Modeling the bacterial flagellum by an elastic network of rigid bodies

Bacteria such as Escherichia coli propel themselves by rotating a bundle of helical filaments, each driven by a rotary motor embedded in the cell membrane. Each filament is an assembly of thousands of copies of the protein flagellin which assumes two different states. We model the filament by an elastic network of rigid bodies that form bonds with one another according to a scheme suggested by Namba and Vondervistz (1997 Q. Rev. Biophys. 30 1-65) and add additional binding sites at the inner part of the rigid body. Our model reproduces the helical parameters of the 12 possible polymorphic configurations very well. We demonstrate that its energetical ground state corresponds to the normal helical form, usually observed in nature, only when inner and outer binding sites of the rigid body have a large axial displacement. This finding correlates directly to the elongated shape of the flagellin molecule. An Ising Hamiltonian in our model directly addresses the two states of the flagellin protein. It contains an external field that represents external parameters which allow us to alter the ground state of the filament.