Mathematical theory of molecular motors and a new approach for uncovering motor mechanism

Molecular motors operate in an environment dominated by thermal fluctuations. A molecular motor may produce an active force at the reaction site to directly move the motor forward. Alternatively a molecular motor may generate a unidirectional motion by rectifying thermal fluctuations. In this case, the chemical reaction establishes free energy barriers to block the backward fluctuations. The effect of the chemical reaction on the motor motion can be represented by the motor potential profile (rectifying barrier and/or active driving force). Different motor mechanisms are characterised by different motor potential profiles. The mathematical theory and properties of molecular motors are discussed and a mathematical framework is developed for extracting the motor potential profile from measured time series of motor position. As an example. we discuss the binding zipper model for the F1 ATPase. which was motivated mainly by the fact that the motor potential profile of the ATPase is nearly a constant slope.