Common basis for cellular motility

Motility is characteristic of life, but a common basis for movement has remained to be identified. Diverse systems in motion shift between two states depending on interactions that turnover at the rate of an applied cycle of force. Although one phase of the force cycle terminates the decay of the most recent state, continuation of the cycle of force regenerates the original decay process in a recursive cycle. By completing a cycle, kinetic energy is transformed into probability of sustaining the most recent state and the system gains a frame of reference for discrete transitions having static rather than time-dependent probability. The probability of completing a recursive cycle is computed with a Markov chain comprised of two equilibrium states and a kinetic intermediate. Given rate constants for the reactions, a random walk reproduces bias and recurrence times of walking motor molecules and bacterial flagellar switching with unrivaled fidelity. INTRODUCTION The time a bacterial flagellar motor rotates in the counterclockwise (CCW) and clockwise (CW) direction is a random variable that depends on ligand binding (1). If the regulation were owing to the decay of a simple equilibrium switch, time intervals of CCW and CW rotation (recurrence times) would be exponentially distributed (1-3), i.e. having a decreasing failure rate (DFR, 4). However, recurrence times are found to have a gamma distribution (1), which exhibits increasing failure rate (IFR, 4). IFR suggests that each switch is a sequence of hidden Markov steps (1-3).