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

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