Dynamics of travelling helicity fronts in bacterial flagella

Abstract

Twenty years ago the experiments of Hotani revealed that flagellar polymorphism (the ability of bacterial flagellar filaments to take on different quaternary structures, specifically helices of different handedness and pitch) can be generated by fluid stresses of the same magnitude as those that occur during natural swimming. Experimental work including the recent crystallization of flagellin, as well as theoretical studies, show how the packing properties and underlying bistability of flagellin may give rise to different static structures. Hotani's experiments showed dynamic nucleation and propagation of domains of opposing handedness on a single flagellum. Here we present the first theory to explain this phenomenon, which is of great relevance to the study of the bundling-unbundling transition in run-and-tumble behaviour of free-swimming bacteria. Our model, based entirely on measurable, physical properties of flagella, bridges the gap between protein-scale statics and cell-scale dynamics. We generate simulations of flagellar motion under fluid stress that exhibit nucleation rates and transition speeds in quantitative agreement with experiment.