Negative viscosity and nonlinear elasticity of muscle cross-bridges

Negative viscosity is found in active fibrillar insect flight muscle when it is stretched, and this nonlinear phenomenon of ‘stretch activation’ allows the muscle to perform oscillatory mechanical work. We show that stretch activation may be a consequence of quite simple cross-bridge kinetics. In the first place, we consider an elementary but instructive two-state model in which cross-bridge attachment depends on stretching a series spring by thermal activation. This model exhibits a mechanical yield point, and the elastic properties are nonlinear. In particular, we show that the two-state system becomes more lossy and unstable as the yield point is approached, although the loss remains positive, so the system cannot perform oscillatory work. A three-state model incorporating tilting of the attached cross-bridge represents the next step towards a more realistic cross-bridge model. Attachment and detachment at the start of the power stroke are treated as in the two-state model, and we assume that tilting is also thermally activated in a manner similar to that suggested by Huxley and Simmons. Detachment at the end of the power stroke is assumed to be completely irreversible, and it is therefore this one non-equilibrium step which is coupled to the ATP hydrolysis that drives the cross-bridge cycle. This simple three-state model displays many of the characteristics of fibrillar insect flight muscle.