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

TL;DR

This paper extends the tube model for biopolymer solutions to include nonlinear effects, revealing insights into shear stiffening, destabilization, and potential shear banding phenomena relevant to biological tissues.

Contribution

It introduces a nonlinear unit-cell model accounting for filament deformation, thermal fluctuations, and large strains, advancing understanding of biopolymer rheology beyond linear approximations.

Findings

Thermal suppression of stiffening in athermal solutions

Broad linear response regime in polymerized actin

Large strain destabilization suggesting shear banding

Abstract

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 rods 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 solutions as indicative of coupling to longitudinal modes. We observe a destabilizing effect of large strains (about 100%), suggesting shear banding as a plausible explanation for the widely observed catastrophic collapse of in-vitro biopolymer 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.