Motor potential profile and a robust method for extracting it from time series of motor positions

Molecular motors are small, and, as a result, motor operation is dominated by high-viscous friction and large thermal fluctuations from the surrounding fluid environment. The small size has hindered, in many ways, the studies of physical mechanisms of molecular motors. For a macroscopic motor, it is possible to observe/record experimentally the internal operation details of the motor. This is not yet possible for molecular motors. The chemical reaction in a molecular motor has many occupancy states, each having a different effect on the motor motion. The overall effect of the chemical reaction on the motor motion can be characterized by the motor potential profile. The potential profile reveals how the motor force changes with position in a motor step, which may lead to insights into how the chemical reaction is coupled to force generation. In this article, we propose a mathematical formulation and a robust method for constructing motor potential profiles from time series of motor positions measured in single molecule experiments. Numerical examples based on simulated data are shown to demonstrate the method. Interestingly, it is the small size of molecular motors (negligible inertia) that makes it possible to recover the potential profile from time series of motor positions. For a macroscopic motor, the variation of driving force within a cycle is smoothed out by the large inertia.