Theory of Crosslinked Bundles of Helical Filaments: Intrinsic Torques in Self-Limiting Biopolymer Assemblies

TL;DR

This paper presents a theoretical model showing how crosslinking proteins induce intrinsic torques in helical biopolymer bundles, leading to self-limiting sizes and superhelical twisting, with implications for understanding biofilament assembly.

Contribution

It introduces a coarse-grained model revealing how crosslinker-induced torques influence the structure and size regulation of helical filament bundles.

Findings

Crosslinking generates intrinsic torques causing bundle supercoiling.

A critical crosslinker density leads to thermodynamically preferred bundle radius.

Bundle twist and size are feedback-regulated by crosslinker stiffness.

Abstract

Inspired by the complex influence of the globular crosslinking proteins on the formation of biofilament bundles in living organisms, we study and analyze a theoretical model for the structure and thermodynamics of bundles of helical filaments assembled in the presence of crosslinking molecules. The helical structure of filaments, a universal feature of biopolymers such as filamentous actin, is shown to generically frustrate the geometry of crosslinking between the "grooves" of two neighboring filaments. We develop a coarse-grained model to investigate the interplay between the geometry of binding and mechanics of both linker and filament distortion, and we show that crosslinking in parallel bundles of helical filaments generates {\it intrinsic torques}, of the type that tend to wind bundle superhelically about its central axis. Crosslinking mediates a non-linear competition between the preference for bundle twist and the size-dependent mechanical cost of filament bending, which in turn gives rise to feedback between the global twist of self-assembled bundles and their lateral size. Finally, we demonstrate that above a critical density of bound crosslinkers, twisted bundles form with a thermodynamically preferred radius that, in turn, increases with a further increase in crosslinking bonds. We identify the {\it stiffness} of crosslinking bonds as a key parameter governing the sensitivity of bundle structure and assembly to the availability and affinity of crosslinkers.