The mechanochemistry of molecular motors

A theory of molecular motors is presented that explains how the energy released in single chemical reactions can generate mechanical motion and force. In the simplest case the fluctuating movements of a motor enzyme are well described by a diffusion process on a two-dimensional potential energy surface, where one dimension is a chemical reaction coordinate and the other is the spatial displacement of the motor. The coupling between chemistry and motion results from the shape of the surface, and motor velocities and forces result from diffusion currents on this surface. This microscopic description is shown to possess an equivalent kinetic mechanism in which the rate constants depend on externally applied forces. By using this equivalence we explore the characteristic properties of several broad classes of motor mechanisms and give general expressions for motor velocity versus load force for any member of each class. We show that in some cases simple plots of 1/velocity vs. 1/concentration can distinguish between classes of motor mechanisms and may be used to determine the step at which movement occurs.