Direct tests of muscle cross-bridge theories: predictions of a Brownian dumbbell model for position-dependent cross-bridge lifetimes and step sizes with an optically trapped actin filament.
Force and displacement events from a single myosin molecule interacting with an actin filament suspended between optically trapped beads (Finer, J. T., R. M. Simmons, and J. A. Spudich. 1994. Nature. 368:113-119) can be interpreted in terms of a generalized cross-bridge model that includes the effects of Brownian forces on the beads. Steady-state distributions of force and displacement can be obtained directly from a generalized Smoluchowski equation for Brownian motion of the actin-bead "dumbbell," and time series from Monte Carlo simulations of the corresponding Langevin equation. When the frequency spectrum of Brownian motion extends beyond cross-bridge transition rates, the inverse mean lifetimes of force/displacement pulses are given by cross-bridge rate constants averaged over a Boltzmann distribution of Brownian noise. These averaged rate constants reflect the strain-dependence of the rate constants for the stationary filament, most faithfully at high trap stiffness. Hence, measurements of the lifetimes and displacements of single events as a function of the resting position of the dumbbell can provide a direct test of different cross-bridge theories of muscle contraction. Quantitative demonstrations are given for Huxley models with 1) faster binding or 2) slower dissociation at positive cross-bridge strain. Predictions for other models can be inferred from the averaging procedure.
Smith
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DA
The Randall Institute, King's College, London WC2B 5RL, United Kingdom. dave@muscle.rai.kcl.ac.uk
D000199:Actins / Q000502:physiology*; D000465:Algorithms; D000818:Animals; D001696:Biomechanical Phenomena; D055592:Biophysical Phenomena; D001703:Biophysics; D008954:Models, Biological; D020409:Molecular Motor Proteins / Q000502:physiology; D009010:Monte Carlo Method; D009119:Muscle Contraction / Q000502:physiology*; D009218:Myosins / Q000502:physiology
D000199:Actins; D020409:Molecular Motor Proteins; D009218:Myosins