Chemomechanical Coupling of Molecular Motors: Thermodynamics, Network Representations, and Balance Conditions

Molecular motors are considered that convert the chemical energy released from the hydrolysis of adenosine triphosphate (ATP) into mechanical work. Such a motor represents a small system that is coupled to a heat reservoir, a work reservoir, and particle reservoirs for ATP, adenosine diphosphate (ADP), and inorganic phosphate (P). The discrete state space of the motor is defined in terms of the chemical composition of its catalytic domains. Each motor state represents an ensemble of molecular conformations that are thermally equilibrated. The motor states together with the possible transitions between neighboring states define a network representation of the motor. The motor dynamics is described by a continuous-time Markov process (or master equation) on this network. The consistency between thermodynamics and network dynamics implies (i) local and nonlocal balance conditions for the transition rates of the motor and (ii) an underlying landscape of internal energies for the motor states. The local balance conditions can be interpreted in terms of constrained equilibria between neighboring motor states; the nonlocal balance conditions pinpoint chemical and/or mechanical nonequilibrium.