Effective medium approach for stiff polymer networks with flexible cross-links

TL;DR

This paper develops an effective medium theory to understand the nonlinear elasticity of stiff biopolymer networks with flexible cross-links, highlighting entropic stiffening effects and matching experimental rheology data.

Contribution

It introduces a novel effective medium model that captures the nonlinear elastic behavior of actin networks with flexible cross-linkers, emphasizing entropic stiffening mechanisms.

Findings

Nonlinear elastic response begins at strains proportional to cross-linker length.

Differential modulus scales linearly with stress in the stiffening regime.

Model predictions align well with experimental rheology measurements.

Abstract

Recent experiments have demonstrated that the nonlinear elasticity of in vitro networks of the biopolymer actin is dramatically altered in the presence of a flexible cross-linker such as the abundant cytoskeletal protein filamin. The basic principles of such networks remain poorly understood. Here we describe an effective medium theory of flexibly cross-linked stiff polymer networks. We argue that the response of the cross-links can be fully attributed to entropic stiffening, while softening due to domain unfolding can be ignored. The network is modeled as a collection of randomly oriented rods connected by flexible cross-links to an elastic continuum. This effective medium is treated in a linear elastic limit as well as in a more general framework, in which the medium self-consistently represents the nonlinear network behavior. This model predicts that the nonlinear elastic response sets in at strains proportional to cross-linker length and inversely proportional to filament length. Furthermore, we find that the differential modulus scales linearly with the stress in the stiffening regime. These results are in excellent agreement with bulk rheology data.