Mathematical simulation of muscle crossbridge cycle and force-velocity relationship

¹ University of British Columbia

^* To whom correspondence should be addressed. E-mail: cseow{at}mrl.ubc.ca.

Submitted on June 30, 2006
Revised on July 27, 2006
Accepted on 15 August 2006

	Abstract

Muscle contraction underlies many essential functions such as breathing, heart beating, locomotion, regulation of blood pressure and airway resistance. Active shortening of muscle is the result of cycling of myosin crossbridges that leads to sliding of myosin filaments relative to actin filaments. In this study, we have developed a computer program that allows us to alter the rates of transitions between any crossbridge-states in a stochastic cycle. The crossbridge-states within the cycle are divided into six attached (between myosin crossbridges and actin filaments) states and one detached state. The population of crossbridges in each of the states is determined by the transition rates throughout the cycle; differential equations describing the transitions are set up as a cyclic matrix. A method for rapidly obtaining steady-state exact solutions for the cyclic matrix has been developed to reduce computation time and avoid divergence problem associated with numerical solutions. In the 7-state model, two power strokes are assumed for each crossbridge cycle, one before the release of inorganic phosphate, and one after. The characteristic hyperbolic force-velocity relationship observed in muscle contraction can be reproduced by the model. Deviation from the single hyperbolic behavior at low velocities can be mimicked by allowing the rate of crossbridge-attachment to vary with velocity. The effects of [ATP], [ADP], and [Pi] are simulated by changing transition rates between specific states. The model has revealed new insights on how the force-velocity characteristics are related to the state transitions in the crossbridge cycle.

Key Words: cyclic matrix, mechanics of contraction, muscle model, steady-state solution