Thermodynamic inference in molecular motors: A martingale approach

Molecular motors are in charge of almost every process in the life cycle of cells, such as protein synthesis, DNA replication, and cell locomotion, hence being of crucial importance for understanding the cellular dynamics. However, given their size scales on the order of nanometers, direct measurements are rather challenging, and the information that can be extracted from them is limited. In this work, we propose strategies based on martingale theory in stochastic thermodynamics to infer thermodynamic properties of molecular motors using a limited amount of available information. In particular, we use two recent theoretical results valid for systems arbitrary far of equilibrium: the integral fluctuation theorem at stopping times and a family of bounds to the maximal excursions of entropy production. The potential of these strategies is illustrated with a simple model for the F1-ATPase rotary molecular motor, where our approach is able to estimate several quantities determining the thermodynamics of the motor, such as the rotational work of the motor performed against an externally applied force or the effective environmental temperature.