A constitutive law for cross-linked actin networks by homogenization techniques

TL;DR

This paper develops a homogenized macroscopic constitutive law for a 2D actin network based on microscopic elastic properties, analyzing stability and implications for actin-driven motion.

Contribution

It introduces a homogenization-based method to derive a macroscopic model from microscopic actin network properties, including stability analysis.

Findings

Thin networks are linearly stable.

Thick networks become unstable beyond a critical thickness.

Stability depends on microscopic elastic constants ratio.

Abstract

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.