Markov Process of Muscle Motors

TL;DR

This paper models muscle molecular motor behavior using a Markov process, deriving an exact solution for the system's nonlinear dynamics in the limit of many motors, enhancing understanding of muscle mechanics.

Contribution

It introduces a Markov process model for muscle motors and provides an exact solution for the nonlinear equations governing their collective behavior.

Findings

Derived an exact solution for the nonlinear system

Analyzed the dynamics of bound and unbound motor states

Provided insights into muscle force generation mechanisms

Abstract

We study a Markov random process describing a muscle molecular motor behavior. Every motor is either bound up with a thin filament or unbound. In the bound state the motor creates a force proportional to its displacement from the neutral position. In both states the motor spend an exponential time depending on the state. The thin filament moves at its velocity proportional to average of all displacements of all motors. We assume that the time which a motor stays at the bound state does not depend on its displacement. Then one can find an exact solution of a non-linear equation appearing in the limit of infinite number of the motors.