http://soft-matter.seas.harvard.edu/api.php?action=feedcontributions&user=Chisholm&feedformat=atomSoft-Matter - User contributions [en]2022-08-11T08:29:16ZUser contributionsMediaWiki 1.24.2http://soft-matter.seas.harvard.edu/index.php?title=The_universal_dynamics_of_cell_spreading&diff=14009The universal dynamics of cell spreading2009-12-05T10:43:19Z<p>Chisholm: </p>
<hr />
<div>Original entry: Naveen Sinha, APPHY 226, Spring 2009<br />
<br />
In numerous biological experiments, cells are plated onto an artificial adhesive surface to study them under a microscope. After being deposited on the surface, they flatten and spread outwards along the surface. This process incorporates many biological reactions, including the diffusion of adhesion receptors and the polymerization of the scaffolding-like actin molecules. However, Prof. Mahadevan and his collaborators show how a variety of cells and surface exhibit a power-law behavior in the contact radius of the colony of cells as a function of time. This can be understood when the cells are modeled as a viscous shell of liquid with a much less viscous interior. <br />
<br />
The basic biological system is shown below. Cells are placed on a surface and Reflectance Contrast Imaging Microscopy is used to measure the contact area as a function of time. <br />
<br />
[[Image:MahadevanUniversalFig01.jpg | 360 px]]<br />
<br />
The length measure used to characterize the system is the radius of a circle with the same area. On a log-log plot, the power law behavior becomes apparent.<br />
<br />
[[Image:MahadevanUniversalFig02.jpg | 360 px]]<br />
<br />
There appear to be two different regimes: (1) an initial diffusive regime with <math>R ~ t^{1/2}</math> and (2) a sub-diffusive region with <math>R ~ t^{1/4}</math>.<br />
<br />
Despite all the biochemical complexities of the spreading process, a simple model that treated the cells as a shell of viscous liquid is sufficient to describe most of the behavior. <br />
<br />
[[Image:MahadevanUniversalFig03.jpg | 360 px]]<br />
<br />
Initially, the power-law can be derived by setting the chance in adhesion energy equal to the viscous energy dissipation. This approximation is valid for when the radius of the contact angle is less than te initial cell radius <math>R_c</math>. The change in contact area is related to the rate of change in the radius by <math>\frac{dA}{dt} = R \frac{dR}{dt}</math>. This can related to the rate of energy gain by multiplying by the adhesion energy per unit area, J, which is the product of the area of each bond and the energy per bond: <math>J R \frac{dR}{dt}</math>. Assuming that the cell cortex has a width w everywhere, the strain is of the order <math>\frac{dR/dt}{w}</math>. This strain acts over a volume approximately equal to <math>R^2 w</math>. The product of the strain, volume, and viscosity leads to an energy dissipation of <math>\eta (\frac{dR}{dt} \frac{1}{w})</math>. By setting this equal to the change in the adhesion energy, we can get the following power law:<br />
<math>R = C \big(\frac{J w}{\eta}\big)^{1/2} t^{1/2}</math>.<br />
<br />
At longer times, when cell has flattened out (i.e. the radius of contact is larger than the initial radius), the viscous energy dissipation occurs throughout the whole volume of the cell. The power law is modified to <math>J R \frac{dR}{dt} = \eta_c \big(\frac{dR}{dt} \frac{1}{w}\big)^2 R^2 w_c</math>. This can be re-arranged to the scaling law:<br />
<math>R ~ \big(\frac{J R_c^3}{\eta_c}\big)^{1/4} t^{1/4}</math>.<br />
<br />
<br />
One prediction of this model is that the properties of the cellular membrane are far more important than the interior of the cell in the cell spreading. One way to test this is by creating two mutants: one in which the microtubules molecules within the cell are unable to polymerize and another in which the actin shell in the cortex is altered.<br />
<br />
[[Image:MahadevanUniversalFig04.jpg | 360 px]]<br />
<br />
Sung Hoon's comment: In the Fig. 4 (a), the Cytochalasin D-treated cell showed linear<br />
behavior. What does the treatment do so that the treated cells spread more quickly?<br />
<br />
Has anyone actually created these mutant cells to test this theory? Is that what you're showing below?<br />
Maybe it's better to write your own captions that get right to your point?<br />
--[[User:Lidiya|Lidiya]] 03:06, 18 February 2009 (UTC)<br />
<br />
This work is important by providing unity to the plethora of information about the molecular mechanics for cell motility and adhesion. It allows future researchers to focus on the aspects of cell structure that are most relevant for thee processes and make refinements to this basic model.<br />
<br />
<br />
-------------------------------------------------------------------------------------------------------------------------------------------------------------<br />
<br />
Second Entry: Nick Chisholm, AP 225, Fall 2009<br />
<br />
==General Information==<br />
'''Authors''': D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan <br />
<br />
'''Publication''': Current Biology '''17''' 694 (2007)<br />
<br />
==Soft Matter Keywords==<br />
[http://soft-matter.seas.harvard.edu/index.php/Adhesion Adhesion], [http://soft-matter.seas.harvard.edu/index.php/Cell Cell], [http://soft-matter.seas.harvard.edu/index.php/Polymerization Polymerization], Viscous<br />
<br />
==Summary==<br />
The authors explore the early stages of cell spreading. In particular, they look at the situation where cells are plated onto artificial adhesive surfaces; they first flatten and deform extensively as they spread. This article presents experimental probing of the dynamics of this spreading process using quantitative visualization and biochemical manipulation with a variety of cell types, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs. Surprisingly, the authors find that the adhesion dynamics of cells follow a universal power-law behavior (i.e. the contact radius is proportional to elapsed time to a certain power), regardless of cell type or adhesion surface. The authors then provide a theoretical model that justifies their experimental results.<br />
<br />
In Figure 1, one can see an image of a cell spreading on a substrate. The image is taken using reflection interference contrast microscopy (RICM).<br />
<br />
[[Image:CellSpreading.png|thumb|300px| Figure 1, taken from [1].]]<br />
<br />
==Soft Matter Discussion==<br />
As is clear by Figure 1, the spreading is isotropic, the authors can define the spreading radius as: <math>R = \sqrt{\frac{A}{\pi}}</math>.<br />
<br />
The contact radius was found as a function of time for various cells and adhesive surfaces; the results are plotted in Figure 2 (careful: it's a logarithmic plot!). From this plot, the authors note two regimes: an initial diffusive regime summarized by the scaling law <math>R \propto t^{1/2}</math>, and later a subdiffusive regime summarized by the scaling law <math>R \propto t^{1/4}</math>. To be completely honest, I'm not quite sure how accurate these scaling laws are, if only derived from the plot in Figure 2. However, I would assume (or, at least, hope) that these plots were also examined without a logarithmic scale, and then fitted using these power-law forms. <br />
<br />
[[Image:ContactRadius.png|thumb|300px| Figure 2, taken from [1].]]<br />
<br />
<br />
In any case, the authors have also developed a theory which would predict these particular scaling laws. I will briefly outline the physical motivation behind this theory, and then derive the scaling laws. Physically, the authors assume that for short times (i.e. times where the radius of the adhesive patch is smaller than the size of the cell), the cell encompasses a viscous shell enclosing a liquid. For long times, where the radius of the adhesive patch is comparable to the size of the cell, the cell is a homogeneous viscous drop. See Figure 3 for details. Note that this model makes sense: for short times, only part of the cell will be touching the surface, whereas for long times most of the cell has already spread, and thus is substantially flattened.<br />
<br />
[[Image:Cells.png|thumb|300px| Figure 3, taken from [1].]]<br />
<br />
<br />
For short times, the contact zone will be disk-like, and the rate of change of the contact area will be: <math>\frac{dA}{dt} \approx R \frac{dR}{dt}</math>. The rate of energy gain is then <math>JR \frac{dR}{dt}</math>, where <math>J</math> is the adhesion energy per unit area. Using Figure 3, one then realizes that there is a characteristic shear strain of order <math>\frac{dR/dt}{w}</math>. The energy dissipation rate due to the viscous flow in the shell is proportional to the product of the shell viscosity (<math>\eta</math>), the square of the shear strain, and the volume over which dissipation occurs (see Figure 3; <math>V = R^{2}w</math>. Thus, it is proportional to: <math>\eta (\frac{dR}{dt} \frac{1}{w})^{2}R^{2}w</math>. By balancing this with the adhesive power, one find the scaling law for the contact radius for short times: <math>R = C(\frac{Jw}{\eta})^{\frac{1}{2}}t^{\frac{1}{2}}, R \leq R_{C}</math>, where <math>C</math> is a dimensionless constant and <math>R_{C}</math> is the initial radius of the cell. This agrees with the experimental results.<br />
<br />
For long times, viscous dissipation occurs in the whole cell (since the contact radius is comparable to the cell size). Now, for a cell of initial height <math>w_{C}</math> and radius <math>R_{C}</math>, we notice that <math>R_{C}^{3} \propto R^{2}w_{C}</math> by volume conservation. The balance of adhesive and viscous power becomes: <math>JR \frac{dR}{dt} \cong \eta_{C} (\frac{dR}{dt} \frac{1}{w_{C}})^{2}R^{2}w_{C}</math>, where <math>\eta_{C}</math> is the effective cell viscosity. The scaling law is thus: <math>R \propto (\frac{JR_{C}^{3}}{\eta_{C}})^{\frac{1}{4}}t^{\frac{1}{4}}, R > R_{C}</math>. Again, this agrees with the experimental results.<br />
<br />
<br />
In addition, in order to test the theory, the authors performed another experiment. For this experiment, they altered the geometry and mechanical structure of the shell of the cell, which lead to a drastic change in the scaling law obtained above. I think this experiment is much more complicated than the value of its explanation is worth, but the results are shown in Figure 4. Note that the black line is for a cell with a normal shell, and the red line is for a cell with a "patchy" shell (meaning parts of it missing). They conclude that their model is justified.<br />
<br />
[[Image:Expt1.png|thumb|300px| Figure 4, taken from [1].]]<br />
<br />
<br />
I think the next step would be to test the altering of the geometric and mechanical structure of the shell of the cell in more than just one (as shown in Figure 4), in order to more accurately conclude that the authors' theory is justified. I'm not entirely sure how one can do this, but certainly they could have done further experiments on different types of cells to ensure that this behavior was universal. <br />
<br />
<br />
Although this paper was quite interesting, I have a hard time trying to think of any relevant application.<br />
<br />
==Reference==<br />
[1] D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan, "The universal dynamics of cell spreading," Current Biology '''17''' 694 (2007).</div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=The_universal_dynamics_of_cell_spreading&diff=14008The universal dynamics of cell spreading2009-12-05T10:41:19Z<p>Chisholm: /* Soft Matter Discussion */</p>
<hr />
<div>Original entry: Naveen Sinha, APPHY 226, Spring 2009<br />
<br />
In numerous biological experiments, cells are plated onto an artificial adhesive surface to study them under a microscope. After being deposited on the surface, they flatten and spread outwards along the surface. This process incorporates many biological reactions, including the diffusion of adhesion receptors and the polymerization of the scaffolding-like actin molecules. However, Prof. Mahadevan and his collaborators show how a variety of cells and surface exhibit a power-law behavior in the contact radius of the colony of cells as a function of time. This can be understood when the cells are modeled as a viscous shell of liquid with a much less viscous interior. <br />
<br />
The basic biological system is shown below. Cells are placed on a surface and Reflectance Contrast Imaging Microscopy is used to measure the contact area as a function of time. <br />
<br />
[[Image:MahadevanUniversalFig01.jpg | 360 px]]<br />
<br />
The length measure used to characterize the system is the radius of a circle with the same area. On a log-log plot, the power law behavior becomes apparent.<br />
<br />
[[Image:MahadevanUniversalFig02.jpg | 360 px]]<br />
<br />
There appear to be two different regimes: (1) an initial diffusive regime with <math>R ~ t^{1/2}</math> and (2) a sub-diffusive region with <math>R ~ t^{1/4}</math>.<br />
<br />
Despite all the biochemical complexities of the spreading process, a simple model that treated the cells as a shell of viscous liquid is sufficient to describe most of the behavior. <br />
<br />
[[Image:MahadevanUniversalFig03.jpg | 360 px]]<br />
<br />
Initially, the power-law can be derived by setting the chance in adhesion energy equal to the viscous energy dissipation. This approximation is valid for when the radius of the contact angle is less than te initial cell radius <math>R_c</math>. The change in contact area is related to the rate of change in the radius by <math>\frac{dA}{dt} = R \frac{dR}{dt}</math>. This can related to the rate of energy gain by multiplying by the adhesion energy per unit area, J, which is the product of the area of each bond and the energy per bond: <math>J R \frac{dR}{dt}</math>. Assuming that the cell cortex has a width w everywhere, the strain is of the order <math>\frac{dR/dt}{w}</math>. This strain acts over a volume approximately equal to <math>R^2 w</math>. The product of the strain, volume, and viscosity leads to an energy dissipation of <math>\eta (\frac{dR}{dt} \frac{1}{w})</math>. By setting this equal to the change in the adhesion energy, we can get the following power law:<br />
<math>R = C \big(\frac{J w}{\eta}\big)^{1/2} t^{1/2}</math>.<br />
<br />
At longer times, when cell has flattened out (i.e. the radius of contact is larger than the initial radius), the viscous energy dissipation occurs throughout the whole volume of the cell. The power law is modified to <math>J R \frac{dR}{dt} = \eta_c \big(\frac{dR}{dt} \frac{1}{w}\big)^2 R^2 w_c</math>. This can be re-arranged to the scaling law:<br />
<math>R ~ \big(\frac{J R_c^3}{\eta_c}\big)^{1/4} t^{1/4}</math>.<br />
<br />
<br />
One prediction of this model is that the properties of the cellular membrane are far more important than the interior of the cell in the cell spreading. One way to test this is by creating two mutants: one in which the microtubules molecules within the cell are unable to polymerize and another in which the actin shell in the cortex is altered.<br />
<br />
[[Image:MahadevanUniversalFig04.jpg | 360 px]]<br />
<br />
Sung Hoon's comment: In the Fig. 4 (a), the Cytochalasin D-treated cell showed linear<br />
behavior. What does the treatment do so that the treated cells spread more quickly?<br />
<br />
Has anyone actually created these mutant cells to test this theory? Is that what you're showing below?<br />
Maybe it's better to write your own captions that get right to your point?<br />
--[[User:Lidiya|Lidiya]] 03:06, 18 February 2009 (UTC)<br />
<br />
This work is important by providing unity to the plethora of information about the molecular mechanics for cell motility and adhesion. It allows future researchers to focus on the aspects of cell structure that are most relevant for thee processes and make refinements to this basic model.<br />
<br />
<br />
-------------------------------------------------------------------------------------------------------------------------------------------------------------<br />
<br />
Second Entry: Nick Chisholm, AP 225, Fall 2009 (In Progress...)<br />
<br />
==General Information==<br />
'''Authors''': D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan <br />
<br />
'''Publication''': Current Biology '''17''' 694 (2007)<br />
<br />
==Soft Matter Keywords==<br />
[http://soft-matter.seas.harvard.edu/index.php/Adhesion Adhesion], [http://soft-matter.seas.harvard.edu/index.php/Cell Cell], [http://soft-matter.seas.harvard.edu/index.php/Polymerization Polymerization], Viscous<br />
<br />
==Summary==<br />
The authors explore the early stages of cell spreading. In particular, they look at the situation where cells are plated onto artificial adhesive surfaces; they first flatten and deform extensively as they spread. This article presents experimental probing of the dynamics of this spreading process using quantitative visualization and biochemical manipulation with a variety of cell types, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs. Surprisingly, the authors find that the adhesion dynamics of cells follow a universal power-law behavior (i.e. the contact radius is proportional to elapsed time to a certain power), regardless of cell type or adhesion surface. The authors then provide a theoretical model that justifies their experimental results.<br />
<br />
In Figure 1, one can see an image of a cell spreading on a substrate. The image is taken using reflection interference contrast microscopy (RICM).<br />
<br />
[[Image:CellSpreading.png|thumb|300px| Figure 1, taken from [1].]]<br />
<br />
==Soft Matter Discussion==<br />
As is clear by Figure 1, the spreading is isotropic, the authors can define the spreading radius as: <math>R = \sqrt{\frac{A}{\pi}}</math>.<br />
<br />
The contact radius was found as a function of time for various cells and adhesive surfaces; the results are plotted in Figure 2 (careful: it's a logarithmic plot!). From this plot, the authors note two regimes: an initial diffusive regime summarized by the scaling law <math>R \propto t^{1/2}</math>, and later a subdiffusive regime summarized by the scaling law <math>R \propto t^{1/4}</math>. To be completely honest, I'm not quite sure how accurate these scaling laws are, if only derived from the plot in Figure 2. However, I would assume (or, at least, hope) that these plots were also examined without a logarithmic scale, and then fitted using these power-law forms. <br />
<br />
[[Image:ContactRadius.png|thumb|300px| Figure 2, taken from [1].]]<br />
<br />
<br />
In any case, the authors have also developed a theory which would predict these particular scaling laws. I will briefly outline the physical motivation behind this theory, and then derive the scaling laws. Physically, the authors assume that for short times (i.e. times where the radius of the adhesive patch is smaller than the size of the cell), the cell encompasses a viscous shell enclosing a liquid. For long times, where the radius of the adhesive patch is comparable to the size of the cell, the cell is a homogeneous viscous drop. See Figure 3 for details. Note that this model makes sense: for short times, only part of the cell will be touching the surface, whereas for long times most of the cell has already spread, and thus is substantially flattened.<br />
<br />
[[Image:Cells.png|thumb|300px| Figure 3, taken from [1].]]<br />
<br />
<br />
For short times, the contact zone will be disk-like, and the rate of change of the contact area will be: <math>\frac{dA}{dt} \approx R \frac{dR}{dt}</math>. The rate of energy gain is then <math>JR \frac{dR}{dt}</math>, where <math>J</math> is the adhesion energy per unit area. Using Figure 3, one then realizes that there is a characteristic shear strain of order <math>\frac{dR/dt}{w}</math>. The energy dissipation rate due to the viscous flow in the shell is proportional to the product of the shell viscosity (<math>\eta</math>), the square of the shear strain, and the volume over which dissipation occurs (see Figure 3; <math>V = R^{2}w</math>. Thus, it is proportional to: <math>\eta (\frac{dR}{dt} \frac{1}{w})^{2}R^{2}w</math>. By balancing this with the adhesive power, one find the scaling law for the contact radius for short times: <math>R = C(\frac{Jw}{\eta})^{\frac{1}{2}}t^{\frac{1}{2}}, R \leq R_{C}</math>, where <math>C</math> is a dimensionless constant and <math>R_{C}</math> is the initial radius of the cell. This agrees with the experimental results.<br />
<br />
For long times, viscous dissipation occurs in the whole cell (since the contact radius is comparable to the cell size). Now, for a cell of initial height <math>w_{C}</math> and radius <math>R_{C}</math>, we notice that <math>R_{C}^{3} \propto R^{2}w_{C}</math> by volume conservation. The balance of adhesive and viscous power becomes: <math>JR \frac{dR}{dt} \cong \eta_{C} (\frac{dR}{dt} \frac{1}{w_{C}})^{2}R^{2}w_{C}</math>, where <math>\eta_{C}</math> is the effective cell viscosity. The scaling law is thus: <math>R \propto (\frac{JR_{C}^{3}}{\eta_{C}})^{\frac{1}{4}}t^{\frac{1}{4}}, R > R_{C}</math>. Again, this agrees with the experimental results.<br />
<br />
<br />
In addition, in order to test the theory, the authors performed another experiment. For this experiment, they altered the geometry and mechanical structure of the shell of the cell, which lead to a drastic change in the scaling law obtained above. I think this experiment is much more complicated than the value of its explanation is worth, but the results are shown in Figure 4. Note that the black line is for a cell with a normal shell, and the red line is for a cell with a "patchy" shell (meaning parts of it missing). They conclude that their model is justified.<br />
<br />
[[Image:Expt1.png|thumb|300px| Figure 4, taken from [1].]]<br />
<br />
<br />
I think the next step would be to test the altering of the geometric and mechanical structure of the shell of the cell in more than just one (as shown in Figure 4), in order to more accurately conclude that the authors' theory is justified. I'm not entirely sure how one can do this, but certainly they could have done further experiments on different types of cells to ensure that this behavior was universal. <br />
<br />
<br />
Although this paper was quite interesting, I have a hard time trying to think of any relevant application.<br />
<br />
==Reference==<br />
[1] D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan, "The universal dynamics of cell spreading," Current Biology '''17''' 694 (2007).</div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=The_universal_dynamics_of_cell_spreading&diff=14007The universal dynamics of cell spreading2009-12-05T10:37:34Z<p>Chisholm: /* Summary */</p>
<hr />
<div>Original entry: Naveen Sinha, APPHY 226, Spring 2009<br />
<br />
In numerous biological experiments, cells are plated onto an artificial adhesive surface to study them under a microscope. After being deposited on the surface, they flatten and spread outwards along the surface. This process incorporates many biological reactions, including the diffusion of adhesion receptors and the polymerization of the scaffolding-like actin molecules. However, Prof. Mahadevan and his collaborators show how a variety of cells and surface exhibit a power-law behavior in the contact radius of the colony of cells as a function of time. This can be understood when the cells are modeled as a viscous shell of liquid with a much less viscous interior. <br />
<br />
The basic biological system is shown below. Cells are placed on a surface and Reflectance Contrast Imaging Microscopy is used to measure the contact area as a function of time. <br />
<br />
[[Image:MahadevanUniversalFig01.jpg | 360 px]]<br />
<br />
The length measure used to characterize the system is the radius of a circle with the same area. On a log-log plot, the power law behavior becomes apparent.<br />
<br />
[[Image:MahadevanUniversalFig02.jpg | 360 px]]<br />
<br />
There appear to be two different regimes: (1) an initial diffusive regime with <math>R ~ t^{1/2}</math> and (2) a sub-diffusive region with <math>R ~ t^{1/4}</math>.<br />
<br />
Despite all the biochemical complexities of the spreading process, a simple model that treated the cells as a shell of viscous liquid is sufficient to describe most of the behavior. <br />
<br />
[[Image:MahadevanUniversalFig03.jpg | 360 px]]<br />
<br />
Initially, the power-law can be derived by setting the chance in adhesion energy equal to the viscous energy dissipation. This approximation is valid for when the radius of the contact angle is less than te initial cell radius <math>R_c</math>. The change in contact area is related to the rate of change in the radius by <math>\frac{dA}{dt} = R \frac{dR}{dt}</math>. This can related to the rate of energy gain by multiplying by the adhesion energy per unit area, J, which is the product of the area of each bond and the energy per bond: <math>J R \frac{dR}{dt}</math>. Assuming that the cell cortex has a width w everywhere, the strain is of the order <math>\frac{dR/dt}{w}</math>. This strain acts over a volume approximately equal to <math>R^2 w</math>. The product of the strain, volume, and viscosity leads to an energy dissipation of <math>\eta (\frac{dR}{dt} \frac{1}{w})</math>. By setting this equal to the change in the adhesion energy, we can get the following power law:<br />
<math>R = C \big(\frac{J w}{\eta}\big)^{1/2} t^{1/2}</math>.<br />
<br />
At longer times, when cell has flattened out (i.e. the radius of contact is larger than the initial radius), the viscous energy dissipation occurs throughout the whole volume of the cell. The power law is modified to <math>J R \frac{dR}{dt} = \eta_c \big(\frac{dR}{dt} \frac{1}{w}\big)^2 R^2 w_c</math>. This can be re-arranged to the scaling law:<br />
<math>R ~ \big(\frac{J R_c^3}{\eta_c}\big)^{1/4} t^{1/4}</math>.<br />
<br />
<br />
One prediction of this model is that the properties of the cellular membrane are far more important than the interior of the cell in the cell spreading. One way to test this is by creating two mutants: one in which the microtubules molecules within the cell are unable to polymerize and another in which the actin shell in the cortex is altered.<br />
<br />
[[Image:MahadevanUniversalFig04.jpg | 360 px]]<br />
<br />
Sung Hoon's comment: In the Fig. 4 (a), the Cytochalasin D-treated cell showed linear<br />
behavior. What does the treatment do so that the treated cells spread more quickly?<br />
<br />
Has anyone actually created these mutant cells to test this theory? Is that what you're showing below?<br />
Maybe it's better to write your own captions that get right to your point?<br />
--[[User:Lidiya|Lidiya]] 03:06, 18 February 2009 (UTC)<br />
<br />
This work is important by providing unity to the plethora of information about the molecular mechanics for cell motility and adhesion. It allows future researchers to focus on the aspects of cell structure that are most relevant for thee processes and make refinements to this basic model.<br />
<br />
<br />
-------------------------------------------------------------------------------------------------------------------------------------------------------------<br />
<br />
Second Entry: Nick Chisholm, AP 225, Fall 2009 (In Progress...)<br />
<br />
==General Information==<br />
'''Authors''': D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan <br />
<br />
'''Publication''': Current Biology '''17''' 694 (2007)<br />
<br />
==Soft Matter Keywords==<br />
[http://soft-matter.seas.harvard.edu/index.php/Adhesion Adhesion], [http://soft-matter.seas.harvard.edu/index.php/Cell Cell], [http://soft-matter.seas.harvard.edu/index.php/Polymerization Polymerization], Viscous<br />
<br />
==Summary==<br />
The authors explore the early stages of cell spreading. In particular, they look at the situation where cells are plated onto artificial adhesive surfaces; they first flatten and deform extensively as they spread. This article presents experimental probing of the dynamics of this spreading process using quantitative visualization and biochemical manipulation with a variety of cell types, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs. Surprisingly, the authors find that the adhesion dynamics of cells follow a universal power-law behavior (i.e. the contact radius is proportional to elapsed time to a certain power), regardless of cell type or adhesion surface. The authors then provide a theoretical model that justifies their experimental results.<br />
<br />
In Figure 1, one can see an image of a cell spreading on a substrate. The image is taken using reflection interference contrast microscopy (RICM).<br />
<br />
[[Image:CellSpreading.png|thumb|300px| Figure 1, taken from [1].]]<br />
<br />
==Soft Matter Discussion==<br />
As is clear by Figure 1, the spreading is isotropic, the authors can define the spreading radius as: <math>R = \sqrt{\frac{A}{\pi}}</math>.<br />
<br />
The contact radius was found as a function of time for various cells, adhesive surfaces, and adhesion receptors; the results are plotted in Figure 2 (careful: it's a logarithmic plot!). From this plot, the authors note two regimes: an initial diffusive regime summarized by the scaling law <math>R \propto t^{1/2}</math>, and later a subdiffusive regime summarized by the scaling law <math>R \propto t^{1/4}</math>. To be completely honest, I'm not quite sure how accurate these scaling laws are, if only derived from the plot in Figure 2. However, I would assume (or, at least, hope) that these plots were also examined without a logarithmic scale, and then fitted using these power-law forms. <br />
<br />
[[Image:ContactRadius.png|thumb|300px| Figure 2, taken from [1].]]<br />
<br />
<br />
In any case, the authors have also developed a theory which would predict these particular scaling laws. I will briefly outline the physical motivation behind this theory, and then derive the scaling laws. Physically, the authors assume that for short times (i.e. times where the radius of the adhesive patch is smaller than the size of the cell), the cell encompasses a viscous shell enclosing a liquid. For long times, where the radius of the adhesive patch is comparable to the size of the cell, the cell is a homogeneous viscous drop. See Figure 3 for details. Note that this model makes sense: for short times, only part of the cell will be touching the surface, whereas for long times most of the cell has already spread, and thus is substantially flattened.<br />
<br />
[[Image:Cells.png|thumb|300px| Figure 3, taken from [1].]]<br />
<br />
<br />
For short times, the contact zone will be disk-like, and the rate of change of the contact area will be: <math>\frac{dA}{dt} \approx R \frac{dR}{dt}</math>. The rate of energy gain is then <math>JR \frac{dR}{dt}</math>, where <math>J</math> is the adhesion energy per unit area. Using Figure 3, one then realizes that there is a characteristic shear strain of order <math>\frac{dR/dt}{w}</math>. The energy dissipation rate due to the viscous flow in the shell is proportional to the product of the shell viscosity (<math>\eta</math>), the square of the shear strain, and the volume over which dissipation occurs (see Figure 3; <math>V = R^{2}w</math>. Thus, it is proportional to: <math>\eta (\frac{dR}{dt} \frac{1}{w})^{2}R^{2}w</math>. By balancing this with the adhesive power, one find the scaling law for the contact radius for short times: <math>R = C(\frac{Jw}{\eta})^{\frac{1}{2}}t^{\frac{1}{2}}, R \leq R_{C}</math>, where <math>C</math> is a dimensionless constant and <math>R_{C}</math> is the initial radius of the cell. This agrees with the experimental results.<br />
<br />
For long times, viscous dissipation occurs in the whole cell (since the contact radius is comparable to the cell size). Now, for a cell of initial height <math>w_{C}</math> and radius <math>R_{C}</math>, we notice that <math>R_{C}^{3} \propto R^{2}w_{C}</math> by volume conservation. The balance of adhesive and viscous power becomes: <math>JR \frac{dR}{dt} \cong \eta_{C} (\frac{dR}{dt} \frac{1}{w_{C}})^{2}R^{2}w_{C}</math>, where <math>\eta_{C}</math> is the effective cell viscosity. The scaling law is thus: <math>R \propto (\frac{JR_{C}^{3}}{\eta_{C}})^{\frac{1}{4}}t^{\frac{1}{4}}, R > R_{C}</math>. Again, this agrees with the experimental results.<br />
<br />
<br />
In addition, in order to test the theory, the authors performed another experiment. For this experiment, they altered the geometry and mechanical structure of the shell of the cell, which lead to a drastic change in the scaling law obtained above. I think this experiment is much more complicated than the value of its explanation is worth, but the results are shown in Figure 4. Note that the black line is for a cell with a normal shell, and the red line is for a cell with a "patchy" shell (meaning parts of it missing). They conclude that their model is justified.<br />
<br />
[[Image:Expt1.png|thumb|300px| Figure 4, taken from [1].]]<br />
<br />
<br />
I found this paper to be quite interesting; the fact that there was such uniformity in how different cells act on different adhesive surfaces<br />
<br />
==Reference==<br />
[1] D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan, "The universal dynamics of cell spreading," Current Biology '''17''' 694 (2007).</div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=The_universal_dynamics_of_cell_spreading&diff=14006The universal dynamics of cell spreading2009-12-05T10:36:42Z<p>Chisholm: /* Soft Matter Discussion */</p>
<hr />
<div>Original entry: Naveen Sinha, APPHY 226, Spring 2009<br />
<br />
In numerous biological experiments, cells are plated onto an artificial adhesive surface to study them under a microscope. After being deposited on the surface, they flatten and spread outwards along the surface. This process incorporates many biological reactions, including the diffusion of adhesion receptors and the polymerization of the scaffolding-like actin molecules. However, Prof. Mahadevan and his collaborators show how a variety of cells and surface exhibit a power-law behavior in the contact radius of the colony of cells as a function of time. This can be understood when the cells are modeled as a viscous shell of liquid with a much less viscous interior. <br />
<br />
The basic biological system is shown below. Cells are placed on a surface and Reflectance Contrast Imaging Microscopy is used to measure the contact area as a function of time. <br />
<br />
[[Image:MahadevanUniversalFig01.jpg | 360 px]]<br />
<br />
The length measure used to characterize the system is the radius of a circle with the same area. On a log-log plot, the power law behavior becomes apparent.<br />
<br />
[[Image:MahadevanUniversalFig02.jpg | 360 px]]<br />
<br />
There appear to be two different regimes: (1) an initial diffusive regime with <math>R ~ t^{1/2}</math> and (2) a sub-diffusive region with <math>R ~ t^{1/4}</math>.<br />
<br />
Despite all the biochemical complexities of the spreading process, a simple model that treated the cells as a shell of viscous liquid is sufficient to describe most of the behavior. <br />
<br />
[[Image:MahadevanUniversalFig03.jpg | 360 px]]<br />
<br />
Initially, the power-law can be derived by setting the chance in adhesion energy equal to the viscous energy dissipation. This approximation is valid for when the radius of the contact angle is less than te initial cell radius <math>R_c</math>. The change in contact area is related to the rate of change in the radius by <math>\frac{dA}{dt} = R \frac{dR}{dt}</math>. This can related to the rate of energy gain by multiplying by the adhesion energy per unit area, J, which is the product of the area of each bond and the energy per bond: <math>J R \frac{dR}{dt}</math>. Assuming that the cell cortex has a width w everywhere, the strain is of the order <math>\frac{dR/dt}{w}</math>. This strain acts over a volume approximately equal to <math>R^2 w</math>. The product of the strain, volume, and viscosity leads to an energy dissipation of <math>\eta (\frac{dR}{dt} \frac{1}{w})</math>. By setting this equal to the change in the adhesion energy, we can get the following power law:<br />
<math>R = C \big(\frac{J w}{\eta}\big)^{1/2} t^{1/2}</math>.<br />
<br />
At longer times, when cell has flattened out (i.e. the radius of contact is larger than the initial radius), the viscous energy dissipation occurs throughout the whole volume of the cell. The power law is modified to <math>J R \frac{dR}{dt} = \eta_c \big(\frac{dR}{dt} \frac{1}{w}\big)^2 R^2 w_c</math>. This can be re-arranged to the scaling law:<br />
<math>R ~ \big(\frac{J R_c^3}{\eta_c}\big)^{1/4} t^{1/4}</math>.<br />
<br />
<br />
One prediction of this model is that the properties of the cellular membrane are far more important than the interior of the cell in the cell spreading. One way to test this is by creating two mutants: one in which the microtubules molecules within the cell are unable to polymerize and another in which the actin shell in the cortex is altered.<br />
<br />
[[Image:MahadevanUniversalFig04.jpg | 360 px]]<br />
<br />
Sung Hoon's comment: In the Fig. 4 (a), the Cytochalasin D-treated cell showed linear<br />
behavior. What does the treatment do so that the treated cells spread more quickly?<br />
<br />
Has anyone actually created these mutant cells to test this theory? Is that what you're showing below?<br />
Maybe it's better to write your own captions that get right to your point?<br />
--[[User:Lidiya|Lidiya]] 03:06, 18 February 2009 (UTC)<br />
<br />
This work is important by providing unity to the plethora of information about the molecular mechanics for cell motility and adhesion. It allows future researchers to focus on the aspects of cell structure that are most relevant for thee processes and make refinements to this basic model.<br />
<br />
<br />
-------------------------------------------------------------------------------------------------------------------------------------------------------------<br />
<br />
Second Entry: Nick Chisholm, AP 225, Fall 2009 (In Progress...)<br />
<br />
==General Information==<br />
'''Authors''': D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan <br />
<br />
'''Publication''': Current Biology '''17''' 694 (2007)<br />
<br />
==Soft Matter Keywords==<br />
[http://soft-matter.seas.harvard.edu/index.php/Adhesion Adhesion], [http://soft-matter.seas.harvard.edu/index.php/Cell Cell], [http://soft-matter.seas.harvard.edu/index.php/Polymerization Polymerization], Viscous<br />
<br />
==Summary==<br />
The authors explore the early stages of cell spreading. In particular, they look at the situation where cells are plated onto artificial adhesive surfaces; they first flatten and deform extensively as they spread. This article presents experimental probing of the dynamics of this spreading process using quantitative visualization and biochemical manipulation with a variety of cell types, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs. Surprisingly, the authors find that the adhesion dynamics of cells follow a universal power-law behavior (i.e. the contact radius is proportional to elapsed time to a certain power). The authors then provide a theoretical model that justifies their experimental results.<br />
<br />
In Figure 1, one can see an image of a cell spreading on a substrate. The image is taken using reflection interference contrast microscopy (RICM).<br />
<br />
[[Image:CellSpreading.png|thumb|300px| Figure 1, taken from [1].]]<br />
<br />
==Soft Matter Discussion==<br />
As is clear by Figure 1, the spreading is isotropic, the authors can define the spreading radius as: <math>R = \sqrt{\frac{A}{\pi}}</math>.<br />
<br />
The contact radius was found as a function of time for various cells, adhesive surfaces, and adhesion receptors; the results are plotted in Figure 2 (careful: it's a logarithmic plot!). From this plot, the authors note two regimes: an initial diffusive regime summarized by the scaling law <math>R \propto t^{1/2}</math>, and later a subdiffusive regime summarized by the scaling law <math>R \propto t^{1/4}</math>. To be completely honest, I'm not quite sure how accurate these scaling laws are, if only derived from the plot in Figure 2. However, I would assume (or, at least, hope) that these plots were also examined without a logarithmic scale, and then fitted using these power-law forms. <br />
<br />
[[Image:ContactRadius.png|thumb|300px| Figure 2, taken from [1].]]<br />
<br />
<br />
In any case, the authors have also developed a theory which would predict these particular scaling laws. I will briefly outline the physical motivation behind this theory, and then derive the scaling laws. Physically, the authors assume that for short times (i.e. times where the radius of the adhesive patch is smaller than the size of the cell), the cell encompasses a viscous shell enclosing a liquid. For long times, where the radius of the adhesive patch is comparable to the size of the cell, the cell is a homogeneous viscous drop. See Figure 3 for details. Note that this model makes sense: for short times, only part of the cell will be touching the surface, whereas for long times most of the cell has already spread, and thus is substantially flattened.<br />
<br />
[[Image:Cells.png|thumb|300px| Figure 3, taken from [1].]]<br />
<br />
<br />
For short times, the contact zone will be disk-like, and the rate of change of the contact area will be: <math>\frac{dA}{dt} \approx R \frac{dR}{dt}</math>. The rate of energy gain is then <math>JR \frac{dR}{dt}</math>, where <math>J</math> is the adhesion energy per unit area. Using Figure 3, one then realizes that there is a characteristic shear strain of order <math>\frac{dR/dt}{w}</math>. The energy dissipation rate due to the viscous flow in the shell is proportional to the product of the shell viscosity (<math>\eta</math>), the square of the shear strain, and the volume over which dissipation occurs (see Figure 3; <math>V = R^{2}w</math>. Thus, it is proportional to: <math>\eta (\frac{dR}{dt} \frac{1}{w})^{2}R^{2}w</math>. By balancing this with the adhesive power, one find the scaling law for the contact radius for short times: <math>R = C(\frac{Jw}{\eta})^{\frac{1}{2}}t^{\frac{1}{2}}, R \leq R_{C}</math>, where <math>C</math> is a dimensionless constant and <math>R_{C}</math> is the initial radius of the cell. This agrees with the experimental results.<br />
<br />
For long times, viscous dissipation occurs in the whole cell (since the contact radius is comparable to the cell size). Now, for a cell of initial height <math>w_{C}</math> and radius <math>R_{C}</math>, we notice that <math>R_{C}^{3} \propto R^{2}w_{C}</math> by volume conservation. The balance of adhesive and viscous power becomes: <math>JR \frac{dR}{dt} \cong \eta_{C} (\frac{dR}{dt} \frac{1}{w_{C}})^{2}R^{2}w_{C}</math>, where <math>\eta_{C}</math> is the effective cell viscosity. The scaling law is thus: <math>R \propto (\frac{JR_{C}^{3}}{\eta_{C}})^{\frac{1}{4}}t^{\frac{1}{4}}, R > R_{C}</math>. Again, this agrees with the experimental results.<br />
<br />
<br />
In addition, in order to test the theory, the authors performed another experiment. For this experiment, they altered the geometry and mechanical structure of the shell of the cell, which lead to a drastic change in the scaling law obtained above. I think this experiment is much more complicated than the value of its explanation is worth, but the results are shown in Figure 4. Note that the black line is for a cell with a normal shell, and the red line is for a cell with a "patchy" shell (meaning parts of it missing). They conclude that their model is justified.<br />
<br />
[[Image:Expt1.png|thumb|300px| Figure 4, taken from [1].]]<br />
<br />
<br />
I found this paper to be quite interesting; the fact that there was such uniformity in how different cells act on different adhesive surfaces<br />
<br />
==Reference==<br />
[1] D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan, "The universal dynamics of cell spreading," Current Biology '''17''' 694 (2007).</div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=The_universal_dynamics_of_cell_spreading&diff=14005The universal dynamics of cell spreading2009-12-05T10:34:01Z<p>Chisholm: /* Soft Matter Discussion */</p>
<hr />
<div>Original entry: Naveen Sinha, APPHY 226, Spring 2009<br />
<br />
In numerous biological experiments, cells are plated onto an artificial adhesive surface to study them under a microscope. After being deposited on the surface, they flatten and spread outwards along the surface. This process incorporates many biological reactions, including the diffusion of adhesion receptors and the polymerization of the scaffolding-like actin molecules. However, Prof. Mahadevan and his collaborators show how a variety of cells and surface exhibit a power-law behavior in the contact radius of the colony of cells as a function of time. This can be understood when the cells are modeled as a viscous shell of liquid with a much less viscous interior. <br />
<br />
The basic biological system is shown below. Cells are placed on a surface and Reflectance Contrast Imaging Microscopy is used to measure the contact area as a function of time. <br />
<br />
[[Image:MahadevanUniversalFig01.jpg | 360 px]]<br />
<br />
The length measure used to characterize the system is the radius of a circle with the same area. On a log-log plot, the power law behavior becomes apparent.<br />
<br />
[[Image:MahadevanUniversalFig02.jpg | 360 px]]<br />
<br />
There appear to be two different regimes: (1) an initial diffusive regime with <math>R ~ t^{1/2}</math> and (2) a sub-diffusive region with <math>R ~ t^{1/4}</math>.<br />
<br />
Despite all the biochemical complexities of the spreading process, a simple model that treated the cells as a shell of viscous liquid is sufficient to describe most of the behavior. <br />
<br />
[[Image:MahadevanUniversalFig03.jpg | 360 px]]<br />
<br />
Initially, the power-law can be derived by setting the chance in adhesion energy equal to the viscous energy dissipation. This approximation is valid for when the radius of the contact angle is less than te initial cell radius <math>R_c</math>. The change in contact area is related to the rate of change in the radius by <math>\frac{dA}{dt} = R \frac{dR}{dt}</math>. This can related to the rate of energy gain by multiplying by the adhesion energy per unit area, J, which is the product of the area of each bond and the energy per bond: <math>J R \frac{dR}{dt}</math>. Assuming that the cell cortex has a width w everywhere, the strain is of the order <math>\frac{dR/dt}{w}</math>. This strain acts over a volume approximately equal to <math>R^2 w</math>. The product of the strain, volume, and viscosity leads to an energy dissipation of <math>\eta (\frac{dR}{dt} \frac{1}{w})</math>. By setting this equal to the change in the adhesion energy, we can get the following power law:<br />
<math>R = C \big(\frac{J w}{\eta}\big)^{1/2} t^{1/2}</math>.<br />
<br />
At longer times, when cell has flattened out (i.e. the radius of contact is larger than the initial radius), the viscous energy dissipation occurs throughout the whole volume of the cell. The power law is modified to <math>J R \frac{dR}{dt} = \eta_c \big(\frac{dR}{dt} \frac{1}{w}\big)^2 R^2 w_c</math>. This can be re-arranged to the scaling law:<br />
<math>R ~ \big(\frac{J R_c^3}{\eta_c}\big)^{1/4} t^{1/4}</math>.<br />
<br />
<br />
One prediction of this model is that the properties of the cellular membrane are far more important than the interior of the cell in the cell spreading. One way to test this is by creating two mutants: one in which the microtubules molecules within the cell are unable to polymerize and another in which the actin shell in the cortex is altered.<br />
<br />
[[Image:MahadevanUniversalFig04.jpg | 360 px]]<br />
<br />
Sung Hoon's comment: In the Fig. 4 (a), the Cytochalasin D-treated cell showed linear<br />
behavior. What does the treatment do so that the treated cells spread more quickly?<br />
<br />
Has anyone actually created these mutant cells to test this theory? Is that what you're showing below?<br />
Maybe it's better to write your own captions that get right to your point?<br />
--[[User:Lidiya|Lidiya]] 03:06, 18 February 2009 (UTC)<br />
<br />
This work is important by providing unity to the plethora of information about the molecular mechanics for cell motility and adhesion. It allows future researchers to focus on the aspects of cell structure that are most relevant for thee processes and make refinements to this basic model.<br />
<br />
<br />
-------------------------------------------------------------------------------------------------------------------------------------------------------------<br />
<br />
Second Entry: Nick Chisholm, AP 225, Fall 2009 (In Progress...)<br />
<br />
==General Information==<br />
'''Authors''': D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan <br />
<br />
'''Publication''': Current Biology '''17''' 694 (2007)<br />
<br />
==Soft Matter Keywords==<br />
[http://soft-matter.seas.harvard.edu/index.php/Adhesion Adhesion], [http://soft-matter.seas.harvard.edu/index.php/Cell Cell], [http://soft-matter.seas.harvard.edu/index.php/Polymerization Polymerization], Viscous<br />
<br />
==Summary==<br />
The authors explore the early stages of cell spreading. In particular, they look at the situation where cells are plated onto artificial adhesive surfaces; they first flatten and deform extensively as they spread. This article presents experimental probing of the dynamics of this spreading process using quantitative visualization and biochemical manipulation with a variety of cell types, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs. Surprisingly, the authors find that the adhesion dynamics of cells follow a universal power-law behavior (i.e. the contact radius is proportional to elapsed time to a certain power). The authors then provide a theoretical model that justifies their experimental results.<br />
<br />
In Figure 1, one can see an image of a cell spreading on a substrate. The image is taken using reflection interference contrast microscopy (RICM).<br />
<br />
[[Image:CellSpreading.png|thumb|300px| Figure 1, taken from [1].]]<br />
<br />
==Soft Matter Discussion==<br />
As is clear by Figure 1, the spreading is isotropic, the authors can define the spreading radius as: <math>R = \sqrt{\frac{A}{\pi}}</math>.<br />
<br />
The contact radius was found as a function of time for various cells, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs; the results are plotted in Figure 2 (careful: it's a logarithmic plot!). From this plot, the authors note two regimes: an initial diffusive regime summarized by the scaling law <math>R \propto t^{1/2}</math>, and later a subdiffusive regime summarized by the scaling law <math>R \propto t^{1/4}</math>. To be completely honest, I'm not quite sure how accurate these scaling laws are, if only derived from the plot in Figure 2. However, I would assume (or, at least, hope) that these plots were also examined without a logarithmic scale, and then fitted using these power-law forms. <br />
<br />
[[Image:ContactRadius.png|thumb|300px| Figure 2, taken from [1].]]<br />
<br />
<br />
