The theory of sliding filament models for muscle contraction. III. Dynamics of the five-state model

Abstract

The five-state model derived in the last paper is shown to provide a unified description of most dynamical behaviour of striated muscle, with a set of rate constants in accord with in-vitro values. It predicts several observed phenomena beyond the scope of older models. Rapid binding of M.ADP.Pi to actin generates a high-frequency tail in the Nyquist plot for AC stiffness, which is only weakly dependent on contraction velocity. Known effects of changes in Ca2+ level are predicted if Ca2+ activates only the phosphate-release step, e.g. in the relaxed-state there is substantial stiffness at high frequencies and weak stiffness at low frequencies. Under partial activation the tension drops with increasing extension speed, and Nyquist plots suggest that the reverse phosphate step should be unaffected by Ca2+. Lowering the phosphate level increases tension and also the first two loop amplitudes of the Nyquist plot. The model also yields an improved tension-velocity characteristic, acceptable length-step response, and simulates Brenner & Eisenberg's "stop and stretch" experiment which is shown to be closely related to isometric activation. Oscillatory length response to small tension steps is shown to be a general feature of any model whose AC stiffness can be fitted by a three-term Kawai formula. The model must be enlarged to include the rigor-state, and to describe the effects of variations in ATP and ADP levels correctly.