Discrete elastic model for stretching-induced flagellar polymorphs

¹  Physics Department, Technical University Munich - 85748 Garching, Germany, EU
²  Yukawa Institute for Theoretical Physics, Kyoto Universiy - Kyoto, 606-8502, Japan

Corresponding author: hwada@yukawa.kyoto-u.ac.jp

Received: 5 February 2008
Accepted: 19 February 2008

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.