The cell as a material

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Original entry: Nefeli Georgoulia, APPHY 226, Spring 2009

Second Entry: Nick Chisholm, AP 225, Fall 2009

Overview

Authors: K.E. Kasza, A.C.Rowat, J. Liu, T.A. Angelini, C.P. Brangwynne, G.H. Koenderink & D.A. Weitz

Source: Current Opinion in Cell Biology, Vol 19, 101-107, (2007)

Soft Matter key words: rheology, elastic behavior, viscous behavior, prestress

Abstract

Fig.1 : K.E. Kasza, A.C.Rowat, J. Liu, T.A. Angelini, C.P. Brangwynne, G.H. Koenderink & D.A. Weitz

This review paper summarizes the advances made in probing and recording the material properties of cells. Experiments in this field can be divided in two broad categories: the shearing of purified cytoskeletal filament networks and the probing of whole cells. Results indicate that the cell is a viscoelastic material. Rheology of semi-flexible biopolymer networks reveals stress-stiffening behavior: an increase in applied stress increases the network's elastic modulus (figure1). This is thought to be a consequence of the 'pulling out' of filament thermal fluctuations at high stress. Although purified filament networks have a linear elasticity much lower than cells, prestressed networks of such filaments display an elasticity similar to that of cells. According to the authors, this suggests that cells themselves are prestressed into a non-linear regime, possibly by molecular motors such as myosin. Cellular prestress has been experimentally confirmed by traction force microscopy, and it is thought to enable cellular response to external mechanical stimuli. In the last part of the paper, all this information is integrated into two competing models that account for cell mechanical behavior.


Soft Matter Snippet

The two models suggested to account for cell mechanical behavior are of soft matter interest:

1) The tensegrity model: According to tensegrity, some components of the cells are under tension, and these forces are balanced by other components of the cell which are under compression. Stress fibers (actin-myosin fibrillar assemblies) are thought to be the tensile components, while microtubules have been shown to bear compressive cellular loads. In fact, figure 2 demonstrates how cutting a stress fiber with laser nanoscissors causes it to snap back. The tensegrity model highlights the role of prestress in determining cell elasticity. It was architecturally inspired and parallels the mechanical behavior of cells to that of buildings!

Fig.2 : K.E. Kasza, A.C.Rowat, J. Liu, T.A. Angelini, C.P. Brangwynne, G.H. Koenderink & D.A. Weitz

2) The soft glassy rheology model: This model suggests that the cell is a soft solid composed of an elastic solid with some non-thermal relaxation processes, such as those generated by molecular motors. The predicted mechanical response displays a characteristic timescale dependance that is set by the effective 'temperature' of these non-thermal fluctuations. Experimental evidence that justify this model include applying large shear stresses on cells by magnetic bead cytometry. In these experiments magnetic beads are attached on the cell membrane and the application of stress induces cell softening, much like the shear-induced melting that characterizes soft glasses.




General Information

Authors: Karen E Kasza, Amy C Rowat, Jiayu Liu, Thomas E Angelini, Clifford P Brangwynne, Gijsje H Koenderink and David A Weitz

Publication: Current Opinions in Cell Biology 19, 101-107 (2007)

Soft Matter Keywords

Viscoelastic, polymer, rheology, cross-linking, prestressed, cell

Summary

This review paper begins by stating that a cell is a viscoelastic material whose dynamic and functional role within a tissue can only be understood if one has an understanding of its material properties. In particular, in vitro studies of model networks of the components of the cytoskeleton and direct studies of the mechanical properties of cells are discussed. The authors state that one of the most common in vitro studies is on filamentous actin (F-actin), which is one of the cytoskeletal filaments, and discuss the different results of probing techniques on this particular system (in particular, stress-stiffening behavior). Methods of measuring cell mechanics are explored, along with their use in attempting to model cellular mechanics. The key experimental data provides evidence that the cell is viscoelastic with nonlinear mechanics, and that internal prestress plays an important role in cell mechanics. A common theme of the review paper is the link between in vitro studies of the components of the cytoskeleton to direct studies of the mechanical properties of cells, stating that both will be required to provide unique insight into the origins of cellular behavior. In conclusion, the authors remind the reader that we are only now beginning to understand some of the mechanical properties of cells.

