  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. Stochastic,
nonequilibrium thermodynamic interpretations of the mathematical equations and
their solutions are presented. Some relevant mathematics, mainly in the field
of stochastic processes, are discussed.