In any case, the authors have also developed a theory which would predict these particular scaling laws. I will briefly outline the physical motivation behind this theory, and then derive the scaling laws. Physically, the authors assume that for short times (i.e. times where the radius of the adhesive patch is smaller than the size of the cell), the cell encompasses a viscous shell enclosing a liquid. For long times, where the radius of the adhesive patch is comparable to the size of the cell, the cell is a homogeneous viscous drop. See Figure 3 for details. Note that this model makes sense: for short times, only part of the cell will be touching the surface, whereas for long times most of the cell has already spread, and thus is substantially flattened.<br />
<br />
[[Image:Cells.png|thumb|300px| Figure 3, taken from [1].]]<br />
<br />
<br />
For short times, the contact zone will be disk-like, and the rate of change of the contact area will be: <math>\frac{dA}{dt} \approx R \frac{dR}{dt}</math>. The rate of energy gain is then <math>JR \frac{dR}{dt}</math>, where <math>J</math> is the adhesion energy per unit area. Using Figure 3, one then realizes that there is a characteristic shear strain of order <math>\frac{dR/dt}{w}</math>. The energy dissipation rate due to the viscous flow in the shell is proportional to the product of the shell viscosity (<math>\eta</math>), the square of the shear strain, and the volume over which dissipation occurs (see Figure 3; <math>V = R^{2}w</math>. Thus, it is proportional to: <math>\eta (\frac{dR}{dt} \frac{1}{w})^{2}R^{2}w</math>. By balancing this with the adhesive power, one find the scaling law for the contact radius for short times: <math>R = C(\frac{Jw}{\eta})^{\frac{1}{2}}t^{\frac{1}{2}}, R \leq R_{C}</math>, where <math>C</math> is a dimensionless constant and <math>R_{C}</math> is the initial radius of the cell. This agrees with the experimental results.<br />
<br />
For long times, viscous dissipation occurs in the whole cell (since the contact radius is comparable to the cell size). Now, for a cell of initial height <math>w_{C}</math> and radius <math>R_{C}</math>, we notice that <math>R_{C}^{3} \propto R^{2}w_{C}</math> by volume conservation. The balance of adhesive and viscous power becomes: <math>JR \frac{dR}{dt} \cong \eta_{C} (\frac{dR}{dt} \frac{1}{w_{C}})^{2}R^{2}w_{C}</math>, where <math>\eta_{C}</math> is the effective cell viscosity. The scaling law is thus: <math>R \propto (\frac{JR_{C}^{3}}{\eta_{C}})^{\frac{1}{4}}t^{\frac{1}{4}}, R > R_{C}</math>. Again, this agrees with the experimental results.<br />
<br />
<br />
In addition, in order to test the theory, the authors performed another experiment. For this experiment, they altered the geometry and mechanical structure of the shell of the cell, which lead to a drastic change in the scaling law obtained above. I think this experiment is much more complicated than the value of its explanation is worth, but the results are shown in Figure 4. Note that the black line is for a cell with a normal shell, and the red line is for a cell with a "patchy" shell (meaning parts of it missing). They conclude that their model is justified.<br />
<br />
[[Image:Expt1.png|thumb|300px| Figure 4, taken from [1].]]<br />
<br />
==Reference==<br />
[1] D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan, "The universal dynamics of cell spreading," Current Biology '''17''' 694 (2007).</div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=The_universal_dynamics_of_cell_spreading&diff=14004The universal dynamics of cell spreading2009-12-05T10:33:07Z<p>Chisholm: /* Soft Matter Discussion */</p>
<hr />
<div>Original entry: Naveen Sinha, APPHY 226, Spring 2009<br />
<br />
In numerous biological experiments, cells are plated onto an artificial adhesive surface to study them under a microscope. After being deposited on the surface, they flatten and spread outwards along the surface. This process incorporates many biological reactions, including the diffusion of adhesion receptors and the polymerization of the scaffolding-like actin molecules. However, Prof. Mahadevan and his collaborators show how a variety of cells and surface exhibit a power-law behavior in the contact radius of the colony of cells as a function of time. This can be understood when the cells are modeled as a viscous shell of liquid with a much less viscous interior. <br />
<br />
The basic biological system is shown below. Cells are placed on a surface and Reflectance Contrast Imaging Microscopy is used to measure the contact area as a function of time. <br />
<br />
[[Image:MahadevanUniversalFig01.jpg | 360 px]]<br />
<br />
The length measure used to characterize the system is the radius of a circle with the same area. On a log-log plot, the power law behavior becomes apparent.<br />
<br />
[[Image:MahadevanUniversalFig02.jpg | 360 px]]<br />
<br />
There appear to be two different regimes: (1) an initial diffusive regime with <math>R ~ t^{1/2}</math> and (2) a sub-diffusive region with <math>R ~ t^{1/4}</math>.<br />
<br />
Despite all the biochemical complexities of the spreading process, a simple model that treated the cells as a shell of viscous liquid is sufficient to describe most of the behavior. <br />
<br />
[[Image:MahadevanUniversalFig03.jpg | 360 px]]<br />
<br />
Initially, the power-law can be derived by setting the chance in adhesion energy equal to the viscous energy dissipation. This approximation is valid for when the radius of the contact angle is less than te initial cell radius <math>R_c</math>. The change in contact area is related to the rate of change in the radius by <math>\frac{dA}{dt} = R \frac{dR}{dt}</math>. This can related to the rate of energy gain by multiplying by the adhesion energy per unit area, J, which is the product of the area of each bond and the energy per bond: <math>J R \frac{dR}{dt}</math>. Assuming that the cell cortex has a width w everywhere, the strain is of the order <math>\frac{dR/dt}{w}</math>. This strain acts over a volume approximately equal to <math>R^2 w</math>. The product of the strain, volume, and viscosity leads to an energy dissipation of <math>\eta (\frac{dR}{dt} \frac{1}{w})</math>. By setting this equal to the change in the adhesion energy, we can get the following power law:<br />
<math>R = C \big(\frac{J w}{\eta}\big)^{1/2} t^{1/2}</math>.<br />
<br />
At longer times, when cell has flattened out (i.e. the radius of contact is larger than the initial radius), the viscous energy dissipation occurs throughout the whole volume of the cell. The power law is modified to <math>J R \frac{dR}{dt} = \eta_c \big(\frac{dR}{dt} \frac{1}{w}\big)^2 R^2 w_c</math>. This can be re-arranged to the scaling law:<br />
<math>R ~ \big(\frac{J R_c^3}{\eta_c}\big)^{1/4} t^{1/4}</math>.<br />
<br />
<br />
One prediction of this model is that the properties of the cellular membrane are far more important than the interior of the cell in the cell spreading. One way to test this is by creating two mutants: one in which the microtubules molecules within the cell are unable to polymerize and another in which the actin shell in the cortex is altered.<br />
<br />
[[Image:MahadevanUniversalFig04.jpg | 360 px]]<br />
<br />
Sung Hoon's comment: In the Fig. 4 (a), the Cytochalasin D-treated cell showed linear<br />
behavior. What does the treatment do so that the treated cells spread more quickly?<br />
<br />
Has anyone actually created these mutant cells to test this theory? Is that what you're showing below?<br />
Maybe it's better to write your own captions that get right to your point?<br />
--[[User:Lidiya|Lidiya]] 03:06, 18 February 2009 (UTC)<br />
<br />
This work is important by providing unity to the plethora of information about the molecular mechanics for cell motility and adhesion. It allows future researchers to focus on the aspects of cell structure that are most relevant for thee processes and make refinements to this basic model.<br />
<br />
<br />
-------------------------------------------------------------------------------------------------------------------------------------------------------------<br />
<br />
Second Entry: Nick Chisholm, AP 225, Fall 2009 (In Progress...)<br />
<br />
==General Information==<br />
'''Authors''': D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan <br />
<br />
'''Publication''': Current Biology '''17''' 694 (2007)<br />
<br />
==Soft Matter Keywords==<br />
[http://soft-matter.seas.harvard.edu/index.php/Adhesion Adhesion], [http://soft-matter.seas.harvard.edu/index.php/Cell Cell], [http://soft-matter.seas.harvard.edu/index.php/Polymerization Polymerization], Viscous<br />
<br />
==Summary==<br />
The authors explore the early stages of cell spreading. In particular, they look at the situation where cells are plated onto artificial adhesive surfaces; they first flatten and deform extensively as they spread. This article presents experimental probing of the dynamics of this spreading process using quantitative visualization and biochemical manipulation with a variety of cell types, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs. Surprisingly, the authors find that the adhesion dynamics of cells follow a universal power-law behavior (i.e. the contact radius is proportional to elapsed time to a certain power). The authors then provide a theoretical model that justifies their experimental results.<br />
<br />
In Figure 1, one can see an image of a cell spreading on a substrate. The image is taken using reflection interference contrast microscopy (RICM).<br />
<br />
[[Image:CellSpreading.png|thumb|300px| Figure 1, taken from [1].]]<br />
<br />
==Soft Matter Discussion==<br />
As is clear by Figure 1, the spreading is isotropic, the authors can define the spreading radius as: <math>R = \sqrt{\frac{A}{\pi}}</math>.<br />
<br />
The contact radius was found as a function of time for various cells, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs; the results are plotted in Figure 2 (careful: it's a logarithmic plot!). From this plot, the authors note two regimes: an initial diffusive regime summarized by the scaling law <math>R \propto t^{1/2}</math>, and later a subdiffusive regime summarized by the scaling law <math>R \propto t^{1/4}</math>. To be completely honest, I'm not quite sure how accurate these scaling laws are, if only derived from the plot in Figure 2. However, I would assume (or, at least, hope) that these plots were also examined without a logarithmic scale, and then fitted using these power-law forms. <br />
<br />
[[Image:ContactRadius.png|thumb|300px| Figure 2, taken from [1].]]<br />
<br />
<br />
In any case, the authors have also developed a theory which would predict these particular scaling laws. I will briefly outline the physical motivation behind this theory, and then derive the scaling laws. Physically, the authors assume that for short times (i.e. times where the radius of the adhesive patch is smaller than the size of the cell), the cell encompasses a viscous shell enclosing a liquid. For long times, where the radius of the adhesive patch is comparable to the size of the cell, the cell is a homogeneous viscous drop. See Figure 3 for details. Note that this model makes sense: for short times, only part of the cell will be touching the surface, whereas for long times most of the cell has already spread, and thus is substantially flattened.<br />
<br />
[[Image:Cells.png|thumb|300px| Figure 3, taken from [1].]]<br />
<br />
<br />
For short times, the contact zone will be disk-like, and the rate of change of the contact area will be: <math>\frac{dA}{dt} \approx R \frac{dR}{dt}</math>. The rate of energy gain is then <math>JR \frac{dR}{dt}</math>, where <math>J</math> is the adhesion energy per unit area. Using Figure 3, one then realizes that there is a characteristic shear strain of order <math>\frac{dR/dt}{w}</math>. The energy dissipation rate due to the viscous flow in the shell is proportional to the product of the shell viscosity (<math>\eta</math>), the square of the shear strain, and the volume over which dissipation occurs (see Figure 3; <math>V = R^{2}w</math>. Thus, it is proportional to: <math>\eta (\frac{dR}{dt} \frac{1}{w})^{2}R^{2}w</math>. By balancing this with the adhesive power, one find the scaling law for the contact radius for short times: <math>R = C(\frac{Jw}{\eta})^{\frac{1}{2}}t^{\frac{1}{2}}, R \leq R_{C}</math>, where <math>C</math> is a dimensionless constant and <math>R_{C}</math> is the initial radius of the cell. This agrees with the experimental results.<br />
<br />
For long times, viscous dissipation occurs in the whole cell (since the contact radius is comparable to the cell size). Now, for a cell of initial height <math>w_{C}</math> and radius <math>R_{C}</math>, we notice that <math>R_{C}^{3} \propto R^{2}w_{C}</math> by volume conservation. The balance of adhesive and viscous power becomes: <math>JR \frac{dR}{dt} \cong \eta_{C} (\frac{dR}{dt} \frac{1}{w_{C}})^{2}R^{2}w_{C}</math>, where <math>\eta_{C}</math> is the effective cell viscosity. The scaling law is thus: <math>R \propto (\frac{JR_{C}^{3}}{\eta_{C}})^{\frac{1}{4}}t^{\frac{1}{4}}, R > R_{C}</math>.<br />
<br />
<br />
In addition, in order to test the theory, the authors performed another experiment. For this experiment, they altered the geometry and mechanical structure of the shell of the cell, which lead to a drastic change in the scaling law obtained above. I think this experiment is much more complicated than the value of its explanation is worth, but the results are shown in Figure 4. Note that the black line is for a cell with a normal shell, and the red line is for a cell with a "patchy" shell (meaning parts of it missing).<br />
<br />
[[Image:Expt1.png|thumb|300px| Figure 4, taken from [1].]]<br />
<br />
==Reference==<br />
[1] D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan, "The universal dynamics of cell spreading," Current Biology '''17''' 694 (2007).</div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=The_universal_dynamics_of_cell_spreading&diff=14003The universal dynamics of cell spreading2009-12-05T10:25:27Z<p>Chisholm: /* Soft Matter Discussion */</p>
<hr />
<div>Original entry: Naveen Sinha, APPHY 226, Spring 2009<br />
<br />
In numerous biological experiments, cells are plated onto an artificial adhesive surface to study them under a microscope. After being deposited on the surface, they flatten and spread outwards along the surface. This process incorporates many biological reactions, including the diffusion of adhesion receptors and the polymerization of the scaffolding-like actin molecules. However, Prof. Mahadevan and his collaborators show how a variety of cells and surface exhibit a power-law behavior in the contact radius of the colony of cells as a function of time. This can be understood when the cells are modeled as a viscous shell of liquid with a much less viscous interior. <br />
<br />
The basic biological system is shown below. Cells are placed on a surface and Reflectance Contrast Imaging Microscopy is used to measure the contact area as a function of time. <br />
<br />
[[Image:MahadevanUniversalFig01.jpg | 360 px]]<br />
<br />
The length measure used to characterize the system is the radius of a circle with the same area. On a log-log plot, the power law behavior becomes apparent.<br />
<br />
[[Image:MahadevanUniversalFig02.jpg | 360 px]]<br />
<br />
There appear to be two different regimes: (1) an initial diffusive regime with <math>R ~ t^{1/2}</math> and (2) a sub-diffusive region with <math>R ~ t^{1/4}</math>.<br />
<br />
Despite all the biochemical complexities of the spreading process, a simple model that treated the cells as a shell of viscous liquid is sufficient to describe most of the behavior. <br />
<br />
[[Image:MahadevanUniversalFig03.jpg | 360 px]]<br />
<br />
Initially, the power-law can be derived by setting the chance in adhesion energy equal to the viscous energy dissipation. This approximation is valid for when the radius of the contact angle is less than te initial cell radius <math>R_c</math>. The change in contact area is related to the rate of change in the radius by <math>\frac{dA}{dt} = R \frac{dR}{dt}</math>. This can related to the rate of energy gain by multiplying by the adhesion energy per unit area, J, which is the product of the area of each bond and the energy per bond: <math>J R \frac{dR}{dt}</math>. Assuming that the cell cortex has a width w everywhere, the strain is of the order <math>\frac{dR/dt}{w}</math>. This strain acts over a volume approximately equal to <math>R^2 w</math>. The product of the strain, volume, and viscosity leads to an energy dissipation of <math>\eta (\frac{dR}{dt} \frac{1}{w})</math>. By setting this equal to the change in the adhesion energy, we can get the following power law:<br />
<math>R = C \big(\frac{J w}{\eta}\big)^{1/2} t^{1/2}</math>.<br />
<br />
At longer times, when cell has flattened out (i.e. the radius of contact is larger than the initial radius), the viscous energy dissipation occurs throughout the whole volume of the cell. The power law is modified to <math>J R \frac{dR}{dt} = \eta_c \big(\frac{dR}{dt} \frac{1}{w}\big)^2 R^2 w_c</math>. This can be re-arranged to the scaling law:<br />
<math>R ~ \big(\frac{J R_c^3}{\eta_c}\big)^{1/4} t^{1/4}</math>.<br />
<br />
<br />
One prediction of this model is that the properties of the cellular membrane are far more important than the interior of the cell in the cell spreading. One way to test this is by creating two mutants: one in which the microtubules molecules within the cell are unable to polymerize and another in which the actin shell in the cortex is altered.<br />
<br />
[[Image:MahadevanUniversalFig04.jpg | 360 px]]<br />
<br />
Sung Hoon's comment: In the Fig. 4 (a), the Cytochalasin D-treated cell showed linear<br />
behavior. What does the treatment do so that the treated cells spread more quickly?<br />
<br />
Has anyone actually created these mutant cells to test this theory? Is that what you're showing below?<br />
Maybe it's better to write your own captions that get right to your point?<br />
--[[User:Lidiya|Lidiya]] 03:06, 18 February 2009 (UTC)<br />
<br />
This work is important by providing unity to the plethora of information about the molecular mechanics for cell motility and adhesion. It allows future researchers to focus on the aspects of cell structure that are most relevant for thee processes and make refinements to this basic model.<br />
<br />
<br />
-------------------------------------------------------------------------------------------------------------------------------------------------------------<br />
<br />
Second Entry: Nick Chisholm, AP 225, Fall 2009 (In Progress...)<br />
<br />
==General Information==<br />
'''Authors''': D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan <br />
<br />
'''Publication''': Current Biology '''17''' 694 (2007)<br />
<br />
==Soft Matter Keywords==<br />
[http://soft-matter.seas.harvard.edu/index.php/Adhesion Adhesion], [http://soft-matter.seas.harvard.edu/index.php/Cell Cell], [http://soft-matter.seas.harvard.edu/index.php/Polymerization Polymerization], Viscous<br />
<br />
==Summary==<br />
The authors explore the early stages of cell spreading. In particular, they look at the situation where cells are plated onto artificial adhesive surfaces; they first flatten and deform extensively as they spread. This article presents experimental probing of the dynamics of this spreading process using quantitative visualization and biochemical manipulation with a variety of cell types, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs. Surprisingly, the authors find that the adhesion dynamics of cells follow a universal power-law behavior (i.e. the contact radius is proportional to elapsed time to a certain power). The authors then provide a theoretical model that justifies their experimental results.<br />
<br />
In Figure 1, one can see an image of a cell spreading on a substrate. The image is taken using reflection interference contrast microscopy (RICM).<br />
<br />
[[Image:CellSpreading.png|thumb|300px| Figure 1, taken from [1].]]<br />
<br />
==Soft Matter Discussion==<br />
As is clear by Figure 1, the spreading is isotropic, the authors can define the spreading radius as: <math>R = \sqrt{\frac{A}{\pi}}</math>.<br />
<br />
The contact radius was found as a function of time for various cells, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs; the results are plotted in Figure 2 (careful: it's a logarithmic plot!). From this plot, the authors note two regimes: an initial diffusive regime summarized by the scaling law <math>R \propto t^{1/2}</math>, and later a subdiffusive regime summarized by the scaling law <math>R \propto t^{1/4}</math>. To be completely honest, I'm not quite sure how accurate these scaling laws are, if only derived from the plot in Figure 2. However, I would assume (or, at least, hope) that these plots were also examined without a logarithmic scale, and then fitted using these power-law forms. <br />
<br />
[[Image:ContactRadius.png|thumb|300px| Figure 2, taken from [1].]]<br />
<br />
<br />
In any case, the authors have also developed a theory which would predict these particular scaling laws. I will briefly outline the physical motivation behind this theory, and then derive the scaling laws. Physically, the authors assume that for short times (i.e. times where the radius of the adhesive patch is smaller than the size of the cell), the cell encompasses a viscous shell enclosing a liquid. For long times, where the radius of the adhesive patch is comparable to the size of the cell, the cell is a homogeneous viscous drop. See Figure 3 for details. Note that this model makes sense: for short times, only part of the cell will be touching the surface, whereas for long times most of the cell has already spread, and thus is substantially flattened.<br />
<br />
[[Image:Cells.png|thumb|300px| Figure 3, taken from [1].]]<br />
<br />
<br />
For short times, the contact zone will be disk-like, and the rate of change of the contact area will be: <math>\frac{dA}{dt} \approx R \frac{dR}{dt}</math>. The rate of energy gain is then <math>JR \frac{dR}{dt}</math>, where <math>J</math> is the adhesion energy per unit area. Using Figure 3, one then realizes that there is a characteristic shear strain of order <math>\frac{dR/dt}{w}</math>. The energy dissipation rate due to the viscous flow in the shell is proportional to the product of the shell viscosity (<math>\eta</math>), the square of the shear strain, and the volume over which dissipation occurs (see Figure 3; <math>V = R^{2}w</math>. Thus, it is proportional to: <math>\eta (\frac{dR}{dt} \frac{1}{w})^{2}R^{2}w</math>. By balancing this with the adhesive power, one find the scaling law for the contact radius for short times: <math>R = C(\frac{Jw}{\eta})^{\frac{1}{2}}t^{\frac{1}{2}}, R \leq R_{C}</math>, where <math>C</math> is a dimensionless constant and <math>R_{C}</math> is the initial radius of the cell. This agrees with the experimental results.<br />
<br />
For long times, viscous dissipation occurs in the whole cell (since the contact radius is comparable to the cell size). <br />
<br />
<br />
In addition, in order to test the theory, the authors performed another experiment. For this experiment, they altered the geometry and mechanical structure of the shell of the cell, which lead to a drastic change in the scaling law obtained above. I think this experiment is much more complicated than the value of its explanation is worth, but the results are shown in Figure 4. Note that the black line is for a cell with a normal shell, and the red line is for a cell with a "patchy" shell (meaning parts of it missing).<br />
<br />
[[Image:Expt1.png|thumb|300px| Figure 4, taken from [1].]]<br />
<br />
==Reference==<br />
[1] D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan, "The universal dynamics of cell spreading," Current Biology '''17''' 694 (2007).</div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=The_universal_dynamics_of_cell_spreading&diff=14002The universal dynamics of cell spreading2009-12-05T10:21:17Z<p>Chisholm: /* Soft Matter Discussion */</p>
<hr />
<div>Original entry: Naveen Sinha, APPHY 226, Spring 2009<br />
<br />
In numerous biological experiments, cells are plated onto an artificial adhesive surface to study them under a microscope. After being deposited on the surface, they flatten and spread outwards along the surface. This process incorporates many biological reactions, including the diffusion of adhesion receptors and the polymerization of the scaffolding-like actin molecules. However, Prof. Mahadevan and his collaborators show how a variety of cells and surface exhibit a power-law behavior in the contact radius of the colony of cells as a function of time. This can be understood when the cells are modeled as a viscous shell of liquid with a much less viscous interior. <br />
<br />
The basic biological system is shown below. Cells are placed on a surface and Reflectance Contrast Imaging Microscopy is used to measure the contact area as a function of time. <br />
<br />
[[Image:MahadevanUniversalFig01.jpg | 360 px]]<br />
<br />
The length measure used to characterize the system is the radius of a circle with the same area. On a log-log plot, the power law behavior becomes apparent.<br />
<br />
[[Image:MahadevanUniversalFig02.jpg | 360 px]]<br />
<br />
There appear to be two different regimes: (1) an initial diffusive regime with <math>R ~ t^{1/2}</math> and (2) a sub-diffusive region with <math>R ~ t^{1/4}</math>.<br />
<br />
Despite all the biochemical complexities of the spreading process, a simple model that treated the cells as a shell of viscous liquid is sufficient to describe most of the behavior. <br />
<br />
[[Image:MahadevanUniversalFig03.jpg | 360 px]]<br />
<br />
Initially, the power-law can be derived by setting the chance in adhesion energy equal to the viscous energy dissipation. This approximation is valid for when the radius of the contact angle is less than te initial cell radius <math>R_c</math>. The change in contact area is related to the rate of change in the radius by <math>\frac{dA}{dt} = R \frac{dR}{dt}</math>. This can related to the rate of energy gain by multiplying by the adhesion energy per unit area, J, which is the product of the area of each bond and the energy per bond: <math>J R \frac{dR}{dt}</math>. Assuming that the cell cortex has a width w everywhere, the strain is of the order <math>\frac{dR/dt}{w}</math>. This strain acts over a volume approximately equal to <math>R^2 w</math>. The product of the strain, volume, and viscosity leads to an energy dissipation of <math>\eta (\frac{dR}{dt} \frac{1}{w})</math>. By setting this equal to the change in the adhesion energy, we can get the following power law:<br />
<math>R = C \big(\frac{J w}{\eta}\big)^{1/2} t^{1/2}</math>.<br />
<br />
At longer times, when cell has flattened out (i.e. the radius of contact is larger than the initial radius), the viscous energy dissipation occurs throughout the whole volume of the cell. The power law is modified to <math>J R \frac{dR}{dt} = \eta_c \big(\frac{dR}{dt} \frac{1}{w}\big)^2 R^2 w_c</math>. This can be re-arranged to the scaling law:<br />
<math>R ~ \big(\frac{J R_c^3}{\eta_c}\big)^{1/4} t^{1/4}</math>.<br />
<br />
<br />
One prediction of this model is that the properties of the cellular membrane are far more important than the interior of the cell in the cell spreading. One way to test this is by creating two mutants: one in which the microtubules molecules within the cell are unable to polymerize and another in which the actin shell in the cortex is altered.<br />
<br />
[[Image:MahadevanUniversalFig04.jpg | 360 px]]<br />
<br />
Sung Hoon's comment: In the Fig. 4 (a), the Cytochalasin D-treated cell showed linear<br />
behavior. What does the treatment do so that the treated cells spread more quickly?<br />
<br />
Has anyone actually created these mutant cells to test this theory? Is that what you're showing below?<br />
Maybe it's better to write your own captions that get right to your point?<br />
--[[User:Lidiya|Lidiya]] 03:06, 18 February 2009 (UTC)<br />
<br />
This work is important by providing unity to the plethora of information about the molecular mechanics for cell motility and adhesion. It allows future researchers to focus on the aspects of cell structure that are most relevant for thee processes and make refinements to this basic model.<br />
<br />
<br />
-------------------------------------------------------------------------------------------------------------------------------------------------------------<br />
<br />
Second Entry: Nick Chisholm, AP 225, Fall 2009 (In Progress...)<br />
<br />
==General Information==<br />
'''Authors''': D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan <br />
<br />
'''Publication''': Current Biology '''17''' 694 (2007)<br />
<br />
==Soft Matter Keywords==<br />
[http://soft-matter.seas.harvard.edu/index.php/Adhesion Adhesion], [http://soft-matter.seas.harvard.edu/index.php/Cell Cell], [http://soft-matter.seas.harvard.edu/index.php/Polymerization Polymerization], Viscous<br />
<br />
==Summary==<br />
The authors explore the early stages of cell spreading. In particular, they look at the situation where cells are plated onto artificial adhesive surfaces; they first flatten and deform extensively as they spread. This article presents experimental probing of the dynamics of this spreading process using quantitative visualization and biochemical manipulation with a variety of cell types, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs. Surprisingly, the authors find that the adhesion dynamics of cells follow a universal power-law behavior (i.e. the contact radius is proportional to elapsed time to a certain power). The authors then provide a theoretical model that justifies their experimental results.<br />
<br />
In Figure 1, one can see an image of a cell spreading on a substrate. The image is taken using reflection interference contrast microscopy (RICM).<br />
<br />
[[Image:CellSpreading.png|thumb|300px| Figure 1, taken from [1].]]<br />
<br />
==Soft Matter Discussion==<br />
As is clear by Figure 1, the spreading is isotropic, the authors can define the spreading radius as: <math>R = \sqrt{\frac{A}{\pi}}</math>.<br />
<br />
The contact radius was found as a function of time for various cells, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs; the results are plotted in Figure 2 (careful: it's a logarithmic plot!). From this plot, the authors note two regimes: an initial diffusive regime summarized by the scaling law <math>R \propto t^{1/2}</math>, and later a subdiffusive regime summarized by the scaling law <math>R \propto t^{1/4}</math>. To be completely honest, I'm not quite sure how accurate these scaling laws are, if only derived from the plot in Figure 2. However, I would assume (or, at least, hope) that these plots were also examined without a logarithmic scale, and then fitted using these power-law forms. <br />
<br />
[[Image:ContactRadius.png|thumb|300px| Figure 2, taken from [1].]]<br />
<br />
<br />
In any case, the authors have also developed a theory which would predict these particular scaling laws. I will briefly outline the physical motivation behind this theory, and then derive the scaling laws. Physically, the authors assume that for short times (i.e. times where the radius of the adhesive patch is smaller than the size of the cell), the cell encompasses a viscous shell enclosing a liquid. For long times, where the radius of the adhesive patch is comparable to the size of the cell, the cell is a homogeneous viscous drop. See Figure 3 for details. Note that this model makes sense: for short times, only part of the cell will be touching the surface, whereas for long times most of the cell has already spread, and thus is substantially flattened.<br />
<br />
[[Image:Cells.png|thumb|300px| Figure 3, taken from [1].]]<br />
<br />
<br />
For short time scales, the contact zone will be disk-like, and the rate of change of the contact area will be: <math>\frac{dA}{dt} \approx R \frac{dR}{dt}</math>. The rate of energy gain is then <math>JR \frac{dR}{dt}</math>, where <math>J</math> is the adhesion energy per unit area. Using Figure 3, one then realizes that there is a characteristic shear strain of order <math>\frac{dR/dt}{w}</math>. The energy dissipation rate due to the viscous flow in the shell is proportional to the product of the shell viscosity (<math>\eta</math>), the square of the shear strain, and the volume over which dissipation occurs (see Figure 3; <math>V = R^{2}w</math>. Thus, it is proportional to: <math>\eta (\frac{dR}{dt} \frac{1}{w})^{2}R^{2}w</math>. By balancing this with the adhesive power, one find the scaling law for the contact radius for short times: <math>R = C(\frac{Jw}{\eta})^{\frac{1}{2}}t^{\frac{1}{2}}, R \leq R_{C}</math>, where <math>C</math> is a dimensionless constant and <math>R_{C}</math> is the initial radius of the cell.<br />
<br />
<br />
In addition, in order to test the theory, the authors performed another experiment. For this experiment, they altered the geometry and mechanical structure of the shell of the cell, which lead to a drastic change in the scaling law obtained above. I think this experiment is much more complicated than the value of its explanation is worth, but the results are shown in Figure 4. Note that the black line is for a cell with a normal shell, and the red line is for a cell with a "patchy" shell (meaning parts of it missing).<br />
<br />
[[Image:Expt1.png|thumb|300px| Figure 4, taken from [1].]]<br />
<br />
==Reference==<br />
[1] D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan, "The universal dynamics of cell spreading," Current Biology '''17''' 694 (2007).</div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=The_universal_dynamics_of_cell_spreading&diff=14001The universal dynamics of cell spreading2009-12-05T10:17:15Z<p>Chisholm: /* Soft Matter Discussion */</p>
<hr />
<div>Original entry: Naveen Sinha, APPHY 226, Spring 2009<br />
<br />
In numerous biological experiments, cells are plated onto an artificial adhesive surface to study them under a microscope. After being deposited on the surface, they flatten and spread outwards along the surface. This process incorporates many biological reactions, including the diffusion of adhesion receptors and the polymerization of the scaffolding-like actin molecules. However, Prof. Mahadevan and his collaborators show how a variety of cells and surface exhibit a power-law behavior in the contact radius of the colony of cells as a function of time. This can be understood when the cells are modeled as a viscous shell of liquid with a much less viscous interior. <br />
<br />
The basic biological system is shown below. Cells are placed on a surface and Reflectance Contrast Imaging Microscopy is used to measure the contact area as a function of time. <br />
<br />
[[Image:MahadevanUniversalFig01.jpg | 360 px]]<br />
<br />
The length measure used to characterize the system is the radius of a circle with the same area. On a log-log plot, the power law behavior becomes apparent.<br />
<br />
[[Image:MahadevanUniversalFig02.jpg | 360 px]]<br />
<br />
There appear to be two different regimes: (1) an initial diffusive regime with <math>R ~ t^{1/2}</math> and (2) a sub-diffusive region with <math>R ~ t^{1/4}</math>.<br />
<br />
Despite all the biochemical complexities of the spreading process, a simple model that treated the cells as a shell of viscous liquid is sufficient to describe most of the behavior. <br />
<br />
[[Image:MahadevanUniversalFig03.jpg | 360 px]]<br />
<br />
Initially, the power-law can be derived by setting the chance in adhesion energy equal to the viscous energy dissipation. This approximation is valid for when the radius of the contact angle is less than te initial cell radius <math>R_c</math>. The change in contact area is related to the rate of change in the radius by <math>\frac{dA}{dt} = R \frac{dR}{dt}</math>. This can related to the rate of energy gain by multiplying by the adhesion energy per unit area, J, which is the product of the area of each bond and the energy per bond: <math>J R \frac{dR}{dt}</math>. Assuming that the cell cortex has a width w everywhere, the strain is of the order <math>\frac{dR/dt}{w}</math>. This strain acts over a volume approximately equal to <math>R^2 w</math>. The product of the strain, volume, and viscosity leads to an energy dissipation of <math>\eta (\frac{dR}{dt} \frac{1}{w})</math>. By setting this equal to the change in the adhesion energy, we can get the following power law:<br />
<math>R = C \big(\frac{J w}{\eta}\big)^{1/2} t^{1/2}</math>.<br />
<br />
At longer times, when cell has flattened out (i.e. the radius of contact is larger than the initial radius), the viscous energy dissipation occurs throughout the whole volume of the cell. The power law is modified to <math>J R \frac{dR}{dt} = \eta_c \big(\frac{dR}{dt} \frac{1}{w}\big)^2 R^2 w_c</math>. This can be re-arranged to the scaling law:<br />
<math>R ~ \big(\frac{J R_c^3}{\eta_c}\big)^{1/4} t^{1/4}</math>.<br />
<br />
<br />
One prediction of this model is that the properties of the cellular membrane are far more important than the interior of the cell in the cell spreading. One way to test this is by creating two mutants: one in which the microtubules molecules within the cell are unable to polymerize and another in which the actin shell in the cortex is altered.<br />
<br />
[[Image:MahadevanUniversalFig04.jpg | 360 px]]<br />
<br />
Sung Hoon's comment: In the Fig. 4 (a), the Cytochalasin D-treated cell showed linear<br />
behavior. What does the treatment do so that the treated cells spread more quickly?<br />
<br />
Has anyone actually created these mutant cells to test this theory? Is that what you're showing below?<br />
Maybe it's better to write your own captions that get right to your point?<br />
--[[User:Lidiya|Lidiya]] 03:06, 18 February 2009 (UTC)<br />
<br />
This work is important by providing unity to the plethora of information about the molecular mechanics for cell motility and adhesion. It allows future researchers to focus on the aspects of cell structure that are most relevant for thee processes and make refinements to this basic model.<br />
<br />
<br />
-------------------------------------------------------------------------------------------------------------------------------------------------------------<br />
<br />
Second Entry: Nick Chisholm, AP 225, Fall 2009 (In Progress...)<br />
<br />
==General Information==<br />
'''Authors''': D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan <br />
<br />
'''Publication''': Current Biology '''17''' 694 (2007)<br />
<br />
==Soft Matter Keywords==<br />
[http://soft-matter.seas.harvard.edu/index.php/Adhesion Adhesion], [http://soft-matter.seas.harvard.edu/index.php/Cell Cell], [http://soft-matter.seas.harvard.edu/index.php/Polymerization Polymerization], Viscous<br />
<br />
==Summary==<br />
The authors explore the early stages of cell spreading. In particular, they look at the situation where cells are plated onto artificial adhesive surfaces; they first flatten and deform extensively as they spread. This article presents experimental probing of the dynamics of this spreading process using quantitative visualization and biochemical manipulation with a variety of cell types, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs. Surprisingly, the authors find that the adhesion dynamics of cells follow a universal power-law behavior (i.e. the contact radius is proportional to elapsed time to a certain power). The authors then provide a theoretical model that justifies their experimental results.<br />
<br />
In Figure 1, one can see an image of a cell spreading on a substrate. The image is taken using reflection interference contrast microscopy (RICM).<br />
<br />
[[Image:CellSpreading.png|thumb|300px| Figure 1, taken from [1].]]<br />
<br />
==Soft Matter Discussion==<br />
As is clear by Figure 1, the spreading is isotropic, the authors can define the spreading radius as: <math>R = \sqrt{\frac{A}{\pi}}</math>.<br />
<br />
The contact radius was found as a function of time for various cells, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs; the results are plotted in Figure 2 (careful: it's a logarithmic plot!). From this plot, the authors note two regimes: an initial diffusive regime summarized by the scaling law <math>R \propto t^{1/2}</math>, and later a subdiffusive regime summarized by the scaling law <math>R \propto t^{1/4}</math>. To be completely honest, I'm not quite sure how accurate these scaling laws are, if only derived from the plot in Figure 2. However, I would assume (or, at least, hope) that these plots were also examined without a logarithmic scale, and then fitted using these power-law forms. <br />
<br />
[[Image:ContactRadius.png|thumb|300px| Figure 2, taken from [1].]]<br />
<br />
<br />
In any case, the authors have also developed a theory which would predict these particular scaling laws. I will briefly outline the physical motivation behind this theory, and then derive the scaling laws. Physically, the authors assume that for small times (i.e. times where the radius of the adhesive patch is smaller than the size of the cell), the cell encompasses a viscous shell enclosing a liquid. For large times, where the radius of the adhesive patch is comparable to the size of the cell, the cell is a homogeneous viscous drop. See Figure 3 for details. Note that this model makes sense: for small times, only part of the cell will be touching the surface, whereas for long times most of the cell has already spread, and thus is substantially flattened.<br />
<br />
[[Image:Cells.png|thumb|300px| Figure 3, taken from [1].]]<br />
<br />
For short time scales, the contact zone will be disk-like, and the rate of change of the contact area will be: <math>\frac{dA}{dt} \approx R \frac{dR}{dt}</math>. The rate of energy gain is then <math>JR \frac{dR}{dt}</math>, where <math>J</math> is the adhesion energy per unit area. Using Figure 3, one then realizes that there is a characteristic shear strain of order <math>\frac{dR/dt}{w}</math>. The energy dissipation rate due to the viscous flow in the shell is proportional to the product of the shell viscosity, the square of the shear strain, and the volume over which dissipation occurs (see Figure 3; <math>V = R^{2}w</math>. Thus, it is proportional to: <math>\eta (\frac{dR}{dt} \frac{1}{w})^{2}R^{2}w</math>.<br />
<br />
In addition, in order to test the theory, the authors performed another experiment. For this experiment, they altered the geometry and mechanical structure of the shell of the cell, which lead to a drastic change in the scaling law obtained above. I think this experiment is much more complicated than the value of its explanation is worth, but the results are shown in Figure 4. Note that the black line is for a cell with a normal shell, and the red line is for a cell with a "patchy" shell (meaning parts of it missing).<br />
<br />
[[Image:Expt1.png|thumb|300px| Figure 4, taken from [1].]]<br />
<br />
==Reference==<br />
[1] D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan, "The universal dynamics of cell spreading," Current Biology '''17''' 694 (2007).</div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=The_universal_dynamics_of_cell_spreading&diff=14000The universal dynamics of cell spreading2009-12-05T10:12:03Z<p>Chisholm: /* Soft Matter Discussion */</p>
<hr />
<div>Original entry: Naveen Sinha, APPHY 226, Spring 2009<br />
<br />
In numerous biological experiments, cells are plated onto an artificial adhesive surface to study them under a microscope. After being deposited on the surface, they flatten and spread outwards along the surface. This process incorporates many biological reactions, including the diffusion of adhesion receptors and the polymerization of the scaffolding-like actin molecules. However, Prof. Mahadevan and his collaborators show how a variety of cells and surface exhibit a power-law behavior in the contact radius of the colony of cells as a function of time. This can be understood when the cells are modeled as a viscous shell of liquid with a much less viscous interior. <br />
<br />
The basic biological system is shown below. Cells are placed on a surface and Reflectance Contrast Imaging Microscopy is used to measure the contact area as a function of time. <br />
<br />
[[Image:MahadevanUniversalFig01.jpg | 360 px]]<br />
<br />
The length measure used to characterize the system is the radius of a circle with the same area. On a log-log plot, the power law behavior becomes apparent.<br />
<br />
[[Image:MahadevanUniversalFig02.jpg | 360 px]]<br />
<br />
There appear to be two different regimes: (1) an initial diffusive regime with <math>R ~ t^{1/2}</math> and (2) a sub-diffusive region with <math>R ~ t^{1/4}</math>.<br />
<br />
Despite all the biochemical complexities of the spreading process, a simple model that treated the cells as a shell of viscous liquid is sufficient to describe most of the behavior. <br />
<br />
[[Image:MahadevanUniversalFig03.jpg | 360 px]]<br />
<br />
Initially, the power-law can be derived by setting the chance in adhesion energy equal to the viscous energy dissipation. This approximation is valid for when the radius of the contact angle is less than te initial cell radius <math>R_c</math>. The change in contact area is related to the rate of change in the radius by <math>\frac{dA}{dt} = R \frac{dR}{dt}</math>. This can related to the rate of energy gain by multiplying by the adhesion energy per unit area, J, which is the product of the area of each bond and the energy per bond: <math>J R \frac{dR}{dt}</math>. Assuming that the cell cortex has a width w everywhere, the strain is of the order <math>\frac{dR/dt}{w}</math>. This strain acts over a volume approximately equal to <math>R^2 w</math>. The product of the strain, volume, and viscosity leads to an energy dissipation of <math>\eta (\frac{dR}{dt} \frac{1}{w})</math>. By setting this equal to the change in the adhesion energy, we can get the following power law:<br />
<math>R = C \big(\frac{J w}{\eta}\big)^{1/2} t^{1/2}</math>.<br />
<br />
At longer times, when cell has flattened out (i.e. the radius of contact is larger than the initial radius), the viscous energy dissipation occurs throughout the whole volume of the cell. The power law is modified to <math>J R \frac{dR}{dt} = \eta_c \big(\frac{dR}{dt} \frac{1}{w}\big)^2 R^2 w_c</math>. This can be re-arranged to the scaling law:<br />
<math>R ~ \big(\frac{J R_c^3}{\eta_c}\big)^{1/4} t^{1/4}</math>.<br />
<br />
<br />
One prediction of this model is that the properties of the cellular membrane are far more important than the interior of the cell in the cell spreading. One way to test this is by creating two mutants: one in which the microtubules molecules within the cell are unable to polymerize and another in which the actin shell in the cortex is altered.<br />
<br />
[[Image:MahadevanUniversalFig04.jpg | 360 px]]<br />
<br />
Sung Hoon's comment: In the Fig. 4 (a), the Cytochalasin D-treated cell showed linear<br />
behavior. What does the treatment do so that the treated cells spread more quickly?<br />
<br />
Has anyone actually created these mutant cells to test this theory? Is that what you're showing below?<br />
Maybe it's better to write your own captions that get right to your point?<br />
--[[User:Lidiya|Lidiya]] 03:06, 18 February 2009 (UTC)<br />
<br />
This work is important by providing unity to the plethora of information about the molecular mechanics for cell motility and adhesion. It allows future researchers to focus on the aspects of cell structure that are most relevant for thee processes and make refinements to this basic model.<br />
<br />
<br />
-------------------------------------------------------------------------------------------------------------------------------------------------------------<br />
<br />
Second Entry: Nick Chisholm, AP 225, Fall 2009 (In Progress...)<br />
<br />
==General Information==<br />
'''Authors''': D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan <br />
<br />
'''Publication''': Current Biology '''17''' 694 (2007)<br />
<br />
==Soft Matter Keywords==<br />
[http://soft-matter.seas.harvard.edu/index.php/Adhesion Adhesion], [http://soft-matter.seas.harvard.edu/index.php/Cell Cell], [http://soft-matter.seas.harvard.edu/index.php/Polymerization Polymerization], Viscous<br />
<br />
==Summary==<br />
The authors explore the early stages of cell spreading. In particular, they look at the situation where cells are plated onto artificial adhesive surfaces; they first flatten and deform extensively as they spread. This article presents experimental probing of the dynamics of this spreading process using quantitative visualization and biochemical manipulation with a variety of cell types, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs. Surprisingly, the authors find that the adhesion dynamics of cells follow a universal power-law behavior (i.e. the contact radius is proportional to elapsed time to a certain power). The authors then provide a theoretical model that justifies their experimental results.<br />
<br />
In Figure 1, one can see an image of a cell spreading on a substrate. The image is taken using reflection interference contrast microscopy (RICM).<br />
<br />
[[Image:CellSpreading.png|thumb|300px| Figure 1, taken from [1].]]<br />
<br />
==Soft Matter Discussion==<br />
As is clear by Figure 1, the spreading is isotropic, the authors can define the spreading radius as: <math>R = \sqrt{\frac{A}{\pi}}</math>.<br />
<br />
The contact radius was found as a function of time for various cells, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs; the results are plotted in Figure 2 (careful: it's a logarithmic plot!). From this plot, the authors note two regimes: an initial diffusive regime summarized by the scaling law <math>R \propto t^{1/2}</math>, and later a subdiffusive regime summarized by the scaling law <math>R \propto t^{1/4}</math>. To be completely honest, I'm not quite sure how accurate these scaling laws are, if only derived from the plot in Figure 2. However, I would assume (or, at least, hope) that these plots were also examined without a logarithmic scale, and then fitted using these power-law forms. <br />
<br />
[[Image:ContactRadius.png|thumb|300px| Figure 2, taken from [1].]]<br />
<br />
<br />
In any case, the authors have also developed a theory which would predict these particular scaling laws. I will briefly outline the physical motivation behind this theory, and then derive the scaling laws. Physically, the authors assume that for small times (i.e. times where the radius of the adhesive patch is smaller than the size of the cell), the cell encompasses a viscous shell enclosing a liquid. For large times, where the radius of the adhesive patch is comparable to the size of the cell, the cell is a homogeneous viscous drop. See Figure 3 for details. Note that this model makes sense: for small times, only part of the cell will be touching the surface, whereas for long times most of the cell has already spread, and thus is substantially flattened.<br />
<br />
[[Image:Cells.png|thumb|300px| Figure 3, taken from [1].]]<br />
