The stochastic chemomechanics of the -ATPase molecular motor

We report a theoretical study of the F 1 -ATPase molecular rotary motor experimentally studied by R. Yasuda, H. Noji, M. Yoshida, K. Kinosita Jr., H. Itoh [Nature 410 (2001) 898]. The motor is modeled as a stochastic process for the angle of its shaft and the chemical state of its catalytic sites. The stochastic process is ruled by six coupled Fokker–Planck equations for the biased diffusion of the angle and the random jumps between the chemical states. The model reproduces the experimental observations that the motor proceeds by substeps and the rotation rate saturates at high concentrations of adenosine triphosphate or at low values of the friction coefficient. Moreover, predictions are made about the dependence of the rotation rate on temperature, and about the behavior of the F 1 motor under the effect of an external torque, especially, in the regime of synthesis of adenosine triphosphate.