A Simple Theory of Motor Protein

A three-state stochastic model of motor protein Qian, Biophys. Chem., (1997)] is further developed to illustrate the relationship between the external load on an individual motor protein in aqueous solution with various ATP concentration and its steady-state velocity. A wide variety of dynamic motor behavior are obtained from this simple model. For the particular case of free-load translocation being the most unfavorable step within the hydrolysis cycle, the load-velocity curve is quasi-linear, v=v max = (c F=Fmax ? c)=(1 ? c), in contrast to the hyperbolic relationship proposed by A.V. Hill for macroscopic muscle. Signiicant deviation from the linearity is expected when the velocity is less than 10% of its maximal (free load) value-a situation under which the processivity of motor diminishes and experimental observations are less certain. We then investigate the dependence of load-velocity curve on ATP (ADP) concentration. It is shown that the free load v max exhibits a Michaelis-Menten like behavior, and the isometric F max increases linearly with ln((ATP]//ADP]). However, the quasi-linear region is independent of the ATP concentration, yielding an apparently ATP-independent maximal force below the true isometric force. Finally, the heat production as function of ATP concentration and external load are calculated. In simple terms and solved with elementary algebra, the present model provides an integrated picture of biochemical kinetics and mechanical energetics of motor proteins.