<br />
For short time scales, the contact zone will be disk-like, and the rate of change of the contact area will be: <math>\frac{dA}{dt} \approx R \frac{dR}{dt}</math>. The rate of energy gain is then <math>JR \frac{dR}{dt}</math>, where <math>J</math> is the adhesion energy per unit area. Using Figure 3, one then realizes that there is a characteristic shear strain of order <math>\frac{dR/dt}{w}</math>. <br />
<br />
In addition, in order to test the theory, the authors performed another experiment. For this experiment, they altered the geometry and mechanical structure of the shell of the cell, which lead to a drastic change in the scaling law obtained above. I think this experiment is much more complicated than the value of its explanation is worth, but the results are shown in Figure 4. Note that the black line is for a cell with a normal shell, and the red line is for a cell with a "patchy" shell (meaning parts of it missing).<br />
<br />
[[Image:Expt1.png|thumb|300px| Figure 4, taken from [1].]]<br />
<br />
==Reference==<br />
[1] D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan, "The universal dynamics of cell spreading," Current Biology '''17''' 694 (2007).</div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=The_universal_dynamics_of_cell_spreading&diff=13999The universal dynamics of cell spreading2009-12-05T10:09:07Z<p>Chisholm: /* Soft Matter Discussion */</p>
<hr />
<div>Original entry: Naveen Sinha, APPHY 226, Spring 2009<br />
<br />
In numerous biological experiments, cells are plated onto an artificial adhesive surface to study them under a microscope. After being deposited on the surface, they flatten and spread outwards along the surface. This process incorporates many biological reactions, including the diffusion of adhesion receptors and the polymerization of the scaffolding-like actin molecules. However, Prof. Mahadevan and his collaborators show how a variety of cells and surface exhibit a power-law behavior in the contact radius of the colony of cells as a function of time. This can be understood when the cells are modeled as a viscous shell of liquid with a much less viscous interior. <br />
<br />
The basic biological system is shown below. Cells are placed on a surface and Reflectance Contrast Imaging Microscopy is used to measure the contact area as a function of time. <br />
<br />
[[Image:MahadevanUniversalFig01.jpg | 360 px]]<br />
<br />
The length measure used to characterize the system is the radius of a circle with the same area. On a log-log plot, the power law behavior becomes apparent.<br />
<br />
[[Image:MahadevanUniversalFig02.jpg | 360 px]]<br />
<br />
There appear to be two different regimes: (1) an initial diffusive regime with <math>R ~ t^{1/2}</math> and (2) a sub-diffusive region with <math>R ~ t^{1/4}</math>.<br />
<br />
Despite all the biochemical complexities of the spreading process, a simple model that treated the cells as a shell of viscous liquid is sufficient to describe most of the behavior. <br />
<br />
[[Image:MahadevanUniversalFig03.jpg | 360 px]]<br />
<br />
Initially, the power-law can be derived by setting the chance in adhesion energy equal to the viscous energy dissipation. This approximation is valid for when the radius of the contact angle is less than te initial cell radius <math>R_c</math>. The change in contact area is related to the rate of change in the radius by <math>\frac{dA}{dt} = R \frac{dR}{dt}</math>. This can related to the rate of energy gain by multiplying by the adhesion energy per unit area, J, which is the product of the area of each bond and the energy per bond: <math>J R \frac{dR}{dt}</math>. Assuming that the cell cortex has a width w everywhere, the strain is of the order <math>\frac{dR/dt}{w}</math>. This strain acts over a volume approximately equal to <math>R^2 w</math>. The product of the strain, volume, and viscosity leads to an energy dissipation of <math>\eta (\frac{dR}{dt} \frac{1}{w})</math>. By setting this equal to the change in the adhesion energy, we can get the following power law:<br />
<math>R = C \big(\frac{J w}{\eta}\big)^{1/2} t^{1/2}</math>.<br />
<br />
At longer times, when cell has flattened out (i.e. the radius of contact is larger than the initial radius), the viscous energy dissipation occurs throughout the whole volume of the cell. The power law is modified to <math>J R \frac{dR}{dt} = \eta_c \big(\frac{dR}{dt} \frac{1}{w}\big)^2 R^2 w_c</math>. This can be re-arranged to the scaling law:<br />
<math>R ~ \big(\frac{J R_c^3}{\eta_c}\big)^{1/4} t^{1/4}</math>.<br />
<br />
<br />
One prediction of this model is that the properties of the cellular membrane are far more important than the interior of the cell in the cell spreading. One way to test this is by creating two mutants: one in which the microtubules molecules within the cell are unable to polymerize and another in which the actin shell in the cortex is altered.<br />
<br />
[[Image:MahadevanUniversalFig04.jpg | 360 px]]<br />
<br />
Sung Hoon's comment: In the Fig. 4 (a), the Cytochalasin D-treated cell showed linear<br />
behavior. What does the treatment do so that the treated cells spread more quickly?<br />
<br />
Has anyone actually created these mutant cells to test this theory? Is that what you're showing below?<br />
Maybe it's better to write your own captions that get right to your point?<br />
--[[User:Lidiya|Lidiya]] 03:06, 18 February 2009 (UTC)<br />
<br />
This work is important by providing unity to the plethora of information about the molecular mechanics for cell motility and adhesion. It allows future researchers to focus on the aspects of cell structure that are most relevant for thee processes and make refinements to this basic model.<br />
<br />
<br />
-------------------------------------------------------------------------------------------------------------------------------------------------------------<br />
<br />
Second Entry: Nick Chisholm, AP 225, Fall 2009 (In Progress...)<br />
<br />
==General Information==<br />
'''Authors''': D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan <br />
<br />
'''Publication''': Current Biology '''17''' 694 (2007)<br />
<br />
==Soft Matter Keywords==<br />
[http://soft-matter.seas.harvard.edu/index.php/Adhesion Adhesion], [http://soft-matter.seas.harvard.edu/index.php/Cell Cell], [http://soft-matter.seas.harvard.edu/index.php/Polymerization Polymerization], Viscous<br />
<br />
==Summary==<br />
The authors explore the early stages of cell spreading. In particular, they look at the situation where cells are plated onto artificial adhesive surfaces; they first flatten and deform extensively as they spread. This article presents experimental probing of the dynamics of this spreading process using quantitative visualization and biochemical manipulation with a variety of cell types, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs. Surprisingly, the authors find that the adhesion dynamics of cells follow a universal power-law behavior (i.e. the contact radius is proportional to elapsed time to a certain power). The authors then provide a theoretical model that justifies their experimental results.<br />
<br />
In Figure 1, one can see an image of a cell spreading on a substrate. The image is taken using reflection interference contrast microscopy (RICM).<br />
<br />
[[Image:CellSpreading.png|thumb|300px| Figure 1, taken from [1].]]<br />
<br />
==Soft Matter Discussion==<br />
As is clear by Figure 1, the spreading is isotropic, the authors can define the spreading radius as: <math>R = \sqrt{\frac{A}{\pi}}</math>.<br />
<br />
The contact radius was found as a function of time for various cells, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs; the results are plotted in Figure 2 (careful: it's a logarithmic plot!). From this plot, the authors note two regimes: an initial diffusive regime summarized by the scaling law <math>R \propto t^{1/2}</math>, and later a subdiffusive regime summarized by the scaling law <math>R \propto t^{1/4}</math>. To be completely honest, I'm not quite sure how accurate these scaling laws are, if only derived from the plot in Figure 2. However, I would assume (or, at least, hope) that these plots were also examined without a logarithmic scale, and then fitted using these power-law forms. <br />
<br />
[[Image:ContactRadius.png|thumb|300px| Figure 2, taken from [1].]]<br />
<br />
<br />
In any case, the authors have also developed a theory which would predict these particular scaling laws. I will briefly outline the physical motivation behind this theory, and then derive the scaling laws. Physically, the authors assume that for small times (i.e. times where the radius of the adhesive patch is smaller than the size of the cell), the cell encompasses a viscous shell enclosing a liquid. For large times, where the radius of the adhesive patch is comparable to the size of the cell, the cell is a homogeneous viscous drop. See Figure 3 for details. Note that this model makes sense: for small times, only part of the cell will be touching the surface, whereas for long times most of the cell has already spread, and thus is substantially flattened.<br />
<br />
[[Image:Cells.png|thumb|300px| Figure 3, taken from [1].]]<br />
<br />
For short time scales, the contact zone will be disk-like, and the rate of change of the contact area will be: <math>\frac{dA}{dt} \approx R \frac{dR}{dt}</math>. The rate of energy gain is then <math>JR \frac{dR}{dt}</math>, where <math>J</math> is the adhesion energy per unit area. <br />
<br />
In addition, in order to test the theory, the authors performed another experiment. For this experiment, they altered the geometry and mechanical structure of the shell of the cell, which lead to a drastic change in the scaling law obtained above. I think this experiment is much more complicated than the value of its explanation is worth, but the results are shown in Figure 4. Note that the black line is for a cell with a normal shell, and the red line is for a cell with a "patchy" shell (meaning parts of it missing).<br />
<br />
[[Image:Expt1.png|thumb|300px| Figure 4, taken from [1].]]<br />
<br />
==Reference==<br />
[1] D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan, "The universal dynamics of cell spreading," Current Biology '''17''' 694 (2007).</div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=The_universal_dynamics_of_cell_spreading&diff=13998The universal dynamics of cell spreading2009-12-05T09:09:20Z<p>Chisholm: /* Summary */</p>
<hr />
<div>Original entry: Naveen Sinha, APPHY 226, Spring 2009<br />
<br />
In numerous biological experiments, cells are plated onto an artificial adhesive surface to study them under a microscope. After being deposited on the surface, they flatten and spread outwards along the surface. This process incorporates many biological reactions, including the diffusion of adhesion receptors and the polymerization of the scaffolding-like actin molecules. However, Prof. Mahadevan and his collaborators show how a variety of cells and surface exhibit a power-law behavior in the contact radius of the colony of cells as a function of time. This can be understood when the cells are modeled as a viscous shell of liquid with a much less viscous interior. <br />
<br />
The basic biological system is shown below. Cells are placed on a surface and Reflectance Contrast Imaging Microscopy is used to measure the contact area as a function of time. <br />
<br />
[[Image:MahadevanUniversalFig01.jpg | 360 px]]<br />
<br />
The length measure used to characterize the system is the radius of a circle with the same area. On a log-log plot, the power law behavior becomes apparent.<br />
<br />
[[Image:MahadevanUniversalFig02.jpg | 360 px]]<br />
<br />
There appear to be two different regimes: (1) an initial diffusive regime with <math>R ~ t^{1/2}</math> and (2) a sub-diffusive region with <math>R ~ t^{1/4}</math>.<br />
<br />
Despite all the biochemical complexities of the spreading process, a simple model that treated the cells as a shell of viscous liquid is sufficient to describe most of the behavior. <br />
<br />
[[Image:MahadevanUniversalFig03.jpg | 360 px]]<br />
<br />
Initially, the power-law can be derived by setting the chance in adhesion energy equal to the viscous energy dissipation. This approximation is valid for when the radius of the contact angle is less than te initial cell radius <math>R_c</math>. The change in contact area is related to the rate of change in the radius by <math>\frac{dA}{dt} = R \frac{dR}{dt}</math>. This can related to the rate of energy gain by multiplying by the adhesion energy per unit area, J, which is the product of the area of each bond and the energy per bond: <math>J R \frac{dR}{dt}</math>. Assuming that the cell cortex has a width w everywhere, the strain is of the order <math>\frac{dR/dt}{w}</math>. This strain acts over a volume approximately equal to <math>R^2 w</math>. The product of the strain, volume, and viscosity leads to an energy dissipation of <math>\eta (\frac{dR}{dt} \frac{1}{w})</math>. By setting this equal to the change in the adhesion energy, we can get the following power law:<br />
<math>R = C \big(\frac{J w}{\eta}\big)^{1/2} t^{1/2}</math>.<br />
<br />
At longer times, when cell has flattened out (i.e. the radius of contact is larger than the initial radius), the viscous energy dissipation occurs throughout the whole volume of the cell. The power law is modified to <math>J R \frac{dR}{dt} = \eta_c \big(\frac{dR}{dt} \frac{1}{w}\big)^2 R^2 w_c</math>. This can be re-arranged to the scaling law:<br />
<math>R ~ \big(\frac{J R_c^3}{\eta_c}\big)^{1/4} t^{1/4}</math>.<br />
<br />
<br />
One prediction of this model is that the properties of the cellular membrane are far more important than the interior of the cell in the cell spreading. One way to test this is by creating two mutants: one in which the microtubules molecules within the cell are unable to polymerize and another in which the actin shell in the cortex is altered.<br />
<br />
[[Image:MahadevanUniversalFig04.jpg | 360 px]]<br />
<br />
Sung Hoon's comment: In the Fig. 4 (a), the Cytochalasin D-treated cell showed linear<br />
behavior. What does the treatment do so that the treated cells spread more quickly?<br />
<br />
Has anyone actually created these mutant cells to test this theory? Is that what you're showing below?<br />
Maybe it's better to write your own captions that get right to your point?<br />
--[[User:Lidiya|Lidiya]] 03:06, 18 February 2009 (UTC)<br />
<br />
This work is important by providing unity to the plethora of information about the molecular mechanics for cell motility and adhesion. It allows future researchers to focus on the aspects of cell structure that are most relevant for thee processes and make refinements to this basic model.<br />
<br />
<br />
-------------------------------------------------------------------------------------------------------------------------------------------------------------<br />
<br />
Second Entry: Nick Chisholm, AP 225, Fall 2009 (In Progress...)<br />
<br />
==General Information==<br />
'''Authors''': D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan <br />
<br />
'''Publication''': Current Biology '''17''' 694 (2007)<br />
<br />
==Soft Matter Keywords==<br />
[http://soft-matter.seas.harvard.edu/index.php/Adhesion Adhesion], [http://soft-matter.seas.harvard.edu/index.php/Cell Cell], [http://soft-matter.seas.harvard.edu/index.php/Polymerization Polymerization], Viscous<br />
<br />
==Summary==<br />
The authors explore the early stages of cell spreading. In particular, they look at the situation where cells are plated onto artificial adhesive surfaces; they first flatten and deform extensively as they spread. This article presents experimental probing of the dynamics of this spreading process using quantitative visualization and biochemical manipulation with a variety of cell types, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs. Surprisingly, the authors find that the adhesion dynamics of cells follow a universal power-law behavior (i.e. the contact radius is proportional to elapsed time to a certain power). The authors then provide a theoretical model that justifies their experimental results.<br />
<br />
In Figure 1, one can see an image of a cell spreading on a substrate. The image is taken using reflection interference contrast microscopy (RICM).<br />
<br />
[[Image:CellSpreading.png|thumb|300px| Figure 1, taken from [1].]]<br />
<br />
==Soft Matter Discussion==<br />
As is clear by Figure 1, the spreading is isotropic, the authors can define the spreading radius as: <math>R = \sqrt{\frac{A}{\pi}}</math>.<br />
<br />
The contact radius was found as a function of time for various cells, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs; the results are plotted in Figure 2 (careful: it's a logarithmic plot!). From this plot, the authors note two regimes: an initial diffusive regime summarized by the scaling law <math>R \propto t^{1/2}</math>, and later a subdiffusive regime summarized by the scaling law <math>R \propto t^{1/4}</math>. To be completely honest, I'm not quite sure how accurate these scaling laws are, if only derived from the plot in Figure 2. However, I would assume (or, at least, hope) that these plots were also examined without a logarithmic scale, and then fitted using these power-law forms. <br />
<br />
[[Image:ContactRadius.png|thumb|300px| Figure 2, taken from [1].]]<br />
<br />
<br />
In any case, the authors have also developed a theory which would predict these particular scaling laws. I will briefly outline the physical motivation behind this theory, and then derive the scaling laws. Physically, the authors assume that for small times (i.e. times where the radius of the adhesive patch is smaller than the size of the cell), the cell encompasses a viscous shell enclosing a liquid. For large times, where the radius of the adhesive patch is comparable to the size of the cell, the cell is a homogeneous viscous drop. See Figure 3 for details. Note that this model makes sense: for small times, only part of the cell will be touching the surface, whereas for long times most of the cell has already spread, and thus is substantially flattened.<br />
<br />
[[Image:Cells.png|thumb|300px| Figure 3, taken from [1].]]<br />
<br />
<br />
<br />
In addition, in order to test the theory, the authors performed another experiment. For this experiment, they altered the geometry and mechanical structure of the shell of the cell, which lead to a drastic change in the scaling law obtained above. I think this experiment is much more complicated than the value of its explanation is worth, but the results are shown in Figure 4. Note that the black line is for a cell with a normal shell, and the red line is for a cell with a "patchy" shell (meaning parts of it missing).<br />
<br />
[[Image:Expt1.png|thumb|300px| Figure 4, taken from [1].]]<br />
<br />
==Reference==<br />
[1] D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan, "The universal dynamics of cell spreading," Current Biology '''17''' 694 (2007).</div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=File:Expt1.png&diff=13997File:Expt1.png2009-12-05T09:08:09Z<p>Chisholm: </p>
<hr />
<div></div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=The_universal_dynamics_of_cell_spreading&diff=13996The universal dynamics of cell spreading2009-12-05T09:08:01Z<p>Chisholm: /* Soft Matter Discussion */</p>
<hr />
<div>Original entry: Naveen Sinha, APPHY 226, Spring 2009<br />
<br />
In numerous biological experiments, cells are plated onto an artificial adhesive surface to study them under a microscope. After being deposited on the surface, they flatten and spread outwards along the surface. This process incorporates many biological reactions, including the diffusion of adhesion receptors and the polymerization of the scaffolding-like actin molecules. However, Prof. Mahadevan and his collaborators show how a variety of cells and surface exhibit a power-law behavior in the contact radius of the colony of cells as a function of time. This can be understood when the cells are modeled as a viscous shell of liquid with a much less viscous interior. <br />
<br />
The basic biological system is shown below. Cells are placed on a surface and Reflectance Contrast Imaging Microscopy is used to measure the contact area as a function of time. <br />
<br />
[[Image:MahadevanUniversalFig01.jpg | 360 px]]<br />
<br />
The length measure used to characterize the system is the radius of a circle with the same area. On a log-log plot, the power law behavior becomes apparent.<br />
<br />
[[Image:MahadevanUniversalFig02.jpg | 360 px]]<br />
<br />
There appear to be two different regimes: (1) an initial diffusive regime with <math>R ~ t^{1/2}</math> and (2) a sub-diffusive region with <math>R ~ t^{1/4}</math>.<br />
<br />
Despite all the biochemical complexities of the spreading process, a simple model that treated the cells as a shell of viscous liquid is sufficient to describe most of the behavior. <br />
<br />
[[Image:MahadevanUniversalFig03.jpg | 360 px]]<br />
<br />
Initially, the power-law can be derived by setting the chance in adhesion energy equal to the viscous energy dissipation. This approximation is valid for when the radius of the contact angle is less than te initial cell radius <math>R_c</math>. The change in contact area is related to the rate of change in the radius by <math>\frac{dA}{dt} = R \frac{dR}{dt}</math>. This can related to the rate of energy gain by multiplying by the adhesion energy per unit area, J, which is the product of the area of each bond and the energy per bond: <math>J R \frac{dR}{dt}</math>. Assuming that the cell cortex has a width w everywhere, the strain is of the order <math>\frac{dR/dt}{w}</math>. This strain acts over a volume approximately equal to <math>R^2 w</math>. The product of the strain, volume, and viscosity leads to an energy dissipation of <math>\eta (\frac{dR}{dt} \frac{1}{w})</math>. By setting this equal to the change in the adhesion energy, we can get the following power law:<br />
<math>R = C \big(\frac{J w}{\eta}\big)^{1/2} t^{1/2}</math>.<br />
<br />
At longer times, when cell has flattened out (i.e. the radius of contact is larger than the initial radius), the viscous energy dissipation occurs throughout the whole volume of the cell. The power law is modified to <math>J R \frac{dR}{dt} = \eta_c \big(\frac{dR}{dt} \frac{1}{w}\big)^2 R^2 w_c</math>. This can be re-arranged to the scaling law:<br />
<math>R ~ \big(\frac{J R_c^3}{\eta_c}\big)^{1/4} t^{1/4}</math>.<br />
<br />
<br />
One prediction of this model is that the properties of the cellular membrane are far more important than the interior of the cell in the cell spreading. One way to test this is by creating two mutants: one in which the microtubules molecules within the cell are unable to polymerize and another in which the actin shell in the cortex is altered.<br />
<br />
[[Image:MahadevanUniversalFig04.jpg | 360 px]]<br />
<br />
Sung Hoon's comment: In the Fig. 4 (a), the Cytochalasin D-treated cell showed linear<br />
behavior. What does the treatment do so that the treated cells spread more quickly?<br />
<br />
Has anyone actually created these mutant cells to test this theory? Is that what you're showing below?<br />
Maybe it's better to write your own captions that get right to your point?<br />
--[[User:Lidiya|Lidiya]] 03:06, 18 February 2009 (UTC)<br />
<br />
This work is important by providing unity to the plethora of information about the molecular mechanics for cell motility and adhesion. It allows future researchers to focus on the aspects of cell structure that are most relevant for thee processes and make refinements to this basic model.<br />
<br />
<br />
-------------------------------------------------------------------------------------------------------------------------------------------------------------<br />
<br />
Second Entry: Nick Chisholm, AP 225, Fall 2009 (In Progress...)<br />
<br />
==General Information==<br />
'''Authors''': D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan <br />
<br />
'''Publication''': Current Biology '''17''' 694 (2007)<br />
<br />
==Soft Matter Keywords==<br />
[http://soft-matter.seas.harvard.edu/index.php/Adhesion Adhesion], [http://soft-matter.seas.harvard.edu/index.php/Cell Cell], [http://soft-matter.seas.harvard.edu/index.php/Polymerization Polymerization], Viscous<br />
<br />
==Summary==<br />
The authors explore the early stages of cell spreading. In particular, they look at the situation where cells are plated onto artificial adhesive surfaces; they first flatten and deform extensively as they spread. This article presents experimental probing of the dynamics of this spreading process using quantitative visualization and biochemical manipulation with a variety of cell types, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs. Surprisingly, the authors find that the adhesion dynamics of cells follow a universal power-law behavior (i.e. the contact radius is proportional to elapsed time to a certain power).<br />
<br />
In Figure 1, one can see an image of a cell spreading on a substrate. The image is taken using reflection interference contrast microscopy (RICM).<br />
<br />
[[Image:CellSpreading.png|thumb|300px| Figure 1, taken from [1].]]<br />
<br />
==Soft Matter Discussion==<br />
As is clear by Figure 1, the spreading is isotropic, the authors can define the spreading radius as: <math>R = \sqrt{\frac{A}{\pi}}</math>.<br />
<br />
The contact radius was found as a function of time for various cells, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs; the results are plotted in Figure 2 (careful: it's a logarithmic plot!). From this plot, the authors note two regimes: an initial diffusive regime summarized by the scaling law <math>R \propto t^{1/2}</math>, and later a subdiffusive regime summarized by the scaling law <math>R \propto t^{1/4}</math>. To be completely honest, I'm not quite sure how accurate these scaling laws are, if only derived from the plot in Figure 2. However, I would assume (or, at least, hope) that these plots were also examined without a logarithmic scale, and then fitted using these power-law forms. <br />
<br />
[[Image:ContactRadius.png|thumb|300px| Figure 2, taken from [1].]]<br />
<br />
<br />
In any case, the authors have also developed a theory which would predict these particular scaling laws. I will briefly outline the physical motivation behind this theory, and then derive the scaling laws. Physically, the authors assume that for small times (i.e. times where the radius of the adhesive patch is smaller than the size of the cell), the cell encompasses a viscous shell enclosing a liquid. For large times, where the radius of the adhesive patch is comparable to the size of the cell, the cell is a homogeneous viscous drop. See Figure 3 for details. Note that this model makes sense: for small times, only part of the cell will be touching the surface, whereas for long times most of the cell has already spread, and thus is substantially flattened.<br />
<br />
[[Image:Cells.png|thumb|300px| Figure 3, taken from [1].]]<br />
<br />
<br />
<br />
In addition, in order to test the theory, the authors performed another experiment. For this experiment, they altered the geometry and mechanical structure of the shell of the cell, which lead to a drastic change in the scaling law obtained above. I think this experiment is much more complicated than the value of its explanation is worth, but the results are shown in Figure 4. Note that the black line is for a cell with a normal shell, and the red line is for a cell with a "patchy" shell (meaning parts of it missing).<br />
<br />
[[Image:Expt1.png|thumb|300px| Figure 4, taken from [1].]]<br />
<br />
==Reference==<br />
[1] D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan, "The universal dynamics of cell spreading," Current Biology '''17''' 694 (2007).</div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=The_universal_dynamics_of_cell_spreading&diff=13995The universal dynamics of cell spreading2009-12-05T09:07:48Z<p>Chisholm: /* Soft Matter Discussion */</p>
<hr />
<div>Original entry: Naveen Sinha, APPHY 226, Spring 2009<br />
<br />
In numerous biological experiments, cells are plated onto an artificial adhesive surface to study them under a microscope. After being deposited on the surface, they flatten and spread outwards along the surface. This process incorporates many biological reactions, including the diffusion of adhesion receptors and the polymerization of the scaffolding-like actin molecules. However, Prof. Mahadevan and his collaborators show how a variety of cells and surface exhibit a power-law behavior in the contact radius of the colony of cells as a function of time. This can be understood when the cells are modeled as a viscous shell of liquid with a much less viscous interior. <br />
<br />
The basic biological system is shown below. Cells are placed on a surface and Reflectance Contrast Imaging Microscopy is used to measure the contact area as a function of time. <br />
<br />
[[Image:MahadevanUniversalFig01.jpg | 360 px]]<br />
<br />
The length measure used to characterize the system is the radius of a circle with the same area. On a log-log plot, the power law behavior becomes apparent.<br />
<br />
[[Image:MahadevanUniversalFig02.jpg | 360 px]]<br />
<br />
There appear to be two different regimes: (1) an initial diffusive regime with <math>R ~ t^{1/2}</math> and (2) a sub-diffusive region with <math>R ~ t^{1/4}</math>.<br />
<br />
Despite all the biochemical complexities of the spreading process, a simple model that treated the cells as a shell of viscous liquid is sufficient to describe most of the behavior. <br />
<br />
[[Image:MahadevanUniversalFig03.jpg | 360 px]]<br />
<br />
Initially, the power-law can be derived by setting the chance in adhesion energy equal to the viscous energy dissipation. This approximation is valid for when the radius of the contact angle is less than te initial cell radius <math>R_c</math>. The change in contact area is related to the rate of change in the radius by <math>\frac{dA}{dt} = R \frac{dR}{dt}</math>. This can related to the rate of energy gain by multiplying by the adhesion energy per unit area, J, which is the product of the area of each bond and the energy per bond: <math>J R \frac{dR}{dt}</math>. Assuming that the cell cortex has a width w everywhere, the strain is of the order <math>\frac{dR/dt}{w}</math>. This strain acts over a volume approximately equal to <math>R^2 w</math>. The product of the strain, volume, and viscosity leads to an energy dissipation of <math>\eta (\frac{dR}{dt} \frac{1}{w})</math>. By setting this equal to the change in the adhesion energy, we can get the following power law:<br />
<math>R = C \big(\frac{J w}{\eta}\big)^{1/2} t^{1/2}</math>.<br />
<br />
At longer times, when cell has flattened out (i.e. the radius of contact is larger than the initial radius), the viscous energy dissipation occurs throughout the whole volume of the cell. The power law is modified to <math>J R \frac{dR}{dt} = \eta_c \big(\frac{dR}{dt} \frac{1}{w}\big)^2 R^2 w_c</math>. This can be re-arranged to the scaling law:<br />
<math>R ~ \big(\frac{J R_c^3}{\eta_c}\big)^{1/4} t^{1/4}</math>.<br />
<br />
<br />
One prediction of this model is that the properties of the cellular membrane are far more important than the interior of the cell in the cell spreading. One way to test this is by creating two mutants: one in which the microtubules molecules within the cell are unable to polymerize and another in which the actin shell in the cortex is altered.<br />
<br />
[[Image:MahadevanUniversalFig04.jpg | 360 px]]<br />
<br />
Sung Hoon's comment: In the Fig. 4 (a), the Cytochalasin D-treated cell showed linear<br />
behavior. What does the treatment do so that the treated cells spread more quickly?<br />
<br />
Has anyone actually created these mutant cells to test this theory? Is that what you're showing below?<br />
Maybe it's better to write your own captions that get right to your point?<br />
--[[User:Lidiya|Lidiya]] 03:06, 18 February 2009 (UTC)<br />
<br />
This work is important by providing unity to the plethora of information about the molecular mechanics for cell motility and adhesion. It allows future researchers to focus on the aspects of cell structure that are most relevant for thee processes and make refinements to this basic model.<br />
<br />
<br />
-------------------------------------------------------------------------------------------------------------------------------------------------------------<br />
<br />
Second Entry: Nick Chisholm, AP 225, Fall 2009 (In Progress...)<br />
<br />
==General Information==<br />
'''Authors''': D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan <br />
<br />
'''Publication''': Current Biology '''17''' 694 (2007)<br />
<br />
==Soft Matter Keywords==<br />
[http://soft-matter.seas.harvard.edu/index.php/Adhesion Adhesion], [http://soft-matter.seas.harvard.edu/index.php/Cell Cell], [http://soft-matter.seas.harvard.edu/index.php/Polymerization Polymerization], Viscous<br />
<br />
==Summary==<br />
The authors explore the early stages of cell spreading. In particular, they look at the situation where cells are plated onto artificial adhesive surfaces; they first flatten and deform extensively as they spread. This article presents experimental probing of the dynamics of this spreading process using quantitative visualization and biochemical manipulation with a variety of cell types, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs. Surprisingly, the authors find that the adhesion dynamics of cells follow a universal power-law behavior (i.e. the contact radius is proportional to elapsed time to a certain power).<br />
<br />
In Figure 1, one can see an image of a cell spreading on a substrate. The image is taken using reflection interference contrast microscopy (RICM).<br />
<br />
[[Image:CellSpreading.png|thumb|300px| Figure 1, taken from [1].]]<br />
<br />
==Soft Matter Discussion==<br />
As is clear by Figure 1, the spreading is isotropic, the authors can define the spreading radius as: <math>R = \sqrt{\frac{A}{\pi}}</math>.<br />
<br />
The contact radius was found as a function of time for various cells, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs; the results are plotted in Figure 2 (careful: it's a logarithmic plot!). From this plot, the authors note two regimes: an initial diffusive regime summarized by the scaling law <math>R \propto t^{1/2}</math>, and later a subdiffusive regime summarized by the scaling law <math>R \propto t^{1/4}</math>. To be completely honest, I'm not quite sure how accurate these scaling laws are, if only derived from the plot in Figure 2. However, I would assume (or, at least, hope) that these plots were also examined without a logarithmic scale, and then fitted using these power-law forms. <br />
<br />
[[Image:ContactRadius.png|thumb|300px| Figure 2, taken from [1].]]<br />
<br />
<br />
In any case, the authors have also developed a theory which would predict these particular scaling laws. I will briefly outline the physical motivation behind this theory, and then derive the scaling laws. Physically, the authors assume that for small times (i.e. times where the radius of the adhesive patch is smaller than the size of the cell), the cell encompasses a viscous shell enclosing a liquid. For large times, where the radius of the adhesive patch is comparable to the size of the cell, the cell is a homogeneous viscous drop. See Figure 3 for details. Note that this model makes sense: for small times, only part of the cell will be touching the surface, whereas for long times most of the cell has already spread, and thus is substantially flattened.<br />
<br />
[[Image:Cells.png|thumb|300px| Figure 3, taken from [1].]]<br />
<br />
<br />
<br />
In addition, in order to test the theory, the authors performed another experiment. For this experiment, they altered the geometry and mechanical structure of the shell of the cell, which lead to a drastic change in the scaling law obtained above. I think this experiment is much more complicated than the value of its explanation is worth, but the results are shown in Figure 4. Note that the black line is for a cell with a normal shell, and the red line is for a cell with a "patchy" shell (meaning parts of it missing).<br />
<br />
[[Image:Expt.png|thumb|300px| Figure 4, taken from [1].]]<br />
<br />
==Reference==<br />
[1] D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan, "The universal dynamics of cell spreading," Current Biology '''17''' 694 (2007).</div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=The_universal_dynamics_of_cell_spreading&diff=13994The universal dynamics of cell spreading2009-12-05T09:07:30Z<p>Chisholm: /* Soft Matter Discussion */</p>
<hr />
<div>Original entry: Naveen Sinha, APPHY 226, Spring 2009<br />
<br />
In numerous biological experiments, cells are plated onto an artificial adhesive surface to study them under a microscope. After being deposited on the surface, they flatten and spread outwards along the surface. This process incorporates many biological reactions, including the diffusion of adhesion receptors and the polymerization of the scaffolding-like actin molecules. However, Prof. Mahadevan and his collaborators show how a variety of cells and surface exhibit a power-law behavior in the contact radius of the colony of cells as a function of time. This can be understood when the cells are modeled as a viscous shell of liquid with a much less viscous interior. <br />
<br />
The basic biological system is shown below. Cells are placed on a surface and Reflectance Contrast Imaging Microscopy is used to measure the contact area as a function of time. <br />
<br />
[[Image:MahadevanUniversalFig01.jpg | 360 px]]<br />
<br />
The length measure used to characterize the system is the radius of a circle with the same area. On a log-log plot, the power law behavior becomes apparent.<br />
<br />
[[Image:MahadevanUniversalFig02.jpg | 360 px]]<br />
<br />
There appear to be two different regimes: (1) an initial diffusive regime with <math>R ~ t^{1/2}</math> and (2) a sub-diffusive region with <math>R ~ t^{1/4}</math>.<br />
<br />
Despite all the biochemical complexities of the spreading process, a simple model that treated the cells as a shell of viscous liquid is sufficient to describe most of the behavior. <br />
<br />
[[Image:MahadevanUniversalFig03.jpg | 360 px]]<br />
<br />
Initially, the power-law can be derived by setting the chance in adhesion energy equal to the viscous energy dissipation. This approximation is valid for when the radius of the contact angle is less than te initial cell radius <math>R_c</math>. The change in contact area is related to the rate of change in the radius by <math>\frac{dA}{dt} = R \frac{dR}{dt}</math>. This can related to the rate of energy gain by multiplying by the adhesion energy per unit area, J, which is the product of the area of each bond and the energy per bond: <math>J R \frac{dR}{dt}</math>. Assuming that the cell cortex has a width w everywhere, the strain is of the order <math>\frac{dR/dt}{w}</math>. This strain acts over a volume approximately equal to <math>R^2 w</math>. The product of the strain, volume, and viscosity leads to an energy dissipation of <math>\eta (\frac{dR}{dt} \frac{1}{w})</math>. By setting this equal to the change in the adhesion energy, we can get the following power law:<br />
<math>R = C \big(\frac{J w}{\eta}\big)^{1/2} t^{1/2}</math>.<br />
<br />
At longer times, when cell has flattened out (i.e. the radius of contact is larger than the initial radius), the viscous energy dissipation occurs throughout the whole volume of the cell. The power law is modified to <math>J R \frac{dR}{dt} = \eta_c \big(\frac{dR}{dt} \frac{1}{w}\big)^2 R^2 w_c</math>. This can be re-arranged to the scaling law:<br />
<math>R ~ \big(\frac{J R_c^3}{\eta_c}\big)^{1/4} t^{1/4}</math>.<br />
<br />
<br />
One prediction of this model is that the properties of the cellular membrane are far more important than the interior of the cell in the cell spreading. One way to test this is by creating two mutants: one in which the microtubules molecules within the cell are unable to polymerize and another in which the actin shell in the cortex is altered.<br />
<br />
[[Image:MahadevanUniversalFig04.jpg | 360 px]]<br />
<br />
Sung Hoon's comment: In the Fig. 4 (a), the Cytochalasin D-treated cell showed linear<br />
behavior. What does the treatment do so that the treated cells spread more quickly?<br />
<br />
Has anyone actually created these mutant cells to test this theory? Is that what you're showing below?<br />
Maybe it's better to write your own captions that get right to your point?<br />
--[[User:Lidiya|Lidiya]] 03:06, 18 February 2009 (UTC)<br />
<br />
This work is important by providing unity to the plethora of information about the molecular mechanics for cell motility and adhesion. It allows future researchers to focus on the aspects of cell structure that are most relevant for thee processes and make refinements to this basic model.<br />
<br />
<br />
-------------------------------------------------------------------------------------------------------------------------------------------------------------<br />
<br />
Second Entry: Nick Chisholm, AP 225, Fall 2009 (In Progress...)<br />
<br />
==General Information==<br />
'''Authors''': D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan <br />
<br />
'''Publication''': Current Biology '''17''' 694 (2007)<br />
<br />
==Soft Matter Keywords==<br />
[http://soft-matter.seas.harvard.edu/index.php/Adhesion Adhesion], [http://soft-matter.seas.harvard.edu/index.php/Cell Cell], [http://soft-matter.seas.harvard.edu/index.php/Polymerization Polymerization], Viscous<br />
<br />
==Summary==<br />
The authors explore the early stages of cell spreading. In particular, they look at the situation where cells are plated onto artificial adhesive surfaces; they first flatten and deform extensively as they spread. This article presents experimental probing of the dynamics of this spreading process using quantitative visualization and biochemical manipulation with a variety of cell types, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs. Surprisingly, the authors find that the adhesion dynamics of cells follow a universal power-law behavior (i.e. the contact radius is proportional to elapsed time to a certain power).<br />
<br />
In Figure 1, one can see an image of a cell spreading on a substrate. The image is taken using reflection interference contrast microscopy (RICM).<br />
<br />
[[Image:CellSpreading.png|thumb|300px| Figure 1, taken from [1].]]<br />
<br />
==Soft Matter Discussion==<br />
As is clear by Figure 1, the spreading is isotropic, the authors can define the spreading radius as: <math>R = \sqrt{\frac{A}{\pi}}</math>.<br />
<br />
The contact radius was found as a function of time for various cells, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs; the results are plotted in Figure 2 (careful: it's a logarithmic plot!). From this plot, the authors note two regimes: an initial diffusive regime summarized by the scaling law <math>R \propto t^{1/2}</math>, and later a subdiffusive regime summarized by the scaling law <math>R \propto t^{1/4}</math>. To be completely honest, I'm not quite sure how accurate these scaling laws are, if only derived from the plot in Figure 2. However, I would assume (or, at least, hope) that these plots were also examined without a logarithmic scale, and then fitted using these power-law forms. <br />
<br />
[[Image:ContactRadius.png|thumb|300px| Figure 2, taken from [1].]]<br />
<br />
<br />
In any case, the authors have also developed a theory which would predict these particular scaling laws. I will briefly outline the physical motivation behind this theory, and then derive the scaling laws. Physically, the authors assume that for small times (i.e. times where the radius of the adhesive patch is smaller than the size of the cell), the cell encompasses a viscous shell enclosing a liquid. For large times, where the radius of the adhesive patch is comparable to the size of the cell, the cell is a homogeneous viscous drop. See Figure 3 for details. Note that this model makes sense: for small times, only part of the cell will be touching the surface, whereas for long times most of the cell has already spread, and thus is substantially flattened.<br />
<br />
[[Image:Cells.png|thumb|300px| Figure 3, taken from [1].]]<br />
<br />
<br />
<br />
In addition, in order to test the theory, the authors performed another experiment. For this experiment, they altered the geometry and mechanical structure of the shell of the cell, which lead to a drastic change in the scaling law obtained above. I think this experiment is much more complicated than the value of its explanation is worth, but the results are shown in Figure 4. Note that the black line is for a cell with a normal shell, and the red line is for a cell with a "patchy" shell (meaning parts of it missing).<br />
<br />
[[Image:Expt.png|thumb|300px| Figure 2, taken from [1].]]<br />
<br />
==Reference==<br />
[1] D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan, "The universal dynamics of cell spreading," Current Biology '''17''' 694 (2007).</div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=The_universal_dynamics_of_cell_spreading&diff=13993The universal dynamics of cell spreading2009-12-05T09:06:32Z<p>Chisholm: /* Soft Matter Discussion */</p>
<hr />
<div>Original entry: Naveen Sinha, APPHY 226, Spring 2009<br />
<br />
In numerous biological experiments, cells are plated onto an artificial adhesive surface to study them under a microscope. After being deposited on the surface, they flatten and spread outwards along the surface. This process incorporates many biological reactions, including the diffusion of adhesion receptors and the polymerization of the scaffolding-like actin molecules. However, Prof. Mahadevan and his collaborators show how a variety of cells and surface exhibit a power-law behavior in the contact radius of the colony of cells as a function of time. This can be understood when the cells are modeled as a viscous shell of liquid with a much less viscous interior. <br />
<br />
The basic biological system is shown below. Cells are placed on a surface and Reflectance Contrast Imaging Microscopy is used to measure the contact area as a function of time. <br />
<br />
[[Image:MahadevanUniversalFig01.jpg | 360 px]]<br />
<br />
The length measure used to characterize the system is the radius of a circle with the same area. On a log-log plot, the power law behavior becomes apparent.<br />
<br />
[[Image:MahadevanUniversalFig02.jpg | 360 px]]<br />
<br />
There appear to be two different regimes: (1) an initial diffusive regime with <math>R ~ t^{1/2}</math> and (2) a sub-diffusive region with <math>R ~ t^{1/4}</math>.<br />
<br />
Despite all the biochemical complexities of the spreading process, a simple model that treated the cells as a shell of viscous liquid is sufficient to describe most of the behavior. <br />
<br />
[[Image:MahadevanUniversalFig03.jpg | 360 px]]<br />
<br />
Initially, the power-law can be derived by setting the chance in adhesion energy equal to the viscous energy dissipation. This approximation is valid for when the radius of the contact angle is less than te initial cell radius <math>R_c</math>. The change in contact area is related to the rate of change in the radius by <math>\frac{dA}{dt} = R \frac{dR}{dt}</math>. This can related to the rate of energy gain by multiplying by the adhesion energy per unit area, J, which is the product of the area of each bond and the energy per bond: <math>J R \frac{dR}{dt}</math>. Assuming that the cell cortex has a width w everywhere, the strain is of the order <math>\frac{dR/dt}{w}</math>. This strain acts over a volume approximately equal to <math>R^2 w</math>. The product of the strain, volume, and viscosity leads to an energy dissipation of <math>\eta (\frac{dR}{dt} \frac{1}{w})</math>. By setting this equal to the change in the adhesion energy, we can get the following power law:<br />
<math>R = C \big(\frac{J w}{\eta}\big)^{1/2} t^{1/2}</math>.<br />
<br />
At longer times, when cell has flattened out (i.e. the radius of contact is larger than the initial radius), the viscous energy dissipation occurs throughout the whole volume of the cell. The power law is modified to <math>J R \frac{dR}{dt} = \eta_c \big(\frac{dR}{dt} \frac{1}{w}\big)^2 R^2 w_c</math>. This can be re-arranged to the scaling law:<br />
<math>R ~ \big(\frac{J R_c^3}{\eta_c}\big)^{1/4} t^{1/4}</math>.<br />
<br />
<br />
One prediction of this model is that the properties of the cellular membrane are far more important than the interior of the cell in the cell spreading. One way to test this is by creating two mutants: one in which the microtubules molecules within the cell are unable to polymerize and another in which the actin shell in the cortex is altered.<br />
<br />
[[Image:MahadevanUniversalFig04.jpg | 360 px]]<br />
<br />
Sung Hoon's comment: In the Fig. 4 (a), the Cytochalasin D-treated cell showed linear<br />
behavior. What does the treatment do so that the treated cells spread more quickly?<br />
<br />
Has anyone actually created these mutant cells to test this theory? Is that what you're showing below?<br />
Maybe it's better to write your own captions that get right to your point?<br />
--[[User:Lidiya|Lidiya]] 03:06, 18 February 2009 (UTC)<br />
<br />
This work is important by providing unity to the plethora of information about the molecular mechanics for cell motility and adhesion. It allows future researchers to focus on the aspects of cell structure that are most relevant for thee processes and make refinements to this basic model.<br />
<br />
<br />
-------------------------------------------------------------------------------------------------------------------------------------------------------------<br />
<br />
Second Entry: Nick Chisholm, AP 225, Fall 2009 (In Progress...)<br />
<br />
==General Information==<br />
'''Authors''': D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan <br />
<br />
'''Publication''': Current Biology '''17''' 694 (2007)<br />
<br />
==Soft Matter Keywords==<br />
[http://soft-matter.seas.harvard.edu/index.php/Adhesion Adhesion], [http://soft-matter.seas.harvard.edu/index.php/Cell Cell], [http://soft-matter.seas.harvard.edu/index.php/Polymerization Polymerization], Viscous<br />
<br />
==Summary==<br />
The authors explore the early stages of cell spreading. In particular, they look at the situation where cells are plated onto artificial adhesive surfaces; they first flatten and deform extensively as they spread. This article presents experimental probing of the dynamics of this spreading process using quantitative visualization and biochemical manipulation with a variety of cell types, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs. Surprisingly, the authors find that the adhesion dynamics of cells follow a universal power-law behavior (i.e. the contact radius is proportional to elapsed time to a certain power).<br />
