Elasto-plastic response of reversibly crosslinked biopolymer bundles

TL;DR

This paper models the mechanical response of reversibly crosslinked biopolymer bundles, revealing how crosslink stiffness influences brittle and ductile failure modes, hysteresis, and long-term plastic deformation.

Contribution

It introduces an analytical model that characterizes failure modes and phase diagrams for biopolymer bundles with reversible crosslinks, emphasizing the role of crosslink stiffness.

Findings

Brittle failure involves sudden crosslink unbinding and loss of integrity.

Ductile failure maintains bundle integrity through crosslink reorganization.

Force-deflection curves show hysteresis and long-lasting plastic deformation.

Abstract

We study the response of F-actin bundles to driving forces through a simple analytical model. We consider two filaments connected by reversibly bound crosslinks and driven by an external force. Two failure modes under load can be defined. \textit{Brittle failure} is observed when crosslinks suddenly and collectively unbind, leading to catastrophic loss of bundle integrity. During \textit{ductile failure}, on the other hand, bundle integrity is maintained, however at the cost of crosslink reorganization and defect formation. We present phase diagrams for the onset of failure, highlighting the importance of the crosslink stiffness for these processes. Crossing the phase boundaries, force-deflection curves display (frequency-dependent) hysteresis loops, reflecting the first-order character of the failure processes. We evidence how the introduction of defects can lead to complex elasto-plastic relaxation processes, once the force is switched off. Depending on, both, the time-scale for defect motion as well as the crosslink stiffness, bundles can remain in a quasi-permanent plastically deformed state for a very long time.