# Collective cell guidance by cooperative intercellular forces

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Written by Kevin Tian, AP 225, Fall 2011

--Ktian 01:26, 20 September 2011 (UTC)

Title: Collective cell guidance by cooperative intercellular forces

Authors: Dhananjay T. Tambe, C. Corey Hardin, Thomas E. Angelini, Kavitha Rajendran, Chan Young Park, Xavier Serra-Picamal, Enhua H. Zhou, Muhammad H. Zaman, James P. Butler, David A. Weitz, Jeffrey J. Fredberg & Xavier Trepat

Journal: Nature Materials 10, 469–475 (2011)

## Paper Summary

Although the behaviors of individual cells is well described, the same cannot be said for cells as part of a "collective". The important case where this occurs is in biological tissues, where cell migration occurs as a collective. Since the understanding of this process has important implications for further developments in health and medicine, the mapping of the stress components of cell-cell boundaries has been performed.

The experimental mapping of these intercellular mechanical stresses was previously inaccessible. However the authors achieved this by using a cell monolayer as an experimental model system. From the analysis of the monolayer, the same mapping was performed for breast-cancer model systems. In observing the stress landscapes it was noted that there was an extremely heterogeneous stress distribution, which combined with observations of the migration directions lead to the coining of a new unexpected unifying physiological principle. This new phenomenon, termed "Plithotaxis", is the principle that cells will migrate and deform in a way that minimizes the local intercellular shear stress. What is unique about this phenomenon is that this is clearly an property of a collective system and not of any individual cell on its own.

## Theory

Figure 1. Taken from article. Illustrain summary of the principles behind MSM and the idea of reorientating the local coordinate system to obtain principle stress orientations.

Monolayer Stress Microscopy

The essential concept here is that once a mapping of the mechanical stresses can be obtained within and between cellular bodies, as well as their directionality, much information can be gleaned about the importance of various factors in cell migration. The major tool that is used in this experiment is a technique developed previously called "Monolayer Stress Microscopy" (MSM).

MSM works on the idea that one can measure the traction forces an advancing cellular monolayer exerts upon a substrate and use that information to compute the intercellular normal and shear stresses. Since the monolayers in question are approximately uniform in the lateral direction, the system is essentially a 2D system, from which the rigorous recovery of line tensions can be performed. One can treat the entire cell collective as a thin elastic sheet with an internal stress tensor, and thus by enforcing mechanical equilibrium one can work from tensions (of the cells on the substrate) to stresses in the sheet.

The tensions are measured by using fluorescent markers embedded near the surface of a collagen-coated polyacrylamide gel substrate. The cells are adherent to this substrate, and thus in the process of migration generate displacements which can be measured. After compensating for drift of the stage, the gel deformations can be used to compute traction. Details of the exact algorithms used can be found in the Supplementary Information for the article.

Principle Stresses

After obtaining the tensions exerted by the monolayer on the gel, through force balancing, one can obtain the line forces throughout the cell sheet. Converting these stresses by using the average monolayer height, we can then create a map of the stresses across the entire cell sheet.

However an important piece of information can be obtained by finding the special orientation in which the local stress tensor is diagonalized. Rotating the local coordinate system to this special orientation allows us to define the two principle stress components $\sigma_{max}$ and $\sigma_(min)$. These orientations become important to the discussion, as the principle of plithotaxis relates to the alignment of the cells with the maximal principle stress axis.

## Experiment

Outline

The article essentially describes the results of two separate experiments with several stages of analysis. Generally speaking the experiments involved the use of the MSM technique to generate a mapping and to observe the relationships between mechanical stresses and biological parameters.

• The First experiment measured and analyzed the stress mapping of the cell monolayer.
• From this it was found that there was high correlation between cell body orientation and the orientation of the maximal principle stress.
• This was done for 2 Cell lines:
• Rat pulmonary microvascular endothelial (RPME) cells (the first line).
• Madin-Darby canine kidney (MDCK) cells (to verify generality of observation).
• The Second experiment two-fold. First, to further assess the generality of the findings of the first; Second, determined the relationship between cell-cell adhesion and the alignment of cell-body orientation and maximal principle stress axis.
• This was done on a series of MCF10A cells (a well-established breast-cancer model system):
• MCF10A Vector cells(used as a control).
• MCF10A cells overexpressing ErbB2/HER-2/neu (stronger cell-cell contact, different morphology).
• MCF10A cells overexpressing 14-3-3$\xi$ (lowered expression of cell-cell junctional markers).
• In addition, cell-cell adhesion was weakened in the MCF10A vector cells through the addition of calcium chelation.

Based on the observations of the previous experiments, additional analysis was performed on the data from the first experiment:

• Analysis was performed to observe whether intercellular stresses are cooperative over large distances. This was expected since the collective migration appeared to be coordinated across the collective.
• Another stage of analysis was performed to determine whether there existed a physical analog of the cooperative cellular motions to be found in glassy systems

## Results

Figure 2. Image of the RPME and MDCK cell lines using optical microscope and MSM techniques. Note the distribution of stress in the monolayer and its lack of homogeneity.

Experiment 1 - Observations

One of the first observations made during the experiments was that the stress mappings were severely heterogeneous. This aspect of the stress was ever prevalent at all points in time, and the persistent nature suggested to the authors of some underlying mechanics of cell migration were at play.

