Cross-link governed dynamics of biopolymer networks

TL;DR

This paper introduces a model for biopolymer networks with transient cross-linking, explaining their complex stress relaxation and frequency-dependent shear modulus through simulations and experiments.

Contribution

The study provides a combined simulation and analytical model that links microscopic cross-linker unbinding to macroscopic rheological behavior in biopolymer networks.

Findings

Broad spectrum of relaxation times from a single microscopic timescale

Power-law dependence of shear modulus on frequency

Quantitative agreement with actin-$\alpha$-Actinin-$4$ network experiments

Abstract

Cytoskeletal networks of biopolymers are cross-linked by a variety of proteins. Experiments have shown that dynamic cross-linking with physiological linker proteins leads to complex stress relaxation and enables network flow at long times. We present a model for the mechanical properties of transient networks. By a combination of simulations and analytical techniques we show that a single microscopic timescale for cross-linker unbinding leads to a broad spectrum of macroscopic relaxation times, resulting in a weak power-law dependence of the shear modulus on frequency. By performing rheological experiments, we demonstrate that our model quantitatively describes the frequency behavior of actin network cross-linked with $\alpha$-Actinin-$4$ over four decades in frequency.