The mathematical theory of molecular motor movement and chemomechanical energy transduction

The mathematical formulation of the model for molecular movement of single motor proteins driven by cyclic biochemical reactions in an aqueous environment leads to a drifted Brownian motion characterized by coupled diffusion equations. In this article, we introduce the basic notion for the continuous model and review some asymptotic solutions for the problem. (For the lattice model see [17,47].) Stochastic, non-equilibrium thermodynamic interpretations of the mathematical equations and their solutions are presented. Some relevant mathematics, mainly in the field of stochastic processes, are discussed.