Biophysical Journal 9: 759-780 (1969)
© 1969 the Biophysical Society

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Isometric Muscle Contraction and the Active State

An Analog Computer

ABSTRACT

From Sandow's excitation-contraction coupling hypothesis and reasonable assumptions I obtain the kinetics of the active state, (AS), and thence, via empirical equations for series elastic and contractile components for frog sartorius around 20°C, the tension, P, and dP/dt vs. time. Assumptions: (a) Rate of Ca⁺² injection is proportional to the Ca gradient, and a permeability, which increases from zero to a limit as the membrane potential rises above a threshold. (b) Released Ca⁺² is bound by the "muscle machinery," M, and removed by a carrier pump. (c) The AS is proportional to the concentration of Ca-M. The kinetic pattern depends mainly upon the mechanism; the time scale was fixed by the amount of Ca⁺² injected. Depending upon the time course and repetition pattern chosen for the action potential, I obtain P and dP/dt, that agree well with experiment, for normal, potentiated, and summed twitches, tetani, and tension redevelopment after a quick release. Upon excitation the AS rises rapidly to 88%, declines thereafter in twitches, but rises slowly in unfused fashion toward 100% in tetani. The knee in dP/dt marks the first maximum in the AS. Potentiators should raise it in tetani as well as in twitches. Velocity and dP/dt show a much higher fusion frequency than P. The model integrates diverse observations. It may be tested by measuring tension and intramyofibrillar Ca⁺² under controlled depolarization.