Dynamics of a bacterial flagellum under reverse rotation

TL;DR

This study models the polymorphic dynamics of bacterial flagella during reverse rotation using an extended Kirchhoff free energy framework, revealing how energy landscape variations influence flagellar states and dynamics.

Contribution

It introduces a detailed energy landscape model to analyze flagellar polymorphism and demonstrates limitations in generating certain intermediate states.

Findings

Flagellum exhibits multiple dynamical states depending on energy parameters.

Tuning the free energy landscape alone cannot produce the full sequence of polymorphic states.

Proposes an ad hoc method to replicate observed polymorphic sequences in bacteria.

Abstract

To initiate tumbling of an E. coli, one of the helical flagella reverses its sense of rotation. It then transforms from its normal form first to the transient semicoiled state and subsequently to the curly-I state. The dynamics of polymorphism is effectively modeled by describing flagellar elasticity through an extended Kirchhoff free energy. However, the complete landscape of the free energy remains undetermined because the ground state energies of the polymorphic forms are not known. We investigate how variations in these ground state energies affect the dynamics of a reversely rotated flagellum of a swimming bacterium. We find that the flagellum exhibits a number of distinct dynamical states and comprehensively summarize them in a state diagram. As a result, we conclude that tuning the landscape of the extended Kirchhoff free energy alone cannot generate the intermediate full-length semicoiled state. However, our model suggests an ad hoc method to realize the sequence of polymorphic states as observed for a real bacterium. Since the elastic properties of bacterial flagella are similar, our findings can easily be extended to other peritrichous bacteria.