The distribution of the local shear and normal stresses were both rather "rugged", in that their spatial variation was comparable in magnitude to the spatial mean values. However the shear stresses were systematically less than local normal stresses. In addition there was found to be a very strong correlation between the isotropy of the stress (when $\sigma_{max} = \sigma_{min}\,\!$), and the orientation of this stress.

Figure 3. Plot of ellipsoids overlaid onto optical image of cell lines. Ellipsoid is plotted with the major axis corresponding to local $\sigma_{max}$ and minor axis to local $\sigma_{min}$. The red arrows indicate direction of the cell migration. Notice there is strong correlation between the two.

Another pattern between the stress orientation and the cell migration direction was also observed. This pattern is particularly evident when a plot of the orientation of the principle stresses is overlaid with cell migration direction as in Figure 3. Just by observation there appears to be some relationship between the alignment of the two directions, however how strong this alignment appears to vary from region to region on the same monolayer.

From this observation it was then noticed that the orientation of the cell body, cell migration direction and maximal principle stress were highly correlated in spite of the independence of their measurements. This appeared to be particularly true in regions of high stress anisotropy.

Experiment 1 - Analysis

It was thus proposed that the maximum local shear stress, given by $\mu = (\sigma_{max}-\sigma_{min})/2\,\!$, would be the quantitative representation of the stress anisotropy. The various regions in the cell monolayer were rank-ordered into quintiles based on $\mu$. The alignment angle between the local maximal principal stress and the local cell migration velocity, $\phi$,was measured for each of these regions. This information was then used to construct a cumulative probability distribution function $\bar{P}(\phi)$; if perfect alignment occurs then all angles $\phi$ would be zero, yielding a step function in probability (0->1). Thus the higher $\bar{P}(\phi)$ is at lower angles, the stronger the alignment.

Figure 4. Plot of the constructed cumulative probability function for the alignment of orientations of local maximal principle stress ad local cell migration velocity. Different colored lines indicate different shear stress quintiles. Upper plot is for RPME cell line, lower plot is for MDCK cell line.

Plotting the results in Figure 4 shows that although there is not perfect correlational alignment, the effect is certainly significant, thus indicating the validity of the observation that such a relationship between the maximal principle stress direction and the cell migration direction.

Figure 5. Plot of the constructed cumulative probability function for the alignment of orientations of local maximal principle stress ad local cell migration velocity for both experimental sets of data. Displayed at the lines for the highest shear stress quintiles, thus demonstrating the greatest amount of alignment in the entire monolayer for each cell line.

Experiment 2 - Observations

It was noted that because of the dependence of the cell migration direction upon the orientation of the principle maximal stresses it was believed that the strength of the cell-cell interactions must have some influence upon this correlation. ErbB2 cells were observed to still move consistently in alignment with the maximum principle stress, however 14-3-3$\xi$ cell lines (which have a decreased expression of cell-cell junctional markers) had very little alignment, if any. This can clearly be seen in the combined cumulative probability distribution plot in Figure 5.

Additionally the cell-cell contacts of the MCF10A vector were weakened through the addition of calcium chelation. This caused a decrease in the strength of the alignment described previously. When the growth medium was returned to normal, the alignment returned to it's regular state. However when E-cadherin antibodies were introduced this reversibility disappeared. The results of this part of the experiment is illustrated in Figure 6.
Figure 6. Plot of the constructed cumulative probability function for the MCF10A cell line modified with calcium chelation and E-cadherin antibodies.

Thus this experiment highlights the importance of the ability of cells to interact and transfer stresses across their interfaces in order for this alignment between maximal principle stress and cell migration.

## Discussion & Conclusions

Further analysis into the cooperativity of the stress revealed that several characteristics were similar to that of glassy systems. In a similar fashion to glassy systems, where particles undergo cooperative motions, the cells 'push' cooperatively by essentially linking together in a collective manner. Eventually this effect causes the individual particles to become trapped by it's neighbor, forming clusters. This increases with increasing system density, up to a limit where eventually the entire system becomes virtually frozen, or like a glass. The cell monolayer appeared to exhibit this similar dynamic, however what the biological significance of this analog is not completely understood. In particular the link between the mechanical intercellular forces and the heterogeneous dynamics is undetermined.

However the importance of this study is the fact that MSM has allowed scientists for probe further into the mechanical details of cell migration for the first time. Interesting observations that require further investigation include the unexpected heterogeneity of the stress distributions, as well as the original of this Plithotaxy, and the reason for the similarities of the glassy dynamics observed in the cell monolayer. The significance isn't that it has answered questions, but allowed for more questions to be asked about this important model system.

## The Soft Matter Connection

This is most clearly relevant to the aspect of surface forces in soft matter physics. This study not only describes a new biological phenomena but highlights the extreme importance of considering these forces in as complete a form as possible. By ignoring the intercellular forces one would essentially ignore a massive gap in the understanding of the dynamics of cell migration. As the authors have noted in the publication, it was impossible to derive any of the collective effects they observed by the consideration of the properties of independent cells. It was only through the careful measurement and observation of the cell monolayer were they able to discover Plithotaxy, a property only observed through the interactions of many cells and the cooperative effect of the stresses distributed along each cell membrane.