Mean First-Passage Time in the Stochastic Theory of Biochemical Processes. Application to Actomyosin Molecular Motor

Many studies performed in recent years indicate a rich stochastic dynamics of transitions between a multitude of conformational substates in native proteins. A slow character of this dynamics is the reason why the steady-state kinetics of biochemical processes involving protein enzymes cannot be described in terms of conventional chemical kinetics, i.e., reaction rate constants. A more sophisticated language of mean first-passage times has to be used. A technique of summing up the stochastic dynamics diagrams is developed, enabling a calculation of the steady-state fluxes for systems of enzymatic reactions controlled and gated by the arbitrary type stochastic dynamics of the enzymatic complex. For a single enzymatic reaction, it is shown that the phenomenological steady-state kinetics of Michaelis–Menten type remains essentially unaltered but the interpretation of its parameters needs substantial change. A possibility of dynamical rather then structural inhibition of enzymatic activity is supposed. Two coupled enzymatic cycles are studied in the context of the biologically important process of free energy transduction. The theoretical tools introduced are applied to elucidate the mechanism of mechanochemical coupling in actomyosin molecular motor. Relations were found between basic parameters of the flux-force dependences: the force stalling the motor, the degree of coupling between the ATPase and the mechanical cycles as well as the asymptotic turnover number, and the mean first-passage times in a random movement between the particular conformational substates of the myosin head. These times are to be determined within a definite model of conformational transition dynamics. The theory proposed, not contradicting the presently available experimental data, is capable to explain the recently demonstrated multiple stepping produced by a single myosin head during just one ATPase cycle.