Shape selection of surface-bound helical filaments: biopolymers on curved membranes

TL;DR

This study develops a theoretical model to analyze how intrinsically-helical biopolymers change shape when bound to curved membranes, revealing their conformations are highly sensitive to surface curvature and interaction strength.

Contribution

It introduces a new theoretical framework combining numerical and asymptotic analysis to understand filament shape adaptation on curved surfaces, highlighting the role of elastic twist-bending coupling.

Findings

Filaments unwind from native twist with increased surface interaction.

Conformations are critically sensitive to surface curvature.

Biopolymers can respond to geometric cues for regulation.

Abstract

Motivated to understand the behavior of biological filaments interacting with membranes of various types, we study a theoretical model for the shape and thermodynamics of intrinsically-helical filaments bound to curved membranes. We show filament-surface interactions lead to a host of non-uniform shape equilibria, in which filaments progressively unwind from their native twist with increasing surface interaction and surface curvature, ultimately adopting uniform-contact curved shapes. The latter effect is due to non-linear coupling between elastic twist and bending of filaments on anisotropically-curved surfaces, such as the cylindrical surfaces considered here. Via a combination of numerical solutions and asymptotic analysis of shape equilibria we show that filament conformations are critically sensitive to the surface curvature in both the strong- and weak-binding limits. These results suggest that local structure of membrane-bound chiral filaments is generically sensitive to the curvature-radius of the surface to which it is bound, even when that radius is much larger than the filament intrinsic pitch. Typical values of elastic parameters and interaction energies for several prokaryotic and eukaryotic filaments indicate that biopolymers are inherently very sensitive to the coupling between twist, interactions and geometry and that this could be exploited for regulation of a variety of processes such as the targeted exertion of forces, signaling and self-assembly in response to geometric cues including the local mean and Gaussian curvatures.