Dynamics of switching at stall reveals non-equilibrium mechanism in the allosteric regulation of the bacterial flagellar switch

Abstract

Behavior of the bacterial flagellar motor depends sensitively on the external loads it drives. Motor switching, which provides the basis for the run-and-tumble behavior of flagellated bacteria, has been studied for motors under zero to high loads, revealing a non-equilibrium effect that is proportional to the motor torque. However, behavior of the motor switching at stall (with maximum torque) remains unclear. An extrapolation from previous studies would suggest maximum non-equilibrium effect for motor switching at stall. Here, we stalled the motor using optical tweezers and studied the motor switching with a high time resolution of about 2 ms. Surprisingly, our results showed exponentially distributed counterclockwise (CCW) and clockwise (CW) intervals, indicating that motor switching at stall is probably an equilibrium process. Combined with previous experiments at other loads, our result suggested that the non-equilibrium effect in motor switching arises from the asymmetry of the torque generation in the CCW and CW directions. By including this non-equilibrium effect in the general Ising-type conformation spread model of the flagellar switch, we consistently explained the motor switching over the whole range of load conditions. We expect to see similar mechanism of non-equilibrium regulation in other molecular machines.