A theory of tension fluctuations due to muscle cross-bridges

We present an analytical theory for the spectrum of tension fluctuations due to muscle cross-bridges. The theory is based upon the Langevin theory of brownian motion, and is illustrated using a simplified three-state model for the cross-bridge cycle, which is intended to model cross-bridges in fibrillar insect flight muscle. Langevin white-noise sources, representing fluctuations in the net transition rates for each step in the cycle, are introduced into the rate equations, and their strengths are adjusted to give the correct mean-square fluctuations in the occupation probabilities. The Langevin theory shows that the noise is closely related to the elastic properties of cross-bridges, and it also shows in detail how each step in the cross-bridge cycle contributes differently to the noise spectrum. We find that the total noise increases with filament displacement. For small filament displacements, the noise is dominated by the power stroke and by dissociation at the end of the cycle. These contributions increase in the region of stretch activation, whilst at larger displacements, where the cross-bridge becomes locked in the strong-binding state, the noise is much larger and is dominated by attachment and detachment at the beginning of the cycle. The cross-bridge properties in this regime are strongly affected by free inorganic phosphate. Finally, we show how the noise spectrum is modified by the inclusion of a series compliance representing a practical force transducer.