Bacterial flagellar bundling and unbundling via polymorphic transformations

Abstract

Multiflagellated bacteria such as E. coli exploit the polymorphic transformations of helical flagella to explore their fluid environment. In these bacteria, a sequence of polymorphic helical forms appears consecutively as the cell "runs" and "tumbles." During a run, the molecular motors that drive the twirling flagella spin counterclockwise, and the flagella form a normal flagellar bundle. Reversing one or more of these motors, from counterclockwise to clockwise, initiates a tumble by inducing shape transformations of the associated filaments, from normal to semicoiled and then to curly 1 forms. The next run begins when the motors switch back to counterclockwise rotations. This causes the flagella to revert from curly 1 back to normal forms. This paper investigates the dynamics of elastic flagella when one or two flagella undergo a full cycle of polymorphic transformations using a computational method in which the flagellar motors are tethered in space and connected via flexible hooks to the filaments. We describe the flagellar filaments and their hooks as elastic rods adopting Kirchhoff rod theory and their hydrodynamic interaction using a generalization of the method of regularized Stokeslets. We also investigate the role of a compliant hook in flagellar bundling.