A mesoscopic model for helical bacterial flagella.

Filaments of bacterial flagella are perfect tubular stackings polymerized out of just one kind of building block: the flagellin protein. Surprisingly, they do not form straight tubes, but exhibit a symmetry-breaking coiling into helical shapes which is essential for their biological function as cell "propeller''. The co-existence of two conformational states for flagellin within the filament is believed to be responsible for the helical shapes by producing local misfit which results in curvature and twist. In this paper, we present a coarse-grained description with an elastic energy functional for the filament derived from its microscopic structure. By minimising this functional we can answer the question of spatial distribution of flagellin states which is crucial for the observed coupling of curvature and twist. Our approach extends a classical theory of Calladine, which had to assume this spatial distribution from the outset.