The Effects of Stator Compliance, Backs Steps, Temperature, and Clockwise Rotation on the Torque-Speed Curve of Bacterial Flagellar Motor

TL;DR

This paper presents a comprehensive model of bacterial flagellar motor dynamics, explaining experimental observations of torque-speed behavior, temperature dependence, and effects of mechanical properties through a thermally activated stepping mechanism and power-stroke potentials.

Contribution

The authors develop a novel model incorporating back-stepping and power-stroke potentials to accurately reproduce and explain various experimental behaviors of bacterial flagellar motors.

Findings

Model reproduces observed torque-speed curves for both clockwise and counterclockwise rotation.

Temperature dependence of motor speed is explained by thermally activated stepping rates.

Changing interaction potentials alters the shape of the torque-speed curve.

Abstract

Rotation of a single bacterial flagellar motor is powered by multiple stators tethered to the cell wall. In a "power-stroke" model the observed independence of the speed at low load on the number of stators is explained by a torque-dependent stepping mechanism independent of the strength of the stator tethering spring. On the other hand, in models that depend solely on the stator spring to explain the observed behavior, exceedingly small stator spring constants are required. To study the dynamics of the motor driven by external forces (such as those exerted by an optical tweezer), back-stepping is introduced when stators are driven far out of equilibrium. Our model with back-stepping reproduces the observed absence of a barrier to backward rotation, as well the behaviors in the high-speed negative-torque regime. Recently measured temperature dependence of the motor speed near zero load (Yuan & Berg 2010 Biophys J) is explained quantitatively by the thermally activated stepping rates in our model. Finally, we suggest that the general mechanical properties of all molecular motors (linear and rotary), characterized by their force(torque)-speed curve, can be determined by their power-stroke potentials and the dependence of the stepping rates on the mechanical state of the motor (force or speed). The torque-speed curve for the clockwise rotating flagellar motor has been observed for the first time recently (Yuan et al. 2010 PNAS). Its quasi-linear behavior is quantitatively reproduced by our model. In particular, we show that concave and convex shapes of the torque-speed curve can be achieved by changing the interaction potential from linear to quadratic form. We also show that reversing the stepping rate dependence on force (torque) can lead to non-monotonicity in the speed-load dependency.