Several Issues in Modeling Molecular Motors

Protein motors play a central role in many cell functions. Understanding the operating principles of molecular motors is crucial to comprehending intracellular protein transport and cell motility. Due to the small size and the negligible inertia of molecular motors, the motor motion is damped by high viscous friction and is subject to large thermal excitations form the surrounding fluid environment. These properties determine that molecular motors behave drastically different from macroscopic motors. There are many levels of modeling for molecular motors: from simple chemical kinetic models with a few discrete states to all atom molecular dynamics simulations. Models at each level represent a compromise between being able to accommodate all aspects of motor operation and being easy to analyze/compute. All these models of different levels are valuable and are contributing to the understanding of the operating mechanism of molecular motors. In most of our studies of molecular motors, we adopt a mathematical framework of an intermediate level. In this framework, the major conformational changes of the motor are treated as continuous motions and changes in the occupancy state at the catalytic sites are modeled as discrete Markov transitions. In this framework, a motor system is described by a system of coupled Fokker-Planck equations, in which each equation corresponds to a chemical occupancy state. In this review, we discuss several issues in modeling molecular motors under this mathematical framework: (1) detailed balance and breaking of detailed balance; (2) motor potential profile and reconstruction of motor potential profile; (3) thermodynamic efficiency, Stokes efficiency and other efficiencies; and (4) numerical solutions of motor systems. In this review, we also examine the derivation of randomness parameter. We like to make it clear that this review is far from being comprehensive. The issues discussed are simply the ones we encounter in our modeling of molecular motors.