<br />
In Figure 1, one can see an image of a cell spreading on a substrate. The image is taken using reflection interference contrast microscopy (RICM).<br />
<br />
[[Image:CellSpreading.png|thumb|300px| Figure 1, taken from [1].]]<br />
<br />
==Soft Matter Discussion==<br />
As is clear by Figure 1, the spreading is isotropic, the authors can define the spreading radius as: <math>R = \sqrt{\frac{A}{\pi}}</math>.<br />
<br />
The contact radius was found as a function of time for various cells, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs; the results are plotted in Figure 2 (careful: it's a logarithmic plot!). From this plot, the authors note two regimes: an initial diffusive regime summarized by the scaling law <math>R \propto t^{1/2}</math>, and later a subdiffusive regime summarized by the scaling law <math>R \propto t^{1/4}</math>. To be completely honest, I'm not quite sure how accurate these scaling laws are, if only derived from the plot in Figure 2. However, I would assume (or, at least, hope) that these plots were also examined without a logarithmic scale, and then fitted using these power-law forms. <br />
<br />
[[Image:ContactRadius.png|thumb|300px| Figure 2, taken from [1].]]<br />
<br />
<br />
In any case, the authors have also developed a theory which would predict these particular scaling laws. I will briefly outline the physical motivation behind this theory, and then derive the scaling laws. Physically, the authors assume that for small times (i.e. times where the radius of the adhesive patch is smaller than the size of the cell), the cell encompasses a viscous shell enclosing a liquid. For large times, where the radius of the adhesive patch is comparable to the size of the cell, the cell is a homogeneous viscous drop. See Figure 3 for details. Note that this model makes sense: for small times, only part of the cell will be touching the surface, whereas for long times most of the cell has already spread, and thus is substantially flattened.<br />
<br />
[[Image:Cells.png|thumb|300px| Figure 3, taken from [1].]]<br />
<br />
<br />
<br />
In addition, in order to test the theory, the authors performed another experiment. For this experiment, they altered the geometry and mechanical structure of the shell of the cell, which lead to a drastic change in the scaling law obtained above. I think this experiment is much more complicated than the value of its explanation is worth, but the results are shown in Figure 4. Note that the black line is for a cell with a normal shell, and the red line is for a cell with a "patchy" shell (meaning parts of it missing).<br />
<br />
==Reference==<br />
[1] D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan, "The universal dynamics of cell spreading," Current Biology '''17''' 694 (2007).</div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=The_universal_dynamics_of_cell_spreading&diff=13989The universal dynamics of cell spreading2009-12-05T08:57:20Z<p>Chisholm: /* Soft Matter Discussion */</p>
<hr />
<div>Original entry: Naveen Sinha, APPHY 226, Spring 2009<br />
<br />
In numerous biological experiments, cells are plated onto an artificial adhesive surface to study them under a microscope. After being deposited on the surface, they flatten and spread outwards along the surface. This process incorporates many biological reactions, including the diffusion of adhesion receptors and the polymerization of the scaffolding-like actin molecules. However, Prof. Mahadevan and his collaborators show how a variety of cells and surface exhibit a power-law behavior in the contact radius of the colony of cells as a function of time. This can be understood when the cells are modeled as a viscous shell of liquid with a much less viscous interior. <br />
<br />
The basic biological system is shown below. Cells are placed on a surface and Reflectance Contrast Imaging Microscopy is used to measure the contact area as a function of time. <br />
<br />
[[Image:MahadevanUniversalFig01.jpg | 360 px]]<br />
<br />
The length measure used to characterize the system is the radius of a circle with the same area. On a log-log plot, the power law behavior becomes apparent.<br />
<br />
[[Image:MahadevanUniversalFig02.jpg | 360 px]]<br />
<br />
There appear to be two different regimes: (1) an initial diffusive regime with <math>R ~ t^{1/2}</math> and (2) a sub-diffusive region with <math>R ~ t^{1/4}</math>.<br />
<br />
Despite all the biochemical complexities of the spreading process, a simple model that treated the cells as a shell of viscous liquid is sufficient to describe most of the behavior. <br />
<br />
[[Image:MahadevanUniversalFig03.jpg | 360 px]]<br />
<br />
Initially, the power-law can be derived by setting the chance in adhesion energy equal to the viscous energy dissipation. This approximation is valid for when the radius of the contact angle is less than te initial cell radius <math>R_c</math>. The change in contact area is related to the rate of change in the radius by <math>\frac{dA}{dt} = R \frac{dR}{dt}</math>. This can related to the rate of energy gain by multiplying by the adhesion energy per unit area, J, which is the product of the area of each bond and the energy per bond: <math>J R \frac{dR}{dt}</math>. Assuming that the cell cortex has a width w everywhere, the strain is of the order <math>\frac{dR/dt}{w}</math>. This strain acts over a volume approximately equal to <math>R^2 w</math>. The product of the strain, volume, and viscosity leads to an energy dissipation of <math>\eta (\frac{dR}{dt} \frac{1}{w})</math>. By setting this equal to the change in the adhesion energy, we can get the following power law:<br />
<math>R = C \big(\frac{J w}{\eta}\big)^{1/2} t^{1/2}</math>.<br />
<br />
At longer times, when cell has flattened out (i.e. the radius of contact is larger than the initial radius), the viscous energy dissipation occurs throughout the whole volume of the cell. The power law is modified to <math>J R \frac{dR}{dt} = \eta_c \big(\frac{dR}{dt} \frac{1}{w}\big)^2 R^2 w_c</math>. This can be re-arranged to the scaling law:<br />
<math>R ~ \big(\frac{J R_c^3}{\eta_c}\big)^{1/4} t^{1/4}</math>.<br />
<br />
<br />
One prediction of this model is that the properties of the cellular membrane are far more important than the interior of the cell in the cell spreading. One way to test this is by creating two mutants: one in which the microtubules molecules within the cell are unable to polymerize and another in which the actin shell in the cortex is altered.<br />
<br />
[[Image:MahadevanUniversalFig04.jpg | 360 px]]<br />
<br />
Sung Hoon's comment: In the Fig. 4 (a), the Cytochalasin D-treated cell showed linear<br />
behavior. What does the treatment do so that the treated cells spread more quickly?<br />
<br />
Has anyone actually created these mutant cells to test this theory? Is that what you're showing below?<br />
Maybe it's better to write your own captions that get right to your point?<br />
--[[User:Lidiya|Lidiya]] 03:06, 18 February 2009 (UTC)<br />
<br />
This work is important by providing unity to the plethora of information about the molecular mechanics for cell motility and adhesion. It allows future researchers to focus on the aspects of cell structure that are most relevant for thee processes and make refinements to this basic model.<br />
<br />
<br />
-------------------------------------------------------------------------------------------------------------------------------------------------------------<br />
<br />
Second Entry: Nick Chisholm, AP 225, Fall 2009 (In Progress...)<br />
<br />
==General Information==<br />
'''Authors''': D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan <br />
<br />
'''Publication''': Current Biology '''17''' 694 (2007)<br />
<br />
==Soft Matter Keywords==<br />
[http://soft-matter.seas.harvard.edu/index.php/Adhesion Adhesion], [http://soft-matter.seas.harvard.edu/index.php/Cell Cell], [http://soft-matter.seas.harvard.edu/index.php/Polymerization Polymerization], Viscous<br />
<br />
==Summary==<br />
The authors explore the early stages of cell spreading. In particular, they look at the situation where cells are plated onto artificial adhesive surfaces; they first flatten and deform extensively as they spread. This article presents experimental probing of the dynamics of this spreading process using quantitative visualization and biochemical manipulation with a variety of cell types, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs. Surprisingly, the authors find that the adhesion dynamics of cells follow a universal power-law behavior (i.e. the contact radius is proportional to elapsed time to a certain power).<br />
<br />
In Figure 1, one can see an image of a cell spreading on a substrate. The image is taken using reflection interference contrast microscopy (RICM).<br />
<br />
[[Image:CellSpreading.png|thumb|300px| Figure 1, taken from [1].]]<br />
<br />
==Soft Matter Discussion==<br />
As is clear by Figure 1, the spreading is isotropic, the authors can define the spreading radius as: <math>R = \sqrt{\frac{A}{\pi}}</math>.<br />
<br />
The contact radius was found as a function of time for various cells, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs; the results are plotted in Figure 2 (careful: it's a logarithmic plot!). From this plot, the authors note two regimes: an initial diffusive regime summarized by the scaling law <math>R \propto t^{1/2}</math>, and later a subdiffusive regime summarized by the scaling law <math>R \propto t^{1/4}</math>. To be completely honest, I'm not quite sure how accurate these scaling laws are, if only derived from the plot in Figure 2. However, I would assume (or, at least, hope) that these plots were also examined without a logarithmic scale, and then fitted using these power-law forms. <br />
<br />
[[Image:ContactRadius.png|thumb|300px| Figure 2, taken from [1].]]<br />
<br />
<br />
In any case, the authors have also developed a theory which would predict these particular scaling laws. I will briefly outline the physical motivation behind this theory, and then derive the scaling laws. Physically, the authors assume that for small times (i.e. times where the radius of the adhesive patch is smaller than the size of the cell), the cell encompasses a viscous shell enclosing a liquid. For large times, where the radius of the adhesive patch is comparable to the size of the cell, the cell is a homogeneous viscous drop. See Figure 3 for details. Note that this model makes sense: for small times, only part of the cell will be touching the surface, whereas for long times most of the cell has already spread, and thus is substantially flattened.<br />
<br />
[[Image:Cells.png|thumb|300px| Figure 3, taken from [1].]]<br />
<br />
==Reference==<br />
[1] D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan, "The universal dynamics of cell spreading," Current Biology '''17''' 694 (2007).</div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=File:Cells.png&diff=13988File:Cells.png2009-12-05T08:55:28Z<p>Chisholm: </p>
<hr />
<div></div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=The_universal_dynamics_of_cell_spreading&diff=13987The universal dynamics of cell spreading2009-12-05T08:55:19Z<p>Chisholm: /* Soft Matter Discussion */</p>
<hr />
<div>Original entry: Naveen Sinha, APPHY 226, Spring 2009<br />
<br />
In numerous biological experiments, cells are plated onto an artificial adhesive surface to study them under a microscope. After being deposited on the surface, they flatten and spread outwards along the surface. This process incorporates many biological reactions, including the diffusion of adhesion receptors and the polymerization of the scaffolding-like actin molecules. However, Prof. Mahadevan and his collaborators show how a variety of cells and surface exhibit a power-law behavior in the contact radius of the colony of cells as a function of time. This can be understood when the cells are modeled as a viscous shell of liquid with a much less viscous interior. <br />
<br />
The basic biological system is shown below. Cells are placed on a surface and Reflectance Contrast Imaging Microscopy is used to measure the contact area as a function of time. <br />
<br />
[[Image:MahadevanUniversalFig01.jpg | 360 px]]<br />
<br />
The length measure used to characterize the system is the radius of a circle with the same area. On a log-log plot, the power law behavior becomes apparent.<br />
<br />
[[Image:MahadevanUniversalFig02.jpg | 360 px]]<br />
<br />
There appear to be two different regimes: (1) an initial diffusive regime with <math>R ~ t^{1/2}</math> and (2) a sub-diffusive region with <math>R ~ t^{1/4}</math>.<br />
<br />
Despite all the biochemical complexities of the spreading process, a simple model that treated the cells as a shell of viscous liquid is sufficient to describe most of the behavior. <br />
<br />
[[Image:MahadevanUniversalFig03.jpg | 360 px]]<br />
<br />
Initially, the power-law can be derived by setting the chance in adhesion energy equal to the viscous energy dissipation. This approximation is valid for when the radius of the contact angle is less than te initial cell radius <math>R_c</math>. The change in contact area is related to the rate of change in the radius by <math>\frac{dA}{dt} = R \frac{dR}{dt}</math>. This can related to the rate of energy gain by multiplying by the adhesion energy per unit area, J, which is the product of the area of each bond and the energy per bond: <math>J R \frac{dR}{dt}</math>. Assuming that the cell cortex has a width w everywhere, the strain is of the order <math>\frac{dR/dt}{w}</math>. This strain acts over a volume approximately equal to <math>R^2 w</math>. The product of the strain, volume, and viscosity leads to an energy dissipation of <math>\eta (\frac{dR}{dt} \frac{1}{w})</math>. By setting this equal to the change in the adhesion energy, we can get the following power law:<br />
<math>R = C \big(\frac{J w}{\eta}\big)^{1/2} t^{1/2}</math>.<br />
<br />
At longer times, when cell has flattened out (i.e. the radius of contact is larger than the initial radius), the viscous energy dissipation occurs throughout the whole volume of the cell. The power law is modified to <math>J R \frac{dR}{dt} = \eta_c \big(\frac{dR}{dt} \frac{1}{w}\big)^2 R^2 w_c</math>. This can be re-arranged to the scaling law:<br />
<math>R ~ \big(\frac{J R_c^3}{\eta_c}\big)^{1/4} t^{1/4}</math>.<br />
<br />
<br />
One prediction of this model is that the properties of the cellular membrane are far more important than the interior of the cell in the cell spreading. One way to test this is by creating two mutants: one in which the microtubules molecules within the cell are unable to polymerize and another in which the actin shell in the cortex is altered.<br />
<br />
[[Image:MahadevanUniversalFig04.jpg | 360 px]]<br />
<br />
Sung Hoon's comment: In the Fig. 4 (a), the Cytochalasin D-treated cell showed linear<br />
behavior. What does the treatment do so that the treated cells spread more quickly?<br />
<br />
Has anyone actually created these mutant cells to test this theory? Is that what you're showing below?<br />
Maybe it's better to write your own captions that get right to your point?<br />
--[[User:Lidiya|Lidiya]] 03:06, 18 February 2009 (UTC)<br />
<br />
This work is important by providing unity to the plethora of information about the molecular mechanics for cell motility and adhesion. It allows future researchers to focus on the aspects of cell structure that are most relevant for thee processes and make refinements to this basic model.<br />
<br />
<br />
-------------------------------------------------------------------------------------------------------------------------------------------------------------<br />
<br />
Second Entry: Nick Chisholm, AP 225, Fall 2009 (In Progress...)<br />
<br />
==General Information==<br />
'''Authors''': D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan <br />
<br />
'''Publication''': Current Biology '''17''' 694 (2007)<br />
<br />
==Soft Matter Keywords==<br />
[http://soft-matter.seas.harvard.edu/index.php/Adhesion Adhesion], [http://soft-matter.seas.harvard.edu/index.php/Cell Cell], [http://soft-matter.seas.harvard.edu/index.php/Polymerization Polymerization], Viscous<br />
<br />
==Summary==<br />
The authors explore the early stages of cell spreading. In particular, they look at the situation where cells are plated onto artificial adhesive surfaces; they first flatten and deform extensively as they spread. This article presents experimental probing of the dynamics of this spreading process using quantitative visualization and biochemical manipulation with a variety of cell types, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs. Surprisingly, the authors find that the adhesion dynamics of cells follow a universal power-law behavior (i.e. the contact radius is proportional to elapsed time to a certain power).<br />
<br />
In Figure 1, one can see an image of a cell spreading on a substrate. The image is taken using reflection interference contrast microscopy (RICM).<br />
<br />
[[Image:CellSpreading.png|thumb|300px| Figure 1, taken from [1].]]<br />
<br />
==Soft Matter Discussion==<br />
As is clear by Figure 1, the spreading is isotropic, the authors can define the spreading radius as: <math>R = \sqrt{\frac{A}{\pi}}</math>.<br />
<br />
The contact radius was found as a function of time for various cells, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs; the results are plotted in Figure 2 (careful: it's a logarithmic plot!). From this plot, the authors note two regimes: an initial diffusive regime summarized by the scaling law <math>R \propto t^{1/2}</math>, and later a subdiffusive regime summarized by the scaling law <math>R \propto t^{1/4}</math>. To be completely honest, I'm not quite sure how accurate these scaling laws are, if only derived from the plot in Figure 2. However, I would assume (or, at least, hope) that these plots were also examined without a logarithmic scale, and then fitted using these power-law forms. <br />
<br />
[[Image:ContactRadius.png|thumb|300px| Figure 2, taken from [1].]]<br />
<br />
<br />
In any case, the authors have also developed a theory which would predict these particular scaling laws. I will briefly outline the physical motivation behind this theory, and then derive the scaling laws. Physically, the authors assume that for small times (i.e. times where the radius of the adhesive patch is smaller than the size of the cell), the cell encompasses a viscous shell enclosing a liquid. For large times, where the radius of the adhesive patch is comparable to the size of the cell, the cell is a homogeneous viscous drop. See Figure 3 for details. <br />
<br />
[[Image:Cells.png|thumb|300px| Figure 3, taken from [1].]]<br />
<br />
==Reference==<br />
[1] D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan, "The universal dynamics of cell spreading," Current Biology '''17''' 694 (2007).</div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=The_universal_dynamics_of_cell_spreading&diff=13982The universal dynamics of cell spreading2009-12-05T08:22:08Z<p>Chisholm: /* Soft Matter Discussion */</p>
<hr />
<div>Original entry: Naveen Sinha, APPHY 226, Spring 2009<br />
<br />
In numerous biological experiments, cells are plated onto an artificial adhesive surface to study them under a microscope. After being deposited on the surface, they flatten and spread outwards along the surface. This process incorporates many biological reactions, including the diffusion of adhesion receptors and the polymerization of the scaffolding-like actin molecules. However, Prof. Mahadevan and his collaborators show how a variety of cells and surface exhibit a power-law behavior in the contact radius of the colony of cells as a function of time. This can be understood when the cells are modeled as a viscous shell of liquid with a much less viscous interior. <br />
<br />
The basic biological system is shown below. Cells are placed on a surface and Reflectance Contrast Imaging Microscopy is used to measure the contact area as a function of time. <br />
<br />
[[Image:MahadevanUniversalFig01.jpg | 360 px]]<br />
<br />
The length measure used to characterize the system is the radius of a circle with the same area. On a log-log plot, the power law behavior becomes apparent.<br />
<br />
[[Image:MahadevanUniversalFig02.jpg | 360 px]]<br />
<br />
There appear to be two different regimes: (1) an initial diffusive regime with <math>R ~ t^{1/2}</math> and (2) a sub-diffusive region with <math>R ~ t^{1/4}</math>.<br />
<br />
Despite all the biochemical complexities of the spreading process, a simple model that treated the cells as a shell of viscous liquid is sufficient to describe most of the behavior. <br />
<br />
[[Image:MahadevanUniversalFig03.jpg | 360 px]]<br />
<br />
Initially, the power-law can be derived by setting the chance in adhesion energy equal to the viscous energy dissipation. This approximation is valid for when the radius of the contact angle is less than te initial cell radius <math>R_c</math>. The change in contact area is related to the rate of change in the radius by <math>\frac{dA}{dt} = R \frac{dR}{dt}</math>. This can related to the rate of energy gain by multiplying by the adhesion energy per unit area, J, which is the product of the area of each bond and the energy per bond: <math>J R \frac{dR}{dt}</math>. Assuming that the cell cortex has a width w everywhere, the strain is of the order <math>\frac{dR/dt}{w}</math>. This strain acts over a volume approximately equal to <math>R^2 w</math>. The product of the strain, volume, and viscosity leads to an energy dissipation of <math>\eta (\frac{dR}{dt} \frac{1}{w})</math>. By setting this equal to the change in the adhesion energy, we can get the following power law:<br />
<math>R = C \big(\frac{J w}{\eta}\big)^{1/2} t^{1/2}</math>.<br />
<br />
At longer times, when cell has flattened out (i.e. the radius of contact is larger than the initial radius), the viscous energy dissipation occurs throughout the whole volume of the cell. The power law is modified to <math>J R \frac{dR}{dt} = \eta_c \big(\frac{dR}{dt} \frac{1}{w}\big)^2 R^2 w_c</math>. This can be re-arranged to the scaling law:<br />
<math>R ~ \big(\frac{J R_c^3}{\eta_c}\big)^{1/4} t^{1/4}</math>.<br />
<br />
<br />
One prediction of this model is that the properties of the cellular membrane are far more important than the interior of the cell in the cell spreading. One way to test this is by creating two mutants: one in which the microtubules molecules within the cell are unable to polymerize and another in which the actin shell in the cortex is altered.<br />
<br />
[[Image:MahadevanUniversalFig04.jpg | 360 px]]<br />
<br />
Sung Hoon's comment: In the Fig. 4 (a), the Cytochalasin D-treated cell showed linear<br />
behavior. What does the treatment do so that the treated cells spread more quickly?<br />
<br />
Has anyone actually created these mutant cells to test this theory? Is that what you're showing below?<br />
Maybe it's better to write your own captions that get right to your point?<br />
--[[User:Lidiya|Lidiya]] 03:06, 18 February 2009 (UTC)<br />
<br />
This work is important by providing unity to the plethora of information about the molecular mechanics for cell motility and adhesion. It allows future researchers to focus on the aspects of cell structure that are most relevant for thee processes and make refinements to this basic model.<br />
<br />
<br />
-------------------------------------------------------------------------------------------------------------------------------------------------------------<br />
<br />
Second Entry: Nick Chisholm, AP 225, Fall 2009 (In Progress...)<br />
<br />
==General Information==<br />
'''Authors''': D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan <br />
<br />
'''Publication''': Current Biology '''17''' 694 (2007)<br />
<br />
==Soft Matter Keywords==<br />
[http://soft-matter.seas.harvard.edu/index.php/Adhesion Adhesion], [http://soft-matter.seas.harvard.edu/index.php/Cell Cell], [http://soft-matter.seas.harvard.edu/index.php/Polymerization Polymerization], Viscous<br />
<br />
==Summary==<br />
The authors explore the early stages of cell spreading. In particular, they look at the situation where cells are plated onto artificial adhesive surfaces; they first flatten and deform extensively as they spread. This article presents experimental probing of the dynamics of this spreading process using quantitative visualization and biochemical manipulation with a variety of cell types, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs. Surprisingly, the authors find that the adhesion dynamics of cells follow a universal power-law behavior (i.e. the contact radius is proportional to elapsed time to a certain power).<br />
<br />
In Figure 1, one can see an image of a cell spreading on a substrate. The image is taken using reflection interference contrast microscopy (RICM).<br />
<br />
[[Image:CellSpreading.png|thumb|300px| Figure 1, taken from [1].]]<br />
<br />
==Soft Matter Discussion==<br />
As is clear by Figure 1, the spreading is isotropic, the authors can define the spreading radius as: <math>R = \sqrt{\frac{A}{\pi}}</math>.<br />
<br />
The contact radius was found as a function of time for various cells, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs; the results are plotted in Figure 2 (careful: it's a logarithmic plot!). From this plot, the authors note two regimes: an initial diffusive regime summarized by the scaling law <math>R \propto t^{1/2}</math>, and later a subdiffusive regime summarized by the scaling law <math>R \propto t^{1/4}</math>. To be completely honest, I'm not quite sure how accurate these scaling laws are, if only derived from the plot in Figure 2. However, I would assume (or, at least, hope) that these plots were also examined without a logarithmic scale, and then fitted using these power-law forms. <br />
<br />
[[Image:ContactRadius.png|thumb|300px| Figure 2, taken from [1].]]<br />
<br />
<br />
In any case, the authors have also developed a theory which would predict these particular scaling laws.<br />
<br />
==Reference==<br />
[1] D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan, "The universal dynamics of cell spreading," Current Biology '''17''' 694 (2007).</div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=The_universal_dynamics_of_cell_spreading&diff=13981The universal dynamics of cell spreading2009-12-05T08:21:43Z<p>Chisholm: /* Soft Matter Discussion */</p>
<hr />
<div>Original entry: Naveen Sinha, APPHY 226, Spring 2009<br />
<br />
In numerous biological experiments, cells are plated onto an artificial adhesive surface to study them under a microscope. After being deposited on the surface, they flatten and spread outwards along the surface. This process incorporates many biological reactions, including the diffusion of adhesion receptors and the polymerization of the scaffolding-like actin molecules. However, Prof. Mahadevan and his collaborators show how a variety of cells and surface exhibit a power-law behavior in the contact radius of the colony of cells as a function of time. This can be understood when the cells are modeled as a viscous shell of liquid with a much less viscous interior. <br />
<br />
The basic biological system is shown below. Cells are placed on a surface and Reflectance Contrast Imaging Microscopy is used to measure the contact area as a function of time. <br />
<br />
[[Image:MahadevanUniversalFig01.jpg | 360 px]]<br />
<br />
The length measure used to characterize the system is the radius of a circle with the same area. On a log-log plot, the power law behavior becomes apparent.<br />
<br />
[[Image:MahadevanUniversalFig02.jpg | 360 px]]<br />
<br />
There appear to be two different regimes: (1) an initial diffusive regime with <math>R ~ t^{1/2}</math> and (2) a sub-diffusive region with <math>R ~ t^{1/4}</math>.<br />
<br />
Despite all the biochemical complexities of the spreading process, a simple model that treated the cells as a shell of viscous liquid is sufficient to describe most of the behavior. <br />
<br />
[[Image:MahadevanUniversalFig03.jpg | 360 px]]<br />
<br />
Initially, the power-law can be derived by setting the chance in adhesion energy equal to the viscous energy dissipation. This approximation is valid for when the radius of the contact angle is less than te initial cell radius <math>R_c</math>. The change in contact area is related to the rate of change in the radius by <math>\frac{dA}{dt} = R \frac{dR}{dt}</math>. This can related to the rate of energy gain by multiplying by the adhesion energy per unit area, J, which is the product of the area of each bond and the energy per bond: <math>J R \frac{dR}{dt}</math>. Assuming that the cell cortex has a width w everywhere, the strain is of the order <math>\frac{dR/dt}{w}</math>. This strain acts over a volume approximately equal to <math>R^2 w</math>. The product of the strain, volume, and viscosity leads to an energy dissipation of <math>\eta (\frac{dR}{dt} \frac{1}{w})</math>. By setting this equal to the change in the adhesion energy, we can get the following power law:<br />
<math>R = C \big(\frac{J w}{\eta}\big)^{1/2} t^{1/2}</math>.<br />
<br />
At longer times, when cell has flattened out (i.e. the radius of contact is larger than the initial radius), the viscous energy dissipation occurs throughout the whole volume of the cell. The power law is modified to <math>J R \frac{dR}{dt} = \eta_c \big(\frac{dR}{dt} \frac{1}{w}\big)^2 R^2 w_c</math>. This can be re-arranged to the scaling law:<br />
<math>R ~ \big(\frac{J R_c^3}{\eta_c}\big)^{1/4} t^{1/4}</math>.<br />
<br />
<br />
One prediction of this model is that the properties of the cellular membrane are far more important than the interior of the cell in the cell spreading. One way to test this is by creating two mutants: one in which the microtubules molecules within the cell are unable to polymerize and another in which the actin shell in the cortex is altered.<br />
<br />
[[Image:MahadevanUniversalFig04.jpg | 360 px]]<br />
<br />
Sung Hoon's comment: In the Fig. 4 (a), the Cytochalasin D-treated cell showed linear<br />
behavior. What does the treatment do so that the treated cells spread more quickly?<br />
<br />
Has anyone actually created these mutant cells to test this theory? Is that what you're showing below?<br />
Maybe it's better to write your own captions that get right to your point?<br />
--[[User:Lidiya|Lidiya]] 03:06, 18 February 2009 (UTC)<br />
<br />
This work is important by providing unity to the plethora of information about the molecular mechanics for cell motility and adhesion. It allows future researchers to focus on the aspects of cell structure that are most relevant for thee processes and make refinements to this basic model.<br />
<br />
<br />
-------------------------------------------------------------------------------------------------------------------------------------------------------------<br />
<br />
Second Entry: Nick Chisholm, AP 225, Fall 2009 (In Progress...)<br />
<br />
==General Information==<br />
'''Authors''': D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan <br />
<br />
'''Publication''': Current Biology '''17''' 694 (2007)<br />
<br />
==Soft Matter Keywords==<br />
[http://soft-matter.seas.harvard.edu/index.php/Adhesion Adhesion], [http://soft-matter.seas.harvard.edu/index.php/Cell Cell], [http://soft-matter.seas.harvard.edu/index.php/Polymerization Polymerization], Viscous<br />
<br />
==Summary==<br />
The authors explore the early stages of cell spreading. In particular, they look at the situation where cells are plated onto artificial adhesive surfaces; they first flatten and deform extensively as they spread. This article presents experimental probing of the dynamics of this spreading process using quantitative visualization and biochemical manipulation with a variety of cell types, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs. Surprisingly, the authors find that the adhesion dynamics of cells follow a universal power-law behavior (i.e. the contact radius is proportional to elapsed time to a certain power).<br />
<br />
In Figure 1, one can see an image of a cell spreading on a substrate. The image is taken using reflection interference contrast microscopy (RICM).<br />
<br />
[[Image:CellSpreading.png|thumb|300px| Figure 1, taken from [1].]]<br />
<br />
==Soft Matter Discussion==<br />
As is clear by Figure 1, the spreading is isotropic, the authors can define the spreading radius as: <math>R = \sqrt{\frac{A}{\pi}}</math>.<br />
<br />
The contact radius was found as a function of time for various cells, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs; the results are plotted in Figure 2 (careful: it's a logarithmic plot!). From this plot, the authors note two regimes: an initial diffusive regime summarized by the scaling law <math>R \propto t^{1/2}</math>, and later a subdiffusive regime summarized by the scaling law <math>R \propto t^{1/4}</math>. To be completely honest, I'm not quite sure how accurate these scaling laws are, if only derived from the plot in Figure 2. However, I would assume (or, at least, hope) that these plots were also examined without a logarithmic scale, and then fitted using these power-law forms. <br />
<br />
[[Image:ContactRadius.png|thumb|300px| Figure 2, taken from [1].]]<br />
<br />
In any case, the authors have also developed a theory which would predict these particular scaling laws.<br />
<br />
==Reference==<br />
[1] D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan, "The universal dynamics of cell spreading," Current Biology '''17''' 694 (2007).</div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=The_universal_dynamics_of_cell_spreading&diff=13978The universal dynamics of cell spreading2009-12-05T08:17:21Z<p>Chisholm: /* Soft Matter Discussion */</p>
<hr />
<div>Original entry: Naveen Sinha, APPHY 226, Spring 2009<br />
<br />
In numerous biological experiments, cells are plated onto an artificial adhesive surface to study them under a microscope. After being deposited on the surface, they flatten and spread outwards along the surface. This process incorporates many biological reactions, including the diffusion of adhesion receptors and the polymerization of the scaffolding-like actin molecules. However, Prof. Mahadevan and his collaborators show how a variety of cells and surface exhibit a power-law behavior in the contact radius of the colony of cells as a function of time. This can be understood when the cells are modeled as a viscous shell of liquid with a much less viscous interior. <br />
<br />
The basic biological system is shown below. Cells are placed on a surface and Reflectance Contrast Imaging Microscopy is used to measure the contact area as a function of time. <br />
<br />
[[Image:MahadevanUniversalFig01.jpg | 360 px]]<br />
<br />
The length measure used to characterize the system is the radius of a circle with the same area. On a log-log plot, the power law behavior becomes apparent.<br />
<br />
[[Image:MahadevanUniversalFig02.jpg | 360 px]]<br />
<br />
There appear to be two different regimes: (1) an initial diffusive regime with <math>R ~ t^{1/2}</math> and (2) a sub-diffusive region with <math>R ~ t^{1/4}</math>.<br />
<br />
Despite all the biochemical complexities of the spreading process, a simple model that treated the cells as a shell of viscous liquid is sufficient to describe most of the behavior. <br />
<br />
[[Image:MahadevanUniversalFig03.jpg | 360 px]]<br />
<br />
Initially, the power-law can be derived by setting the chance in adhesion energy equal to the viscous energy dissipation. This approximation is valid for when the radius of the contact angle is less than te initial cell radius <math>R_c</math>. The change in contact area is related to the rate of change in the radius by <math>\frac{dA}{dt} = R \frac{dR}{dt}</math>. This can related to the rate of energy gain by multiplying by the adhesion energy per unit area, J, which is the product of the area of each bond and the energy per bond: <math>J R \frac{dR}{dt}</math>. Assuming that the cell cortex has a width w everywhere, the strain is of the order <math>\frac{dR/dt}{w}</math>. This strain acts over a volume approximately equal to <math>R^2 w</math>. The product of the strain, volume, and viscosity leads to an energy dissipation of <math>\eta (\frac{dR}{dt} \frac{1}{w})</math>. By setting this equal to the change in the adhesion energy, we can get the following power law:<br />
<math>R = C \big(\frac{J w}{\eta}\big)^{1/2} t^{1/2}</math>.<br />
<br />
At longer times, when cell has flattened out (i.e. the radius of contact is larger than the initial radius), the viscous energy dissipation occurs throughout the whole volume of the cell. The power law is modified to <math>J R \frac{dR}{dt} = \eta_c \big(\frac{dR}{dt} \frac{1}{w}\big)^2 R^2 w_c</math>. This can be re-arranged to the scaling law:<br />
<math>R ~ \big(\frac{J R_c^3}{\eta_c}\big)^{1/4} t^{1/4}</math>.<br />
<br />
<br />
One prediction of this model is that the properties of the cellular membrane are far more important than the interior of the cell in the cell spreading. One way to test this is by creating two mutants: one in which the microtubules molecules within the cell are unable to polymerize and another in which the actin shell in the cortex is altered.<br />
<br />
[[Image:MahadevanUniversalFig04.jpg | 360 px]]<br />
<br />
Sung Hoon's comment: In the Fig. 4 (a), the Cytochalasin D-treated cell showed linear<br />
behavior. What does the treatment do so that the treated cells spread more quickly?<br />
<br />
Has anyone actually created these mutant cells to test this theory? Is that what you're showing below?<br />
Maybe it's better to write your own captions that get right to your point?<br />
--[[User:Lidiya|Lidiya]] 03:06, 18 February 2009 (UTC)<br />
<br />
This work is important by providing unity to the plethora of information about the molecular mechanics for cell motility and adhesion. It allows future researchers to focus on the aspects of cell structure that are most relevant for thee processes and make refinements to this basic model.<br />
<br />
<br />
-------------------------------------------------------------------------------------------------------------------------------------------------------------<br />
<br />
Second Entry: Nick Chisholm, AP 225, Fall 2009 (In Progress...)<br />
<br />
==General Information==<br />
'''Authors''': D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan <br />
<br />
'''Publication''': Current Biology '''17''' 694 (2007)<br />
<br />
==Soft Matter Keywords==<br />
[http://soft-matter.seas.harvard.edu/index.php/Adhesion Adhesion], [http://soft-matter.seas.harvard.edu/index.php/Cell Cell], [http://soft-matter.seas.harvard.edu/index.php/Polymerization Polymerization], Viscous<br />
<br />
==Summary==<br />
The authors explore the early stages of cell spreading. In particular, they look at the situation where cells are plated onto artificial adhesive surfaces; they first flatten and deform extensively as they spread. This article presents experimental probing of the dynamics of this spreading process using quantitative visualization and biochemical manipulation with a variety of cell types, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs. Surprisingly, the authors find that the adhesion dynamics of cells follow a universal power-law behavior (i.e. the contact radius is proportional to elapsed time to a certain power).<br />
<br />
In Figure 1, one can see an image of a cell spreading on a substrate. The image is taken using reflection interference contrast microscopy (RICM).<br />
<br />
[[Image:CellSpreading.png|thumb|300px| Figure 1, taken from [1].]]<br />
<br />
==Soft Matter Discussion==<br />
As is clear by Figure 1, the spreading is isotropic, the authors can define the spreading radius as: <math>R = \sqrt{\frac{A}{\pi}}</math>.<br />
<br />
The contact radius was found as a function of time for various cells, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs; the results are plotted in Figure 2 (careful: it's a logarithmic plot!). From this plot, the authors note two regimes: an initial diffusive regime summarized by the scaling law <math>R \propto t^{1/2}</math>, and later a subdiffusive regime summarized by the scaling law <math>R \propto t^{1/4}</math>. <br />
<br />
[[Image:ContactRadius.png|thumb|300px| Figure 2, taken from [1].]]<br />
<br />
==Reference==<br />
[1] D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan, "The universal dynamics of cell spreading," Current Biology '''17''' 694 (2007).</div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=The_universal_dynamics_of_cell_spreading&diff=13977The universal dynamics of cell spreading2009-12-05T08:16:03Z<p>Chisholm: /* Soft Matter Discussion */</p>
<hr />
<div>Original entry: Naveen Sinha, APPHY 226, Spring 2009<br />
<br />
In numerous biological experiments, cells are plated onto an artificial adhesive surface to study them under a microscope. After being deposited on the surface, they flatten and spread outwards along the surface. This process incorporates many biological reactions, including the diffusion of adhesion receptors and the polymerization of the scaffolding-like actin molecules. However, Prof. Mahadevan and his collaborators show how a variety of cells and surface exhibit a power-law behavior in the contact radius of the colony of cells as a function of time. This can be understood when the cells are modeled as a viscous shell of liquid with a much less viscous interior. <br />
<br />
The basic biological system is shown below. Cells are placed on a surface and Reflectance Contrast Imaging Microscopy is used to measure the contact area as a function of time. <br />
<br />
[[Image:MahadevanUniversalFig01.jpg | 360 px]]<br />
<br />
The length measure used to characterize the system is the radius of a circle with the same area. On a log-log plot, the power law behavior becomes apparent.<br />
<br />
[[Image:MahadevanUniversalFig02.jpg | 360 px]]<br />
<br />
There appear to be two different regimes: (1) an initial diffusive regime with <math>R ~ t^{1/2}</math> and (2) a sub-diffusive region with <math>R ~ t^{1/4}</math>.<br />
<br />
Despite all the biochemical complexities of the spreading process, a simple model that treated the cells as a shell of viscous liquid is sufficient to describe most of the behavior. <br />
<br />
[[Image:MahadevanUniversalFig03.jpg | 360 px]]<br />
<br />
Initially, the power-law can be derived by setting the chance in adhesion energy equal to the viscous energy dissipation. This approximation is valid for when the radius of the contact angle is less than te initial cell radius <math>R_c</math>. The change in contact area is related to the rate of change in the radius by <math>\frac{dA}{dt} = R \frac{dR}{dt}</math>. This can related to the rate of energy gain by multiplying by the adhesion energy per unit area, J, which is the product of the area of each bond and the energy per bond: <math>J R \frac{dR}{dt}</math>. Assuming that the cell cortex has a width w everywhere, the strain is of the order <math>\frac{dR/dt}{w}</math>. This strain acts over a volume approximately equal to <math>R^2 w</math>. The product of the strain, volume, and viscosity leads to an energy dissipation of <math>\eta (\frac{dR}{dt} \frac{1}{w})</math>. By setting this equal to the change in the adhesion energy, we can get the following power law:<br />
<math>R = C \big(\frac{J w}{\eta}\big)^{1/2} t^{1/2}</math>.<br />
<br />
At longer times, when cell has flattened out (i.e. the radius of contact is larger than the initial radius), the viscous energy dissipation occurs throughout the whole volume of the cell. The power law is modified to <math>J R \frac{dR}{dt} = \eta_c \big(\frac{dR}{dt} \frac{1}{w}\big)^2 R^2 w_c</math>. This can be re-arranged to the scaling law:<br />
<math>R ~ \big(\frac{J R_c^3}{\eta_c}\big)^{1/4} t^{1/4}</math>.<br />
<br />
<br />
One prediction of this model is that the properties of the cellular membrane are far more important than the interior of the cell in the cell spreading. One way to test this is by creating two mutants: one in which the microtubules molecules within the cell are unable to polymerize and another in which the actin shell in the cortex is altered.<br />
<br />
[[Image:MahadevanUniversalFig04.jpg | 360 px]]<br />
<br />
Sung Hoon's comment: In the Fig. 4 (a), the Cytochalasin D-treated cell showed linear<br />
behavior. What does the treatment do so that the treated cells spread more quickly?<br />
<br />
Has anyone actually created these mutant cells to test this theory? Is that what you're showing below?<br />
Maybe it's better to write your own captions that get right to your point?<br />
--[[User:Lidiya|Lidiya]] 03:06, 18 February 2009 (UTC)<br />
<br />
This work is important by providing unity to the plethora of information about the molecular mechanics for cell motility and adhesion. It allows future researchers to focus on the aspects of cell structure that are most relevant for thee processes and make refinements to this basic model.<br />
<br />
<br />
-------------------------------------------------------------------------------------------------------------------------------------------------------------<br />
<br />
Second Entry: Nick Chisholm, AP 225, Fall 2009 (In Progress...)<br />
<br />
==General Information==<br />
'''Authors''': D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan <br />
<br />
'''Publication''': Current Biology '''17''' 694 (2007)<br />
<br />
==Soft Matter Keywords==<br />
[http://soft-matter.seas.harvard.edu/index.php/Adhesion Adhesion], [http://soft-matter.seas.harvard.edu/index.php/Cell Cell], [http://soft-matter.seas.harvard.edu/index.php/Polymerization Polymerization], Viscous<br />
<br />
==Summary==<br />
The authors explore the early stages of cell spreading. In particular, they look at the situation where cells are plated onto artificial adhesive surfaces; they first flatten and deform extensively as they spread. This article presents experimental probing of the dynamics of this spreading process using quantitative visualization and biochemical manipulation with a variety of cell types, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs. Surprisingly, the authors find that the adhesion dynamics of cells follow a universal power-law behavior (i.e. the contact radius is proportional to elapsed time to a certain power).<br />
<br />
In Figure 1, one can see an image of a cell spreading on a substrate. The image is taken using reflection interference contrast microscopy (RICM).<br />
<br />
[[Image:CellSpreading.png|thumb|300px| Figure 1, taken from [1].]]<br />
<br />
==Soft Matter Discussion==<br />
As is clear by Figure 1, the spreading is isotropic, the authors can define the spreading radius as: <math>R = \sqrt{\frac{A}{\pi}}</math>.<br />
<br />
The contact radius was found as a function of time for various cells, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs; the results are plotted in Figure 2 (careful: it's a logarithmic plot!). From this plot, the authors notw to regimes: an initial diffusive regime summarized by the scaling law <math>R \propto t^{1/2}</math><br />
<br />
[[Image:ContactRadius.png|thumb|300px| Figure 2, taken from [1].]]<br />
<br />
==Reference==<br />
[1] D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan, "The universal dynamics of cell spreading," Current Biology '''17''' 694 (2007).</div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=The_universal_dynamics_of_cell_spreading&diff=13976The universal dynamics of cell spreading2009-12-05T08:15:41Z<p>Chisholm: /* Soft Matter Discussion */</p>
<hr />
<div>Original entry: Naveen Sinha, APPHY 226, Spring 2009<br />
<br />
In numerous biological experiments, cells are plated onto an artificial adhesive surface to study them under a microscope. After being deposited on the surface, they flatten and spread outwards along the surface. This process incorporates many biological reactions, including the diffusion of adhesion receptors and the polymerization of the scaffolding-like actin molecules. However, Prof. Mahadevan and his collaborators show how a variety of cells and surface exhibit a power-law behavior in the contact radius of the colony of cells as a function of time. This can be understood when the cells are modeled as a viscous shell of liquid with a much less viscous interior. <br />
<br />
The basic biological system is shown below. Cells are placed on a surface and Reflectance Contrast Imaging Microscopy is used to measure the contact area as a function of time. <br />
<br />
[[Image:MahadevanUniversalFig01.jpg | 360 px]]<br />
<br />
The length measure used to characterize the system is the radius of a circle with the same area. On a log-log plot, the power law behavior becomes apparent.<br />
<br />
[[Image:MahadevanUniversalFig02.jpg | 360 px]]<br />
<br />
There appear to be two different regimes: (1) an initial diffusive regime with <math>R ~ t^{1/2}</math> and (2) a sub-diffusive region with <math>R ~ t^{1/4}</math>.<br />
<br />
Despite all the biochemical complexities of the spreading process, a simple model that treated the cells as a shell of viscous liquid is sufficient to describe most of the behavior. <br />
<br />
[[Image:MahadevanUniversalFig03.jpg | 360 px]]<br />
<br />
Initially, the power-law can be derived by setting the chance in adhesion energy equal to the viscous energy dissipation. This approximation is valid for when the radius of the contact angle is less than te initial cell radius <math>R_c</math>. The change in contact area is related to the rate of change in the radius by <math>\frac{dA}{dt} = R \frac{dR}{dt}</math>. This can related to the rate of energy gain by multiplying by the adhesion energy per unit area, J, which is the product of the area of each bond and the energy per bond: <math>J R \frac{dR}{dt}</math>. Assuming that the cell cortex has a width w everywhere, the strain is of the order <math>\frac{dR/dt}{w}</math>. This strain acts over a volume approximately equal to <math>R^2 w</math>. The product of the strain, volume, and viscosity leads to an energy dissipation of <math>\eta (\frac{dR}{dt} \frac{1}{w})</math>. By setting this equal to the change in the adhesion energy, we can get the following power law:<br />
<math>R = C \big(\frac{J w}{\eta}\big)^{1/2} t^{1/2}</math>.<br />
<br />
At longer times, when cell has flattened out (i.e. the radius of contact is larger than the initial radius), the viscous energy dissipation occurs throughout the whole volume of the cell. The power law is modified to <math>J R \frac{dR}{dt} = \eta_c \big(\frac{dR}{dt} \frac{1}{w}\big)^2 R^2 w_c</math>. This can be re-arranged to the scaling law:<br />
<math>R ~ \big(\frac{J R_c^3}{\eta_c}\big)^{1/4} t^{1/4}</math>.<br />
<br />
<br />
One prediction of this model is that the properties of the cellular membrane are far more important than the interior of the cell in the cell spreading. One way to test this is by creating two mutants: one in which the microtubules molecules within the cell are unable to polymerize and another in which the actin shell in the cortex is altered.<br />
