Molecular model of muscle contraction

Molecular model of muscle contraction

T. A. J. Duke*

Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE, United Kingdom

Communicated by Andrew Huxley, University of Cambridge, Cambridge, United Kingdom (received for review February 13, 1998)

Abstract

A quantitative stochastic model of the mechanochemical cycle of myosin, the protein that drives muscle contraction, is proposed. It is based on three premises: (i) the myosin head incorporates a lever arm, whose equilibrium position adjusts as each of the products of ATP hydrolysis dissociates from the nucleotide pocket; (ii) the chemical reaction rates are modified according to the work done in moving the arm; and (iii) the compliance of myosin’s elastic element is designed to permit many molecules to work together efficiently. The model has a minimal number of parameters and provides an explanation, at the molecular level, of many of the mechanical and thermodynamic properties of steadily shortening muscle. In particular, the inflexion in the force–velocity curve at a force approaching the isometric load is reproduced. Moreover, the model indicates that when large numbers of myosin molecules act collectively, their chemical cycles can be synchronized, and that this leads to stepwise motion of the thin filament. The oscillatory transient response of muscle to abrupt changes of load is interpreted in this light.

Footnotes

↵ * To whom reprint requests should be addressed. e-mail: td18{at}cam.ac.uk.
↵ ** e.g., after a step change that brings T ₁ to zero, fewer than 25% of myosin molecules have a bound head that changes conformation.
↵ † The typical time between chemical events is τ _chem = 1/Nk _bind. After an individual molecular transition, the filaments return to mechanical equilibrium by sliding through a displacement of order d/N in a time of order τ _visc = ηL/NK, where η is the viscosity of the surrounding fluid and L is the filament length.
↵ ‡ It should be noted, however, that filament compliance is not negligible (24, 25), so the relation between stiffness and number of attached cross-bridges is not a direct one.
↵ § Note that series compliance effectively reduces the spring constant K and thereby the value of ɛ₁. Thus, in single-molecule experiments, elimination of extra compliance is essential for the detection of effects associated with the condition ɛ₁ > 1, such as inhibition of the power stroke.
↵ ‖ Interestingly, a 3.5-nm movement on ADP release has been detected in smooth muscle myosin (35), suggesting stronger regulation of the proportion of bound heads in this motor protein.
↵ ¶ Previous theoretical models (14–18) solve differential equations for the probability distributions under the assumption that a steady state exists and consequently preclude the generation of stepwise motion by the mechanism described here, but might permit transient damped oscillations on other sets of assumptions.
ABBREVIATIONS:

M,

myosin;

A,

actin