Linear rheology of reversibly cross-linked biopolymer networks

TL;DR

This paper models the frequency-dependent rheological response of biopolymer networks with reversible cross-links, revealing complex behaviors influenced by linker dynamics and providing insights into biological network mechanics.

Contribution

It introduces a simple model for reversible cross-linking in biopolymer networks and analyzes its impact on rheological properties through simulations.

Findings

A low frequency peak in the loss modulus appears with long linker lifetimes.

The storage modulus decays from its plateau, indicating additional relaxation.

Reversible and irreversible linkers' ratio controls network relaxation behavior.

Abstract

We suggest a simple model for reversible cross-links, binding and unbinding to/from a network of semiflexible polymers. The resulting frequency dependent response of the network to an applied shear is calculated via Brownian dynamics simulations. It is shown to be rather complex with the timescale of the linkers competing with the excitations of the network. If the lifetime of the linkers is the longest timescale, as is indeed the case in most biological networks, then a distinct low frequency peak of the loss modulus develops. The storage modulus shows a corresponding decay from its plateau value, which for irreversible cross-linkers extends all the way to the static limit. This additional relaxation mechanism can be controlled by the relative weight of reversible and irreversible linkers.