<br />
[[Image:MahadevanUniversalFig04.jpg | 360 px]]<br />
<br />
Sung Hoon's comment: In the Fig. 4 (a), the Cytochalasin D-treated cell showed linear<br />
behavior. What does the treatment do so that the treated cells spread more quickly?<br />
<br />
Has anyone actually created these mutant cells to test this theory? Is that what you're showing below?<br />
Maybe it's better to write your own captions that get right to your point?<br />
--[[User:Lidiya|Lidiya]] 03:06, 18 February 2009 (UTC)<br />
<br />
This work is important by providing unity to the plethora of information about the molecular mechanics for cell motility and adhesion. It allows future researchers to focus on the aspects of cell structure that are most relevant for thee processes and make refinements to this basic model.<br />
<br />
<br />
-------------------------------------------------------------------------------------------------------------------------------------------------------------<br />
<br />
Second Entry: Nick Chisholm, AP 225, Fall 2009 (In Progress...)<br />
<br />
==General Information==<br />
'''Authors''': D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan <br />
<br />
'''Publication''': Current Biology '''17''' 694 (2007)<br />
<br />
==Soft Matter Keywords==<br />
[http://soft-matter.seas.harvard.edu/index.php/Adhesion Adhesion], [http://soft-matter.seas.harvard.edu/index.php/Cell Cell], [http://soft-matter.seas.harvard.edu/index.php/Polymerization Polymerization], Viscous<br />
<br />
==Summary==<br />
The authors explore the early stages of cell spreading. In particular, they look at the situation where cells are plated onto artificial adhesive surfaces; they first flatten and deform extensively as they spread. This article presents experimental probing of the dynamics of this spreading process using quantitative visualization and biochemical manipulation with a variety of cell types, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs. Surprisingly, the authors find that the adhesion dynamics of cells follow a universal power-law behavior (i.e. the contact radius is proportional to elapsed time to a certain power).<br />
<br />
In Figure 1, one can see an image of a cell spreading on a substrate. The image is taken using reflection interference contrast microscopy (RICM).<br />
<br />
[[Image:CellSpreading.png|thumb|300px| Figure 1, taken from [1].]]<br />
<br />
==Soft Matter Discussion==<br />
As is clear by Figure 1, the spreading is isotropic, the authors can define the spreading radius as: <math>R = \sqrt{\frac{A}{\pi}}</math>.<br />
<br />
The contact radius was found as a function of time for various cells, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs; the results are plotted in Figure 2 (careful: it's a logarithmic plot!). From this plot, the authors notw to regimes: an initial diffusive regime summarized by the scaling law <math>R \sim t^{1/2}</math><br />
<br />
[[Image:ContactRadius.png|thumb|300px| Figure 2, taken from [1].]]<br />
<br />
==Reference==<br />
[1] D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan, "The universal dynamics of cell spreading," Current Biology '''17''' 694 (2007).</div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=The_universal_dynamics_of_cell_spreading&diff=13975The universal dynamics of cell spreading2009-12-05T08:15:31Z<p>Chisholm: /* Soft Matter Discussion */</p>
<hr />
<div>Original entry: Naveen Sinha, APPHY 226, Spring 2009<br />
<br />
In numerous biological experiments, cells are plated onto an artificial adhesive surface to study them under a microscope. After being deposited on the surface, they flatten and spread outwards along the surface. This process incorporates many biological reactions, including the diffusion of adhesion receptors and the polymerization of the scaffolding-like actin molecules. However, Prof. Mahadevan and his collaborators show how a variety of cells and surface exhibit a power-law behavior in the contact radius of the colony of cells as a function of time. This can be understood when the cells are modeled as a viscous shell of liquid with a much less viscous interior. <br />
<br />
The basic biological system is shown below. Cells are placed on a surface and Reflectance Contrast Imaging Microscopy is used to measure the contact area as a function of time. <br />
<br />
[[Image:MahadevanUniversalFig01.jpg | 360 px]]<br />
<br />
The length measure used to characterize the system is the radius of a circle with the same area. On a log-log plot, the power law behavior becomes apparent.<br />
<br />
[[Image:MahadevanUniversalFig02.jpg | 360 px]]<br />
<br />
There appear to be two different regimes: (1) an initial diffusive regime with <math>R ~ t^{1/2}</math> and (2) a sub-diffusive region with <math>R ~ t^{1/4}</math>.<br />
<br />
Despite all the biochemical complexities of the spreading process, a simple model that treated the cells as a shell of viscous liquid is sufficient to describe most of the behavior. <br />
<br />
[[Image:MahadevanUniversalFig03.jpg | 360 px]]<br />
<br />
Initially, the power-law can be derived by setting the chance in adhesion energy equal to the viscous energy dissipation. This approximation is valid for when the radius of the contact angle is less than te initial cell radius <math>R_c</math>. The change in contact area is related to the rate of change in the radius by <math>\frac{dA}{dt} = R \frac{dR}{dt}</math>. This can related to the rate of energy gain by multiplying by the adhesion energy per unit area, J, which is the product of the area of each bond and the energy per bond: <math>J R \frac{dR}{dt}</math>. Assuming that the cell cortex has a width w everywhere, the strain is of the order <math>\frac{dR/dt}{w}</math>. This strain acts over a volume approximately equal to <math>R^2 w</math>. The product of the strain, volume, and viscosity leads to an energy dissipation of <math>\eta (\frac{dR}{dt} \frac{1}{w})</math>. By setting this equal to the change in the adhesion energy, we can get the following power law:<br />
<math>R = C \big(\frac{J w}{\eta}\big)^{1/2} t^{1/2}</math>.<br />
<br />
At longer times, when cell has flattened out (i.e. the radius of contact is larger than the initial radius), the viscous energy dissipation occurs throughout the whole volume of the cell. The power law is modified to <math>J R \frac{dR}{dt} = \eta_c \big(\frac{dR}{dt} \frac{1}{w}\big)^2 R^2 w_c</math>. This can be re-arranged to the scaling law:<br />
<math>R ~ \big(\frac{J R_c^3}{\eta_c}\big)^{1/4} t^{1/4}</math>.<br />
<br />
<br />
One prediction of this model is that the properties of the cellular membrane are far more important than the interior of the cell in the cell spreading. One way to test this is by creating two mutants: one in which the microtubules molecules within the cell are unable to polymerize and another in which the actin shell in the cortex is altered.<br />
<br />
[[Image:MahadevanUniversalFig04.jpg | 360 px]]<br />
<br />
Sung Hoon's comment: In the Fig. 4 (a), the Cytochalasin D-treated cell showed linear<br />
behavior. What does the treatment do so that the treated cells spread more quickly?<br />
<br />
Has anyone actually created these mutant cells to test this theory? Is that what you're showing below?<br />
Maybe it's better to write your own captions that get right to your point?<br />
--[[User:Lidiya|Lidiya]] 03:06, 18 February 2009 (UTC)<br />
<br />
This work is important by providing unity to the plethora of information about the molecular mechanics for cell motility and adhesion. It allows future researchers to focus on the aspects of cell structure that are most relevant for thee processes and make refinements to this basic model.<br />
<br />
<br />
-------------------------------------------------------------------------------------------------------------------------------------------------------------<br />
<br />
Second Entry: Nick Chisholm, AP 225, Fall 2009 (In Progress...)<br />
<br />
==General Information==<br />
'''Authors''': D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan <br />
<br />
'''Publication''': Current Biology '''17''' 694 (2007)<br />
<br />
==Soft Matter Keywords==<br />
[http://soft-matter.seas.harvard.edu/index.php/Adhesion Adhesion], [http://soft-matter.seas.harvard.edu/index.php/Cell Cell], [http://soft-matter.seas.harvard.edu/index.php/Polymerization Polymerization], Viscous<br />
<br />
==Summary==<br />
The authors explore the early stages of cell spreading. In particular, they look at the situation where cells are plated onto artificial adhesive surfaces; they first flatten and deform extensively as they spread. This article presents experimental probing of the dynamics of this spreading process using quantitative visualization and biochemical manipulation with a variety of cell types, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs. Surprisingly, the authors find that the adhesion dynamics of cells follow a universal power-law behavior (i.e. the contact radius is proportional to elapsed time to a certain power).<br />
<br />
In Figure 1, one can see an image of a cell spreading on a substrate. The image is taken using reflection interference contrast microscopy (RICM).<br />
<br />
[[Image:CellSpreading.png|thumb|300px| Figure 1, taken from [1].]]<br />
<br />
==Soft Matter Discussion==<br />
As is clear by Figure 1, the spreading is isotropic, the authors can define the spreading radius as: <math>R = \sqrt{\frac{A}{\pi}}</math>.<br />
<br />
The contact radius was found as a function of time for various cells, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs; the results are plotted in Figure 2 (careful: it's a logarithmic plot!). From this plot, the authors notw to regimes: an initial diffusive regime summarized by the scaling law <math>R \simeq t^{1/2}</math><br />
<br />
[[Image:ContactRadius.png|thumb|300px| Figure 2, taken from [1].]]<br />
<br />
==Reference==<br />
[1] D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan, "The universal dynamics of cell spreading," Current Biology '''17''' 694 (2007).</div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=The_universal_dynamics_of_cell_spreading&diff=13974The universal dynamics of cell spreading2009-12-05T08:14:39Z<p>Chisholm: /* Soft Matter Discussion */</p>
<hr />
<div>Original entry: Naveen Sinha, APPHY 226, Spring 2009<br />
<br />
In numerous biological experiments, cells are plated onto an artificial adhesive surface to study them under a microscope. After being deposited on the surface, they flatten and spread outwards along the surface. This process incorporates many biological reactions, including the diffusion of adhesion receptors and the polymerization of the scaffolding-like actin molecules. However, Prof. Mahadevan and his collaborators show how a variety of cells and surface exhibit a power-law behavior in the contact radius of the colony of cells as a function of time. This can be understood when the cells are modeled as a viscous shell of liquid with a much less viscous interior. <br />
<br />
The basic biological system is shown below. Cells are placed on a surface and Reflectance Contrast Imaging Microscopy is used to measure the contact area as a function of time. <br />
<br />
[[Image:MahadevanUniversalFig01.jpg | 360 px]]<br />
<br />
The length measure used to characterize the system is the radius of a circle with the same area. On a log-log plot, the power law behavior becomes apparent.<br />
<br />
[[Image:MahadevanUniversalFig02.jpg | 360 px]]<br />
<br />
There appear to be two different regimes: (1) an initial diffusive regime with <math>R ~ t^{1/2}</math> and (2) a sub-diffusive region with <math>R ~ t^{1/4}</math>.<br />
<br />
Despite all the biochemical complexities of the spreading process, a simple model that treated the cells as a shell of viscous liquid is sufficient to describe most of the behavior. <br />
<br />
[[Image:MahadevanUniversalFig03.jpg | 360 px]]<br />
<br />
Initially, the power-law can be derived by setting the chance in adhesion energy equal to the viscous energy dissipation. This approximation is valid for when the radius of the contact angle is less than te initial cell radius <math>R_c</math>. The change in contact area is related to the rate of change in the radius by <math>\frac{dA}{dt} = R \frac{dR}{dt}</math>. This can related to the rate of energy gain by multiplying by the adhesion energy per unit area, J, which is the product of the area of each bond and the energy per bond: <math>J R \frac{dR}{dt}</math>. Assuming that the cell cortex has a width w everywhere, the strain is of the order <math>\frac{dR/dt}{w}</math>. This strain acts over a volume approximately equal to <math>R^2 w</math>. The product of the strain, volume, and viscosity leads to an energy dissipation of <math>\eta (\frac{dR}{dt} \frac{1}{w})</math>. By setting this equal to the change in the adhesion energy, we can get the following power law:<br />
<math>R = C \big(\frac{J w}{\eta}\big)^{1/2} t^{1/2}</math>.<br />
<br />
At longer times, when cell has flattened out (i.e. the radius of contact is larger than the initial radius), the viscous energy dissipation occurs throughout the whole volume of the cell. The power law is modified to <math>J R \frac{dR}{dt} = \eta_c \big(\frac{dR}{dt} \frac{1}{w}\big)^2 R^2 w_c</math>. This can be re-arranged to the scaling law:<br />
<math>R ~ \big(\frac{J R_c^3}{\eta_c}\big)^{1/4} t^{1/4}</math>.<br />
<br />
<br />
One prediction of this model is that the properties of the cellular membrane are far more important than the interior of the cell in the cell spreading. One way to test this is by creating two mutants: one in which the microtubules molecules within the cell are unable to polymerize and another in which the actin shell in the cortex is altered.<br />
<br />
[[Image:MahadevanUniversalFig04.jpg | 360 px]]<br />
<br />
Sung Hoon's comment: In the Fig. 4 (a), the Cytochalasin D-treated cell showed linear<br />
behavior. What does the treatment do so that the treated cells spread more quickly?<br />
<br />
Has anyone actually created these mutant cells to test this theory? Is that what you're showing below?<br />
Maybe it's better to write your own captions that get right to your point?<br />
--[[User:Lidiya|Lidiya]] 03:06, 18 February 2009 (UTC)<br />
<br />
This work is important by providing unity to the plethora of information about the molecular mechanics for cell motility and adhesion. It allows future researchers to focus on the aspects of cell structure that are most relevant for thee processes and make refinements to this basic model.<br />
<br />
<br />
-------------------------------------------------------------------------------------------------------------------------------------------------------------<br />
<br />
Second Entry: Nick Chisholm, AP 225, Fall 2009 (In Progress...)<br />
<br />
==General Information==<br />
'''Authors''': D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan <br />
<br />
'''Publication''': Current Biology '''17''' 694 (2007)<br />
<br />
==Soft Matter Keywords==<br />
[http://soft-matter.seas.harvard.edu/index.php/Adhesion Adhesion], [http://soft-matter.seas.harvard.edu/index.php/Cell Cell], [http://soft-matter.seas.harvard.edu/index.php/Polymerization Polymerization], Viscous<br />
<br />
==Summary==<br />
The authors explore the early stages of cell spreading. In particular, they look at the situation where cells are plated onto artificial adhesive surfaces; they first flatten and deform extensively as they spread. This article presents experimental probing of the dynamics of this spreading process using quantitative visualization and biochemical manipulation with a variety of cell types, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs. Surprisingly, the authors find that the adhesion dynamics of cells follow a universal power-law behavior (i.e. the contact radius is proportional to elapsed time to a certain power).<br />
<br />
In Figure 1, one can see an image of a cell spreading on a substrate. The image is taken using reflection interference contrast microscopy (RICM).<br />
<br />
[[Image:CellSpreading.png|thumb|300px| Figure 1, taken from [1].]]<br />
<br />
==Soft Matter Discussion==<br />
As is clear by Figure 1, the spreading is isotropic, the authors can define the spreading radius as: <math>R = \sqrt{\frac{A}{\pi}}</math>.<br />
<br />
The contact radius was found as a function of time for various cells, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs; the results are plotted in Figure 2 (careful: it's a logarithmic plot!). From this plot, the authors notw to regimes: an initial diffusive regime summarized by the scaling law <math>R \sim t^{1/2}</math><br />
<br />
[[Image:ContactRadius.png|thumb|300px| Figure 2, taken from [1].]]<br />
<br />
==Reference==<br />
[1] D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan, "The universal dynamics of cell spreading," Current Biology '''17''' 694 (2007).</div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=The_universal_dynamics_of_cell_spreading&diff=13973The universal dynamics of cell spreading2009-12-05T08:14:01Z<p>Chisholm: /* Soft Matter Discussion */</p>
<hr />
<div>Original entry: Naveen Sinha, APPHY 226, Spring 2009<br />
<br />
In numerous biological experiments, cells are plated onto an artificial adhesive surface to study them under a microscope. After being deposited on the surface, they flatten and spread outwards along the surface. This process incorporates many biological reactions, including the diffusion of adhesion receptors and the polymerization of the scaffolding-like actin molecules. However, Prof. Mahadevan and his collaborators show how a variety of cells and surface exhibit a power-law behavior in the contact radius of the colony of cells as a function of time. This can be understood when the cells are modeled as a viscous shell of liquid with a much less viscous interior. <br />
<br />
The basic biological system is shown below. Cells are placed on a surface and Reflectance Contrast Imaging Microscopy is used to measure the contact area as a function of time. <br />
<br />
[[Image:MahadevanUniversalFig01.jpg | 360 px]]<br />
<br />
The length measure used to characterize the system is the radius of a circle with the same area. On a log-log plot, the power law behavior becomes apparent.<br />
<br />
[[Image:MahadevanUniversalFig02.jpg | 360 px]]<br />
<br />
There appear to be two different regimes: (1) an initial diffusive regime with <math>R ~ t^{1/2}</math> and (2) a sub-diffusive region with <math>R ~ t^{1/4}</math>.<br />
<br />
Despite all the biochemical complexities of the spreading process, a simple model that treated the cells as a shell of viscous liquid is sufficient to describe most of the behavior. <br />
<br />
[[Image:MahadevanUniversalFig03.jpg | 360 px]]<br />
<br />
Initially, the power-law can be derived by setting the chance in adhesion energy equal to the viscous energy dissipation. This approximation is valid for when the radius of the contact angle is less than te initial cell radius <math>R_c</math>. The change in contact area is related to the rate of change in the radius by <math>\frac{dA}{dt} = R \frac{dR}{dt}</math>. This can related to the rate of energy gain by multiplying by the adhesion energy per unit area, J, which is the product of the area of each bond and the energy per bond: <math>J R \frac{dR}{dt}</math>. Assuming that the cell cortex has a width w everywhere, the strain is of the order <math>\frac{dR/dt}{w}</math>. This strain acts over a volume approximately equal to <math>R^2 w</math>. The product of the strain, volume, and viscosity leads to an energy dissipation of <math>\eta (\frac{dR}{dt} \frac{1}{w})</math>. By setting this equal to the change in the adhesion energy, we can get the following power law:<br />
<math>R = C \big(\frac{J w}{\eta}\big)^{1/2} t^{1/2}</math>.<br />
<br />
At longer times, when cell has flattened out (i.e. the radius of contact is larger than the initial radius), the viscous energy dissipation occurs throughout the whole volume of the cell. The power law is modified to <math>J R \frac{dR}{dt} = \eta_c \big(\frac{dR}{dt} \frac{1}{w}\big)^2 R^2 w_c</math>. This can be re-arranged to the scaling law:<br />
<math>R ~ \big(\frac{J R_c^3}{\eta_c}\big)^{1/4} t^{1/4}</math>.<br />
<br />
<br />
One prediction of this model is that the properties of the cellular membrane are far more important than the interior of the cell in the cell spreading. One way to test this is by creating two mutants: one in which the microtubules molecules within the cell are unable to polymerize and another in which the actin shell in the cortex is altered.<br />
<br />
[[Image:MahadevanUniversalFig04.jpg | 360 px]]<br />
<br />
Sung Hoon's comment: In the Fig. 4 (a), the Cytochalasin D-treated cell showed linear<br />
behavior. What does the treatment do so that the treated cells spread more quickly?<br />
<br />
Has anyone actually created these mutant cells to test this theory? Is that what you're showing below?<br />
Maybe it's better to write your own captions that get right to your point?<br />
--[[User:Lidiya|Lidiya]] 03:06, 18 February 2009 (UTC)<br />
<br />
This work is important by providing unity to the plethora of information about the molecular mechanics for cell motility and adhesion. It allows future researchers to focus on the aspects of cell structure that are most relevant for thee processes and make refinements to this basic model.<br />
<br />
<br />
-------------------------------------------------------------------------------------------------------------------------------------------------------------<br />
<br />
Second Entry: Nick Chisholm, AP 225, Fall 2009 (In Progress...)<br />
<br />
==General Information==<br />
'''Authors''': D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan <br />
<br />
'''Publication''': Current Biology '''17''' 694 (2007)<br />
<br />
==Soft Matter Keywords==<br />
[http://soft-matter.seas.harvard.edu/index.php/Adhesion Adhesion], [http://soft-matter.seas.harvard.edu/index.php/Cell Cell], [http://soft-matter.seas.harvard.edu/index.php/Polymerization Polymerization], Viscous<br />
<br />
==Summary==<br />
The authors explore the early stages of cell spreading. In particular, they look at the situation where cells are plated onto artificial adhesive surfaces; they first flatten and deform extensively as they spread. This article presents experimental probing of the dynamics of this spreading process using quantitative visualization and biochemical manipulation with a variety of cell types, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs. Surprisingly, the authors find that the adhesion dynamics of cells follow a universal power-law behavior (i.e. the contact radius is proportional to elapsed time to a certain power).<br />
<br />
In Figure 1, one can see an image of a cell spreading on a substrate. The image is taken using reflection interference contrast microscopy (RICM).<br />
<br />
[[Image:CellSpreading.png|thumb|300px| Figure 1, taken from [1].]]<br />
<br />
==Soft Matter Discussion==<br />
As is clear by Figure 1, the spreading is isotropic, the authors can define the spreading radius as: <math>R = \sqrt{\frac{A}{\pi}}</math>.<br />
<br />
The contact radius was found as a function of time for various cells, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs; the results are plotted in Figure 2 (careful: it's a logarithmic plot!). From this plot, the authors notw to regimes: an initial diffusive regime summarized by the scaling law <math>R \proportional t^{1/2}</math><br />
<br />
[[Image:ContactRadius.png|thumb|300px| Figure 2, taken from [1].]]<br />
<br />
==Reference==<br />
[1] D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan, "The universal dynamics of cell spreading," Current Biology '''17''' 694 (2007).</div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=File:ContactRadius.png&diff=13970File:ContactRadius.png2009-12-05T08:05:00Z<p>Chisholm: </p>
<hr />
<div></div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=The_universal_dynamics_of_cell_spreading&diff=13969The universal dynamics of cell spreading2009-12-05T08:04:49Z<p>Chisholm: /* Soft Matter Discussion */</p>
<hr />
<div>Original entry: Naveen Sinha, APPHY 226, Spring 2009<br />
<br />
In numerous biological experiments, cells are plated onto an artificial adhesive surface to study them under a microscope. After being deposited on the surface, they flatten and spread outwards along the surface. This process incorporates many biological reactions, including the diffusion of adhesion receptors and the polymerization of the scaffolding-like actin molecules. However, Prof. Mahadevan and his collaborators show how a variety of cells and surface exhibit a power-law behavior in the contact radius of the colony of cells as a function of time. This can be understood when the cells are modeled as a viscous shell of liquid with a much less viscous interior. <br />
<br />
The basic biological system is shown below. Cells are placed on a surface and Reflectance Contrast Imaging Microscopy is used to measure the contact area as a function of time. <br />
<br />
[[Image:MahadevanUniversalFig01.jpg | 360 px]]<br />
<br />
The length measure used to characterize the system is the radius of a circle with the same area. On a log-log plot, the power law behavior becomes apparent.<br />
<br />
[[Image:MahadevanUniversalFig02.jpg | 360 px]]<br />
<br />
There appear to be two different regimes: (1) an initial diffusive regime with <math>R ~ t^{1/2}</math> and (2) a sub-diffusive region with <math>R ~ t^{1/4}</math>.<br />
<br />
Despite all the biochemical complexities of the spreading process, a simple model that treated the cells as a shell of viscous liquid is sufficient to describe most of the behavior. <br />
<br />
[[Image:MahadevanUniversalFig03.jpg | 360 px]]<br />
<br />
Initially, the power-law can be derived by setting the chance in adhesion energy equal to the viscous energy dissipation. This approximation is valid for when the radius of the contact angle is less than te initial cell radius <math>R_c</math>. The change in contact area is related to the rate of change in the radius by <math>\frac{dA}{dt} = R \frac{dR}{dt}</math>. This can related to the rate of energy gain by multiplying by the adhesion energy per unit area, J, which is the product of the area of each bond and the energy per bond: <math>J R \frac{dR}{dt}</math>. Assuming that the cell cortex has a width w everywhere, the strain is of the order <math>\frac{dR/dt}{w}</math>. This strain acts over a volume approximately equal to <math>R^2 w</math>. The product of the strain, volume, and viscosity leads to an energy dissipation of <math>\eta (\frac{dR}{dt} \frac{1}{w})</math>. By setting this equal to the change in the adhesion energy, we can get the following power law:<br />
<math>R = C \big(\frac{J w}{\eta}\big)^{1/2} t^{1/2}</math>.<br />
<br />
At longer times, when cell has flattened out (i.e. the radius of contact is larger than the initial radius), the viscous energy dissipation occurs throughout the whole volume of the cell. The power law is modified to <math>J R \frac{dR}{dt} = \eta_c \big(\frac{dR}{dt} \frac{1}{w}\big)^2 R^2 w_c</math>. This can be re-arranged to the scaling law:<br />
<math>R ~ \big(\frac{J R_c^3}{\eta_c}\big)^{1/4} t^{1/4}</math>.<br />
<br />
<br />
One prediction of this model is that the properties of the cellular membrane are far more important than the interior of the cell in the cell spreading. One way to test this is by creating two mutants: one in which the microtubules molecules within the cell are unable to polymerize and another in which the actin shell in the cortex is altered.<br />
<br />
[[Image:MahadevanUniversalFig04.jpg | 360 px]]<br />
<br />
Sung Hoon's comment: In the Fig. 4 (a), the Cytochalasin D-treated cell showed linear<br />
behavior. What does the treatment do so that the treated cells spread more quickly?<br />
<br />
Has anyone actually created these mutant cells to test this theory? Is that what you're showing below?<br />
Maybe it's better to write your own captions that get right to your point?<br />
--[[User:Lidiya|Lidiya]] 03:06, 18 February 2009 (UTC)<br />
<br />
This work is important by providing unity to the plethora of information about the molecular mechanics for cell motility and adhesion. It allows future researchers to focus on the aspects of cell structure that are most relevant for thee processes and make refinements to this basic model.<br />
<br />
<br />
-------------------------------------------------------------------------------------------------------------------------------------------------------------<br />
<br />
Second Entry: Nick Chisholm, AP 225, Fall 2009 (In Progress...)<br />
<br />
==General Information==<br />
'''Authors''': D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan <br />
<br />
'''Publication''': Current Biology '''17''' 694 (2007)<br />
<br />
==Soft Matter Keywords==<br />
[http://soft-matter.seas.harvard.edu/index.php/Adhesion Adhesion], [http://soft-matter.seas.harvard.edu/index.php/Cell Cell], [http://soft-matter.seas.harvard.edu/index.php/Polymerization Polymerization], Viscous<br />
<br />
==Summary==<br />
The authors explore the early stages of cell spreading. In particular, they look at the situation where cells are plated onto artificial adhesive surfaces; they first flatten and deform extensively as they spread. This article presents experimental probing of the dynamics of this spreading process using quantitative visualization and biochemical manipulation with a variety of cell types, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs. Surprisingly, the authors find that the adhesion dynamics of cells follow a universal power-law behavior (i.e. the contact radius is proportional to elapsed time to a certain power).<br />
<br />
In Figure 1, one can see an image of a cell spreading on a substrate. The image is taken using reflection interference contrast microscopy (RICM).<br />
<br />
[[Image:CellSpreading.png|thumb|300px| Figure 1, taken from [1].]]<br />
<br />
==Soft Matter Discussion==<br />
As is clear by Figure 1, the spreading is isotropic, the authors can define the spreading radius as: <math>R = \sqrt{\frac{A}{\pi}}</math>.<br />
<br />
[[Image:ContactRadius.png|thumb|300px| Figure 2, taken from [1].]]<br />
<br />
==Reference==<br />
[1] D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan, "The universal dynamics of cell spreading," Current Biology '''17''' 694 (2007).</div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=The_universal_dynamics_of_cell_spreading&diff=13966The universal dynamics of cell spreading2009-12-05T07:50:13Z<p>Chisholm: /* Soft Matter Discussion */</p>
<hr />
<div>Original entry: Naveen Sinha, APPHY 226, Spring 2009<br />
<br />
In numerous biological experiments, cells are plated onto an artificial adhesive surface to study them under a microscope. After being deposited on the surface, they flatten and spread outwards along the surface. This process incorporates many biological reactions, including the diffusion of adhesion receptors and the polymerization of the scaffolding-like actin molecules. However, Prof. Mahadevan and his collaborators show how a variety of cells and surface exhibit a power-law behavior in the contact radius of the colony of cells as a function of time. This can be understood when the cells are modeled as a viscous shell of liquid with a much less viscous interior. <br />
<br />
The basic biological system is shown below. Cells are placed on a surface and Reflectance Contrast Imaging Microscopy is used to measure the contact area as a function of time. <br />
<br />
[[Image:MahadevanUniversalFig01.jpg | 360 px]]<br />
<br />
The length measure used to characterize the system is the radius of a circle with the same area. On a log-log plot, the power law behavior becomes apparent.<br />
<br />
[[Image:MahadevanUniversalFig02.jpg | 360 px]]<br />
<br />
There appear to be two different regimes: (1) an initial diffusive regime with <math>R ~ t^{1/2}</math> and (2) a sub-diffusive region with <math>R ~ t^{1/4}</math>.<br />
<br />
Despite all the biochemical complexities of the spreading process, a simple model that treated the cells as a shell of viscous liquid is sufficient to describe most of the behavior. <br />
<br />
[[Image:MahadevanUniversalFig03.jpg | 360 px]]<br />
<br />
Initially, the power-law can be derived by setting the chance in adhesion energy equal to the viscous energy dissipation. This approximation is valid for when the radius of the contact angle is less than te initial cell radius <math>R_c</math>. The change in contact area is related to the rate of change in the radius by <math>\frac{dA}{dt} = R \frac{dR}{dt}</math>. This can related to the rate of energy gain by multiplying by the adhesion energy per unit area, J, which is the product of the area of each bond and the energy per bond: <math>J R \frac{dR}{dt}</math>. Assuming that the cell cortex has a width w everywhere, the strain is of the order <math>\frac{dR/dt}{w}</math>. This strain acts over a volume approximately equal to <math>R^2 w</math>. The product of the strain, volume, and viscosity leads to an energy dissipation of <math>\eta (\frac{dR}{dt} \frac{1}{w})</math>. By setting this equal to the change in the adhesion energy, we can get the following power law:<br />
<math>R = C \big(\frac{J w}{\eta}\big)^{1/2} t^{1/2}</math>.<br />
<br />
At longer times, when cell has flattened out (i.e. the radius of contact is larger than the initial radius), the viscous energy dissipation occurs throughout the whole volume of the cell. The power law is modified to <math>J R \frac{dR}{dt} = \eta_c \big(\frac{dR}{dt} \frac{1}{w}\big)^2 R^2 w_c</math>. This can be re-arranged to the scaling law:<br />
<math>R ~ \big(\frac{J R_c^3}{\eta_c}\big)^{1/4} t^{1/4}</math>.<br />
<br />
<br />
One prediction of this model is that the properties of the cellular membrane are far more important than the interior of the cell in the cell spreading. One way to test this is by creating two mutants: one in which the microtubules molecules within the cell are unable to polymerize and another in which the actin shell in the cortex is altered.<br />
<br />
[[Image:MahadevanUniversalFig04.jpg | 360 px]]<br />
<br />
Sung Hoon's comment: In the Fig. 4 (a), the Cytochalasin D-treated cell showed linear<br />
behavior. What does the treatment do so that the treated cells spread more quickly?<br />
<br />
Has anyone actually created these mutant cells to test this theory? Is that what you're showing below?<br />
Maybe it's better to write your own captions that get right to your point?<br />
--[[User:Lidiya|Lidiya]] 03:06, 18 February 2009 (UTC)<br />
<br />
This work is important by providing unity to the plethora of information about the molecular mechanics for cell motility and adhesion. It allows future researchers to focus on the aspects of cell structure that are most relevant for thee processes and make refinements to this basic model.<br />
<br />
<br />
-------------------------------------------------------------------------------------------------------------------------------------------------------------<br />
<br />
Second Entry: Nick Chisholm, AP 225, Fall 2009 (In Progress...)<br />
<br />
==General Information==<br />
'''Authors''': D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan <br />
<br />
'''Publication''': Current Biology '''17''' 694 (2007)<br />
<br />
==Soft Matter Keywords==<br />
[http://soft-matter.seas.harvard.edu/index.php/Adhesion Adhesion], [http://soft-matter.seas.harvard.edu/index.php/Cell Cell], [http://soft-matter.seas.harvard.edu/index.php/Polymerization Polymerization], Viscous<br />
<br />
==Summary==<br />
The authors explore the early stages of cell spreading. In particular, they look at the situation where cells are plated onto artificial adhesive surfaces; they first flatten and deform extensively as they spread. This article presents experimental probing of the dynamics of this spreading process using quantitative visualization and biochemical manipulation with a variety of cell types, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs. Surprisingly, the authors find that the adhesion dynamics of cells follow a universal power-law behavior (i.e. the contact radius is proportional to elapsed time to a certain power).<br />
<br />
In Figure 1, one can see an image of a cell spreading on a substrate. The image is taken using reflection interference contrast microscopy (RICM).<br />
<br />
[[Image:CellSpreading.png|thumb|300px| Figure 1, taken from [1].]]<br />
<br />
==Soft Matter Discussion==<br />
As is clear by Figure 1, the spreading is isotropic, the authors can define the spreading radius as: <math>R = \sqrt{\frac{A}{\pi}}</math>.<br />
<br />
==Reference==<br />
[1] D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan, "The universal dynamics of cell spreading," Current Biology '''17''' 694 (2007).</div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=The_universal_dynamics_of_cell_spreading&diff=13965The universal dynamics of cell spreading2009-12-05T07:49:54Z<p>Chisholm: /* Summary */</p>
<hr />
<div>Original entry: Naveen Sinha, APPHY 226, Spring 2009<br />
<br />
In numerous biological experiments, cells are plated onto an artificial adhesive surface to study them under a microscope. After being deposited on the surface, they flatten and spread outwards along the surface. This process incorporates many biological reactions, including the diffusion of adhesion receptors and the polymerization of the scaffolding-like actin molecules. However, Prof. Mahadevan and his collaborators show how a variety of cells and surface exhibit a power-law behavior in the contact radius of the colony of cells as a function of time. This can be understood when the cells are modeled as a viscous shell of liquid with a much less viscous interior. <br />
<br />
The basic biological system is shown below. Cells are placed on a surface and Reflectance Contrast Imaging Microscopy is used to measure the contact area as a function of time. <br />
<br />
[[Image:MahadevanUniversalFig01.jpg | 360 px]]<br />
<br />
The length measure used to characterize the system is the radius of a circle with the same area. On a log-log plot, the power law behavior becomes apparent.<br />
<br />
[[Image:MahadevanUniversalFig02.jpg | 360 px]]<br />
<br />
There appear to be two different regimes: (1) an initial diffusive regime with <math>R ~ t^{1/2}</math> and (2) a sub-diffusive region with <math>R ~ t^{1/4}</math>.<br />
<br />
Despite all the biochemical complexities of the spreading process, a simple model that treated the cells as a shell of viscous liquid is sufficient to describe most of the behavior. <br />
<br />
[[Image:MahadevanUniversalFig03.jpg | 360 px]]<br />
<br />
Initially, the power-law can be derived by setting the chance in adhesion energy equal to the viscous energy dissipation. This approximation is valid for when the radius of the contact angle is less than te initial cell radius <math>R_c</math>. The change in contact area is related to the rate of change in the radius by <math>\frac{dA}{dt} = R \frac{dR}{dt}</math>. This can related to the rate of energy gain by multiplying by the adhesion energy per unit area, J, which is the product of the area of each bond and the energy per bond: <math>J R \frac{dR}{dt}</math>. Assuming that the cell cortex has a width w everywhere, the strain is of the order <math>\frac{dR/dt}{w}</math>. This strain acts over a volume approximately equal to <math>R^2 w</math>. The product of the strain, volume, and viscosity leads to an energy dissipation of <math>\eta (\frac{dR}{dt} \frac{1}{w})</math>. By setting this equal to the change in the adhesion energy, we can get the following power law:<br />
<math>R = C \big(\frac{J w}{\eta}\big)^{1/2} t^{1/2}</math>.<br />
<br />
At longer times, when cell has flattened out (i.e. the radius of contact is larger than the initial radius), the viscous energy dissipation occurs throughout the whole volume of the cell. The power law is modified to <math>J R \frac{dR}{dt} = \eta_c \big(\frac{dR}{dt} \frac{1}{w}\big)^2 R^2 w_c</math>. This can be re-arranged to the scaling law:<br />
<math>R ~ \big(\frac{J R_c^3}{\eta_c}\big)^{1/4} t^{1/4}</math>.<br />
<br />
<br />
One prediction of this model is that the properties of the cellular membrane are far more important than the interior of the cell in the cell spreading. One way to test this is by creating two mutants: one in which the microtubules molecules within the cell are unable to polymerize and another in which the actin shell in the cortex is altered.<br />
<br />
[[Image:MahadevanUniversalFig04.jpg | 360 px]]<br />
<br />
Sung Hoon's comment: In the Fig. 4 (a), the Cytochalasin D-treated cell showed linear<br />
behavior. What does the treatment do so that the treated cells spread more quickly?<br />
<br />
Has anyone actually created these mutant cells to test this theory? Is that what you're showing below?<br />
Maybe it's better to write your own captions that get right to your point?<br />
--[[User:Lidiya|Lidiya]] 03:06, 18 February 2009 (UTC)<br />
<br />
This work is important by providing unity to the plethora of information about the molecular mechanics for cell motility and adhesion. It allows future researchers to focus on the aspects of cell structure that are most relevant for thee processes and make refinements to this basic model.<br />
<br />
<br />
-------------------------------------------------------------------------------------------------------------------------------------------------------------<br />
<br />
Second Entry: Nick Chisholm, AP 225, Fall 2009 (In Progress...)<br />
<br />
==General Information==<br />
'''Authors''': D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan <br />
<br />
'''Publication''': Current Biology '''17''' 694 (2007)<br />
<br />
==Soft Matter Keywords==<br />
[http://soft-matter.seas.harvard.edu/index.php/Adhesion Adhesion], [http://soft-matter.seas.harvard.edu/index.php/Cell Cell], [http://soft-matter.seas.harvard.edu/index.php/Polymerization Polymerization], Viscous<br />
<br />
==Summary==<br />
The authors explore the early stages of cell spreading. In particular, they look at the situation where cells are plated onto artificial adhesive surfaces; they first flatten and deform extensively as they spread. This article presents experimental probing of the dynamics of this spreading process using quantitative visualization and biochemical manipulation with a variety of cell types, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs. Surprisingly, the authors find that the adhesion dynamics of cells follow a universal power-law behavior (i.e. the contact radius is proportional to elapsed time to a certain power).<br />
<br />
In Figure 1, one can see an image of a cell spreading on a substrate. The image is taken using reflection interference contrast microscopy (RICM).<br />
<br />
[[Image:CellSpreading.png|thumb|300px| Figure 1, taken from [1].]]<br />
<br />
==Soft Matter Discussion==<br />
<br />
==Reference==<br />
[1] D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan, "The universal dynamics of cell spreading," Current Biology '''17''' 694 (2007).</div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=The_universal_dynamics_of_cell_spreading&diff=13964The universal dynamics of cell spreading2009-12-05T07:49:12Z<p>Chisholm: /* Summary */</p>
<hr />
<div>Original entry: Naveen Sinha, APPHY 226, Spring 2009<br />
<br />
In numerous biological experiments, cells are plated onto an artificial adhesive surface to study them under a microscope. After being deposited on the surface, they flatten and spread outwards along the surface. This process incorporates many biological reactions, including the diffusion of adhesion receptors and the polymerization of the scaffolding-like actin molecules. However, Prof. Mahadevan and his collaborators show how a variety of cells and surface exhibit a power-law behavior in the contact radius of the colony of cells as a function of time. This can be understood when the cells are modeled as a viscous shell of liquid with a much less viscous interior. <br />
<br />
The basic biological system is shown below. Cells are placed on a surface and Reflectance Contrast Imaging Microscopy is used to measure the contact area as a function of time. <br />
<br />
[[Image:MahadevanUniversalFig01.jpg | 360 px]]<br />
<br />
The length measure used to characterize the system is the radius of a circle with the same area. On a log-log plot, the power law behavior becomes apparent.<br />
<br />
[[Image:MahadevanUniversalFig02.jpg | 360 px]]<br />
<br />
There appear to be two different regimes: (1) an initial diffusive regime with <math>R ~ t^{1/2}</math> and (2) a sub-diffusive region with <math>R ~ t^{1/4}</math>.<br />
<br />
Despite all the biochemical complexities of the spreading process, a simple model that treated the cells as a shell of viscous liquid is sufficient to describe most of the behavior. <br />
<br />
[[Image:MahadevanUniversalFig03.jpg | 360 px]]<br />
<br />
Initially, the power-law can be derived by setting the chance in adhesion energy equal to the viscous energy dissipation. This approximation is valid for when the radius of the contact angle is less than te initial cell radius <math>R_c</math>. The change in contact area is related to the rate of change in the radius by <math>\frac{dA}{dt} = R \frac{dR}{dt}</math>. This can related to the rate of energy gain by multiplying by the adhesion energy per unit area, J, which is the product of the area of each bond and the energy per bond: <math>J R \frac{dR}{dt}</math>. Assuming that the cell cortex has a width w everywhere, the strain is of the order <math>\frac{dR/dt}{w}</math>. This strain acts over a volume approximately equal to <math>R^2 w</math>. The product of the strain, volume, and viscosity leads to an energy dissipation of <math>\eta (\frac{dR}{dt} \frac{1}{w})</math>. By setting this equal to the change in the adhesion energy, we can get the following power law:<br />
<math>R = C \big(\frac{J w}{\eta}\big)^{1/2} t^{1/2}</math>.<br />
<br />
At longer times, when cell has flattened out (i.e. the radius of contact is larger than the initial radius), the viscous energy dissipation occurs throughout the whole volume of the cell. The power law is modified to <math>J R \frac{dR}{dt} = \eta_c \big(\frac{dR}{dt} \frac{1}{w}\big)^2 R^2 w_c</math>. This can be re-arranged to the scaling law:<br />
<math>R ~ \big(\frac{J R_c^3}{\eta_c}\big)^{1/4} t^{1/4}</math>.<br />
<br />
<br />
One prediction of this model is that the properties of the cellular membrane are far more important than the interior of the cell in the cell spreading. One way to test this is by creating two mutants: one in which the microtubules molecules within the cell are unable to polymerize and another in which the actin shell in the cortex is altered.<br />
<br />
[[Image:MahadevanUniversalFig04.jpg | 360 px]]<br />
<br />
Sung Hoon's comment: In the Fig. 4 (a), the Cytochalasin D-treated cell showed linear<br />
behavior. What does the treatment do so that the treated cells spread more quickly?<br />
<br />
Has anyone actually created these mutant cells to test this theory? Is that what you're showing below?<br />
Maybe it's better to write your own captions that get right to your point?<br />
--[[User:Lidiya|Lidiya]] 03:06, 18 February 2009 (UTC)<br />
<br />
This work is important by providing unity to the plethora of information about the molecular mechanics for cell motility and adhesion. It allows future researchers to focus on the aspects of cell structure that are most relevant for thee processes and make refinements to this basic model.<br />
<br />
<br />
-------------------------------------------------------------------------------------------------------------------------------------------------------------<br />
<br />
Second Entry: Nick Chisholm, AP 225, Fall 2009 (In Progress...)<br />
<br />
==General Information==<br />
'''Authors''': D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan <br />
<br />
'''Publication''': Current Biology '''17''' 694 (2007)<br />
<br />
==Soft Matter Keywords==<br />
[http://soft-matter.seas.harvard.edu/index.php/Adhesion Adhesion], [http://soft-matter.seas.harvard.edu/index.php/Cell Cell], [http://soft-matter.seas.harvard.edu/index.php/Polymerization Polymerization], Viscous<br />
<br />
==Summary==<br />
The authors explore the early stages of cell spreading. In particular, they look at the situation where cells are plated onto artificial adhesive surfaces; they first flatten and deform extensively as they spread. This article presents experimental probing of the dynamics of this spreading process using quantitative visualization and biochemical manipulation with a variety of cell types, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs. Surprisingly, the authors find that the adhesion dynamics of cells follow a universal power-law behavior (i.e. the contact radius is proportional to elapsed time to a certain power).<br />
<br />
In Figure 1, one can see an image of a cell spreading on a substrate. The image is taken using reflection interference contrast microscopy (RICM). Since the spreading is isotropic, the authors can define the spreading radius as: <math>R = \sqrt{\frac{A}{\pi}}</math>.<br />
<br />
[[Image:CellSpreading.png|thumb|300px| Figure 1, taken from [1].]]<br />
<br />
==Soft Matter Discussion==<br />
<br />
==Reference==<br />
[1] D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan, "The universal dynamics of cell spreading," Current Biology '''17''' 694 (2007).</div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=The_universal_dynamics_of_cell_spreading&diff=13963The universal dynamics of cell spreading2009-12-05T07:48:54Z<p>Chisholm: /* Summary */</p>
<hr />
<div>Original entry: Naveen Sinha, APPHY 226, Spring 2009<br />
<br />
In numerous biological experiments, cells are plated onto an artificial adhesive surface to study them under a microscope. After being deposited on the surface, they flatten and spread outwards along the surface. This process incorporates many biological reactions, including the diffusion of adhesion receptors and the polymerization of the scaffolding-like actin molecules. However, Prof. Mahadevan and his collaborators show how a variety of cells and surface exhibit a power-law behavior in the contact radius of the colony of cells as a function of time. This can be understood when the cells are modeled as a viscous shell of liquid with a much less viscous interior. <br />
<br />
The basic biological system is shown below. Cells are placed on a surface and Reflectance Contrast Imaging Microscopy is used to measure the contact area as a function of time. <br />
<br />
[[Image:MahadevanUniversalFig01.jpg | 360 px]]<br />
<br />
The length measure used to characterize the system is the radius of a circle with the same area. On a log-log plot, the power law behavior becomes apparent.<br />
<br />
[[Image:MahadevanUniversalFig02.jpg | 360 px]]<br />
<br />
There appear to be two different regimes: (1) an initial diffusive regime with <math>R ~ t^{1/2}</math> and (2) a sub-diffusive region with <math>R ~ t^{1/4}</math>.<br />
