Dynamics of bacterial flagella: bundling and polymorphism
School of Engineering, Brown University
(October 14, 2003 3:00 PM - 4:00 PM)
E. coli and Salmonella swim using several flagella, each of which consist of a rotary motor, a universal joint known as the hook, and a helical filament which acts a propeller. For propulsion, the filaments wrap into a bundle when the motors turn counter-clockwise. We built a scale model to study the interplay of hydrodynamics and elasticity in this process. Our model shows how the filaments wrap around each other, and allows us to determine which characteristic timescales govern bundling. The filament is normally left-handed in the absence of external stress, but undergoes mechanical phase transitions to other helical states ("polymorphs") in response to external torque. The filament is made of identical flagellin protein subunits which are organized into eleven protofilaments which wind around the filament. We develop an effective theory in which the flagellin subunits and their connections along the protofilaments are modeled with a non-convex potential. A helical spring represents the other connections of the subunits, and introduces a twist-stretch coupling and an element of frustration in our model. We solve for the ground states and the phase diagram for filament shapes.