Theory of asynchronous oscillations in loaded insect flight muscle

Abstract

A quantitative theory of the oscillatory behavior of loaded insect flight muscle is presented and is derived from the sliding filament model by calculating its nonlinear response to length changes out to third order. Oscillations may occur when the resonant frequency of the muscle and its load lie within the range of the negative second loop of the Nyquist plot for linear a.c. stiffness. They also require the total d.c. stiffness to exceed a threshold value, which may explain why these oscillations are not normally observed in other muscles. The tension-length loops and waveforms, the oscillatory power output, and their variation with load damping are in good agreement with observations. The rise in ATPase hydrolysis rate with oscillatory power is predicted, but the effect is sensitive to details of the sliding filament model. The model also shows a slow growth of oscillations after Ca2+ activation. The even slower rate of decay after deactivation is attributed to cooperative binding in the absence of calcium. Also, the tension responses to large imposed a.c. length changes agree with experiment and show figure-of-eight loops at higher frequencies. Stretch activation effects will require a modification of the theory but are not essential because these oscillations arise from the instability indicated by the negative second loop of the Nyquist plot, which is universal to all striated muscle.