<br />
Despite all the biochemical complexities of the spreading process, a simple model that treated the cells as a shell of viscous liquid is sufficient to describe most of the behavior. <br />
<br />
[[Image:MahadevanUniversalFig03.jpg | 360 px]]<br />
<br />
Initially, the power-law can be derived by setting the chance in adhesion energy equal to the viscous energy dissipation. This approximation is valid for when the radius of the contact angle is less than te initial cell radius <math>R_c</math>. The change in contact area is related to the rate of change in the radius by <math>\frac{dA}{dt} = R \frac{dR}{dt}</math>. This can related to the rate of energy gain by multiplying by the adhesion energy per unit area, J, which is the product of the area of each bond and the energy per bond: <math>J R \frac{dR}{dt}</math>. Assuming that the cell cortex has a width w everywhere, the strain is of the order <math>\frac{dR/dt}{w}</math>. This strain acts over a volume approximately equal to <math>R^2 w</math>. The product of the strain, volume, and viscosity leads to an energy dissipation of <math>\eta (\frac{dR}{dt} \frac{1}{w})</math>. By setting this equal to the change in the adhesion energy, we can get the following power law:<br />
<math>R = C \big(\frac{J w}{\eta}\big)^{1/2} t^{1/2}</math>.<br />
<br />
At longer times, when cell has flattened out (i.e. the radius of contact is larger than the initial radius), the viscous energy dissipation occurs throughout the whole volume of the cell. The power law is modified to <math>J R \frac{dR}{dt} = \eta_c \big(\frac{dR}{dt} \frac{1}{w}\big)^2 R^2 w_c</math>. This can be re-arranged to the scaling law:<br />
<math>R ~ \big(\frac{J R_c^3}{\eta_c}\big)^{1/4} t^{1/4}</math>.<br />
<br />
<br />
One prediction of this model is that the properties of the cellular membrane are far more important than the interior of the cell in the cell spreading. One way to test this is by creating two mutants: one in which the microtubules molecules within the cell are unable to polymerize and another in which the actin shell in the cortex is altered.<br />
<br />
[[Image:MahadevanUniversalFig04.jpg | 360 px]]<br />
<br />
Sung Hoon's comment: In the Fig. 4 (a), the Cytochalasin D-treated cell showed linear<br />
behavior. What does the treatment do so that the treated cells spread more quickly?<br />
<br />
Has anyone actually created these mutant cells to test this theory? Is that what you're showing below?<br />
Maybe it's better to write your own captions that get right to your point?<br />
--[[User:Lidiya|Lidiya]] 03:06, 18 February 2009 (UTC)<br />
<br />
This work is important by providing unity to the plethora of information about the molecular mechanics for cell motility and adhesion. It allows future researchers to focus on the aspects of cell structure that are most relevant for thee processes and make refinements to this basic model.<br />
<br />
<br />
-------------------------------------------------------------------------------------------------------------------------------------------------------------<br />
<br />
Second Entry: Nick Chisholm, AP 225, Fall 2009 (In Progress...)<br />
<br />
==General Information==<br />
'''Authors''': D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan <br />
<br />
'''Publication''': Current Biology '''17''' 694 (2007)<br />
<br />
==Soft Matter Keywords==<br />
[http://soft-matter.seas.harvard.edu/index.php/Adhesion Adhesion], [http://soft-matter.seas.harvard.edu/index.php/Cell Cell], [http://soft-matter.seas.harvard.edu/index.php/Polymerization Polymerization], Viscous<br />
<br />
==Summary==<br />
The authors explore the early stages of cell spreading. In particular, they look at the situation where cells are plated onto artificial adhesive surfaces; they first flatten and deform extensively as they spread. This article presents experimental probing of the dynamics of this spreading process using quantitative visualization and biochemical manipulation with a variety of cell types, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs. Surprisingly, the authors find that the adhesion dynamics of cells follow a universal power-law behavior (i.e. the contact radius is proportional to elapsed time to a certain power).<br />
<br />
In Figure 1, one can see an image of a cell spreading on a substrate. The image is taken using reflection interference contrast microscopy (RICM). Since the spreading is isotropic, the authors can define the spreading radius as: <math>R = \sqrt{8}</math>.<br />
<br />
[[Image:CellSpreading.png|thumb|300px| Figure 1, taken from [1].]]<br />
<br />
==Soft Matter Discussion==<br />
<br />
==Reference==<br />
[1] D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan, "The universal dynamics of cell spreading," Current Biology '''17''' 694 (2007).</div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=The_universal_dynamics_of_cell_spreading&diff=13962The universal dynamics of cell spreading2009-12-05T07:48:45Z<p>Chisholm: /* Summary */</p>
<hr />
<div>Original entry: Naveen Sinha, APPHY 226, Spring 2009<br />
<br />
In numerous biological experiments, cells are plated onto an artificial adhesive surface to study them under a microscope. After being deposited on the surface, they flatten and spread outwards along the surface. This process incorporates many biological reactions, including the diffusion of adhesion receptors and the polymerization of the scaffolding-like actin molecules. However, Prof. Mahadevan and his collaborators show how a variety of cells and surface exhibit a power-law behavior in the contact radius of the colony of cells as a function of time. This can be understood when the cells are modeled as a viscous shell of liquid with a much less viscous interior. <br />
<br />
The basic biological system is shown below. Cells are placed on a surface and Reflectance Contrast Imaging Microscopy is used to measure the contact area as a function of time. <br />
<br />
[[Image:MahadevanUniversalFig01.jpg | 360 px]]<br />
<br />
The length measure used to characterize the system is the radius of a circle with the same area. On a log-log plot, the power law behavior becomes apparent.<br />
<br />
[[Image:MahadevanUniversalFig02.jpg | 360 px]]<br />
<br />
There appear to be two different regimes: (1) an initial diffusive regime with <math>R ~ t^{1/2}</math> and (2) a sub-diffusive region with <math>R ~ t^{1/4}</math>.<br />
<br />
Despite all the biochemical complexities of the spreading process, a simple model that treated the cells as a shell of viscous liquid is sufficient to describe most of the behavior. <br />
<br />
[[Image:MahadevanUniversalFig03.jpg | 360 px]]<br />
<br />
Initially, the power-law can be derived by setting the chance in adhesion energy equal to the viscous energy dissipation. This approximation is valid for when the radius of the contact angle is less than te initial cell radius <math>R_c</math>. The change in contact area is related to the rate of change in the radius by <math>\frac{dA}{dt} = R \frac{dR}{dt}</math>. This can related to the rate of energy gain by multiplying by the adhesion energy per unit area, J, which is the product of the area of each bond and the energy per bond: <math>J R \frac{dR}{dt}</math>. Assuming that the cell cortex has a width w everywhere, the strain is of the order <math>\frac{dR/dt}{w}</math>. This strain acts over a volume approximately equal to <math>R^2 w</math>. The product of the strain, volume, and viscosity leads to an energy dissipation of <math>\eta (\frac{dR}{dt} \frac{1}{w})</math>. By setting this equal to the change in the adhesion energy, we can get the following power law:<br />
<math>R = C \big(\frac{J w}{\eta}\big)^{1/2} t^{1/2}</math>.<br />
<br />
At longer times, when cell has flattened out (i.e. the radius of contact is larger than the initial radius), the viscous energy dissipation occurs throughout the whole volume of the cell. The power law is modified to <math>J R \frac{dR}{dt} = \eta_c \big(\frac{dR}{dt} \frac{1}{w}\big)^2 R^2 w_c</math>. This can be re-arranged to the scaling law:<br />
<math>R ~ \big(\frac{J R_c^3}{\eta_c}\big)^{1/4} t^{1/4}</math>.<br />
<br />
<br />
One prediction of this model is that the properties of the cellular membrane are far more important than the interior of the cell in the cell spreading. One way to test this is by creating two mutants: one in which the microtubules molecules within the cell are unable to polymerize and another in which the actin shell in the cortex is altered.<br />
<br />
[[Image:MahadevanUniversalFig04.jpg | 360 px]]<br />
<br />
Sung Hoon's comment: In the Fig. 4 (a), the Cytochalasin D-treated cell showed linear<br />
behavior. What does the treatment do so that the treated cells spread more quickly?<br />
<br />
Has anyone actually created these mutant cells to test this theory? Is that what you're showing below?<br />
Maybe it's better to write your own captions that get right to your point?<br />
--[[User:Lidiya|Lidiya]] 03:06, 18 February 2009 (UTC)<br />
<br />
This work is important by providing unity to the plethora of information about the molecular mechanics for cell motility and adhesion. It allows future researchers to focus on the aspects of cell structure that are most relevant for thee processes and make refinements to this basic model.<br />
<br />
<br />
-------------------------------------------------------------------------------------------------------------------------------------------------------------<br />
<br />
Second Entry: Nick Chisholm, AP 225, Fall 2009 (In Progress...)<br />
<br />
==General Information==<br />
'''Authors''': D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan <br />
<br />
'''Publication''': Current Biology '''17''' 694 (2007)<br />
<br />
==Soft Matter Keywords==<br />
[http://soft-matter.seas.harvard.edu/index.php/Adhesion Adhesion], [http://soft-matter.seas.harvard.edu/index.php/Cell Cell], [http://soft-matter.seas.harvard.edu/index.php/Polymerization Polymerization], Viscous<br />
<br />
==Summary==<br />
The authors explore the early stages of cell spreading. In particular, they look at the situation where cells are plated onto artificial adhesive surfaces; they first flatten and deform extensively as they spread. This article presents experimental probing of the dynamics of this spreading process using quantitative visualization and biochemical manipulation with a variety of cell types, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs. Surprisingly, the authors find that the adhesion dynamics of cells follow a universal power-law behavior (i.e. the contact radius is proportional to elapsed time to a certain power).<br />
<br />
In Figure 1, one can see an image of a cell spreading on a substrate. The image is taken using reflection interference contrast microscopy (RICM). Since the spreading is isotropic, the authors can define the spreading radius as: <math>R = \Sqrt{8}</math>.<br />
<br />
[[Image:CellSpreading.png|thumb|300px| Figure 1, taken from [1].]]<br />
<br />
==Soft Matter Discussion==<br />
<br />
==Reference==<br />
[1] D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan, "The universal dynamics of cell spreading," Current Biology '''17''' 694 (2007).</div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=The_universal_dynamics_of_cell_spreading&diff=13961The universal dynamics of cell spreading2009-12-05T07:48:34Z<p>Chisholm: /* Summary */</p>
<hr />
<div>Original entry: Naveen Sinha, APPHY 226, Spring 2009<br />
<br />
In numerous biological experiments, cells are plated onto an artificial adhesive surface to study them under a microscope. After being deposited on the surface, they flatten and spread outwards along the surface. This process incorporates many biological reactions, including the diffusion of adhesion receptors and the polymerization of the scaffolding-like actin molecules. However, Prof. Mahadevan and his collaborators show how a variety of cells and surface exhibit a power-law behavior in the contact radius of the colony of cells as a function of time. This can be understood when the cells are modeled as a viscous shell of liquid with a much less viscous interior. <br />
<br />
The basic biological system is shown below. Cells are placed on a surface and Reflectance Contrast Imaging Microscopy is used to measure the contact area as a function of time. <br />
<br />
[[Image:MahadevanUniversalFig01.jpg | 360 px]]<br />
<br />
The length measure used to characterize the system is the radius of a circle with the same area. On a log-log plot, the power law behavior becomes apparent.<br />
<br />
[[Image:MahadevanUniversalFig02.jpg | 360 px]]<br />
<br />
There appear to be two different regimes: (1) an initial diffusive regime with <math>R ~ t^{1/2}</math> and (2) a sub-diffusive region with <math>R ~ t^{1/4}</math>.<br />
<br />
Despite all the biochemical complexities of the spreading process, a simple model that treated the cells as a shell of viscous liquid is sufficient to describe most of the behavior. <br />
<br />
[[Image:MahadevanUniversalFig03.jpg | 360 px]]<br />
<br />
Initially, the power-law can be derived by setting the chance in adhesion energy equal to the viscous energy dissipation. This approximation is valid for when the radius of the contact angle is less than te initial cell radius <math>R_c</math>. The change in contact area is related to the rate of change in the radius by <math>\frac{dA}{dt} = R \frac{dR}{dt}</math>. This can related to the rate of energy gain by multiplying by the adhesion energy per unit area, J, which is the product of the area of each bond and the energy per bond: <math>J R \frac{dR}{dt}</math>. Assuming that the cell cortex has a width w everywhere, the strain is of the order <math>\frac{dR/dt}{w}</math>. This strain acts over a volume approximately equal to <math>R^2 w</math>. The product of the strain, volume, and viscosity leads to an energy dissipation of <math>\eta (\frac{dR}{dt} \frac{1}{w})</math>. By setting this equal to the change in the adhesion energy, we can get the following power law:<br />
<math>R = C \big(\frac{J w}{\eta}\big)^{1/2} t^{1/2}</math>.<br />
<br />
At longer times, when cell has flattened out (i.e. the radius of contact is larger than the initial radius), the viscous energy dissipation occurs throughout the whole volume of the cell. The power law is modified to <math>J R \frac{dR}{dt} = \eta_c \big(\frac{dR}{dt} \frac{1}{w}\big)^2 R^2 w_c</math>. This can be re-arranged to the scaling law:<br />
<math>R ~ \big(\frac{J R_c^3}{\eta_c}\big)^{1/4} t^{1/4}</math>.<br />
<br />
<br />
One prediction of this model is that the properties of the cellular membrane are far more important than the interior of the cell in the cell spreading. One way to test this is by creating two mutants: one in which the microtubules molecules within the cell are unable to polymerize and another in which the actin shell in the cortex is altered.<br />
<br />
[[Image:MahadevanUniversalFig04.jpg | 360 px]]<br />
<br />
Sung Hoon's comment: In the Fig. 4 (a), the Cytochalasin D-treated cell showed linear<br />
behavior. What does the treatment do so that the treated cells spread more quickly?<br />
<br />
Has anyone actually created these mutant cells to test this theory? Is that what you're showing below?<br />
Maybe it's better to write your own captions that get right to your point?<br />
--[[User:Lidiya|Lidiya]] 03:06, 18 February 2009 (UTC)<br />
<br />
This work is important by providing unity to the plethora of information about the molecular mechanics for cell motility and adhesion. It allows future researchers to focus on the aspects of cell structure that are most relevant for thee processes and make refinements to this basic model.<br />
<br />
<br />
-------------------------------------------------------------------------------------------------------------------------------------------------------------<br />
<br />
Second Entry: Nick Chisholm, AP 225, Fall 2009 (In Progress...)<br />
<br />
==General Information==<br />
'''Authors''': D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan <br />
<br />
'''Publication''': Current Biology '''17''' 694 (2007)<br />
<br />
==Soft Matter Keywords==<br />
[http://soft-matter.seas.harvard.edu/index.php/Adhesion Adhesion], [http://soft-matter.seas.harvard.edu/index.php/Cell Cell], [http://soft-matter.seas.harvard.edu/index.php/Polymerization Polymerization], Viscous<br />
<br />
==Summary==<br />
The authors explore the early stages of cell spreading. In particular, they look at the situation where cells are plated onto artificial adhesive surfaces; they first flatten and deform extensively as they spread. This article presents experimental probing of the dynamics of this spreading process using quantitative visualization and biochemical manipulation with a variety of cell types, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs. Surprisingly, the authors find that the adhesion dynamics of cells follow a universal power-law behavior (i.e. the contact radius is proportional to elapsed time to a certain power).<br />
<br />
In Figure 1, one can see an image of a cell spreading on a substrate. The image is taken using reflection interference contrast microscopy (RICM). Since the spreading is isotropic, the authors can define the spreading radius as: <math>R = \Sqrt{\frac{A}{\pi}}}</math>.<br />
<br />
[[Image:CellSpreading.png|thumb|300px| Figure 1, taken from [1].]]<br />
<br />
==Soft Matter Discussion==<br />
<br />
==Reference==<br />
[1] D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan, "The universal dynamics of cell spreading," Current Biology '''17''' 694 (2007).</div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=The_universal_dynamics_of_cell_spreading&diff=13959The universal dynamics of cell spreading2009-12-05T07:48:24Z<p>Chisholm: /* Summary */</p>
<hr />
<div>Original entry: Naveen Sinha, APPHY 226, Spring 2009<br />
<br />
In numerous biological experiments, cells are plated onto an artificial adhesive surface to study them under a microscope. After being deposited on the surface, they flatten and spread outwards along the surface. This process incorporates many biological reactions, including the diffusion of adhesion receptors and the polymerization of the scaffolding-like actin molecules. However, Prof. Mahadevan and his collaborators show how a variety of cells and surface exhibit a power-law behavior in the contact radius of the colony of cells as a function of time. This can be understood when the cells are modeled as a viscous shell of liquid with a much less viscous interior. <br />
<br />
The basic biological system is shown below. Cells are placed on a surface and Reflectance Contrast Imaging Microscopy is used to measure the contact area as a function of time. <br />
<br />
[[Image:MahadevanUniversalFig01.jpg | 360 px]]<br />
<br />
The length measure used to characterize the system is the radius of a circle with the same area. On a log-log plot, the power law behavior becomes apparent.<br />
<br />
[[Image:MahadevanUniversalFig02.jpg | 360 px]]<br />
<br />
There appear to be two different regimes: (1) an initial diffusive regime with <math>R ~ t^{1/2}</math> and (2) a sub-diffusive region with <math>R ~ t^{1/4}</math>.<br />
<br />
Despite all the biochemical complexities of the spreading process, a simple model that treated the cells as a shell of viscous liquid is sufficient to describe most of the behavior. <br />
<br />
[[Image:MahadevanUniversalFig03.jpg | 360 px]]<br />
<br />
Initially, the power-law can be derived by setting the chance in adhesion energy equal to the viscous energy dissipation. This approximation is valid for when the radius of the contact angle is less than te initial cell radius <math>R_c</math>. The change in contact area is related to the rate of change in the radius by <math>\frac{dA}{dt} = R \frac{dR}{dt}</math>. This can related to the rate of energy gain by multiplying by the adhesion energy per unit area, J, which is the product of the area of each bond and the energy per bond: <math>J R \frac{dR}{dt}</math>. Assuming that the cell cortex has a width w everywhere, the strain is of the order <math>\frac{dR/dt}{w}</math>. This strain acts over a volume approximately equal to <math>R^2 w</math>. The product of the strain, volume, and viscosity leads to an energy dissipation of <math>\eta (\frac{dR}{dt} \frac{1}{w})</math>. By setting this equal to the change in the adhesion energy, we can get the following power law:<br />
<math>R = C \big(\frac{J w}{\eta}\big)^{1/2} t^{1/2}</math>.<br />
<br />
At longer times, when cell has flattened out (i.e. the radius of contact is larger than the initial radius), the viscous energy dissipation occurs throughout the whole volume of the cell. The power law is modified to <math>J R \frac{dR}{dt} = \eta_c \big(\frac{dR}{dt} \frac{1}{w}\big)^2 R^2 w_c</math>. This can be re-arranged to the scaling law:<br />
<math>R ~ \big(\frac{J R_c^3}{\eta_c}\big)^{1/4} t^{1/4}</math>.<br />
<br />
<br />
One prediction of this model is that the properties of the cellular membrane are far more important than the interior of the cell in the cell spreading. One way to test this is by creating two mutants: one in which the microtubules molecules within the cell are unable to polymerize and another in which the actin shell in the cortex is altered.<br />
<br />
[[Image:MahadevanUniversalFig04.jpg | 360 px]]<br />
<br />
Sung Hoon's comment: In the Fig. 4 (a), the Cytochalasin D-treated cell showed linear<br />
behavior. What does the treatment do so that the treated cells spread more quickly?<br />
<br />
Has anyone actually created these mutant cells to test this theory? Is that what you're showing below?<br />
Maybe it's better to write your own captions that get right to your point?<br />
--[[User:Lidiya|Lidiya]] 03:06, 18 February 2009 (UTC)<br />
<br />
This work is important by providing unity to the plethora of information about the molecular mechanics for cell motility and adhesion. It allows future researchers to focus on the aspects of cell structure that are most relevant for thee processes and make refinements to this basic model.<br />
<br />
<br />
-------------------------------------------------------------------------------------------------------------------------------------------------------------<br />
<br />
Second Entry: Nick Chisholm, AP 225, Fall 2009 (In Progress...)<br />
<br />
==General Information==<br />
'''Authors''': D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan <br />
<br />
'''Publication''': Current Biology '''17''' 694 (2007)<br />
<br />
==Soft Matter Keywords==<br />
[http://soft-matter.seas.harvard.edu/index.php/Adhesion Adhesion], [http://soft-matter.seas.harvard.edu/index.php/Cell Cell], [http://soft-matter.seas.harvard.edu/index.php/Polymerization Polymerization], Viscous<br />
<br />
==Summary==<br />
The authors explore the early stages of cell spreading. In particular, they look at the situation where cells are plated onto artificial adhesive surfaces; they first flatten and deform extensively as they spread. This article presents experimental probing of the dynamics of this spreading process using quantitative visualization and biochemical manipulation with a variety of cell types, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs. Surprisingly, the authors find that the adhesion dynamics of cells follow a universal power-law behavior (i.e. the contact radius is proportional to elapsed time to a certain power).<br />
<br />
In Figure 1, one can see an image of a cell spreading on a substrate. The image is taken using reflection interference contrast microscopy (RICM). Since the spreading is isotropic, the authors can define the spreading radius as: <math>R = \Sqrt{\frac{A}{\pi}}</math>.<br />
<br />
[[Image:CellSpreading.png|thumb|300px| Figure 1, taken from [1].]]<br />
<br />
==Soft Matter Discussion==<br />
<br />
==Reference==<br />
[1] D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan, "The universal dynamics of cell spreading," Current Biology '''17''' 694 (2007).</div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=File:CellSpreading.png&diff=13955File:CellSpreading.png2009-12-05T07:42:11Z<p>Chisholm: </p>
<hr />
<div></div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=The_universal_dynamics_of_cell_spreading&diff=13954The universal dynamics of cell spreading2009-12-05T07:42:01Z<p>Chisholm: /* Summary */</p>
<hr />
<div>Original entry: Naveen Sinha, APPHY 226, Spring 2009<br />
<br />
In numerous biological experiments, cells are plated onto an artificial adhesive surface to study them under a microscope. After being deposited on the surface, they flatten and spread outwards along the surface. This process incorporates many biological reactions, including the diffusion of adhesion receptors and the polymerization of the scaffolding-like actin molecules. However, Prof. Mahadevan and his collaborators show how a variety of cells and surface exhibit a power-law behavior in the contact radius of the colony of cells as a function of time. This can be understood when the cells are modeled as a viscous shell of liquid with a much less viscous interior. <br />
<br />
The basic biological system is shown below. Cells are placed on a surface and Reflectance Contrast Imaging Microscopy is used to measure the contact area as a function of time. <br />
<br />
[[Image:MahadevanUniversalFig01.jpg | 360 px]]<br />
<br />
The length measure used to characterize the system is the radius of a circle with the same area. On a log-log plot, the power law behavior becomes apparent.<br />
<br />
[[Image:MahadevanUniversalFig02.jpg | 360 px]]<br />
<br />
There appear to be two different regimes: (1) an initial diffusive regime with <math>R ~ t^{1/2}</math> and (2) a sub-diffusive region with <math>R ~ t^{1/4}</math>.<br />
<br />
Despite all the biochemical complexities of the spreading process, a simple model that treated the cells as a shell of viscous liquid is sufficient to describe most of the behavior. <br />
<br />
[[Image:MahadevanUniversalFig03.jpg | 360 px]]<br />
<br />
Initially, the power-law can be derived by setting the chance in adhesion energy equal to the viscous energy dissipation. This approximation is valid for when the radius of the contact angle is less than te initial cell radius <math>R_c</math>. The change in contact area is related to the rate of change in the radius by <math>\frac{dA}{dt} = R \frac{dR}{dt}</math>. This can related to the rate of energy gain by multiplying by the adhesion energy per unit area, J, which is the product of the area of each bond and the energy per bond: <math>J R \frac{dR}{dt}</math>. Assuming that the cell cortex has a width w everywhere, the strain is of the order <math>\frac{dR/dt}{w}</math>. This strain acts over a volume approximately equal to <math>R^2 w</math>. The product of the strain, volume, and viscosity leads to an energy dissipation of <math>\eta (\frac{dR}{dt} \frac{1}{w})</math>. By setting this equal to the change in the adhesion energy, we can get the following power law:<br />
<math>R = C \big(\frac{J w}{\eta}\big)^{1/2} t^{1/2}</math>.<br />
<br />
At longer times, when cell has flattened out (i.e. the radius of contact is larger than the initial radius), the viscous energy dissipation occurs throughout the whole volume of the cell. The power law is modified to <math>J R \frac{dR}{dt} = \eta_c \big(\frac{dR}{dt} \frac{1}{w}\big)^2 R^2 w_c</math>. This can be re-arranged to the scaling law:<br />
<math>R ~ \big(\frac{J R_c^3}{\eta_c}\big)^{1/4} t^{1/4}</math>.<br />
<br />
<br />
One prediction of this model is that the properties of the cellular membrane are far more important than the interior of the cell in the cell spreading. One way to test this is by creating two mutants: one in which the microtubules molecules within the cell are unable to polymerize and another in which the actin shell in the cortex is altered.<br />
<br />
[[Image:MahadevanUniversalFig04.jpg | 360 px]]<br />
<br />
Sung Hoon's comment: In the Fig. 4 (a), the Cytochalasin D-treated cell showed linear<br />
behavior. What does the treatment do so that the treated cells spread more quickly?<br />
<br />
Has anyone actually created these mutant cells to test this theory? Is that what you're showing below?<br />
Maybe it's better to write your own captions that get right to your point?<br />
--[[User:Lidiya|Lidiya]] 03:06, 18 February 2009 (UTC)<br />
<br />
This work is important by providing unity to the plethora of information about the molecular mechanics for cell motility and adhesion. It allows future researchers to focus on the aspects of cell structure that are most relevant for thee processes and make refinements to this basic model.<br />
<br />
<br />
-------------------------------------------------------------------------------------------------------------------------------------------------------------<br />
<br />
Second Entry: Nick Chisholm, AP 225, Fall 2009 (In Progress...)<br />
<br />
==General Information==<br />
'''Authors''': D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan <br />
<br />
'''Publication''': Current Biology '''17''' 694 (2007)<br />
<br />
==Soft Matter Keywords==<br />
[http://soft-matter.seas.harvard.edu/index.php/Adhesion Adhesion], [http://soft-matter.seas.harvard.edu/index.php/Cell Cell], [http://soft-matter.seas.harvard.edu/index.php/Polymerization Polymerization], Viscous<br />
<br />
==Summary==<br />
The authors explore the early stages of cell spreading. In particular, they look at the situation where cells are plated onto artificial adhesive surfaces; they first flatten and deform extensively as they spread. This article presents experimental probing of the dynamics of this spreading process using quantitative visualization and biochemical manipulation with a variety of cell types, adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs. Surprisingly, the authors find that the adhesion dynamics of cells follow a universal power-law behavior (i.e. the contact radius is proportional to elapsed time to a certain power).<br />
<br />
<br />
<br />
[[Image:CellSpreading.png|thumb|300px| Figure 1, taken from [1].]]<br />
<br />
==Soft Matter Discussion==<br />
<br />
==Reference==<br />
[1] D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan, "The universal dynamics of cell spreading," Current Biology '''17''' 694 (2007).</div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=Gravitational_stability_of_suspensions_of_attractive_colloidal_particles&diff=13408Gravitational stability of suspensions of attractive colloidal particles2009-11-30T20:18:48Z<p>Chisholm: </p>
<hr />
<div>==Reference==<br />
<br />
'''Gravitational Stability of Suspension of Attractive Colloidal Particles'''<br />
<br />
Kim C, Liu Y, Kuhnle A, Hess S, Viereck S, Danner T, Mahadevan L, Weitz DA.<br />
<br />
Physical Review Letters '''99''': 028303 (2007)<br />
<br />
==Depletion Attraction==<br />
<br />
The attraction between particles in a [[colloidal suspension]] must overcome the pull of gravity if the suspension is to be stable. The alternative is gradual sedimentation and [[phase separation]] of the particles. There are many applications in which gradual onset of a [[phase separation]] severely limits the useful life of a product. <br />
<br />
One way to overcome sedimentation is through [[depletion attraction]], in which a polymer added to the suspension increases the attraction between particles. This occurs because the polymer is excluded from regions between particles when the distance between particles less than the size of the polymer. The result is regions between particles which are severely depleted of the polymer. This causes a net osmotic force which pushes the particles towards each other. The range and strength of this attractive force can be varied by changing the size of the polymer and the polymer concentration, respectively.<br />
<br />
==Experimental System==<br />
[[Image:Kim2007 fig1inset.jpg|thumb|Emulsion height H was measured by time-lapse imaging]]<br />
<br />
The goal was to measure the effect of particle volume fraction <math>\phi</math> on the [[compressional modulus]] <math>K(\phi)</math>. The colloidal suspension consisted of a surfactant-stabilized emulsion of paraffin oil in water. The emulsion samples had varying [[hydrodynamic radius|hydrodynamic radii]] R, but the volume fraction <math>\phi_0</math> and oil-water density mismatch <math>\Delta \rho</math> were constant. Depletion attraction was induced by adding either nonadsorbing polymer polyvinylpyrrolidon (PVP) or a surfactant - which was either Lutensol T08 or Lutensol A8). Time lapse images of the creaming emulsions were collected in order to observe the evolution of the clear fluid phase. The volume fraction at different times <math>\phi(t)</math> was measured by skimming sample off the top 2 mm of the emulsion, then weighing it, drying it, and weighing it again.<br />
<br />
==Stress as a Function of Steady-State Volume Fraction==<br />
<br />
An emulsion with an initial height <math>H_0</math> will cream and eventually approach a steady-state <math>H_\infin</math> that has a corresponding volume fraction <math>\phi_\infin</math> (which, as explained in the experimental section, can be experimentally measured.) Increasing <math>H_0</math> decreases both <math>H_\infin</math> and <math>\phi_\infin</math>. The buoyant stress in an emulsion is:<br />
<br />
<math><br />
\sigma = \Delta \rho g \phi_0 H_0<br />
</math><br />
<br />
By measuring <math>\phi_\infin </math> and <math>H_\infin</math> while varying <math>H_0</math>, surfactant concentration <math>c_m</math>, and micelle size <math>r</math>, the <math>\sigma \left (\phi_\infin \right)</math> can be experimentally derived.<br />
<br />
[[Image:Kim2007 fig2.jpg|thumb|center|upright=2|<math>\sigma</math> as a function of <math>\phi_\infin</math>. Inset: <math>-\frac{\sigma}{\alpha}</math> as a function of <math>\phi_c - \phi_\infin</math>]]<br />
<br />
The data points can be fit to functions in the form:<br />
<br />
<math><br />
\sigma \left (\phi_\infin \right) = -\alpha \frac{\phi_\infin-\phi_g}{\phi_c-\phi_\infin}<br />
</math><br />
<br />
where <math>\phi_c = 0.64</math> is the theoretical maximum for random close packing of uniform spheres; <math>\phi_g=0.03</math> is the minimum concentration required for gelation (which is independent of <math>c_m</math> and <math>r</math>); and <math>\alpha</math> is a stiffness parameter that depends on <math>c_m</math> and <math>r</math>.<br />
<br />
Which can be related to the compressional modulus K by:<br />
<br />
<math><br />
K(\phi) = -\phi \frac{\partial \sigma}{\partial \phi}<br />
= \alpha \phi_\infin \frac{\phi_\infin-\phi_g}{\left (\phi_c-\phi_\infin \right)^2}<br />
</math><br />
<br />
==Scaling Parameter as a Function of the Hydrodynamic Radius and Micelle Size==<br />
Unlike hard sphere suspensions in which K and osmotic pressure scale with thermal energy, the experiment above shows that <math>\sigma(\phi)</math> and <math>K(\phi)</math> scale with the stiffness parameter <math>\alpha</math>. <math>\alpha</math> should reflect the inter-particle attraction, and dimensional analysis shows that it scales with <math>\frac{U}{r R^2}</math><br />
<br />
==References==<br />
* Pusey PN, Pirie AD, Poon WCK. Dynamics of colloid-polymer mixtures. ''Physica A'' '''201''': 322-331 (1993).<br />
<br />
<br />
<br />
<br />
<br />
-------------------------------------------------------------------------------------------------------------------------------------------------------------<br />
Second Entry: Nick Chisholm, AP 225, Fall 2009<br />
<br />
==General Information==<br />
'''Authors''': C. Kim, Y. Liu, A. Kuhnle, S. Hess, S. Viereck, T. Danner, L. Mahadevan, and D. Weitz<br />
<br />
'''Publication''': PRL '''99''' 028303 (2007)<br />
<br />
==Soft Matter Keywords==<br />
[http://soft-matter.seas.harvard.edu/index.php/Compression_Modulus Compressional Modulus], Colloidal Suspension, [http://soft-matter.seas.harvard.edu/index.php/Emulsion Emulsion], Phase Separation<br />
<br />
==Summary==<br />
The authors present a means by which to stabilize suspensions of attractive colloidal particles against gravitationally-induced sedimentation or creaming. Their idea is to cause a depletion interaction between the colloidal particles by introducing nonadsorbing particles or polymers to the suspension. This causes a weak attraction between the particles, which then results in a solid-like network or gel of the particles that helps support their buoyant weight. Under shear, this network or gel can be made to easily yield, allowing the suspension to flow.<br />
<br />
Other means by which to stabilize these suspensions against gravitationally-induced sedimentation or creaming include density matching the particles to the suspending fluid, restricting the size of the particles so that their Brownian motion keeps them suspended, or by increasing the viscosity of the suspending fluid in order to slow down the phase separation. These methods are often not feasible, thus creating the motivation for this paper.<br />
<br />
How does this depletion interaction work? Well, the polymers are only able to occupy regions where their size is smaller than the spacing between the colloid particles. This results in regions of lower concentration of polymer, and the osmotic pressure of the polymer pushes the colloid particles together.<br />
<br />
==Soft Matter Discussion==<br />
In order to quantify the effectiveness of this method, one must measure the [http://soft-matter.seas.harvard.edu/index.php/Compressional_Modulus compressional modulus]. This compressional modulus may be represented as:<br />
<br />
<math>K(\phi) = -\phi \partial \sigma / \partial \phi</math>, where <math>\phi</math> is the volume fraction and <math>\sigma</math> is the stress (force per unit area).<br />
<br />
<br />
Note that one can change the initial height of the emulsion, <math>H_{0}</math> (the emulsion is in a tube; it was found the meniscus does not have any effect on the results). This effectively allows manipulation of the buoyant stress of the emulsion, since the sample is a gel and thus the emulsion at the top feels the full buoyant stress of the suspensions below. As the sample creams, the initial volume fraction at the top, <math>\phi_{0}</math>, increases to the final volume fraction, <math>\phi_{\infin}</math>. Note that <math>H_{0}</math> sets the magnitude of the stress, <math>\sigma = \Delta \rho g \phi_{0} H_{0}</math> (where <math>\Delta \rho</math> is the difference in density between the colloids and the suspending fluid.)<br />
<br />
<br />
<math>\phi_{\infin}</math> and <math>\sigma_{\infin}</math> are measured experimentally; the specific behavior of <math>\sigma_{\infin}</math> depends on both <math>r</math> (micelle size) and <math>c_{m}</math> (nonadsorbing polymer concentration above the critical micelle concentration), but in every case the data diverges as <math>\phi_{\infin}</math> approaches <math>\phi_{c} \approx 0.64</math>, the maximum value for random close packing of uniform spheres. Thus, the data is fit with functional form:<br />
<br />
<math>\sigma(\phi_{\infin}) = -\alpha(r, c_{m}) \frac{\phi_{\infin} - \phi_{g}}{\phi_{c} - \phi_{\infin}}</math>,<br />
<br />
where <math>\alpha(r, c_{m})</math> is called the stiffness parameter. Note that <math>\phi_{g} = 0.03</math> is the minimum concentration required for gelation. This equation matches very well with experimental data. See Figure 1.<br />
<br />
[[Image:Stress.png|thumb|300px| Figure 1, taken from [1].]]<br />
<br />
From the functional form for <math>\sigma(\phi_{\infin})</math>, <math>K(\phi_{\infin})</math> can be determined easily to be:<br />
<br />
<math>K(\phi_{\infin}) = \alpha(r, c_{m}) \phi_{\infin} \frac{\phi_{c} - \phi_{g}}{(\phi_{c} - \phi_{\infin})^{2}}</math>.<br />
<br />
<br />
The stiffness parameter should reflect the attraction between neighboring particles; it has units of stress, so one expect it to be the attractive force divided by the area of the interparticle bond. This would mean:<br />
<br />
<math>\alpha(r, c_{m}) \approx U/rR^{2}</math>, where <math>R</math> is the hydrodynamic radii.<br />
<br />
This matches well with experiment.<br />
<br />
<br />
Since we can control <math>\phi_{\infin}</math>, we can control <math>K(\phi_{\infin})</math>, and thus control the stability of the suspension against gravitational creaming; this is what the authors claim.<br />
<br />
<br />
Personally, I would have liked to see more of an effort on the part of the authors to explain how one can control, exactly, <math>\phi_{\infin}</math> with the addition of polymer. I am not entirely convinced that this is easily possible (at least, I'm not convinced it's as simple as the authors seem to insinuate).<br />
<br />
<br />
One application of this work is clear: increase in shelf life of commercial products. It would be interesting to consider the commercial products for which this work would be most desirable, and see if a nonadsorbing polymer can be easily found. I wonder if these nonadsorbing polymers would actually have adverse effects on how the emulsion performs when used for the purpose they were original created.<br />
<br />
==References==<br />
[1] C. Kim, Y. Liu, A. Kuhnle, S. Hess, S. Viereck, T. Danner, L. Mahadevan, and D. Weitz, "Gravitational stability of suspensions of attractive colloidal particles," PRL '''99''' 028303 (2007).<br />
<br />
[2] D. Marenduzzo, K. Finan, and P. R. Cook, "The depletion attraction: an underappreciated force driving cellular organization," The Journal of Cell Biology, Volume 175, Number 5, 681-686 (2006).</div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=Gravitational_stability_of_suspensions_of_attractive_colloidal_particles&diff=13407Gravitational stability of suspensions of attractive colloidal particles2009-11-30T20:16:45Z<p>Chisholm: /* Soft Matter Discussion */</p>
<hr />
<div>==Reference==<br />
<br />
'''Gravitational Stability of Suspension of Attractive Colloidal Particles'''<br />
<br />
Kim C, Liu Y, Kuhnle A, Hess S, Viereck S, Danner T, Mahadevan L, Weitz DA.<br />
<br />
Physical Review Letters '''99''': 028303 (2007)<br />
<br />
==Depletion Attraction==<br />
<br />
The attraction between particles in a [[colloidal suspension]] must overcome the pull of gravity if the suspension is to be stable. The alternative is gradual sedimentation and [[phase separation]] of the particles. There are many applications in which gradual onset of a [[phase separation]] severely limits the useful life of a product. <br />
<br />
One way to overcome sedimentation is through [[depletion attraction]], in which a polymer added to the suspension increases the attraction between particles. This occurs because the polymer is excluded from regions between particles when the distance between particles less than the size of the polymer. The result is regions between particles which are severely depleted of the polymer. This causes a net osmotic force which pushes the particles towards each other. The range and strength of this attractive force can be varied by changing the size of the polymer and the polymer concentration, respectively.<br />
<br />
==Experimental System==<br />
[[Image:Kim2007 fig1inset.jpg|thumb|Emulsion height H was measured by time-lapse imaging]]<br />
<br />
The goal was to measure the effect of particle volume fraction <math>\phi</math> on the [[compressional modulus]] <math>K(\phi)</math>. The colloidal suspension consisted of a surfactant-stabilized emulsion of paraffin oil in water. The emulsion samples had varying [[hydrodynamic radius|hydrodynamic radii]] R, but the volume fraction <math>\phi_0</math> and oil-water density mismatch <math>\Delta \rho</math> were constant. Depletion attraction was induced by adding either nonadsorbing polymer polyvinylpyrrolidon (PVP) or a surfactant - which was either Lutensol T08 or Lutensol A8). Time lapse images of the creaming emulsions were collected in order to observe the evolution of the clear fluid phase. The volume fraction at different times <math>\phi(t)</math> was measured by skimming sample off the top 2 mm of the emulsion, then weighing it, drying it, and weighing it again.<br />
<br />
==Stress as a Function of Steady-State Volume Fraction==<br />
<br />
An emulsion with an initial height <math>H_0</math> will cream and eventually approach a steady-state <math>H_\infin</math> that has a corresponding volume fraction <math>\phi_\infin</math> (which, as explained in the experimental section, can be experimentally measured.) Increasing <math>H_0</math> decreases both <math>H_\infin</math> and <math>\phi_\infin</math>. The buoyant stress in an emulsion is:<br />
<br />
<math><br />
\sigma = \Delta \rho g \phi_0 H_0<br />
</math><br />
<br />
By measuring <math>\phi_\infin </math> and <math>H_\infin</math> while varying <math>H_0</math>, surfactant concentration <math>c_m</math>, and micelle size <math>r</math>, the <math>\sigma \left (\phi_\infin \right)</math> can be experimentally derived.<br />
<br />
[[Image:Kim2007 fig2.jpg|thumb|center|upright=2|<math>\sigma</math> as a function of <math>\phi_\infin</math>. Inset: <math>-\frac{\sigma}{\alpha}</math> as a function of <math>\phi_c - \phi_\infin</math>]]<br />
<br />
The data points can be fit to functions in the form:<br />
<br />
<math><br />
\sigma \left (\phi_\infin \right) = -\alpha \frac{\phi_\infin-\phi_g}{\phi_c-\phi_\infin}<br />
</math><br />
<br />
where <math>\phi_c = 0.64</math> is the theoretical maximum for random close packing of uniform spheres; <math>\phi_g=0.03</math> is the minimum concentration required for gelation (which is independent of <math>c_m</math> and <math>r</math>); and <math>\alpha</math> is a stiffness parameter that depends on <math>c_m</math> and <math>r</math>.<br />
<br />
Which can be related to the compressional modulus K by:<br />
<br />
<math><br />
K(\phi) = -\phi \frac{\partial \sigma}{\partial \phi}<br />
= \alpha \phi_\infin \frac{\phi_\infin-\phi_g}{\left (\phi_c-\phi_\infin \right)^2}<br />
</math><br />
<br />
==Scaling Parameter as a Function of the Hydrodynamic Radius and Micelle Size==<br />
Unlike hard sphere suspensions in which K and osmotic pressure scale with thermal energy, the experiment above shows that <math>\sigma(\phi)</math> and <math>K(\phi)</math> scale with the stiffness parameter <math>\alpha</math>. <math>\alpha</math> should reflect the inter-particle attraction, and dimensional analysis shows that it scales with <math>\frac{U}{r R^2}</math><br />
<br />
==References==<br />
* Pusey PN, Pirie AD, Poon WCK. Dynamics of colloid-polymer mixtures. ''Physica A'' '''201''': 322-331 (1993).<br />
<br />
<br />
<br />
<br />
<br />
-------------------------------------------------------------------------------------------------------------------------------------------------------------<br />
Second Entry: Nick Chisholm, AP 225, Fall 2009 (In Progress...)<br />
<br />
==General Information==<br />
'''Authors''': C. Kim, Y. Liu, A. Kuhnle, S. Hess, S. Viereck, T. Danner, L. Mahadevan, and D. Weitz<br />
<br />
'''Publication''': PRL '''99''' 028303 (2007)<br />
<br />
==Soft Matter Keywords==<br />
[http://soft-matter.seas.harvard.edu/index.php/Compression_Modulus Compressional Modulus], Colloidal Suspension, [http://soft-matter.seas.harvard.edu/index.php/Emulsion Emulsion], Phase Separation<br />
<br />
==Summary==<br />
The authors present a means by which to stabilize suspensions of attractive colloidal particles against gravitationally-induced sedimentation or creaming. Their idea is to cause a depletion interaction between the colloidal particles by introducing nonadsorbing particles or polymers to the suspension. This causes a weak attraction between the particles, which then results in a solid-like network or gel of the particles that helps support their buoyant weight. Under shear, this network or gel can be made to easily yield, allowing the suspension to flow.<br />
<br />
Other means by which to stabilize these suspensions against gravitationally-induced sedimentation or creaming include density matching the particles to the suspending fluid, restricting the size of the particles so that their Brownian motion keeps them suspended, or by increasing the viscosity of the suspending fluid in order to slow down the phase separation. These methods are often not feasible, thus creating the motivation for this paper.<br />
<br />
How does this depletion interaction work? Well, the polymers are only able to occupy regions where their size is smaller than the spacing between the colloid particles. This results in regions of lower concentration of polymer, and the osmotic pressure of the polymer pushes the colloid particles together.<br />
<br />
==Soft Matter Discussion==<br />
In order to quantify the effectiveness of this method, one must measure the [http://soft-matter.seas.harvard.edu/index.php/Compressional_Modulus compressional modulus]. This compressional modulus may be represented as:<br />
<br />
<math>K(\phi) = -\phi \partial \sigma / \partial \phi</math>, where <math>\phi</math> is the volume fraction and <math>\sigma</math> is the stress (force per unit area).<br />
<br />
<br />
Note that one can change the initial height of the emulsion, <math>H_{0}</math> (the emulsion is in a tube; it was found the meniscus does not have any effect on the results). This effectively allows manipulation of the buoyant stress of the emulsion, since the sample is a gel and thus the emulsion at the top feels the full buoyant stress of the suspensions below. As the sample creams, the initial volume fraction at the top, <math>\phi_{0}</math>, increases to the final volume fraction, <math>\phi_{\infin}</math>. Note that <math>H_{0}</math> sets the magnitude of the stress, <math>\sigma = \Delta \rho g \phi_{0} H_{0}</math> (where <math>\Delta \rho</math> is the difference in density between the colloids and the suspending fluid.)<br />
<br />
<br />
<math>\phi_{\infin}</math> and <math>\sigma_{\infin}</math> are measured experimentally; the specific behavior of <math>\sigma_{\infin}</math> depends on both <math>r</math> (micelle size) and <math>c_{m}</math> (nonadsorbing polymer concentration above the critical micelle concentration), but in every case the data diverges as <math>\phi_{\infin}</math> approaches <math>\phi_{c} \approx 0.64</math>, the maximum value for random close packing of uniform spheres. Thus, the data is fit with functional form:<br />
<br />
<math>\sigma(\phi_{\infin}) = -\alpha(r, c_{m}) \frac{\phi_{\infin} - \phi_{g}}{\phi_{c} - \phi_{\infin}}</math>,<br />
<br />
where <math>\alpha(r, c_{m})</math> is called the stiffness parameter. Note that <math>\phi_{g} = 0.03</math> is the minimum concentration required for gelation. This equation matches very well with experimental data. See Figure 1.<br />
<br />
[[Image:Stress.png|thumb|300px| Figure 1, taken from [1].]]<br />
<br />
From the functional form for <math>\sigma(\phi_{\infin})</math>, <math>K(\phi_{\infin})</math> can be determined easily to be:<br />
<br />
<math>K(\phi_{\infin}) = \alpha(r, c_{m}) \phi_{\infin} \frac{\phi_{c} - \phi_{g}}{(\phi_{c} - \phi_{\infin})^{2}}</math>.<br />
