Second Chance Mechanism Explains Dwell Time Distributions of Myosin and Dynein

Abstract

We reproduced experimental dwell time distributions of head and tail labeled dynein and myosin V at low and high [ATP] with a continuous time Markov chain (CTMC) that we developed using second chance mechanics (SCM) (doi: 10.1371/ journal.pone.0041098). SCM is a non-equilibrium kinetic model. If work is done by cycles of force acting on protein interactions, SCM determines the probability that the displaced interaction is restored before the proteins separate. For a two headed molecule with a chemo-mechanical cycle, one phase of the cycle displaces a head from its site of interaction while another phase provides a second chance for it to bind. A minimum CTMC consists of three observed states of the motor, i.e. unbound (C), bound by two heads (m1), and bound with one head (m2). The transition between m1 and m2 has unitary probability and marks a physical displacement. Other state transitions have stochastic probabilities determined by the time derivative of the CTMC at steady-state given a set of transition rates. Derived probabilities form the initial distribution of a Markov matrix based on the CTMC. We simulated the stationary probability distribution of the Markov matrix by a Monte Carlo scheme of CTMC. Each step of the CTMC includes a waiting time based on catalytic rates of bound or unbound motor domains and the waiting times of each step are exponentially distributed. The dwell times of the simulated CTMC are gamma distributed because a minimum of two steps is required to complete a dwell period. Hence, the gamma distributed dwell times of myosin V and dynein may be explained by a series of delays, i.e.one to wait for favorable binding of the unbound head and another to wait for the displacement of a bound head.