用均匀化技术研究交联肌动蛋白网络的本构关系
A constitutive law for cross-linked actin networks by homogenization techniques
摘要：
受肌动蛋白驱动的微米大小的珠子的推进实验的启发，我们开发和研究一个最小的力学模型的刚性弹性细丝从圆柱体的表面生长的二维网络。从网络结构及其微观力学行为的离散模型出发，利用均匀化技术导出了宏观本构关系。我们计算了轴对称平衡态，并研究了它的线性稳定性依赖于微观力学性质。我们发现，薄网络是线性稳定的，而厚网络是不稳定的。稳定性变化的临界厚度取决于微观弹性常数的比值。随着网络厚度的增加，内部网络层上的压缩载荷的增加引起不稳定性。本文所采用的均质化方法结合更精细的微观模型可以作为研究聚合肌动蛋白网络演化和肌动蛋白驱动运动机制的基础。
英文摘要：
Inspired by experiments on the actin driven propulsion of micrometer sized beads we develop and study a minimal mechanical model of a two-dimensional network of stiff elastic filaments grown from the surface of a cylinder. Starting out from a discrete model of the network structure and of its microscopic mechanical behavior we derive a macroscopic constitutive law by homogenization techniques. We calculate the axisymmetric equilibrium state and study its linear stability depending on the microscopic mechanical properties. We find that thin networks are linearly stable, whereas thick networks are unstable. The critical thickness for the change in stability depends on the ratio of the microscopic elastic constants. The instability is induced by the increase in the compressive load on the inner network layers as the thickness of the network increases. The here employed homogenization approach combined with more elaborate microscopic models can serve as a basis to study the evolution of polymerizing actin networks and the mechanism of actin driven motion.
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