<br />
<br />
The stiffness parameter should reflect the attraction between neighboring particles; it has units of stress, so one expect it to be the attractive force divided by the area of the interparticle bond. This would mean:<br />
<br />
<math>\alpha(r, c_{m}) \approx U/rR^{2}</math>, where <math>R</math> is the hydrodynamic radii.<br />
<br />
This matches well with experiment.<br />
<br />
<br />
Since we can control <math>\phi_{\infin}</math>, we can control <math>K(\phi_{\infin})</math>, and thus control the stability of the suspension against gravitational creaming; this is what the authors claim.<br />
<br />
<br />
Personally, I would have liked to see more of an effort on the part of the authors to explain how one can control, exactly, <math>\phi_{\infin}</math> with the addition of polymer. I am not entirely convinced that this is easily possible (at least, I'm not convinced it's as simple as the authors seem to insinuate).<br />
<br />
<br />
One application of this work is clear: increase in shelf life of commercial products. It would be interesting to consider the commercial products for which this work would be most desirable, and see if a nonadsorbing polymer can be easily found. I wonder if these nonadsorbing polymers would actually have adverse effects on how the emulsion performs when used for the purpose they were original created.<br />
<br />
==References==<br />
[1] C. Kim, Y. Liu, A. Kuhnle, S. Hess, S. Viereck, T. Danner, L. Mahadevan, and D. Weitz, "Gravitational stability of suspensions of attractive colloidal particles," PRL '''99''' 028303 (2007).<br />
<br />
[2] D. Marenduzzo, K. Finan, and P. R. Cook, "The depletion attraction: an underappreciated force driving cellular organization," The Journal of Cell Biology, Volume 175, Number 5, 681-686 (2006).</div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=Gravitational_stability_of_suspensions_of_attractive_colloidal_particles&diff=13406Gravitational stability of suspensions of attractive colloidal particles2009-11-30T20:16:06Z<p>Chisholm: /* Soft Matter Discussion */</p>
<hr />
<div>==Reference==<br />
<br />
'''Gravitational Stability of Suspension of Attractive Colloidal Particles'''<br />
<br />
Kim C, Liu Y, Kuhnle A, Hess S, Viereck S, Danner T, Mahadevan L, Weitz DA.<br />
<br />
Physical Review Letters '''99''': 028303 (2007)<br />
<br />
==Depletion Attraction==<br />
<br />
The attraction between particles in a [[colloidal suspension]] must overcome the pull of gravity if the suspension is to be stable. The alternative is gradual sedimentation and [[phase separation]] of the particles. There are many applications in which gradual onset of a [[phase separation]] severely limits the useful life of a product. <br />
<br />
One way to overcome sedimentation is through [[depletion attraction]], in which a polymer added to the suspension increases the attraction between particles. This occurs because the polymer is excluded from regions between particles when the distance between particles less than the size of the polymer. The result is regions between particles which are severely depleted of the polymer. This causes a net osmotic force which pushes the particles towards each other. The range and strength of this attractive force can be varied by changing the size of the polymer and the polymer concentration, respectively.<br />
<br />
==Experimental System==<br />
[[Image:Kim2007 fig1inset.jpg|thumb|Emulsion height H was measured by time-lapse imaging]]<br />
<br />
The goal was to measure the effect of particle volume fraction <math>\phi</math> on the [[compressional modulus]] <math>K(\phi)</math>. The colloidal suspension consisted of a surfactant-stabilized emulsion of paraffin oil in water. The emulsion samples had varying [[hydrodynamic radius|hydrodynamic radii]] R, but the volume fraction <math>\phi_0</math> and oil-water density mismatch <math>\Delta \rho</math> were constant. Depletion attraction was induced by adding either nonadsorbing polymer polyvinylpyrrolidon (PVP) or a surfactant - which was either Lutensol T08 or Lutensol A8). Time lapse images of the creaming emulsions were collected in order to observe the evolution of the clear fluid phase. The volume fraction at different times <math>\phi(t)</math> was measured by skimming sample off the top 2 mm of the emulsion, then weighing it, drying it, and weighing it again.<br />
<br />
==Stress as a Function of Steady-State Volume Fraction==<br />
<br />
An emulsion with an initial height <math>H_0</math> will cream and eventually approach a steady-state <math>H_\infin</math> that has a corresponding volume fraction <math>\phi_\infin</math> (which, as explained in the experimental section, can be experimentally measured.) Increasing <math>H_0</math> decreases both <math>H_\infin</math> and <math>\phi_\infin</math>. The buoyant stress in an emulsion is:<br />
<br />
<math><br />
\sigma = \Delta \rho g \phi_0 H_0<br />
</math><br />
<br />
By measuring <math>\phi_\infin </math> and <math>H_\infin</math> while varying <math>H_0</math>, surfactant concentration <math>c_m</math>, and micelle size <math>r</math>, the <math>\sigma \left (\phi_\infin \right)</math> can be experimentally derived.<br />
<br />
[[Image:Kim2007 fig2.jpg|thumb|center|upright=2|<math>\sigma</math> as a function of <math>\phi_\infin</math>. Inset: <math>-\frac{\sigma}{\alpha}</math> as a function of <math>\phi_c - \phi_\infin</math>]]<br />
<br />
The data points can be fit to functions in the form:<br />
<br />
<math><br />
\sigma \left (\phi_\infin \right) = -\alpha \frac{\phi_\infin-\phi_g}{\phi_c-\phi_\infin}<br />
</math><br />
<br />
where <math>\phi_c = 0.64</math> is the theoretical maximum for random close packing of uniform spheres; <math>\phi_g=0.03</math> is the minimum concentration required for gelation (which is independent of <math>c_m</math> and <math>r</math>); and <math>\alpha</math> is a stiffness parameter that depends on <math>c_m</math> and <math>r</math>.<br />
<br />
Which can be related to the compressional modulus K by:<br />
<br />
<math><br />
K(\phi) = -\phi \frac{\partial \sigma}{\partial \phi}<br />
= \alpha \phi_\infin \frac{\phi_\infin-\phi_g}{\left (\phi_c-\phi_\infin \right)^2}<br />
</math><br />
<br />
==Scaling Parameter as a Function of the Hydrodynamic Radius and Micelle Size==<br />
Unlike hard sphere suspensions in which K and osmotic pressure scale with thermal energy, the experiment above shows that <math>\sigma(\phi)</math> and <math>K(\phi)</math> scale with the stiffness parameter <math>\alpha</math>. <math>\alpha</math> should reflect the inter-particle attraction, and dimensional analysis shows that it scales with <math>\frac{U}{r R^2}</math><br />
<br />
==References==<br />
* Pusey PN, Pirie AD, Poon WCK. Dynamics of colloid-polymer mixtures. ''Physica A'' '''201''': 322-331 (1993).<br />
<br />
<br />
<br />
<br />
<br />
-------------------------------------------------------------------------------------------------------------------------------------------------------------<br />
Second Entry: Nick Chisholm, AP 225, Fall 2009 (In Progress...)<br />
<br />
==General Information==<br />
'''Authors''': C. Kim, Y. Liu, A. Kuhnle, S. Hess, S. Viereck, T. Danner, L. Mahadevan, and D. Weitz<br />
<br />
'''Publication''': PRL '''99''' 028303 (2007)<br />
<br />
==Soft Matter Keywords==<br />
[http://soft-matter.seas.harvard.edu/index.php/Compression_Modulus Compressional Modulus], Colloidal Suspension, [http://soft-matter.seas.harvard.edu/index.php/Emulsion Emulsion], Phase Separation<br />
<br />
==Summary==<br />
The authors present a means by which to stabilize suspensions of attractive colloidal particles against gravitationally-induced sedimentation or creaming. Their idea is to cause a depletion interaction between the colloidal particles by introducing nonadsorbing particles or polymers to the suspension. This causes a weak attraction between the particles, which then results in a solid-like network or gel of the particles that helps support their buoyant weight. Under shear, this network or gel can be made to easily yield, allowing the suspension to flow.<br />
<br />
Other means by which to stabilize these suspensions against gravitationally-induced sedimentation or creaming include density matching the particles to the suspending fluid, restricting the size of the particles so that their Brownian motion keeps them suspended, or by increasing the viscosity of the suspending fluid in order to slow down the phase separation. These methods are often not feasible, thus creating the motivation for this paper.<br />
<br />
How does this depletion interaction work? Well, the polymers are only able to occupy regions where their size is smaller than the spacing between the colloid particles. This results in regions of lower concentration of polymer, and the osmotic pressure of the polymer pushes the colloid particles together.<br />
<br />
==Soft Matter Discussion==<br />
In order to quantify the effectiveness of this method, one must measure the [http://soft-matter.seas.harvard.edu/index.php/Compressional_Modulus compressional modulus]. This compressional modulus may be represented as:<br />
<br />
<math>K(\phi) = -\phi \partial \sigma / \partial \phi</math>, where <math>\phi</math> is the volume fraction and <math>\sigma</math> is the stress (force per unit area).<br />
<br />
<br />
Note that one can change the initial height of the emulsion, <math>H_{0}</math> (the emulsion is in a tube; it was found the meniscus does not have any effect on the results). This effectively allows manipulation of the buoyant stress of the emulsion, since the sample is a gel and thus the emulsion at the top feels the full buoyant stress of the suspensions below. As the sample creams, the initial volume fraction at the top, <math>\phi_{0}</math>, increases to the final volume fraction, <math>\phi_{\infin}</math>. Note that <math>H_{0}</math> sets the magnitude of the stress, <math>\sigma = \Delta \rho g \phi_{0} H_{0}</math> (where <math>\Delta \rho</math> is the difference in density between the colloids and the suspending fluid.)<br />
<br />
<br />
<math>\phi_{\infin}</math> and <math>\sigma_{\infin}</math> are measured experimentally; the specific behavior of <math>\sigma_{\infin}</math> depends on both <math>r</math> (micelle size) and <math>c_{m}</math> (nonadsorbing polymer concentration above the critical micelle concentration), but in every case the data diverges as <math>\phi_{\infin}</math> approaches <math>\phi_{c} \approx 0.64</math>, the maximum value for random close packing of uniform spheres. Thus, the data is fit with functional form:<br />
<br />
<math>\sigma(\phi_{\infin}) = -\alpha(r, c_{m}) \frac{\phi_{\infin} - \phi_{g}}{\phi_{c} - \phi_{\infin}}</math>,<br />
<br />
where <math>\alpha</math> is called the stiffness parameter. Note that <math>\phi_{g} = 0.03</math> is the minimum concentration required for gelation. This equation matches very well with experimental data. See Figure 1.<br />
<br />
[[Image:Stress.png|thumb|300px| Figure 1, taken from [1].]]<br />
<br />
From the functional form for <math>\sigma(\phi(\infin))</math>, <math>K(\phi_{\infin})</math> can be determined easily to be:<br />
<br />
<math>K(\phi_{\infin}) = \alpha(r, c_{m}) \phi_{\infin} \frac{\phi_{c} - \phi_{g}}{(\phi_{c} - \phi_{\infin})^{2}}</math>.<br />
<br />
<br />
The stiffness parameter should reflect the attraction between neighboring particles; it has units of stress, so one expect it to be the attractive force divided by the area of the interparticle bond. This would mean:<br />
<br />
<math>\alpha(r, c_{m}) \approx U/rR^{2}</math>, where <math>R</math> is the hydrodynamic radii.<br />
<br />
This matches well with experiment.<br />
<br />
<br />
Since we can control <math>\phi_{\infin}</math>, we can control <math>K(\phi_{\infin})</math>, and thus control the stability of the suspension against gravitational creaming; this is what the authors claim.<br />
<br />
<br />
Personally, I would have liked to see more of an effort on the part of the authors to explain how one can control, exactly, <math>\phi_{\infin}</math> with the addition of polymer. I am not entirely convinced that this is easily possible (at least, I'm not convinced it's as simple as the authors seem to insinuate).<br />
<br />
<br />
One application of this work is clear: increase in shelf life of commercial products. It would be interesting to consider the commercial products for which this work would be most desirable, and see if a nonadsorbing polymer can be easily found. I wonder if these nonadsorbing polymers would actually have adverse effects on how the emulsion performs when used for the purpose they were original created.<br />
<br />
==References==<br />
[1] C. Kim, Y. Liu, A. Kuhnle, S. Hess, S. Viereck, T. Danner, L. Mahadevan, and D. Weitz, "Gravitational stability of suspensions of attractive colloidal particles," PRL '''99''' 028303 (2007).<br />
<br />
[2] D. Marenduzzo, K. Finan, and P. R. Cook, "The depletion attraction: an underappreciated force driving cellular organization," The Journal of Cell Biology, Volume 175, Number 5, 681-686 (2006).</div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=Gravitational_stability_of_suspensions_of_attractive_colloidal_particles&diff=13405Gravitational stability of suspensions of attractive colloidal particles2009-11-30T20:15:35Z<p>Chisholm: /* Soft Matter Discussion */</p>
<hr />
<div>==Reference==<br />
<br />
'''Gravitational Stability of Suspension of Attractive Colloidal Particles'''<br />
<br />
Kim C, Liu Y, Kuhnle A, Hess S, Viereck S, Danner T, Mahadevan L, Weitz DA.<br />
<br />
Physical Review Letters '''99''': 028303 (2007)<br />
<br />
==Depletion Attraction==<br />
<br />
The attraction between particles in a [[colloidal suspension]] must overcome the pull of gravity if the suspension is to be stable. The alternative is gradual sedimentation and [[phase separation]] of the particles. There are many applications in which gradual onset of a [[phase separation]] severely limits the useful life of a product. <br />
<br />
One way to overcome sedimentation is through [[depletion attraction]], in which a polymer added to the suspension increases the attraction between particles. This occurs because the polymer is excluded from regions between particles when the distance between particles less than the size of the polymer. The result is regions between particles which are severely depleted of the polymer. This causes a net osmotic force which pushes the particles towards each other. The range and strength of this attractive force can be varied by changing the size of the polymer and the polymer concentration, respectively.<br />
<br />
==Experimental System==<br />
[[Image:Kim2007 fig1inset.jpg|thumb|Emulsion height H was measured by time-lapse imaging]]<br />
<br />
The goal was to measure the effect of particle volume fraction <math>\phi</math> on the [[compressional modulus]] <math>K(\phi)</math>. The colloidal suspension consisted of a surfactant-stabilized emulsion of paraffin oil in water. The emulsion samples had varying [[hydrodynamic radius|hydrodynamic radii]] R, but the volume fraction <math>\phi_0</math> and oil-water density mismatch <math>\Delta \rho</math> were constant. Depletion attraction was induced by adding either nonadsorbing polymer polyvinylpyrrolidon (PVP) or a surfactant - which was either Lutensol T08 or Lutensol A8). Time lapse images of the creaming emulsions were collected in order to observe the evolution of the clear fluid phase. The volume fraction at different times <math>\phi(t)</math> was measured by skimming sample off the top 2 mm of the emulsion, then weighing it, drying it, and weighing it again.<br />
<br />
==Stress as a Function of Steady-State Volume Fraction==<br />
<br />
An emulsion with an initial height <math>H_0</math> will cream and eventually approach a steady-state <math>H_\infin</math> that has a corresponding volume fraction <math>\phi_\infin</math> (which, as explained in the experimental section, can be experimentally measured.) Increasing <math>H_0</math> decreases both <math>H_\infin</math> and <math>\phi_\infin</math>. The buoyant stress in an emulsion is:<br />
<br />
<math><br />
\sigma = \Delta \rho g \phi_0 H_0<br />
</math><br />
<br />
By measuring <math>\phi_\infin </math> and <math>H_\infin</math> while varying <math>H_0</math>, surfactant concentration <math>c_m</math>, and micelle size <math>r</math>, the <math>\sigma \left (\phi_\infin \right)</math> can be experimentally derived.<br />
<br />
[[Image:Kim2007 fig2.jpg|thumb|center|upright=2|<math>\sigma</math> as a function of <math>\phi_\infin</math>. Inset: <math>-\frac{\sigma}{\alpha}</math> as a function of <math>\phi_c - \phi_\infin</math>]]<br />
<br />
The data points can be fit to functions in the form:<br />
<br />
<math><br />
\sigma \left (\phi_\infin \right) = -\alpha \frac{\phi_\infin-\phi_g}{\phi_c-\phi_\infin}<br />
</math><br />
<br />
where <math>\phi_c = 0.64</math> is the theoretical maximum for random close packing of uniform spheres; <math>\phi_g=0.03</math> is the minimum concentration required for gelation (which is independent of <math>c_m</math> and <math>r</math>); and <math>\alpha</math> is a stiffness parameter that depends on <math>c_m</math> and <math>r</math>.<br />
<br />
Which can be related to the compressional modulus K by:<br />
<br />
<math><br />
K(\phi) = -\phi \frac{\partial \sigma}{\partial \phi}<br />
= \alpha \phi_\infin \frac{\phi_\infin-\phi_g}{\left (\phi_c-\phi_\infin \right)^2}<br />
</math><br />
<br />
==Scaling Parameter as a Function of the Hydrodynamic Radius and Micelle Size==<br />
Unlike hard sphere suspensions in which K and osmotic pressure scale with thermal energy, the experiment above shows that <math>\sigma(\phi)</math> and <math>K(\phi)</math> scale with the stiffness parameter <math>\alpha</math>. <math>\alpha</math> should reflect the inter-particle attraction, and dimensional analysis shows that it scales with <math>\frac{U}{r R^2}</math><br />
<br />
==References==<br />
* Pusey PN, Pirie AD, Poon WCK. Dynamics of colloid-polymer mixtures. ''Physica A'' '''201''': 322-331 (1993).<br />
<br />
<br />
<br />
<br />
<br />
-------------------------------------------------------------------------------------------------------------------------------------------------------------<br />
Second Entry: Nick Chisholm, AP 225, Fall 2009 (In Progress...)<br />
<br />
==General Information==<br />
'''Authors''': C. Kim, Y. Liu, A. Kuhnle, S. Hess, S. Viereck, T. Danner, L. Mahadevan, and D. Weitz<br />
<br />
'''Publication''': PRL '''99''' 028303 (2007)<br />
<br />
==Soft Matter Keywords==<br />
[http://soft-matter.seas.harvard.edu/index.php/Compression_Modulus Compressional Modulus], Colloidal Suspension, [http://soft-matter.seas.harvard.edu/index.php/Emulsion Emulsion], Phase Separation<br />
<br />
==Summary==<br />
The authors present a means by which to stabilize suspensions of attractive colloidal particles against gravitationally-induced sedimentation or creaming. Their idea is to cause a depletion interaction between the colloidal particles by introducing nonadsorbing particles or polymers to the suspension. This causes a weak attraction between the particles, which then results in a solid-like network or gel of the particles that helps support their buoyant weight. Under shear, this network or gel can be made to easily yield, allowing the suspension to flow.<br />
<br />
Other means by which to stabilize these suspensions against gravitationally-induced sedimentation or creaming include density matching the particles to the suspending fluid, restricting the size of the particles so that their Brownian motion keeps them suspended, or by increasing the viscosity of the suspending fluid in order to slow down the phase separation. These methods are often not feasible, thus creating the motivation for this paper.<br />
<br />
How does this depletion interaction work? Well, the polymers are only able to occupy regions where their size is smaller than the spacing between the colloid particles. This results in regions of lower concentration of polymer, and the osmotic pressure of the polymer pushes the colloid particles together.<br />
<br />
==Soft Matter Discussion==<br />
In order to quantify the effectiveness of this method, one must measure the [http://soft-matter.seas.harvard.edu/index.php/Compressional_Modulus compressional modulus]. This compressional modulus may be represented as:<br />
<br />
<math>K(\phi) = -\phi \partial \sigma / \partial \phi</math>, where <math>\phi</math> is the volume fraction and <math>\sigma</math> is the stress (force per unit area).<br />
<br />
<br />
Note that one can change the initial height of the emulsion, <math>H_{0}</math> (the emulsion is in a tube; it was found the meniscus does not have any effect on the results). This effectively allows manipulation of the buoyant stress of the emulsion, since the sample is a gel and thus the emulsion at the top feels the full buoyant stress of the suspensions below. As the sample creams, the initial volume fraction at the top, <math>\phi_{0}</math>, increases to the final volume fraction, <math>\phi_{\infin}</math>. Note that <math>H_{0}</math> sets the magnitude of the stress, <math>\sigma = \Delta \rho g \phi_{0} H_{0}</math> (where <math>\Delta \rho</math> is the difference in density between the colloids and the suspending fluid.)<br />
<br />
<br />
<math>\phi_{\infin}</math> and <math>\sigma_{\infin}</math> are measured experimentally; the specific behavior of <math>\sigma_{\infin}</math> depends on both <math>r</math> (micelle size) and <math>c_{m}</math> (nonadsorbing polymer concentration above the critical micelle concentration), but in every case the data diverges as <math>\phi_{\infin}</math> approaches <math>\phi_{c} \approx 0.64</math>, the maximum value for random close packing of uniform spheres. Thus, the data is fit with functional form:<br />
<br />
<math>\sigma(\phi_{\infin}) = -\alpha(r, c_{m}) \frac{\phi_{\infin} - \phi_{g}}{\phi_{c} - \phi_{\infin}}</math>,<br />
<br />
where <math>\alpha</math> is called the stiffness parameter. Note that <math>\phi_{g} = 0.03</math> is the minimum concentration required for gelation. This equation matches very well with experimental data. See Figure 1.<br />
<br />
[[Image:Stress.png|thumb|300px| Figure 1, taken from [1].]]<br />
<br />
From the functional form for <math>\sigma(\phi(\infin))</math>, <math>K(\phi_{\infin})</math> can be determined easily to be:<br />
<br />
<math>K(\phi_{\infin}) = \alpha(r, c_{m}) \phi_{\infin} \frac{\phi_{c} - \phi_{g}}{(\phi_{c} - \phi_{\infin})^{2}}</math>.<br />
<br />
<br />
The stiffness parameter should reflect the attraction between neighboring particles; it has units of stress, so one expect it to be the attractive force divided by the area of the interparticle bond. This would mean:<br />
<br />
<math>\alpha(r, c_{m}) \approx U/rR^{2}</math>, where <math>R</math> is the hydrodynamic radii.<br />
<br />
This matches well with experiment.<br />
<br />
<br />
Since we can control <math>\phi_{\infin}</math>, we can control <math>K(\phi_{\infin})</math>, and thus control the stability of the suspension against gravitational gelation; this is what the authors claim.<br />
<br />
<br />
Personally, I would have liked to see more of an effort on the part of the authors to explain how one can control, exactly, <math>\phi_{\infin}</math> with the addition of polymer. I am not entirely convinced that this is easily possible (at least, I'm not convinced it's as simple as the authors seem to insinuate).<br />
<br />
<br />
One application of this work ia clear: increase in shelf life of commercial products. It would be interesting to consider the commercial products for which this work would be most desirable, and see if a nonadsorbing polymer can be easily found. I wonder if these nonadsorbing polymers would actually have adverse effects on how the emulsion performs when used for the purpose they were original created.<br />
<br />
==References==<br />
[1] C. Kim, Y. Liu, A. Kuhnle, S. Hess, S. Viereck, T. Danner, L. Mahadevan, and D. Weitz, "Gravitational stability of suspensions of attractive colloidal particles," PRL '''99''' 028303 (2007).<br />
<br />
[2] D. Marenduzzo, K. Finan, and P. R. Cook, "The depletion attraction: an underappreciated force driving cellular organization," The Journal of Cell Biology, Volume 175, Number 5, 681-686 (2006).</div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=Gravitational_stability_of_suspensions_of_attractive_colloidal_particles&diff=13404Gravitational stability of suspensions of attractive colloidal particles2009-11-30T20:14:01Z<p>Chisholm: /* Soft Matter Discussion */</p>
<hr />
<div>==Reference==<br />
<br />
'''Gravitational Stability of Suspension of Attractive Colloidal Particles'''<br />
<br />
Kim C, Liu Y, Kuhnle A, Hess S, Viereck S, Danner T, Mahadevan L, Weitz DA.<br />
<br />
Physical Review Letters '''99''': 028303 (2007)<br />
<br />
==Depletion Attraction==<br />
<br />
The attraction between particles in a [[colloidal suspension]] must overcome the pull of gravity if the suspension is to be stable. The alternative is gradual sedimentation and [[phase separation]] of the particles. There are many applications in which gradual onset of a [[phase separation]] severely limits the useful life of a product. <br />
<br />
One way to overcome sedimentation is through [[depletion attraction]], in which a polymer added to the suspension increases the attraction between particles. This occurs because the polymer is excluded from regions between particles when the distance between particles less than the size of the polymer. The result is regions between particles which are severely depleted of the polymer. This causes a net osmotic force which pushes the particles towards each other. The range and strength of this attractive force can be varied by changing the size of the polymer and the polymer concentration, respectively.<br />
<br />
==Experimental System==<br />
[[Image:Kim2007 fig1inset.jpg|thumb|Emulsion height H was measured by time-lapse imaging]]<br />
<br />
The goal was to measure the effect of particle volume fraction <math>\phi</math> on the [[compressional modulus]] <math>K(\phi)</math>. The colloidal suspension consisted of a surfactant-stabilized emulsion of paraffin oil in water. The emulsion samples had varying [[hydrodynamic radius|hydrodynamic radii]] R, but the volume fraction <math>\phi_0</math> and oil-water density mismatch <math>\Delta \rho</math> were constant. Depletion attraction was induced by adding either nonadsorbing polymer polyvinylpyrrolidon (PVP) or a surfactant - which was either Lutensol T08 or Lutensol A8). Time lapse images of the creaming emulsions were collected in order to observe the evolution of the clear fluid phase. The volume fraction at different times <math>\phi(t)</math> was measured by skimming sample off the top 2 mm of the emulsion, then weighing it, drying it, and weighing it again.<br />
<br />
==Stress as a Function of Steady-State Volume Fraction==<br />
<br />
An emulsion with an initial height <math>H_0</math> will cream and eventually approach a steady-state <math>H_\infin</math> that has a corresponding volume fraction <math>\phi_\infin</math> (which, as explained in the experimental section, can be experimentally measured.) Increasing <math>H_0</math> decreases both <math>H_\infin</math> and <math>\phi_\infin</math>. The buoyant stress in an emulsion is:<br />
<br />
<math><br />
\sigma = \Delta \rho g \phi_0 H_0<br />
</math><br />
<br />
By measuring <math>\phi_\infin </math> and <math>H_\infin</math> while varying <math>H_0</math>, surfactant concentration <math>c_m</math>, and micelle size <math>r</math>, the <math>\sigma \left (\phi_\infin \right)</math> can be experimentally derived.<br />
<br />
[[Image:Kim2007 fig2.jpg|thumb|center|upright=2|<math>\sigma</math> as a function of <math>\phi_\infin</math>. Inset: <math>-\frac{\sigma}{\alpha}</math> as a function of <math>\phi_c - \phi_\infin</math>]]<br />
<br />
The data points can be fit to functions in the form:<br />
<br />
<math><br />
\sigma \left (\phi_\infin \right) = -\alpha \frac{\phi_\infin-\phi_g}{\phi_c-\phi_\infin}<br />
</math><br />
<br />
where <math>\phi_c = 0.64</math> is the theoretical maximum for random close packing of uniform spheres; <math>\phi_g=0.03</math> is the minimum concentration required for gelation (which is independent of <math>c_m</math> and <math>r</math>); and <math>\alpha</math> is a stiffness parameter that depends on <math>c_m</math> and <math>r</math>.<br />
<br />
Which can be related to the compressional modulus K by:<br />
<br />
<math><br />
K(\phi) = -\phi \frac{\partial \sigma}{\partial \phi}<br />
= \alpha \phi_\infin \frac{\phi_\infin-\phi_g}{\left (\phi_c-\phi_\infin \right)^2}<br />
</math><br />
<br />
==Scaling Parameter as a Function of the Hydrodynamic Radius and Micelle Size==<br />
Unlike hard sphere suspensions in which K and osmotic pressure scale with thermal energy, the experiment above shows that <math>\sigma(\phi)</math> and <math>K(\phi)</math> scale with the stiffness parameter <math>\alpha</math>. <math>\alpha</math> should reflect the inter-particle attraction, and dimensional analysis shows that it scales with <math>\frac{U}{r R^2}</math><br />
<br />
==References==<br />
* Pusey PN, Pirie AD, Poon WCK. Dynamics of colloid-polymer mixtures. ''Physica A'' '''201''': 322-331 (1993).<br />
<br />
<br />
<br />
<br />
<br />
-------------------------------------------------------------------------------------------------------------------------------------------------------------<br />
Second Entry: Nick Chisholm, AP 225, Fall 2009 (In Progress...)<br />
<br />
==General Information==<br />
'''Authors''': C. Kim, Y. Liu, A. Kuhnle, S. Hess, S. Viereck, T. Danner, L. Mahadevan, and D. Weitz<br />
<br />
'''Publication''': PRL '''99''' 028303 (2007)<br />
<br />
==Soft Matter Keywords==<br />
[http://soft-matter.seas.harvard.edu/index.php/Compression_Modulus Compressional Modulus], Colloidal Suspension, [http://soft-matter.seas.harvard.edu/index.php/Emulsion Emulsion], Phase Separation<br />
<br />
==Summary==<br />
The authors present a means by which to stabilize suspensions of attractive colloidal particles against gravitationally-induced sedimentation or creaming. Their idea is to cause a depletion interaction between the colloidal particles by introducing nonadsorbing particles or polymers to the suspension. This causes a weak attraction between the particles, which then results in a solid-like network or gel of the particles that helps support their buoyant weight. Under shear, this network or gel can be made to easily yield, allowing the suspension to flow.<br />
<br />
Other means by which to stabilize these suspensions against gravitationally-induced sedimentation or creaming include density matching the particles to the suspending fluid, restricting the size of the particles so that their Brownian motion keeps them suspended, or by increasing the viscosity of the suspending fluid in order to slow down the phase separation. These methods are often not feasible, thus creating the motivation for this paper.<br />
<br />
How does this depletion interaction work? Well, the polymers are only able to occupy regions where their size is smaller than the spacing between the colloid particles. This results in regions of lower concentration of polymer, and the osmotic pressure of the polymer pushes the colloid particles together.<br />
<br />
==Soft Matter Discussion==<br />
In order to quantify the effectiveness of this method, one must measure the [http://soft-matter.seas.harvard.edu/index.php/Compressional_Modulus compressional modulus]. This compressional modulus may be represented as:<br />
<br />
<math>K(\phi) = -\phi \partial \sigma / \partial \phi</math>, where <math>\phi</math> is the volume fraction and <math>\sigma</math> is the stress (force per unit area).<br />
<br />
<br />
Note that one can change the initial height of the emulsion, <math>H_{0}</math> (the emulsion is in a tube; it was found the meniscus does not have any effect on the results). This effectively allows manipulation of the buoyant stress of the emulsion, since the sample is a gel and thus the emulsion at the top feels the full buoyant stress of the suspensions below. As the sample creams, the initial volume fraction at the top, <math>\phi_{0}</math>, increases to the final volume fraction, <math>\phi_{\infin}</math>. Note that <math>H_{0}</math> sets the magnitude of the stress, <math>\sigma = \Delta \rho g \phi_{0} H_{0}</math> (where <math>\Delta \rho</math> is the difference in density between the colloids and the suspending fluid.)<br />
<br />
<br />
<math>\phi_{\infin}</math> and <math>\sigma_{\infin}</math> are measured experimentally; the specific behavior of <math>\sigma_{\infin}</math> depends on both <math>r</math> (micelle size) and <math>c_{m}</math> (nonadsorbing polymer concentration above the critical micelle concentration), but in every case the data diverges as <math>\phi_{\infin}</math> approaches <math>\phi_{c} \approx 0.64</math>, the maximum value for random close packing of uniform spheres. Thus, the data is fit with functional form:<br />
<br />
<math>\sigma(\phi_{\infin}) = -\alpha(r, c_{m}) \frac{\phi_{\infin} - \phi_{g}}{\phi_{c} - \phi_{\infin}}</math>,<br />
<br />
where <math>\alpha</math> is called the stiffness parameter. Note that <math>\phi_{g} = 0.03</math> is the minimum concentration required for gelation. This equation matches very well with experimental data. See Figure 1.<br />
<br />
[[Image:Stress.png|thumb|300px| Figure 1, taken from [1].]]<br />
<br />
From the functional form for <math>\sigma(\phi(\infin))</math>, <math>K(\phi_{\infin})</math> can be determined easily to be:<br />
<br />
<math>K(\phi_{\infin}) = \alpha(r, c_{m}) \phi_{\infin} \frac{\phi_{c} - \phi_{g}}{(\phi_{c} - \phi_{\infin})^{2}}</math>.<br />
<br />
<br />
The stiffness parameter should reflect the attraction between neighboring particles; it has units of stress, so one expect it to be the attractive force divided by the area of the interparticle bond. This would mean:<br />
<br />
<math>\alpha(r, c_{m}) \approx U/rR^{2}</math>, where <math>R</math> is the hydrodynamic radii.<br />
<br />
This matches well with experiment.<br />
<br />
<br />
Since we can control <math>\phi_{\infin}</math>, we can control <math>K(\phi_{\infin})</math>, and thus control the stability of the suspension against gravitational sedimentation; this is what the authors claim.<br />
<br />
<br />
Personally, I would have liked to see more of an effort on the part of the authors to explain how one can control, exactly, <math>\phi_{\infin}</math> with the addition of polymer. I am not entirely convinced that this is easily possible (at least, I'm not convinced it's as simple as the authors seem to insinuate).<br />
<br />
<br />
One application of this work ia clear: increase in shelf life of commercial products. It would be interesting to consider the commercial products for which this work would be most desirable, and see if a nonadsorbing polymer can be easily found. I wonder if these nonadsorbing polymers would actually have adverse effects on how the emulsion performs when used for the purpose they were original created.<br />
<br />
==References==<br />
[1] C. Kim, Y. Liu, A. Kuhnle, S. Hess, S. Viereck, T. Danner, L. Mahadevan, and D. Weitz, "Gravitational stability of suspensions of attractive colloidal particles," PRL '''99''' 028303 (2007).<br />
<br />
[2] D. Marenduzzo, K. Finan, and P. R. Cook, "The depletion attraction: an underappreciated force driving cellular organization," The Journal of Cell Biology, Volume 175, Number 5, 681-686 (2006).</div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=Gravitational_stability_of_suspensions_of_attractive_colloidal_particles&diff=13403Gravitational stability of suspensions of attractive colloidal particles2009-11-30T20:11:56Z<p>Chisholm: /* Soft Matter Discussion */</p>
<hr />
<div>==Reference==<br />
<br />
'''Gravitational Stability of Suspension of Attractive Colloidal Particles'''<br />
<br />
Kim C, Liu Y, Kuhnle A, Hess S, Viereck S, Danner T, Mahadevan L, Weitz DA.<br />
<br />
Physical Review Letters '''99''': 028303 (2007)<br />
<br />
==Depletion Attraction==<br />
<br />
The attraction between particles in a [[colloidal suspension]] must overcome the pull of gravity if the suspension is to be stable. The alternative is gradual sedimentation and [[phase separation]] of the particles. There are many applications in which gradual onset of a [[phase separation]] severely limits the useful life of a product. <br />
<br />
One way to overcome sedimentation is through [[depletion attraction]], in which a polymer added to the suspension increases the attraction between particles. This occurs because the polymer is excluded from regions between particles when the distance between particles less than the size of the polymer. The result is regions between particles which are severely depleted of the polymer. This causes a net osmotic force which pushes the particles towards each other. The range and strength of this attractive force can be varied by changing the size of the polymer and the polymer concentration, respectively.<br />
<br />
==Experimental System==<br />
[[Image:Kim2007 fig1inset.jpg|thumb|Emulsion height H was measured by time-lapse imaging]]<br />
<br />
The goal was to measure the effect of particle volume fraction <math>\phi</math> on the [[compressional modulus]] <math>K(\phi)</math>. The colloidal suspension consisted of a surfactant-stabilized emulsion of paraffin oil in water. The emulsion samples had varying [[hydrodynamic radius|hydrodynamic radii]] R, but the volume fraction <math>\phi_0</math> and oil-water density mismatch <math>\Delta \rho</math> were constant. Depletion attraction was induced by adding either nonadsorbing polymer polyvinylpyrrolidon (PVP) or a surfactant - which was either Lutensol T08 or Lutensol A8). Time lapse images of the creaming emulsions were collected in order to observe the evolution of the clear fluid phase. The volume fraction at different times <math>\phi(t)</math> was measured by skimming sample off the top 2 mm of the emulsion, then weighing it, drying it, and weighing it again.<br />
<br />
==Stress as a Function of Steady-State Volume Fraction==<br />
<br />
An emulsion with an initial height <math>H_0</math> will cream and eventually approach a steady-state <math>H_\infin</math> that has a corresponding volume fraction <math>\phi_\infin</math> (which, as explained in the experimental section, can be experimentally measured.) Increasing <math>H_0</math> decreases both <math>H_\infin</math> and <math>\phi_\infin</math>. The buoyant stress in an emulsion is:<br />
<br />
<math><br />
\sigma = \Delta \rho g \phi_0 H_0<br />
</math><br />
<br />
By measuring <math>\phi_\infin </math> and <math>H_\infin</math> while varying <math>H_0</math>, surfactant concentration <math>c_m</math>, and micelle size <math>r</math>, the <math>\sigma \left (\phi_\infin \right)</math> can be experimentally derived.<br />
<br />
[[Image:Kim2007 fig2.jpg|thumb|center|upright=2|<math>\sigma</math> as a function of <math>\phi_\infin</math>. Inset: <math>-\frac{\sigma}{\alpha}</math> as a function of <math>\phi_c - \phi_\infin</math>]]<br />
<br />
The data points can be fit to functions in the form:<br />
<br />
<math><br />
\sigma \left (\phi_\infin \right) = -\alpha \frac{\phi_\infin-\phi_g}{\phi_c-\phi_\infin}<br />
</math><br />
<br />
where <math>\phi_c = 0.64</math> is the theoretical maximum for random close packing of uniform spheres; <math>\phi_g=0.03</math> is the minimum concentration required for gelation (which is independent of <math>c_m</math> and <math>r</math>); and <math>\alpha</math> is a stiffness parameter that depends on <math>c_m</math> and <math>r</math>.<br />
<br />
Which can be related to the compressional modulus K by:<br />
<br />
<math><br />
K(\phi) = -\phi \frac{\partial \sigma}{\partial \phi}<br />
= \alpha \phi_\infin \frac{\phi_\infin-\phi_g}{\left (\phi_c-\phi_\infin \right)^2}<br />
</math><br />
<br />
==Scaling Parameter as a Function of the Hydrodynamic Radius and Micelle Size==<br />
Unlike hard sphere suspensions in which K and osmotic pressure scale with thermal energy, the experiment above shows that <math>\sigma(\phi)</math> and <math>K(\phi)</math> scale with the stiffness parameter <math>\alpha</math>. <math>\alpha</math> should reflect the inter-particle attraction, and dimensional analysis shows that it scales with <math>\frac{U}{r R^2}</math><br />
<br />
==References==<br />
* Pusey PN, Pirie AD, Poon WCK. Dynamics of colloid-polymer mixtures. ''Physica A'' '''201''': 322-331 (1993).<br />
<br />
<br />
<br />
<br />
<br />
-------------------------------------------------------------------------------------------------------------------------------------------------------------<br />
Second Entry: Nick Chisholm, AP 225, Fall 2009 (In Progress...)<br />
<br />
==General Information==<br />
'''Authors''': C. Kim, Y. Liu, A. Kuhnle, S. Hess, S. Viereck, T. Danner, L. Mahadevan, and D. Weitz<br />
<br />
'''Publication''': PRL '''99''' 028303 (2007)<br />
<br />
==Soft Matter Keywords==<br />
[http://soft-matter.seas.harvard.edu/index.php/Compression_Modulus Compressional Modulus], Colloidal Suspension, [http://soft-matter.seas.harvard.edu/index.php/Emulsion Emulsion], Phase Separation<br />
<br />
==Summary==<br />
The authors present a means by which to stabilize suspensions of attractive colloidal particles against gravitationally-induced sedimentation or creaming. Their idea is to cause a depletion interaction between the colloidal particles by introducing nonadsorbing particles or polymers to the suspension. This causes a weak attraction between the particles, which then results in a solid-like network or gel of the particles that helps support their buoyant weight. Under shear, this network or gel can be made to easily yield, allowing the suspension to flow.<br />
<br />
Other means by which to stabilize these suspensions against gravitationally-induced sedimentation or creaming include density matching the particles to the suspending fluid, restricting the size of the particles so that their Brownian motion keeps them suspended, or by increasing the viscosity of the suspending fluid in order to slow down the phase separation. These methods are often not feasible, thus creating the motivation for this paper.<br />
<br />
How does this depletion interaction work? Well, the polymers are only able to occupy regions where their size is smaller than the spacing between the colloid particles. This results in regions of lower concentration of polymer, and the osmotic pressure of the polymer pushes the colloid particles together.<br />
<br />
==Soft Matter Discussion==<br />
In order to quantify the effectiveness of this method, one must measure the [http://soft-matter.seas.harvard.edu/index.php/Compressional_Modulus compressional modulus]. This compressional modulus may be represented as:<br />
<br />
<math>K(\phi) = -\phi \partial \sigma / \partial \phi</math>, where <math>\phi</math> is the volume fraction and <math>\sigma</math> is the stress (force per unit area).<br />
<br />
<br />
Note that one can change the initial height of the emulsion, <math>H_{0}</math> (the emulsion is in a tube; it was found the meniscus does not have any effect on the results). This effectively allows manipulation of the buoyant stress of the emulsion, since the sample is a gel and thus the emulsion at the top feels the full buoyant stress of the suspensions below. As the sample creams, the initial volume fraction at the top, <math>\phi_{0}</math>, increases to the final volume fraction, <math>\phi_{\infin}</math>. Note that <math>H_{0}</math> sets the magnitude of the stress, <math>\sigma = \Delta \rho g \phi_{0} H_{0}</math> (where <math>\Delta \rho</math> is the difference in density between the colloids and the suspending fluid.)<br />
<br />
<br />
<math>\phi_{\infin}</math> and <math>\sigma(\infin)</math> are measured experimentally; the specific behavior of <math>\sigma(\infin)</math> depends on both <math>r</math> (micelle size) and <math>c_{m}</math> (nonadsorbing polymer concentration above the critical micelle concentration), but in every case the data diverges as <math>\phi(\infin)</math> approaches <math>\phi_{c} \approx 0.64</math>, the maximum value for random close packing of uniform spheres. Thus, the data is fit with functional form:<br />
<br />
<math>\sigma(\phi(\infin)) = -\alpha(r, c_{m}) \frac{\phi_{\infin} - \phi_{g}}{\phi_{c} - \phi_{\infin}}</math>,<br />
<br />
where <math>\alpha</math> is called the stiffness parameter. Note that <math>\phi_{g} = 0.03</math> is the minimum concentration required for gelation. This equation matches very well with experimental data. See Figure 1.<br />
<br />
[[Image:Stress.png|thumb|300px| Figure 1, taken from [1].]]<br />
<br />
From the functional form for <math>\sigma(\phi(\infin))</math>, <math>K(\phi_{\infin})</math> can be determined easily to be:<br />
<br />
<math>K(\phi_{\infin}) = \alpha(r, c_{m}) \phi_{\infin} \frac{\phi_{c} - \phi_{g}}{(\phi_{c} - \phi_{\infin})^{2}}</math>.<br />
<br />
<br />
The stiffness parameter should reflect the attraction between neighboring particles; it has units of stress, so one expect it to be the attractive force divided by the area of the interparticle bond. This would mean:<br />
<br />
<math>\alpha(r, c_{m}) \approx U/rR^{2}</math>, where <math>R</math> is the hydrodynamic radii.<br />
<br />
This matches well with experiment.<br />
<br />
<br />
Since we can control <math>\phi_{\infin}</math>, we can control <math>K(\phi_{\infin})</math>, and thus control the stability of the suspension against gravitational sedimentation; this is what the authors claim.<br />
<br />
<br />
Personally, I would have liked to see more of an effort on the part of the authors to explain how one can control, exactly, <math>\phi_{\infin}</math> with the addition of polymer. I am not entirely convinced that this is easily possible (at least, I'm not convinced it's as simple as the authors seem to insinuate).<br />
<br />
<br />
One application of this work ia clear: increase in shelf life of commercial products. It would be interesting to consider the commercial products for which this work would be most desirable, and see if a nonadsorbing polymer can be easily found. I wonder if these nonadsorbing polymers would actually have adverse effects on how the emulsion performs when used for the purpose they were original created.<br />
<br />
==References==<br />
[1] C. Kim, Y. Liu, A. Kuhnle, S. Hess, S. Viereck, T. Danner, L. Mahadevan, and D. Weitz, "Gravitational stability of suspensions of attractive colloidal particles," PRL '''99''' 028303 (2007).<br />
<br />
[2] D. Marenduzzo, K. Finan, and P. R. Cook, "The depletion attraction: an underappreciated force driving cellular organization," The Journal of Cell Biology, Volume 175, Number 5, 681-686 (2006).</div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=Gravitational_stability_of_suspensions_of_attractive_colloidal_particles&diff=13402Gravitational stability of suspensions of attractive colloidal particles2009-11-30T20:07:47Z<p>Chisholm: /* Summary */</p>
<hr />
<div>==Reference==<br />
<br />
'''Gravitational Stability of Suspension of Attractive Colloidal Particles'''<br />
<br />
Kim C, Liu Y, Kuhnle A, Hess S, Viereck S, Danner T, Mahadevan L, Weitz DA.<br />
<br />
Physical Review Letters '''99''': 028303 (2007)<br />
<br />
==Depletion Attraction==<br />
<br />
The attraction between particles in a [[colloidal suspension]] must overcome the pull of gravity if the suspension is to be stable. The alternative is gradual sedimentation and [[phase separation]] of the particles. There are many applications in which gradual onset of a [[phase separation]] severely limits the useful life of a product. <br />
<br />
One way to overcome sedimentation is through [[depletion attraction]], in which a polymer added to the suspension increases the attraction between particles. This occurs because the polymer is excluded from regions between particles when the distance between particles less than the size of the polymer. The result is regions between particles which are severely depleted of the polymer. This causes a net osmotic force which pushes the particles towards each other. The range and strength of this attractive force can be varied by changing the size of the polymer and the polymer concentration, respectively.<br />
<br />
==Experimental System==<br />
[[Image:Kim2007 fig1inset.jpg|thumb|Emulsion height H was measured by time-lapse imaging]]<br />
<br />
The goal was to measure the effect of particle volume fraction <math>\phi</math> on the [[compressional modulus]] <math>K(\phi)</math>. The colloidal suspension consisted of a surfactant-stabilized emulsion of paraffin oil in water. The emulsion samples had varying [[hydrodynamic radius|hydrodynamic radii]] R, but the volume fraction <math>\phi_0</math> and oil-water density mismatch <math>\Delta \rho</math> were constant. Depletion attraction was induced by adding either nonadsorbing polymer polyvinylpyrrolidon (PVP) or a surfactant - which was either Lutensol T08 or Lutensol A8). Time lapse images of the creaming emulsions were collected in order to observe the evolution of the clear fluid phase. The volume fraction at different times <math>\phi(t)</math> was measured by skimming sample off the top 2 mm of the emulsion, then weighing it, drying it, and weighing it again.<br />
<br />
==Stress as a Function of Steady-State Volume Fraction==<br />
<br />
An emulsion with an initial height <math>H_0</math> will cream and eventually approach a steady-state <math>H_\infin</math> that has a corresponding volume fraction <math>\phi_\infin</math> (which, as explained in the experimental section, can be experimentally measured.) Increasing <math>H_0</math> decreases both <math>H_\infin</math> and <math>\phi_\infin</math>. The buoyant stress in an emulsion is:<br />
<br />
<math><br />
\sigma = \Delta \rho g \phi_0 H_0<br />
</math><br />
<br />
By measuring <math>\phi_\infin </math> and <math>H_\infin</math> while varying <math>H_0</math>, surfactant concentration <math>c_m</math>, and micelle size <math>r</math>, the <math>\sigma \left (\phi_\infin \right)</math> can be experimentally derived.<br />
<br />
[[Image:Kim2007 fig2.jpg|thumb|center|upright=2|<math>\sigma</math> as a function of <math>\phi_\infin</math>. Inset: <math>-\frac{\sigma}{\alpha}</math> as a function of <math>\phi_c - \phi_\infin</math>]]<br />
<br />
The data points can be fit to functions in the form:<br />
<br />
<math><br />
\sigma \left (\phi_\infin \right) = -\alpha \frac{\phi_\infin-\phi_g}{\phi_c-\phi_\infin}<br />
</math><br />
<br />
where <math>\phi_c = 0.64</math> is the theoretical maximum for random close packing of uniform spheres; <math>\phi_g=0.03</math> is the minimum concentration required for gelation (which is independent of <math>c_m</math> and <math>r</math>); and <math>\alpha</math> is a stiffness parameter that depends on <math>c_m</math> and <math>r</math>.<br />
