Disordered biopolymer filament bundles: Topological defects and kinks

TL;DR

This paper investigates how biopolymer filament bundles can develop long-lived localized kinks due to topological defects, with analytical, numerical, and experimental insights into stabilization mechanisms and transitions.

Contribution

It introduces new mechanisms for kink stabilization in biopolymer bundles, highlighting topologically protected states and analyzing their transition to straight configurations.

Findings

Kinks can be stabilized by filament length differences, dislocations, or braiding.

High cross-link concentration leads to topologically protected kinked states.

Transition from kinked to straight bundles is characterized analytically and numerically.

Abstract

Bundles of stiff filaments are ubiquitous in the living world, found both in the cytoskeleton and in the extracellular medium. These bundles are typically held together by smaller cross-linking molecules. We demonstrate analytically, numerically and experimentally that such bundles can be kinked, i.e., have localized regions of high curvature that are long-lived metastable states. We propose three possible mechanisms of kink stabilization: a difference in trapped length of the filament segments between two cross links; a dislocation where the endpoint of a filament occurs within the bundle, and the braiding of the filaments in the bundle. At a high concentration of cross links, the last two effects lead to the topologically protected kinked states. Finally, we explore numerically and analytically the transition of the metastable kinked state to the stable straight bundle.