Nonlinear elasticity of composite networks of stiff biopolymers with flexible linkers

Motivated by recent experiments showing novel rheological properties of biopolymer networks, we develop an effective medium theory for rigid filaments cross-linked by flexible linkers. Specifically, we treat such a network as a collection of randomly oriented stiff polymers mechanically connected by highly compliant cross-linkers to an elastic continuum, which effectively represents the surrounding network. For cross-links with a finite compliance, we find a smooth cross-over between two distinct elastic regimes. Starting from a linear elastic regime dominated by cross-link elasticity, the network begins to stiffen significantly as the cross-links reach full compliance. We extend this model to a self-consistent one, in which the effective medium reflects the non-linear elastic properties of the cross-linked network. This model yields a cross-over to a nonlinear regime that is consistent with recent experimental studies of the cellular cytoskeletal polymer F-actinwith filamin cross-links$^1$. \par\vspace*{0.2cm} $1.$ \hspace*{0.25cm} ML Gardel, F Nakamura, J Hartwig JC Crocker, TP Stossel, DA Weitz, \textbf{103}, 1762 Proc. Nat. Ac. Sci. (2006).