Geometry of flexible filament cohesion: Better contact through twist?

TL;DR

This paper investigates how filament flexibility and helical geometry influence cohesive interactions, revealing universal preferences for non-zero helical skew and geometric limits in filament contact.

Contribution

It introduces two theoretical models of flexible filament cohesion considering helical geometry, highlighting the role of twist in filament interactions.

Findings

Universal preference for non-zero helical skew in filament cohesion

Cohesion approaches a geometric limit in the vanishing interaction range

Different interaction potentials lead to distinct filament stability regimes

Abstract

Cohesive interactions between filamentous molecules have broad implications for a range of biological and synthetic materials. While long-standing theoretical approaches have addressed the problem of inter-filament forces from the limit of infinitely rigid rods, the ability of flexible filaments to deform intra-filament shape in response to changes in inter-filament geometry has a profound affect on the nature of cohesive interactions. In this paper, we study two theoretical models of inter-filament cohesion in the opposite limit, in which filaments are sufficiently flexible to maintain cohesive contact along their contours, and address, in particular, the role played by helical-interfilament geometry in defining interactions. Specifically, we study models of featureless, tubular filaments interacting via 1) pair-wise Lennard-Jones (LJ) interactions between surface elements and 2) depletion-induced filament binding stabilized by electrostatic surface repulsion. Analysis of these models reveals a universal preference for cohesive filament interactions for non-zero helical skew, and further, that in the asymptotic limit of vanishing interaction range relative to filament diameter, the skew-dependence of cohesion approaches a geometrically defined limit described purely by the close-packing geometry of twisted tubular filaments. We further analyze non-universal features of the skew-dependence of cohesion at small-twist for both potentials, and argue that in the LJ model the pair-wise surface attraction generically destabilizes parallel filaments, while in the second model, pair-wise electrostatic repulsion in combination with non-pairwise additivity of depletion leads to a meta-stable parallel state.