Soft Matter Discussion

Firstly, an important definition is prestress: to introduce internal stresses that counteract the affect of applied force.

As one would suspect, cells are soft machines. Thus, the mechanical behavior of cells is of a soft matter nature, and the probing techniques for this behavior are also of interest.

Reconstituted Cellular Networks

  • The most common reconstituted cellular networks are networks of F-actin. F-actin is a semi-flexible (not completely flexible, nor completely rigid) polymer. The individual filaments are soft enough to have shape fluctuations which are induced by thermal fluctuations, and these shape fluctuations cause a change in their elasticity for short extensions of the filaments. At higher extensions, the thermal fluctuations are "pulled out", which causes a large increase in elasticity; effectively, this is stiffening. The key point here is that with a large applied stress, the elastic modulus of the F-actin increases dramatically due to nonlinear rheology, and this corresponds to a stiffening of the F-actin. Figure 1 shows this applied shear stress to strain relationship in graphical form.
Figure 1. Taken from [1].

Measurements of Cell Mechanics

  • Atomic Force Microscopy (AFM): Performs micro-indentation to probe local viscoelastic properties of a single cell.
  • Magnetic Twisting Cytometry (MTC): Applies a local stress to a specific region of a cell by twisting or pulling a small magnetic bead attached to the cell. Then, the resulting displacement is measured using video microscopy or laser particle tracking. This measurement is reliant on the nature of the bead placement on the cell, so it is not a very robust measurement of elastic and viscous properties.
  • Micropipette Aspiration Coupled to Confocal Microscopy: Used to probe the nucleus of the cell, and have shown that the nucleus acts like an elastic shell.
  • Probe Particles: In this technique, probe particles are sent to specific locations in the cell to determine local behavior. The interpretation of these results for determining the elastic constant is based on the idea that particle motion is driven only by thermal fluctuations, however the authors argue that recent work has shown that this is too simplistic of a model: motor proteins and other non-equilibrium processes also play a role.
  • Traction Force Microscopy: A substrate whose deformation is measurable balances the contractile stress in the cell in order to measure the prestress in the cytoskeleton.

In the review paper, these experimental techniques are not discussed extensively, however, if interested in any of them the paper provides references to papers that do discuss them extensively. As you may notice, each of these techniques shares a similar characteristic: they measure a deformation in response to a force. When all of the data is combined, certain traits are noticed: at timescales shorter than a fraction of a second, the effects reflect those of individual filaments and elasticity increases; at timescales between a fraction of a second and several tens of seconds, the cell is primarily elastic; at timescales greater than thirty seconds, cell remodeling leads to additional relaxation.

Modeling Cell Mechanics

  • Tensegrity Model: The basic underlying principle is that the components of the cell that are under tension have their forces balanced by other components that are under compression. In Figure 2a, one can see stress fibers that have been cut and are snapping back. In Figure 2b, microtubulues are shown to carry compressive loads; these compressive loads can be held because the cytoskeleton structurally reinforces the microtubules. Clearly, this model particularly emphasizes the effect of prestress in determining elasticity.
Figure 2. Taken from [1].
  • Soft Glassy Rheology (SGR): This model attempts to describe cell elasticity by proposing that the material of the cell is composed of an elastic solid with some relaxation process driven by non-thermal stress fluctuations. MTC measurements (described above) confirm this model holds but only at intermediate timescales. By applying a large shear stress using MTC, the cell temporarily softens (much like the shear-induced melting and rejuvenation that is typical for soft glasses).

Reference

[1] Karen E Kasza, Amy C Rowat, Jiayu Liu, Thomas E Angelini, Clifford P Brangwynne, Gijsje H Koenderink and David A Weitz, "The cell as a material," Current Opinions in Cell Biology 19, 101-107 (2007)