Discrete elastic model for stretching-induced flagellar polymorphs

TL;DR

This paper presents a discrete elastic rod model that captures the reversible shape transformations of bacterial flagella under force, aligning well with experimental observations and revealing key mechanical behaviors.

Contribution

Introduces a novel discrete elastic model with two helical states and a spin variable to simulate flagellar polymorph transformations under tension.

Findings

Shape transitions driven by domain wall dynamics.

Critical force scales with model parameters.

Stretching rate affects elasticity and buckling behavior.

Abstract

Force-induced reversible transformations between coiled and normal polymorphs of bacterial flagella have been observed in recent optical-tweezer experiment. We introduce a discrete elastic rod model with two competing helical states governed by a fluctuating spin-like variable that represents the underlying conformational states of flagellin monomers. Using hybrid Brownian dynamics Monte-Carlo simulations, we show that a helix undergoes shape transitions dominated by domain wall nucleation and motion in response to externally applied uniaxial tension. A scaling argument for the critical force is presented in good agreement with experimental and simulation results. Stretching rate-dependent elasticity including a buckling instability are found, also consistent with the experiment.