Theoretical Prediction of Run Speed Distribution for a Molecular Motor

Processive molecular motors are large proteins that “walk” along filaments in a cell, transforming chemical energy into mechanical work. These microscopic motors behave, at least qualitatively, like macroscopic walking machines. The dynamics and stability of macroscopic walkers are understood by analysis of “stride functions” (Poincaré maps from one step to the next). We show that molecular motors have linear, probabilistic stride functions. Using these functions, we derive expressions for three measurable distributions: step period, run length and average run speed. The former two distributions are well known, the latter is new. We validate our calculation with simulations of a realistic model for Myosin Va (a molecular motor). The parameters of the run speed distribution specify both the run-length and step period distributions. As step-period distributions are difficult to measure under physiologically relevant conditions, this technique provides new information. Finally, we discuss the effects of variable step size and experimental error.