Cell-scale Models of Mechanosensation



There are clear differences between cells adhered to soft and cells adhered to stiff surfaces.  On stiff surfaces, cells spread out and form stable connections to the surface (adhesion complexes), while their cytoskeleton contains numerous stress fibers, cross-linked bundles of actin that include the molecular motor non-muscle myosin II.  Conversely, on soft surfaces, cells are more rounded, adhesions are fewer and more transient, and few if any stress fibers form (see Fig 1).  It is thought that the interaction between the substrate, the adhesion complexes, stress fibers (including myosin) and the cytoskeleton are responsible for these stiffness-dependent adaptations.  Thus, any model for cell mechanosensation must capture each of these systems and their interactions.




Figure 1: Cells, drawn from Fig. 1b of Geiger, Spatz and Bershadsky (2009) [1].  The soft surface has a Young's modulus of 10kPa, the stiff surface a Young's modulus of 100 kPa.  On stiffer surfaces, cells form more adhesion complexes and stress fibers.  These differences involve the interaction of three different systems: adhesion complexes, the cytoskeleton and the molecular motor myosin.










Reference: Walcott, S, Sun, S. X., A mechanical model of actin stress fiber formation and substrate elasticity sensing in adherent cells. 
Proceedings of the National Academy of Sciences, Volume 107, pages 7757-62, 2010.  PDF


In collaboration with Sean Sun, I developed a model that replicates surface stiffness dependent differences in cytoskeleton organization.  The model is based on a theory that describes the behavior of two filaments or sheets that approach each other in the presence of proteins that transiently bind one to the other.  In this system, the cross-linking proteins oppose relative motion of the two filaments or sheets.  In the limit that this motion is slow the cross-linkers provide a viscous drag, with a drag constant that can be related to various molecular-mechanical properties of the system (see theory and also [2]).


When this model is applied to adhesion complexes, the drag constant depends on surface stiffness, becoming smaller on soft surfaces.  Therefore, for a constant force, adhesions slide faster on soft surfaces.  Since myosin force decreases as sliding speed increases, myosin applies smaller forces on the cytoskeleton when a cell is on a soft surface.  Applying the drag model to the cytoskeleton, maximal drag occurs when overlapping actin filaments are aligned.  Consequently, as force is applied to the cytoskeleton, actin molecules aggregate and align in a direction parallel to that force (see Fig. 2).  The larger the force, the faster this aggregation occurs.  As actin is constantly being broken down, if stress fibers are not formed rapidly, they will be broken down before they can form.  Therefore, on stiff surfaces, adhesions slide slowly, myosin generates large forces, and actin aggregations (stress fibers) form quickly before they can be broken down.  Alternatively, on soft surfaces, adhesions slide quickly, myosin generates small forces, and stress fibers do not form because they are broken down before they can form.  These results are qualitatively in agreement with experimental observations.  The model, and ideas therein, can also describe how cells react when placed on a surface of variable stiffness [3] and how cells spread [4].


The model demonstrates a potential mechanism whereby cells can sense their mechanical environment.  That this mechanism is based in molecular mechanics serves as a contrast to more biochemically-based explanations.  The challenge of future work is to determine what mechanisms cells actually use. 





[1] Geiger, B.,  Spatz, J.P., and Bershadsky, A. D., Environmental sensing through focal adhesions, Nature Reviews Molecular Cell Biology, Volume 10, pages 21-23, 2009.


[2] Leibler, S., and Huse, D. A., Porters and rowers: a unified stochastic model of motor proteins. Journal of Cell Biology, Volume 121, pages 1357-1368, 1993.


[3] Harland, B, Walcott, S., Sun, S. X., Adhesion dynamics and durotaxis in migrating cells. Physical Biology, Volume 8, Article number 015011, 2011.


[4] Krzyszczyk, P. and Wolgemuth, C. W., Mechanosensing can result from adhesion molecule dynamics, Biophysical Journal, Volume 101, pages L53-L55, 2011.




Ben Harland

Sean Sun