Second-Chance Signal Transduction is a Model for Bacterial Flagellar Switching and Tropomyosin-Based Motility

Abstract

The reversal of flagellar motion (switching) results from the interaction between a switch complex of the flagellar rotor and a torque-generating unit (motor unit) of the stator. To explain the steeply cooperative switching response to ligand, present models propose allosteric interaction between subunits of the rotor but have yet to address the reaction that stimulates a motor unit to reverse directions. An individual motor unit could exist in ground and excited states corresponding to counterclockwise and clockwise rotation, respectively. After a passing ligand-bound switch complex excites a motor unit, the independent decay rate of the excited state determines the probability that a fresh switch complex will reach the dwell site owing to the steady-state rotation of the rotor before the motor unit returns to ground state. Here, we derive an analytical expression, based on our muscle model, for the energy coupling between a switch complex and a motor unit in the stator complex of a flagellum, and demonstrate that it accounts for the cooperative switching response without the need for allostery. This analytic function becomes the Hill equation as a special case. We found that the analytical result can be reproduced by simulation if the motion of the rotor provides a motor unit with a second chance to remain excited and the outputs from multiple independent motor units are constrained to a single all-or-none event. A motor unit and switch complex represent switch and reader components of a mathematically defined signal transduction mechanism in which energy coupling is driven by steady-state and regulated by stochastic ligand binding. By homology, tropomyosin and myosin are modeled in a second chance process as reader and switch respectively. This work was supported by NSF grant MCB-0508203.