MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

A mesoscopic model for helical bacterial flagella

Benjamin Friedrich


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 rods, 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.

lattice-rotation-model, bacterial flagella, polymorphism, multi-state control problem

Related publications

2006 Repository Open Access
Benjamin Friedrich

A mesoscopic model for helical bacterial flagella

In: Journal of mathematical biology, 53 (2006) 1, pp. 162-178