Molecular motors: thermodynamics and the random walk

The biochemical cycle of a molecular motor provides the essential link betw een its thermodynamics and kinetics. The thermodynamics of the cycle determ ine the motor's ability to perform mechanical work, whilst the kinetics of the cycle govern its stochastic behaviour. We concentrate here on tightly c oupled, processive molecular motors, such as kinesin and myosin V, which hy drolyse one molecule of ATP per forward step. Thermodynamics require that, when such a motor pulls against a constant load f, the ratio of the forward and backward products of the rate constants for its cycle is exp[-(DeltaG + u(0)f)/kT], where -DeltaG is the free energy available from ATP hydrolysi s and u(0) is the motor's step size. A hypothetical one-state motor can the refore act as a chemically driven ratchet executing a biased random walk. T reating this random walk as a diffusion problem, we calculate the forward v elocity upsilon and the diffusion coefficient D and we find that its random ness parameter r is determined solely by thermodynamics. However, real mole cular motors pass through several states at each attachment site. They sati sfy a modified diffusion equation that follows directly from the rate equat ions for the biochemical cycle and their effective diffusion coefficient is reduced to D-upsilon2-tau, where tau is the time-constant for the motor to reach the steady state. Hence, the randomness of multistate motors is redu ced compared with the one-state case and can be used for determining iota. Our analysis therefore demonstrates the intimate relationship between the b iochemical cycle, the force-velocity relation and the random motion of mole cular motors.