A unit-cell approach to the nonlinear rheology of biopolymer solutions

We propose a nonlinear extension of the standard tube model for semidilute solutions of freely-sliding semiflexible polymers. Non-affine filament deformations at the entanglement scale, the renormalisation of direct interactions by thermal fluctuations, and the geometry of large deformations are systematically taken into account. The stiffening response predicted for athermal solutions of stiff rods1 is found to be thermally suppressed. Instead, we obtain a broad linear response regime, supporting the interpretation of shear stiffening at finite frequencies in polymerised actin solutions2,3 as indicative of coupling to longitudinal modes. We observe a destabilizing effect of large strains (∼100%), suggesting shear banding as a plausible explanation for the widely observed catastrophic collapse of in vitrobiopolymer solutions, usually attributed to network damage. In combination with friction-type interactions, our analysis provides an analytically tractable framework to address the nonlinear viscoplasticity of biological tissue on a molecular basis.