From Conformational Spread to Allosteric and Cooperative models of E. coli flagellar motor

Escherichia coli swims using flagella activated by rotary motors. The direction of rotation of the motors is indirectly regulated by the binding of a single messenger protein. The conformational spread model has been shown to accurately describe the equilibrium properties as well as the dynamics of the flagellar motor. In this paper we study this model from an analytic point of view. By exploiting the separation of timescales observed in experiments, we show how to reduce the conformational spread model to a coarse-grained, cooperative binding model. We show that this simplified model reproduces very well the dynamics of the motor switch.