Weakly nonlinear rheology of transiently crosslinked biopolymer gels

TL;DR

This paper presents a theoretical study of how reversible crosslinking affects the linear rheological spectra of biopolymer gels, revealing bond breaking as a significant nonlinear effect even at small amplitudes.

Contribution

It introduces an analytical model predicting the absorption peak in rheological spectra of crosslinked biopolymer solutions, supported by numerical simulations, highlighting nonlinear bond-breaking effects.

Findings

Reversible crosslinking causes a distinct absorption peak in rheological spectra.

Bond breaking is a nonlinear, non-equilibrium effect significant at small amplitudes.

The model can help infer biochemical binding properties from rheological data.

Abstract

Recent experimental investigations have revealed a non-Maxwellian absorption pattern in the rheological spectra of actin gels, which was interpreted in terms of transient bonds. Here we examine the consequences of reversible crosslinking on the apparent linear spectra of biopolymer solutions theoretically. For a schematic model consisting of a reversibly crosslinked power-law fluid we obtain a simple analytical prediction for the position of the absorption peak, which is backed up by a numerical evaluation of the inelastic glassy wormlike chain model. This establishes bond breaking as a nonlinear non-equilibrium effect that can already be significant for very small driving amplitudes. Our results may be useful for inferring binding affinities and reaction rates of biochemical crosslinkers from rheological measurements of {\it in-vitro} reconstituted cytoskeletal gels.