Yuval Janni, Safran Samuel A
Department of Materials and Interfaces, Weizmann Institute of Science, Rehovot, Israel.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Apr;87(4):042703. doi: 10.1103/PhysRevE.87.042703. Epub 2013 Apr 10.
Cells probe their mechanical environment and can change the organization of their cytoskeletons when the elastic and viscous properties of their environment are modified. We use a model in which the forces exerted by small, contractile acto-myosin filaments (e.g., nascent stress fibers in stem cells) on the extracellular matrix are modeled as local force dipoles. In some cases, the strain field caused by these force dipoles propagates quickly enough so that only static elastic interactions need be considered. On the other hand, in the case of significant energy dissipation, strain propagation is slower and may be eliminated completely by the relaxation of the cellular cytoskeleton (e.g., by cross-link dissociation). Here, we consider several dissipative mechanisms that affect the propagation of the strain field in adhered cells and consider these effects on the interaction between force dipoles and their resulting mutual orientations. This is a first step in understanding the development of orientational (nematic) or layering (smectic) order in the cytoskeleton. We use the theory to estimate the propagation time of the strain fields over a cellular distance for different mechanisms and find that in some cases it can be of the order of seconds, thus competing with the cytoskeletal relaxation time. Furthermore, for a simple system of two force dipoles, we predict that in some cases the orientation of force dipoles might change significantly with time, e.g., for short times the dipoles exhibit parallel alignment while for later times they align perpendicularly.
细胞会探测其力学环境，并且当环境的弹性和粘性特性发生改变时，它们能够改变细胞骨架的组织形式。我们使用一种模型，其中由小的、收缩性的肌动蛋白-肌球蛋白丝（例如干细胞中的新生应力纤维）施加在细胞外基质上的力被建模为局域力偶极。在某些情况下，由这些力偶极引起的应变场传播得足够快，以至于只需要考虑静态弹性相互作用。另一方面，在存在显著能量耗散的情况下，应变传播较慢，并且可能会因细胞骨架的松弛（例如通过交联解离）而完全消除。在此，我们考虑几种影响附着细胞中应变场传播的耗散机制，并研究这些机制对力偶极之间相互作用及其最终相互取向的影响。这是理解细胞骨架中取向（向列相）或分层（近晶相）有序结构发展的第一步。我们使用该理论来估计不同机制下应变场在细胞距离上的传播时间，发现某些情况下其可能达到秒量级，从而与细胞骨架的松弛时间相当。此外，对于由两个力偶极组成的简单系统，我们预测在某些情况下力偶极的取向可能会随时间发生显著变化，例如，在短时间内偶极呈现平行排列，而在稍后时间它们垂直排列。
