A three-state model for oscillation in muscle: Sinusoidal analysis

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Abstract
The crossbridge mechanism leading to oscillation in insect flight muscle is studied theoretically based on a three-state model proposed by Nishiyamaet al. [Biochim. biophys. Acta460, 523–36 (1977)]. Skeletal muscle as well as insect flight muscle shows oscillatory contraction. We demonstrate this oscillatory contraction in muscle by choosing proper rate constants among the three states of the model. It is established that our model gives out not only Hill's force-velocity relation but also other mechanical properties of skeletal muscle. The model is then compared with two types of experiment by Kawai & Brandt [J. Musc. Res. Cell Motility1, 279–303 (1980)] and by Steiger & Rüegg [Pflügers Arch.307, 1–21 (1969)]. Kawai & Brandt obtained the Nyquist plot showing the relation between the phase shift and the amplitude of tension change in response to sinusoidal length changes at various frequencies. Steiger & Rüegg studied the power output and ATPase activity at various frequencies of the length change. Our theoretical results are in good agreement with the results of these two experiments. To determine the crossbridge mechanism which produces the positive power output, spatio-temporal crossbridge distributions in the three states are calculated. It is shown that, after the stretching phase of sinusoidal change in muscle length, the delayed rise of tension is caused by attachment of crossbridges to the active state via the preactive state while the delayed fall is caused by detachment from the active state after release. To obtain the oscillatory property it is not necessary to assume that stretch in muscle length increases the attaching rate as originally proposed by Thorson & White [Biophys. J.9, 360–90 (1969)].

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