Mathematical simulation of muscle crossbridge cycle and force-velocity relationship

Chin, L., Yue, P., Feng, J. J. & Seow, C. Y.

Biophys. J. 91, 3653-3663 (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 developed a computer program that allowed us to alter the rates of transitions between any crossbridge states in a stochastic cycle. The crossbridge states within the cycle were divided into attached (between myosin crossbridges and actin filaments) and detached states. The population of crossbridges in each of the states was determined by the transition rates throughout the cycle; differential equations describing the transitions were set up as a cyclic matrix. A method for rapidly obtaining steady-state solutions for the cyclic matrix was developed to allow the computer to display results of simulation almost instantly; the immediate feedback was found very helpful in model development and refinement. In a 7-state model, two power strokes were assumed for each crossbridge cycle, one before phosphate release, and one after. The characteristic hyperbolic force-velocity relationship observed in muscle contraction was reproduced by the model. Deviation from the single hyperbolic behavior at low velocities was mimicked by allowing the rate of crossbridge attachment to vary with velocity. The effects of [ATP], [ADP], and [Pi] were simulated by changing transition rates between specific states in the cycle. The model has revealed new insights on how the force-velocity characteristics are related to the state transitions in the crossbridge cycle.