A simple theory of motor protein kinetics and energetics. II

A three-state stochastic model of motor protein [Qian, Biophys. Chem. 67 (1 997) pp. 263-267] is further developed to illustrate the relationship betwe en the external load on an individual motor protein in aqueous solution wit h various ATP concentrations and its steady-state velocity. A wide variety of dynamic motor behavior are obtained from this simple model. For the part icular case of free-load translocation being the most unfavorable step with in the hydrolysis cycle, the load-velocity curve is quasi-linear, upsilon/u psilon(max) = (C-F/Fmax - c)/(1 - c), in contrast to the hyperbolic relatio nship proposed by A.V. Hill for macroscopic muscle. Significant deviation f rom the linearity is expected when the velocity is less than 10% of its max imal (free-load) value - a situation under which the processivity of motor diminishes and experimental observations are less certain. We then investig ate the dependence of load-velocity curve on ATP (ADP) concentration. It is shown that the free load upsilon(max) exhibits a Michaelis-Menten like beh avior, and the isometric F-max increases linearly with In([ATP]/[ADP]). How ever, the quasi-linear region is independent of the ATP concentration, yiel ding an apparently ATP-independent maximal force below the true isometric f orce. Finally, the heat production as a function of ATP concentration and e xternal load are calculated. In simple terms and solved with elementary alg ebra, the present model provides an integrated picture of biochemical kinet ics and mechanical energetics of motor proteins. (C) 2000 Elsevier Science B.V. All rights reserved.