Cooperative stator assembly of bacterial flagellar motor for autonomous torque regulation

Cooperativity has a central place in biological regulation, providing robust and highly-sensitive regulation. The bacterial flagellar motor (BFM) implements autonomous torque regulation by the nonequilibrium structure of the stators; the stators assemble at high load and disperse at low load. It would be natural to suppose that the stator packing is affected by stator-stator interaction. However, the cooperativity among the stators has rarely been explored. Here, we evaluated the energetics and kinetics of the stator assembly by combining dynamic load control of a single motor and the trajectory analysis based on statistical mechanics. We demonstrate that the BFM exploits the dynamic cooperativity of the stator binding for the autonomous torque regulation. The cooperative assembly leads to a discontinuous phase transition and hysteresis, which may implement torque regulation with high sensitivity and robustness.