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

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.

12 pages, 8 figures

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Cited by in corpus (9)

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• Non-local fluctuation correlations in active gels
• Stiffening of Red Blood Cells Induced by Disordered Cytoskeleton Structures: A Joint Theory-experiment Study
• Elastic response of filamentous networks with compliant crosslinks
• Stress relaxation through crosslink unbinding in cytoskeletal networks
• Nonlinear Poisson effect in affine semiflexible polymer networks
• Sulfo-SMCC Prevents Annealing of Taxol-Stabilized Microtubules In Vitro
• Filament turnover is essential for continuous long range contractile flow in a model actomyosin cortex