Isometric muscle contraction and the active state: an analog computer study.

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 degrees 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.