<br />
Which can be related to the compressional modulus K by:<br />
<br />
<math><br />
K(\phi) = -\phi \frac{\partial \sigma}{\partial \phi}<br />
= \alpha \phi_\infin \frac{\phi_\infin-\phi_g}{\left (\phi_c-\phi_\infin \right)^2}<br />
</math><br />
<br />
==Scaling Parameter as a Function of the Hydrodynamic Radius and Micelle Size==<br />
Unlike hard sphere suspensions in which K and osmotic pressure scale with thermal energy, the experiment above shows that <math>\sigma(\phi)</math> and <math>K(\phi)</math> scale with the stiffness parameter <math>\alpha</math>. <math>\alpha</math> should reflect the inter-particle attraction, and dimensional analysis shows that it scales with <math>\frac{U}{r R^2}</math><br />
<br />
==References==<br />
* Pusey PN, Pirie AD, Poon WCK. Dynamics of colloid-polymer mixtures. ''Physica A'' '''201''': 322-331 (1993).<br />
<br />
<br />
<br />
<br />
<br />
-------------------------------------------------------------------------------------------------------------------------------------------------------------<br />
Second Entry: Nick Chisholm, AP 225, Fall 2009 (In Progress...)<br />
<br />
==General Information==<br />
'''Authors''': C. Kim, Y. Liu, A. Kuhnle, S. Hess, S. Viereck, T. Danner, L. Mahadevan, and D. Weitz<br />
<br />
'''Publication''': PRL '''99''' 028303 (2007)<br />
<br />
==Soft Matter Keywords==<br />
[http://soft-matter.seas.harvard.edu/index.php/Compression_Modulus Compressional Modulus], Colloidal Suspension, [http://soft-matter.seas.harvard.edu/index.php/Emulsion Emulsion], Phase Separation<br />
<br />
==Summary==<br />
The authors present a means by which to stabilize suspensions of attractive colloidal particles against gravitationally-induced sedimentation or creaming. Their idea is to cause a depletion interaction between the colloidal particles by introducing nonadsorbing particles or polymers to the suspension. This causes a weak attraction between the particles, which then results in a solid-like network or gel of the particles that helps support their buoyant weight. Under shear, this network or gel can be made to easily yield, allowing the suspension to flow.<br />
<br />
Other means by which to stabilize these suspensions against gravitationally-induced sedimentation or creaming include density matching the particles to the suspending fluid, restricting the size of the particles so that their Brownian motion keeps them suspended, or by increasing the viscosity of the suspending fluid in order to slow down the phase separation. These methods are often not feasible, thus creating the motivation for this paper.<br />
<br />
How does this depletion interaction work? Well, the polymers are only able to occupy regions where their size is smaller than the spacing between the colloid particles. This results in regions of lower concentration of polymer, and the osmotic pressure of the polymer pushes the colloid particles together.<br />
<br />
==Soft Matter Discussion==<br />
In order to quantify the effectiveness of this method, one must measure the [http://soft-matter.seas.harvard.edu/index.php/Compressional_Modulus compressional modulus]. This compressional modulus may be represented as:<br />
<br />
<math>K(\phi) = -\phi \partial \sigma / \partial \phi</math>, where <math>\phi</math> is the volume fraction and <math>\sigma</math> is the stress (force per unit area).<br />
<br />
<br />
Note that one can change the initial height of the emulsion, <math>H_{0}</math>. This effectively allows manipulation of the buoyant stress of the emulsion, since the sample is a gel and thus the emulsion at the top feels the full buoyant stress of the suspensions below. As the sample creams, the initial volume fraction at the top, <math>\phi_{0}</math>, increases to the final volume fraction, <math>\phi_{\infin}</math>. Note that <math>H_{0}</math> sets the magnitude of the stress, <math>\sigma = \Delta \rho g \phi_{0} H_{0}</math> (where <math>\Delta \rho</math> is the difference in density between the colloids and the suspending fluid.)<br />
<br />
<br />
<math>\phi_{\infin}</math> and <math>\sigma(\infin)</math> are measured experimentally; the specific behavior of <math>\sigma(\infin)</math> depends on both <math>r</math> (micelle size) and <math>c_{m}</math> (nonadsorbing polymer concentration above the critical micelle concentration), but in every case the data diverges as <math>\phi(\infin)</math> approaches <math>\phi_{c} \approx 0.64</math>, the maximum value for random close packing of uniform spheres. Thus, the data is fit with functional form:<br />
<br />
<math>\sigma(\phi(\infin)) = -\alpha(r, c_{m}) \frac{\phi_{\infin} - \phi_{g}}{\phi_{c} - \phi_{\infin}}</math>,<br />
<br />
where <math>\alpha</math> is called the stiffness parameter. Note that <math>\phi_{g} = 0.03</math> is the minimum concentration required for gelation. This equation matches very well with experimental data. See Figure 1.<br />
<br />
[[Image:Stress.png|thumb|300px| Figure 1, taken from [1].]]<br />
<br />
From the functional form for <math>\sigma(\phi(\infin))</math>, <math>K(\phi_{\infin})</math> can be determined easily to be:<br />
<br />
<math>K(\phi_{\infin}) = \alpha(r, c_{m}) \phi_{\infin} \frac{\phi_{c} - \phi_{g}}{(\phi_{c} - \phi_{\infin})^{2}}</math>.<br />
<br />
<br />
The stiffness parameter should reflect the attraction between neighboring particles; it has units of stress, so one expect it to be the attractive force divided by the area of the interparticle bond. This would mean:<br />
<br />
<math>\alpha(r, c_{m}) \approx U/rR^{2}</math>, where <math>R</math> is the hydrodynamic radii.<br />
<br />
This matches well with experiment.<br />
<br />
<br />
Since we can control <math>\phi_{\infin}</math>, we can control <math>K(\phi_{\infin})</math>, and thus control the stability of the suspension against gravitational sedimentation; this is what the authors claim.<br />
<br />
<br />
Personally, I would have liked to see more of an effort on the part of the authors to explain how one can control, exactly, <math>\phi_{\infin}</math> with the addition of polymer. I am not entirely convinced that this is easily possible (at least, I'm not convinced it's as simple as the authors seem to insinuate).<br />
<br />
<br />
One application of this work ia clear: increase in shelf life of commercial products. It would be interesting to consider the commercial products for which this work would be most desirable, and see if a nonadsorbing polymer can be easily found. I wonder if these nonadsorbing polymers would actually have adverse effects on how the emulsion performs when used for the purpose they were original created.<br />
<br />
==References==<br />
[1] C. Kim, Y. Liu, A. Kuhnle, S. Hess, S. Viereck, T. Danner, L. Mahadevan, and D. Weitz, "Gravitational stability of suspensions of attractive colloidal particles," PRL '''99''' 028303 (2007).<br />
<br />
[2] D. Marenduzzo, K. Finan, and P. R. Cook, "The depletion attraction: an underappreciated force driving cellular organization," The Journal of Cell Biology, Volume 175, Number 5, 681-686 (2006).</div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=Gravitational_stability_of_suspensions_of_attractive_colloidal_particles&diff=13401Gravitational stability of suspensions of attractive colloidal particles2009-11-30T19:55:25Z<p>Chisholm: /* Soft Matter Discussion */</p>
<hr />
<div>==Reference==<br />
<br />
'''Gravitational Stability of Suspension of Attractive Colloidal Particles'''<br />
<br />
Kim C, Liu Y, Kuhnle A, Hess S, Viereck S, Danner T, Mahadevan L, Weitz DA.<br />
<br />
Physical Review Letters '''99''': 028303 (2007)<br />
<br />
==Depletion Attraction==<br />
<br />
The attraction between particles in a [[colloidal suspension]] must overcome the pull of gravity if the suspension is to be stable. The alternative is gradual sedimentation and [[phase separation]] of the particles. There are many applications in which gradual onset of a [[phase separation]] severely limits the useful life of a product. <br />
<br />
One way to overcome sedimentation is through [[depletion attraction]], in which a polymer added to the suspension increases the attraction between particles. This occurs because the polymer is excluded from regions between particles when the distance between particles less than the size of the polymer. The result is regions between particles which are severely depleted of the polymer. This causes a net osmotic force which pushes the particles towards each other. The range and strength of this attractive force can be varied by changing the size of the polymer and the polymer concentration, respectively.<br />
<br />
==Experimental System==<br />
[[Image:Kim2007 fig1inset.jpg|thumb|Emulsion height H was measured by time-lapse imaging]]<br />
<br />
The goal was to measure the effect of particle volume fraction <math>\phi</math> on the [[compressional modulus]] <math>K(\phi)</math>. The colloidal suspension consisted of a surfactant-stabilized emulsion of paraffin oil in water. The emulsion samples had varying [[hydrodynamic radius|hydrodynamic radii]] R, but the volume fraction <math>\phi_0</math> and oil-water density mismatch <math>\Delta \rho</math> were constant. Depletion attraction was induced by adding either nonadsorbing polymer polyvinylpyrrolidon (PVP) or a surfactant - which was either Lutensol T08 or Lutensol A8). Time lapse images of the creaming emulsions were collected in order to observe the evolution of the clear fluid phase. The volume fraction at different times <math>\phi(t)</math> was measured by skimming sample off the top 2 mm of the emulsion, then weighing it, drying it, and weighing it again.<br />
<br />
==Stress as a Function of Steady-State Volume Fraction==<br />
<br />
An emulsion with an initial height <math>H_0</math> will cream and eventually approach a steady-state <math>H_\infin</math> that has a corresponding volume fraction <math>\phi_\infin</math> (which, as explained in the experimental section, can be experimentally measured.) Increasing <math>H_0</math> decreases both <math>H_\infin</math> and <math>\phi_\infin</math>. The buoyant stress in an emulsion is:<br />
<br />
<math><br />
\sigma = \Delta \rho g \phi_0 H_0<br />
</math><br />
<br />
By measuring <math>\phi_\infin </math> and <math>H_\infin</math> while varying <math>H_0</math>, surfactant concentration <math>c_m</math>, and micelle size <math>r</math>, the <math>\sigma \left (\phi_\infin \right)</math> can be experimentally derived.<br />
<br />
[[Image:Kim2007 fig2.jpg|thumb|center|upright=2|<math>\sigma</math> as a function of <math>\phi_\infin</math>. Inset: <math>-\frac{\sigma}{\alpha}</math> as a function of <math>\phi_c - \phi_\infin</math>]]<br />
<br />
The data points can be fit to functions in the form:<br />
<br />
<math><br />
\sigma \left (\phi_\infin \right) = -\alpha \frac{\phi_\infin-\phi_g}{\phi_c-\phi_\infin}<br />
</math><br />
<br />
where <math>\phi_c = 0.64</math> is the theoretical maximum for random close packing of uniform spheres; <math>\phi_g=0.03</math> is the minimum concentration required for gelation (which is independent of <math>c_m</math> and <math>r</math>); and <math>\alpha</math> is a stiffness parameter that depends on <math>c_m</math> and <math>r</math>.<br />
<br />
Which can be related to the compressional modulus K by:<br />
<br />
<math><br />
K(\phi) = -\phi \frac{\partial \sigma}{\partial \phi}<br />
= \alpha \phi_\infin \frac{\phi_\infin-\phi_g}{\left (\phi_c-\phi_\infin \right)^2}<br />
</math><br />
<br />
==Scaling Parameter as a Function of the Hydrodynamic Radius and Micelle Size==<br />
Unlike hard sphere suspensions in which K and osmotic pressure scale with thermal energy, the experiment above shows that <math>\sigma(\phi)</math> and <math>K(\phi)</math> scale with the stiffness parameter <math>\alpha</math>. <math>\alpha</math> should reflect the inter-particle attraction, and dimensional analysis shows that it scales with <math>\frac{U}{r R^2}</math><br />
<br />
==References==<br />
* Pusey PN, Pirie AD, Poon WCK. Dynamics of colloid-polymer mixtures. ''Physica A'' '''201''': 322-331 (1993).<br />
<br />
<br />
<br />
<br />
<br />
-------------------------------------------------------------------------------------------------------------------------------------------------------------<br />
Second Entry: Nick Chisholm, AP 225, Fall 2009 (In Progress...)<br />
<br />
==General Information==<br />
'''Authors''': C. Kim, Y. Liu, A. Kuhnle, S. Hess, S. Viereck, T. Danner, L. Mahadevan, and D. Weitz<br />
<br />
'''Publication''': PRL '''99''' 028303 (2007)<br />
<br />
==Soft Matter Keywords==<br />
[http://soft-matter.seas.harvard.edu/index.php/Compression_Modulus Compressional Modulus], Colloidal Suspension, [http://soft-matter.seas.harvard.edu/index.php/Emulsion Emulsion], Phase Separation<br />
<br />
==Summary==<br />
The authors present a means by which to stabilize suspensions of attractive colloidal particles against gravitationally-induced sedimentation or creaming. Their idea is to cause a depletion interaction between the colloidal particles by introducing nonadsorbing particles or polymers to the suspension. This causes a weak attraction between the particles, which then results in a solid-like network or gel of the particles that helps support their buoyant weight. Under shear, this network or gel easily yields, allowing the suspension to flow.<br />
<br />
Other means by which to stabilize these suspensions against gravitationally-induced sedimentation or creaming include density matching the particles to the suspending fluid, restricting the size of the particles so that their Brownian motion keeps them suspended, or by increasing the viscosity of the suspending fluid in order to slow down the phase separation. These methods are often not feasible, thus creating the motivation for this paper.<br />
<br />
How does this depletion interaction work? Well, the polymers are only able to occupy regions where their size is smaller than the spacing between the colloid particles. This results in regions of lower concentration of polymer, and the osmotic pressure of the polymer pushes the colloid particles together.<br />
<br />
==Soft Matter Discussion==<br />
In order to quantify the effectiveness of this method, one must measure the [http://soft-matter.seas.harvard.edu/index.php/Compressional_Modulus compressional modulus]. This compressional modulus may be represented as:<br />
<br />
<math>K(\phi) = -\phi \partial \sigma / \partial \phi</math>, where <math>\phi</math> is the volume fraction and <math>\sigma</math> is the stress (force per unit area).<br />
<br />
<br />
Note that one can change the initial height of the emulsion, <math>H_{0}</math>. This effectively allows manipulation of the buoyant stress of the emulsion, since the sample is a gel and thus the emulsion at the top feels the full buoyant stress of the suspensions below. As the sample creams, the initial volume fraction at the top, <math>\phi_{0}</math>, increases to the final volume fraction, <math>\phi_{\infin}</math>. Note that <math>H_{0}</math> sets the magnitude of the stress, <math>\sigma = \Delta \rho g \phi_{0} H_{0}</math> (where <math>\Delta \rho</math> is the difference in density between the colloids and the suspending fluid.)<br />
<br />
<br />
<math>\phi_{\infin}</math> and <math>\sigma(\infin)</math> are measured experimentally; the specific behavior of <math>\sigma(\infin)</math> depends on both <math>r</math> (micelle size) and <math>c_{m}</math> (nonadsorbing polymer concentration above the critical micelle concentration), but in every case the data diverges as <math>\phi(\infin)</math> approaches <math>\phi_{c} \approx 0.64</math>, the maximum value for random close packing of uniform spheres. Thus, the data is fit with functional form:<br />
<br />
<math>\sigma(\phi(\infin)) = -\alpha(r, c_{m}) \frac{\phi_{\infin} - \phi_{g}}{\phi_{c} - \phi_{\infin}}</math>,<br />
<br />
where <math>\alpha</math> is called the stiffness parameter. Note that <math>\phi_{g} = 0.03</math> is the minimum concentration required for gelation. This equation matches very well with experimental data. See Figure 1.<br />
<br />
[[Image:Stress.png|thumb|300px| Figure 1, taken from [1].]]<br />
<br />
From the functional form for <math>\sigma(\phi(\infin))</math>, <math>K(\phi_{\infin})</math> can be determined easily to be:<br />
<br />
<math>K(\phi_{\infin}) = \alpha(r, c_{m}) \phi_{\infin} \frac{\phi_{c} - \phi_{g}}{(\phi_{c} - \phi_{\infin})^{2}}</math>.<br />
<br />
<br />
The stiffness parameter should reflect the attraction between neighboring particles; it has units of stress, so one expect it to be the attractive force divided by the area of the interparticle bond. This would mean:<br />
<br />
<math>\alpha(r, c_{m}) \approx U/rR^{2}</math>, where <math>R</math> is the hydrodynamic radii.<br />
<br />
This matches well with experiment.<br />
<br />
<br />
Since we can control <math>\phi_{\infin}</math>, we can control <math>K(\phi_{\infin})</math>, and thus control the stability of the suspension against gravitational sedimentation; this is what the authors claim.<br />
<br />
<br />
Personally, I would have liked to see more of an effort on the part of the authors to explain how one can control, exactly, <math>\phi_{\infin}</math> with the addition of polymer. I am not entirely convinced that this is easily possible (at least, I'm not convinced it's as simple as the authors seem to insinuate).<br />
<br />
<br />
One application of this work ia clear: increase in shelf life of commercial products. It would be interesting to consider the commercial products for which this work would be most desirable, and see if a nonadsorbing polymer can be easily found. I wonder if these nonadsorbing polymers would actually have adverse effects on how the emulsion performs when used for the purpose they were original created.<br />
<br />
==References==<br />
[1] C. Kim, Y. Liu, A. Kuhnle, S. Hess, S. Viereck, T. Danner, L. Mahadevan, and D. Weitz, "Gravitational stability of suspensions of attractive colloidal particles," PRL '''99''' 028303 (2007).<br />
<br />
[2] D. Marenduzzo, K. Finan, and P. R. Cook, "The depletion attraction: an underappreciated force driving cellular organization," The Journal of Cell Biology, Volume 175, Number 5, 681-686 (2006).</div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=Gravitational_stability_of_suspensions_of_attractive_colloidal_particles&diff=13400Gravitational stability of suspensions of attractive colloidal particles2009-11-30T19:51:40Z<p>Chisholm: /* Soft Matter Discussion */</p>
<hr />
<div>==Reference==<br />
<br />
'''Gravitational Stability of Suspension of Attractive Colloidal Particles'''<br />
<br />
Kim C, Liu Y, Kuhnle A, Hess S, Viereck S, Danner T, Mahadevan L, Weitz DA.<br />
<br />
Physical Review Letters '''99''': 028303 (2007)<br />
<br />
==Depletion Attraction==<br />
<br />
The attraction between particles in a [[colloidal suspension]] must overcome the pull of gravity if the suspension is to be stable. The alternative is gradual sedimentation and [[phase separation]] of the particles. There are many applications in which gradual onset of a [[phase separation]] severely limits the useful life of a product. <br />
<br />
One way to overcome sedimentation is through [[depletion attraction]], in which a polymer added to the suspension increases the attraction between particles. This occurs because the polymer is excluded from regions between particles when the distance between particles less than the size of the polymer. The result is regions between particles which are severely depleted of the polymer. This causes a net osmotic force which pushes the particles towards each other. The range and strength of this attractive force can be varied by changing the size of the polymer and the polymer concentration, respectively.<br />
<br />
==Experimental System==<br />
[[Image:Kim2007 fig1inset.jpg|thumb|Emulsion height H was measured by time-lapse imaging]]<br />
<br />
The goal was to measure the effect of particle volume fraction <math>\phi</math> on the [[compressional modulus]] <math>K(\phi)</math>. The colloidal suspension consisted of a surfactant-stabilized emulsion of paraffin oil in water. The emulsion samples had varying [[hydrodynamic radius|hydrodynamic radii]] R, but the volume fraction <math>\phi_0</math> and oil-water density mismatch <math>\Delta \rho</math> were constant. Depletion attraction was induced by adding either nonadsorbing polymer polyvinylpyrrolidon (PVP) or a surfactant - which was either Lutensol T08 or Lutensol A8). Time lapse images of the creaming emulsions were collected in order to observe the evolution of the clear fluid phase. The volume fraction at different times <math>\phi(t)</math> was measured by skimming sample off the top 2 mm of the emulsion, then weighing it, drying it, and weighing it again.<br />
<br />
==Stress as a Function of Steady-State Volume Fraction==<br />
<br />
An emulsion with an initial height <math>H_0</math> will cream and eventually approach a steady-state <math>H_\infin</math> that has a corresponding volume fraction <math>\phi_\infin</math> (which, as explained in the experimental section, can be experimentally measured.) Increasing <math>H_0</math> decreases both <math>H_\infin</math> and <math>\phi_\infin</math>. The buoyant stress in an emulsion is:<br />
<br />
<math><br />
\sigma = \Delta \rho g \phi_0 H_0<br />
</math><br />
<br />
By measuring <math>\phi_\infin </math> and <math>H_\infin</math> while varying <math>H_0</math>, surfactant concentration <math>c_m</math>, and micelle size <math>r</math>, the <math>\sigma \left (\phi_\infin \right)</math> can be experimentally derived.<br />
<br />
[[Image:Kim2007 fig2.jpg|thumb|center|upright=2|<math>\sigma</math> as a function of <math>\phi_\infin</math>. Inset: <math>-\frac{\sigma}{\alpha}</math> as a function of <math>\phi_c - \phi_\infin</math>]]<br />
<br />
The data points can be fit to functions in the form:<br />
<br />
<math><br />
\sigma \left (\phi_\infin \right) = -\alpha \frac{\phi_\infin-\phi_g}{\phi_c-\phi_\infin}<br />
</math><br />
<br />
where <math>\phi_c = 0.64</math> is the theoretical maximum for random close packing of uniform spheres; <math>\phi_g=0.03</math> is the minimum concentration required for gelation (which is independent of <math>c_m</math> and <math>r</math>); and <math>\alpha</math> is a stiffness parameter that depends on <math>c_m</math> and <math>r</math>.<br />
<br />
Which can be related to the compressional modulus K by:<br />
<br />
<math><br />
K(\phi) = -\phi \frac{\partial \sigma}{\partial \phi}<br />
= \alpha \phi_\infin \frac{\phi_\infin-\phi_g}{\left (\phi_c-\phi_\infin \right)^2}<br />
</math><br />
<br />
==Scaling Parameter as a Function of the Hydrodynamic Radius and Micelle Size==<br />
Unlike hard sphere suspensions in which K and osmotic pressure scale with thermal energy, the experiment above shows that <math>\sigma(\phi)</math> and <math>K(\phi)</math> scale with the stiffness parameter <math>\alpha</math>. <math>\alpha</math> should reflect the inter-particle attraction, and dimensional analysis shows that it scales with <math>\frac{U}{r R^2}</math><br />
<br />
==References==<br />
* Pusey PN, Pirie AD, Poon WCK. Dynamics of colloid-polymer mixtures. ''Physica A'' '''201''': 322-331 (1993).<br />
<br />
<br />
<br />
<br />
<br />
-------------------------------------------------------------------------------------------------------------------------------------------------------------<br />
Second Entry: Nick Chisholm, AP 225, Fall 2009 (In Progress...)<br />
<br />
==General Information==<br />
'''Authors''': C. Kim, Y. Liu, A. Kuhnle, S. Hess, S. Viereck, T. Danner, L. Mahadevan, and D. Weitz<br />
<br />
'''Publication''': PRL '''99''' 028303 (2007)<br />
<br />
==Soft Matter Keywords==<br />
[http://soft-matter.seas.harvard.edu/index.php/Compression_Modulus Compressional Modulus], Colloidal Suspension, [http://soft-matter.seas.harvard.edu/index.php/Emulsion Emulsion], Phase Separation<br />
<br />
==Summary==<br />
The authors present a means by which to stabilize suspensions of attractive colloidal particles against gravitationally-induced sedimentation or creaming. Their idea is to cause a depletion interaction between the colloidal particles by introducing nonadsorbing particles or polymers to the suspension. This causes a weak attraction between the particles, which then results in a solid-like network or gel of the particles that helps support their buoyant weight. Under shear, this network or gel easily yields, allowing the suspension to flow.<br />
<br />
Other means by which to stabilize these suspensions against gravitationally-induced sedimentation or creaming include density matching the particles to the suspending fluid, restricting the size of the particles so that their Brownian motion keeps them suspended, or by increasing the viscosity of the suspending fluid in order to slow down the phase separation. These methods are often not feasible, thus creating the motivation for this paper.<br />
<br />
How does this depletion interaction work? Well, the polymers are only able to occupy regions where their size is smaller than the spacing between the colloid particles. This results in regions of lower concentration of polymer, and the osmotic pressure of the polymer pushes the colloid particles together.<br />
<br />
==Soft Matter Discussion==<br />
In order to quantify the effectiveness of this method, one must measure the [http://soft-matter.seas.harvard.edu/index.php/Compressional_Modulus compressional modulus]. This compressional modulus may be represented as:<br />
<br />
<math>K(\phi) = -\phi \partial \sigma / \partial \phi</math>, where <math>\phi</math> is the volume fraction and <math>\sigma</math> is the stress (force per unit area).<br />
<br />
<br />
Note that one can change the initial height of the emulsion, <math>H_{0}</math>. This effectively allows manipulation of the buoyant stress of the emulsion, since the sample is a gel and thus the emulsion at the top feels the full buoyant stress of the suspensions below. As the sample creams, the initial volume fraction at the top, <math>\phi_{0}</math>, increases to the final volume fraction, <math>\phi_{\infin}</math>. Note that <math>H_{0}</math> sets the magnitude of the stress, <math>\sigma = \Delta \rho g \phi_{0} H_{0}</math> (where <math>\Delta \rho</math> is the difference in density between the colloids and the suspending fluid.)<br />
<br />
<br />
<math>\phi_{\infin}</math> and <math>\sigma(\infin)</math> are measured experimentally; the specific behavior of <math>\sigma(\infin)</math> depends on both <math>r</math> (micelle size) and <math>c_{m}</math> (nonadsorbing polymer concentration above the critical micelle concentration), but in every case the data diverges as <math>\phi(\infin)</math> approaches <math>\phi_{c} \approx 0.64</math>, the maximum value for random close packing of uniform spheres. Thus, the data is fit with functional form:<br />
<br />
<math>\sigma(\phi(\infin)) = -\alpha(r, c_{m}) \frac{\phi_{\infin} - \phi_{g}}{\phi_{c} - \phi_{\infin}}</math>,<br />
<br />
where <math>\alpha</math> is called the stiffness parameter. Note that <math>\phi_{g} = 0.03</math> is the minimum concentration required for gelation. This equation matches very well with experimental data. See Figure 1.<br />
<br />
[[Image:Stress.png|thumb|300px| Figure 1, taken from [1].]]<br />
<br />
From the functional form for <math>\sigma(\phi(\infin))</math>, <math>K(\phi_{\infin})</math> can be determined easily to be:<br />
<br />
<math>K(\phi_{\infin}) = \alpha(r, c_{m}) \phi_{\infin} \frac{\phi_{c} - \phi_{g}}{(\phi_{c} - \phi_{\infin})^{2}}</math>.<br />
<br />
<br />
The stiffness parameter should reflect the attraction between neighboring particles; it has units of stress, so one expect it to be the attractive force divided by the area of the interparticle bond. This would mean:<br />
<br />
<math>\alpha(r, c_{m}) \approx U/rR^{2}</math>, where <math>R</math> is the hydrodynamic radii.<br />
<br />
This matches well with experiment.<br />
<br />
<br />
Since we can control <math>\phi_{\infin}</math>, we can control <math>K(\phi_{\infin})</math>, and thus control the stability of the suspension against gravitational sedimentation; this is what the authors claim.<br />
<br />
<br />
Personally, I would have liked to see more of an effort on the part of the authors to explain how one can control, exactly, <math>\phi_{\infin}</math> with the addition of polymer. I am not entirely convinced that this is easily possible (at least, I'm not convinced it's as simple as they seem to insinuate).<br />
<br />
==References==<br />
[1] C. Kim, Y. Liu, A. Kuhnle, S. Hess, S. Viereck, T. Danner, L. Mahadevan, and D. Weitz, "Gravitational stability of suspensions of attractive colloidal particles," PRL '''99''' 028303 (2007).<br />
<br />
[2] D. Marenduzzo, K. Finan, and P. R. Cook, "The depletion attraction: an underappreciated force driving cellular organization," The Journal of Cell Biology, Volume 175, Number 5, 681-686 (2006).</div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=Gravitational_stability_of_suspensions_of_attractive_colloidal_particles&diff=13399Gravitational stability of suspensions of attractive colloidal particles2009-11-30T19:50:39Z<p>Chisholm: /* Soft Matter Discussion */</p>
<hr />
<div>==Reference==<br />
<br />
'''Gravitational Stability of Suspension of Attractive Colloidal Particles'''<br />
<br />
Kim C, Liu Y, Kuhnle A, Hess S, Viereck S, Danner T, Mahadevan L, Weitz DA.<br />
<br />
Physical Review Letters '''99''': 028303 (2007)<br />
<br />
==Depletion Attraction==<br />
<br />
The attraction between particles in a [[colloidal suspension]] must overcome the pull of gravity if the suspension is to be stable. The alternative is gradual sedimentation and [[phase separation]] of the particles. There are many applications in which gradual onset of a [[phase separation]] severely limits the useful life of a product. <br />
<br />
One way to overcome sedimentation is through [[depletion attraction]], in which a polymer added to the suspension increases the attraction between particles. This occurs because the polymer is excluded from regions between particles when the distance between particles less than the size of the polymer. The result is regions between particles which are severely depleted of the polymer. This causes a net osmotic force which pushes the particles towards each other. The range and strength of this attractive force can be varied by changing the size of the polymer and the polymer concentration, respectively.<br />
<br />
==Experimental System==<br />
[[Image:Kim2007 fig1inset.jpg|thumb|Emulsion height H was measured by time-lapse imaging]]<br />
<br />
The goal was to measure the effect of particle volume fraction <math>\phi</math> on the [[compressional modulus]] <math>K(\phi)</math>. The colloidal suspension consisted of a surfactant-stabilized emulsion of paraffin oil in water. The emulsion samples had varying [[hydrodynamic radius|hydrodynamic radii]] R, but the volume fraction <math>\phi_0</math> and oil-water density mismatch <math>\Delta \rho</math> were constant. Depletion attraction was induced by adding either nonadsorbing polymer polyvinylpyrrolidon (PVP) or a surfactant - which was either Lutensol T08 or Lutensol A8). Time lapse images of the creaming emulsions were collected in order to observe the evolution of the clear fluid phase. The volume fraction at different times <math>\phi(t)</math> was measured by skimming sample off the top 2 mm of the emulsion, then weighing it, drying it, and weighing it again.<br />
<br />
==Stress as a Function of Steady-State Volume Fraction==<br />
<br />
An emulsion with an initial height <math>H_0</math> will cream and eventually approach a steady-state <math>H_\infin</math> that has a corresponding volume fraction <math>\phi_\infin</math> (which, as explained in the experimental section, can be experimentally measured.) Increasing <math>H_0</math> decreases both <math>H_\infin</math> and <math>\phi_\infin</math>. The buoyant stress in an emulsion is:<br />
<br />
<math><br />
\sigma = \Delta \rho g \phi_0 H_0<br />
</math><br />
<br />
By measuring <math>\phi_\infin </math> and <math>H_\infin</math> while varying <math>H_0</math>, surfactant concentration <math>c_m</math>, and micelle size <math>r</math>, the <math>\sigma \left (\phi_\infin \right)</math> can be experimentally derived.<br />
<br />
[[Image:Kim2007 fig2.jpg|thumb|center|upright=2|<math>\sigma</math> as a function of <math>\phi_\infin</math>. Inset: <math>-\frac{\sigma}{\alpha}</math> as a function of <math>\phi_c - \phi_\infin</math>]]<br />
<br />
The data points can be fit to functions in the form:<br />
<br />
<math><br />
\sigma \left (\phi_\infin \right) = -\alpha \frac{\phi_\infin-\phi_g}{\phi_c-\phi_\infin}<br />
</math><br />
<br />
where <math>\phi_c = 0.64</math> is the theoretical maximum for random close packing of uniform spheres; <math>\phi_g=0.03</math> is the minimum concentration required for gelation (which is independent of <math>c_m</math> and <math>r</math>); and <math>\alpha</math> is a stiffness parameter that depends on <math>c_m</math> and <math>r</math>.<br />
<br />
Which can be related to the compressional modulus K by:<br />
<br />
<math><br />
K(\phi) = -\phi \frac{\partial \sigma}{\partial \phi}<br />
= \alpha \phi_\infin \frac{\phi_\infin-\phi_g}{\left (\phi_c-\phi_\infin \right)^2}<br />
</math><br />
<br />
==Scaling Parameter as a Function of the Hydrodynamic Radius and Micelle Size==<br />
Unlike hard sphere suspensions in which K and osmotic pressure scale with thermal energy, the experiment above shows that <math>\sigma(\phi)</math> and <math>K(\phi)</math> scale with the stiffness parameter <math>\alpha</math>. <math>\alpha</math> should reflect the inter-particle attraction, and dimensional analysis shows that it scales with <math>\frac{U}{r R^2}</math><br />
<br />
==References==<br />
* Pusey PN, Pirie AD, Poon WCK. Dynamics of colloid-polymer mixtures. ''Physica A'' '''201''': 322-331 (1993).<br />
<br />
<br />
<br />
<br />
<br />
-------------------------------------------------------------------------------------------------------------------------------------------------------------<br />
Second Entry: Nick Chisholm, AP 225, Fall 2009 (In Progress...)<br />
<br />
==General Information==<br />
'''Authors''': C. Kim, Y. Liu, A. Kuhnle, S. Hess, S. Viereck, T. Danner, L. Mahadevan, and D. Weitz<br />
<br />
'''Publication''': PRL '''99''' 028303 (2007)<br />
<br />
==Soft Matter Keywords==<br />
[http://soft-matter.seas.harvard.edu/index.php/Compression_Modulus Compressional Modulus], Colloidal Suspension, [http://soft-matter.seas.harvard.edu/index.php/Emulsion Emulsion], Phase Separation<br />
<br />
==Summary==<br />
The authors present a means by which to stabilize suspensions of attractive colloidal particles against gravitationally-induced sedimentation or creaming. Their idea is to cause a depletion interaction between the colloidal particles by introducing nonadsorbing particles or polymers to the suspension. This causes a weak attraction between the particles, which then results in a solid-like network or gel of the particles that helps support their buoyant weight. Under shear, this network or gel easily yields, allowing the suspension to flow.<br />
<br />
Other means by which to stabilize these suspensions against gravitationally-induced sedimentation or creaming include density matching the particles to the suspending fluid, restricting the size of the particles so that their Brownian motion keeps them suspended, or by increasing the viscosity of the suspending fluid in order to slow down the phase separation. These methods are often not feasible, thus creating the motivation for this paper.<br />
<br />
How does this depletion interaction work? Well, the polymers are only able to occupy regions where their size is smaller than the spacing between the colloid particles. This results in regions of lower concentration of polymer, and the osmotic pressure of the polymer pushes the colloid particles together.<br />
<br />
==Soft Matter Discussion==<br />
In order to quantify the effectiveness of this method, one must measure the [http://soft-matter.seas.harvard.edu/index.php/Compressional_Modulus compressional modulus]. This compressional modulus may be represented as:<br />
<br />
<math>K(\phi) = -\phi \partial \sigma / \partial \phi</math>, where <math>\phi</math> is the volume fraction and <math>\sigma</math> is the stress (force per unit area).<br />
<br />
<br />
Note that one can change the initial height of the emulsion, <math>H_{0}</math>. This effectively allows manipulation of the buoyant stress of the emulsion, since the sample is a gel and thus the emulsion at the top feels the full buoyant stress of the suspensions below. As the sample creams, the initial volume fraction at the top, <math>\phi_{0}</math>, increases to the final volume fraction, <math>\phi_{\infin}</math>. Note that <math>H_{0}</math> sets the magnitude of the stress, <math>\sigma = \Delta \rho g \phi_{0} H_{0}</math> (where <math>\Delta \rho</math> is the difference in density between the colloids and the suspending fluid.)<br />
<br />
<br />
<math>\phi_{\infin}</math> and <math>\sigma(\infin)</math> are measured experimentally; the specific behavior of <math>\sigma(\infin)</math> depends on both <math>r</math> (micelle size) and <math>c_{m}</math> (nonadsorbing polymer concentration above the critical micelle concentration), but in every case the data diverges as <math>\phi(\infin)</math> approaches <math>\phi_{c} \approx 0.64</math>, the maximum value for random close packing of uniform spheres. Thus, the data is fit with functional form:<br />
<br />
<math>\sigma(\phi(\infin)) = -\alpha(r, c_{m}) \frac{\phi_{\infin} - \phi_{g}}{\phi_{c} - \phi_{\infin}}</math>,<br />
<br />
where <math>\alpha</math> is called the stiffness parameter. Note that <math>\phi_{g} = 0.03</math> is the minimum concentration required for gelation. This equation matches very well with experimental data. See Figure 1.<br />
<br />
[[Image:Stress.png|thumb|300px| Figure 1, taken from [1].]]<br />
<br />
From the functional form for <math>\sigma(\phi(\infin))</math>, <math>K(\phi_{\infin})</math> can be determined easily to be:<br />
<br />
<math>K(\phi_{\infin}) = \alpha(r, c_{m}) \phi_{\infin} \frac{\phi_{c} - \phi_{g}}{(\phi_{c} - \phi_{\infin})^{2}}</math>.<br />
<br />
<br />
The stiffness parameter should reflect the attraction between neighboring particles; it has units of stress, so one expect it to be the attractive force divided by the area of the interparticle bond. This would mean:<br />
<br />
<math>\alpha(r, c_{m}) \approx U/rR^{2}</math>.<br />
<br />
This matches well with experiment.<br />
<br />
<br />
Since we can control <math>\phi_{\infin}</math>, we can control <math>K(\phi_{\infin})</math>, and thus control the stability of the suspension against gravitational sedimentation; this is what the authors claim.<br />
<br />
<br />
Personally, I would have liked to see more of an effort on the part of the authors to explain how one can control, exactly, <math>\phi_{\infin}</math> with the addition of polymer. I am not entirely convinced that this is easily possible (at least, I'm not convinced it's as simple as they seem to insinuate).<br />
<br />
==References==<br />
[1] C. Kim, Y. Liu, A. Kuhnle, S. Hess, S. Viereck, T. Danner, L. Mahadevan, and D. Weitz, "Gravitational stability of suspensions of attractive colloidal particles," PRL '''99''' 028303 (2007).<br />
<br />
[2] D. Marenduzzo, K. Finan, and P. R. Cook, "The depletion attraction: an underappreciated force driving cellular organization," The Journal of Cell Biology, Volume 175, Number 5, 681-686 (2006).</div>Chisholmhttp://soft-matter.seas.harvard.edu/index.php?title=Gravitational_stability_of_suspensions_of_attractive_colloidal_particles&diff=13398Gravitational stability of suspensions of attractive colloidal particles2009-11-30T19:47:52Z<p>Chisholm: /* Soft Matter Discussion */</p>
<hr />
<div>==Reference==<br />
<br />
'''Gravitational Stability of Suspension of Attractive Colloidal Particles'''<br />
<br />
Kim C, Liu Y, Kuhnle A, Hess S, Viereck S, Danner T, Mahadevan L, Weitz DA.<br />
<br />
Physical Review Letters '''99''': 028303 (2007)<br />
<br />
==Depletion Attraction==<br />
<br />
The attraction between particles in a [[colloidal suspension]] must overcome the pull of gravity if the suspension is to be stable. The alternative is gradual sedimentation and [[phase separation]] of the particles. There are many applications in which gradual onset of a [[phase separation]] severely limits the useful life of a product. <br />
<br />
One way to overcome sedimentation is through [[depletion attraction]], in which a polymer added to the suspension increases the attraction between particles. This occurs because the polymer is excluded from regions between particles when the distance between particles less than the size of the polymer. The result is regions between particles which are severely depleted of the polymer. This causes a net osmotic force which pushes the particles towards each other. The range and strength of this attractive force can be varied by changing the size of the polymer and the polymer concentration, respectively.<br />
<br />
==Experimental System==<br />
[[Image:Kim2007 fig1inset.jpg|thumb|Emulsion height H was measured by time-lapse imaging]]<br />
<br />
The goal was to measure the effect of particle volume fraction <math>\phi</math> on the [[compressional modulus]] <math>K(\phi)</math>. The colloidal suspension consisted of a surfactant-stabilized emulsion of paraffin oil in water. The emulsion samples had varying [[hydrodynamic radius|hydrodynamic radii]] R, but the volume fraction <math>\phi_0</math> and oil-water density mismatch <math>\Delta \rho</math> were constant. Depletion attraction was induced by adding either nonadsorbing polymer polyvinylpyrrolidon (PVP) or a surfactant - which was either Lutensol T08 or Lutensol A8). Time lapse images of the creaming emulsions were collected in order to observe the evolution of the clear fluid phase. The volume fraction at different times <math>\phi(t)</math> was measured by skimming sample off the top 2 mm of the emulsion, then weighing it, drying it, and weighing it again.<br />
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==Stress as a Function of Steady-State Volume Fraction==<br />
<br />
An emulsion with an initial height <math>H_0</math> will cream and eventually approach a steady-state <math>H_\infin</math> that has a corresponding volume fraction <math>\phi_\infin</math> (which, as explained in the experimental section, can be experimentally measured.) Increasing <math>H_0</math> decreases both <math>H_\infin</math> and <math>\phi_\infin</math>. The buoyant stress in an emulsion is:<br />
<br />
<math><br />
\sigma = \Delta \rho g \phi_0 H_0<br />
</math><br />
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By measuring <math>\phi_\infin </math> and <math>H_\infin</math> while varying <math>H_0</math>, surfactant concentration <math>c_m</math>, and micelle size <math>r</math>, the <math>\sigma \left (\phi_\infin \right)</math> can be experimentally derived.<br />
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[[Image:Kim2007 fig2.jpg|thumb|center|upright=2|<math>\sigma</math> as a function of <math>\phi_\infin</math>. Inset: <math>-\frac{\sigma}{\alpha}</math> as a function of <math>\phi_c - \phi_\infin</math>]]<br />
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The data points can be fit to functions in the form:<br />
<br />
<math><br />
\sigma \left (\phi_\infin \right) = -\alpha \frac{\phi_\infin-\phi_g}{\phi_c-\phi_\infin}<br />
</math><br />
<br />
where <math>\phi_c = 0.64</math> is the theoretical maximum for random close packing of uniform spheres; <math>\phi_g=0.03</math> is the minimum concentration required for gelation (which is independent of <math>c_m</math> and <math>r</math>); and <math>\alpha</math> is a stiffness parameter that depends on <math>c_m</math> and <math>r</math>.<br />
<br />
Which can be related to the compressional modulus K by:<br />
<br />
<math><br />
K(\phi) = -\phi \frac{\partial \sigma}{\partial \phi}<br />
= \alpha \phi_\infin \frac{\phi_\infin-\phi_g}{\left (\phi_c-\phi_\infin \right)^2}<br />
</math><br />
<br />
==Scaling Parameter as a Function of the Hydrodynamic Radius and Micelle Size==<br />
Unlike hard sphere suspensions in which K and osmotic pressure scale with thermal energy, the experiment above shows that <math>\sigma(\phi)</math> and <math>K(\phi)</math> scale with the stiffness parameter <math>\alpha</math>. <math>\alpha</math> should reflect the inter-particle attraction, and dimensional analysis shows that it scales with <math>\frac{U}{r R^2}</math><br />
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==References==<br />
* Pusey PN, Pirie AD, Poon WCK. Dynamics of colloid-polymer mixtures. ''Physica A'' '''201''': 322-331 (1993).<br />
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Second Entry: Nick Chisholm, AP 225, Fall 2009 (In Progress...)<br />
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==General Information==<br />
'''Authors''': C. Kim, Y. Liu, A. Kuhnle, S. Hess, S. Viereck, T. Danner, L. Mahadevan, and D. Weitz<br />
<br />
'''Publication''': PRL '''99''' 028303 (2007)<br />
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==Soft Matter Keywords==<br />
[http://soft-matter.seas.harvard.edu/index.php/Compression_Modulus Compressional Modulus], Colloidal Suspension, [http://soft-matter.seas.harvard.edu/index.php/Emulsion Emulsion], Phase Separation<br />
<br />
==Summary==<br />
The authors present a means by which to stabilize suspensions of attractive colloidal particles against gravitationally-induced sedimentation or creaming. Their idea is to cause a depletion interaction between the colloidal particles by introducing nonadsorbing particles or polymers to the suspension. This causes a weak attraction between the particles, which then results in a solid-like network or gel of the particles that helps support their buoyant weight. Under shear, this network or gel easily yields, allowing the suspension to flow.<br />
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Other means by which to stabilize these suspensions against gravitationally-induced sedimentation or creaming include density matching the particles to the suspending fluid, restricting the size of the particles so that their Brownian motion keeps them suspended, or by increasing the viscosity of the suspending fluid in order to slow down the phase separation. These methods are often not feasible, thus creating the motivation for this paper.<br />
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How does this depletion interaction work? Well, the polymers are only able to occupy regions where their size is smaller than the spacing between the colloid particles. This results in regions of lower concentration of polymer, and the osmotic pressure of the polymer pushes the colloid particles together.<br />
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==Soft Matter Discussion==<br />
In order to quantify the effectiveness of this method, one must measure the [http://soft-matter.seas.harvard.edu/index.php/Compressional_Modulus compressional modulus]. This compressional modulus may be represented as:<br />
<br />
<math>K(\phi) = -\phi \partial \sigma / \partial \phi</math>, where <math>\phi</math> is the volume fraction and <math>\sigma</math> is the stress (force per unit area).<br />
<br />
<br />
Note that one can change the initial height of the emulsion, <math>H_{0}</math>. This effectively allows manipulation of the buoyant stress of the emulsion, since the sample is a gel and thus the emulsion at the top feels the full buoyant stress of the suspensions below. As the sample creams, the initial volume fraction at the top, <math>\phi_{0}</math>, increases to the final volume fraction, <math>\phi_{\infin}</math>. Note that <math>H_{0}</math> sets the magnitude of the stress, <math>\sigma = \Delta \rho g \phi_{0} H_{0}</math> (where <math>\Delta \rho</math> is the difference in density between the colloids and the suspending fluid.)<br />
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<math>\phi_{\infin}</math> and <math>\sigma(\infin)</math> are measured experimentally; the specific behavior of <math>\sigma(\infin)</math> depends on both <math>r</math> and <math>c_{m}</math>, but in every case the data diverges as <math>\phi(\infin)</math> approaches <math>\phi_{c} \approx 0.64</math>, the maximum value for random close packing of uniform spheres. Thus, the data is fit with functional form:<br />
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<math>\sigma(\phi(\infin)) = -\alpha(r, c_{m}) \frac{\phi_{\infin} - \phi_{g}}{\phi_{c} - \phi_{\infin}}</math>,<br />
<br />
where <math>\alpha</math> is called the stiffness parameter. Note that <math>\phi_{g} = 0.03</math> is the minimum concentration required for gelation. This equation matches very well with experimental data. See Figure 1.<br />
<br />
[[Image:Stress.png|thumb|300px| Figure 1, taken from [1].]]<br />
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From the functional form for <math>\sigma(\phi(\infin))</math>, <math>K(\phi_{\infin})</math> can be determined easily to be:<br />
<br />
<math>K(\phi_{\infin}) = \alpha(r, c_{m}) \phi_{\infin} \frac{\phi_{c} - \phi_{g}}{(\phi_{c} - \phi_{\infin})^{2}}</math>.<br />
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The stiffness parameter should reflect the attraction between neighboring particles; it has units of stress, so one expect it to be the attractive force divided by the area of the interparticle bond. This would mean:<br />
<br />
<math>\alpha(r, c_{m}) \approx U/rR^{2}</math>.<br />
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This matches well with experiment.<br />
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<br />
Since we can control <math>\phi_{\infin}</math>, we can control <math>K(\phi_{\infin})</math>, and thus control the stability of the suspension against gravitational sedimentation; this is what the authors claim.<br />
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Personally, I would have liked to see more of an effort on the part of the authors to explain how one can control, exactly, <math>\phi_{\infin}</math> with the addition of polymer. I am not entirely convinced that this is easily possible (at least, I'm not convinced it's as simple as they seem to insinuate).<br />
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==References==<br />
[1] C. Kim, Y. Liu, A. Kuhnle, S. Hess, S. Viereck, T. Danner, L. Mahadevan, and D. Weitz, "Gravitational stability of suspensions of attractive colloidal particles," PRL '''99''' 028303 (2007).<br />
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[2] D. Marenduzzo, K. Finan, and P. R. Cook, "The depletion attraction: an underappreciated force driving cellular organization," The Journal of Cell Biology, Volume 175, Number 5, 681-686 (2006).</div>Chisholm