Perturbed equilibria of myosin binding in airway smooth muscle: Bond-length distributions, mechanics, and ATP metabolism

We carried out a detailed mathematical analysis of the effects of length fl uctuations on the dynamically evolving cross-bridge distributions, simulati ng those that occur in airway smooth muscle during breathing. We used the l atch regulation scheme of Hai and Murphy (Am. J. Physiol. Cell Physiol. 255 :C86-C94, 1988) integrated with Huxley's sliding filament theory of muscle contraction. This analysis showed that imposed length fluctuations decrease the mean number of attached bridges, depress muscle force and stiffness, a nd increase force-length hysteresis. At frequencies >0.1 Hz, the bond-lengt h distribution of slowly cycling latch bridges changed little over the stre tch cycle and contributed almost elastically to muscle force, but the rapid ly cycling cross-bridge distribution changed substantially and dominated th e hysteresis. By contrast, at frequencies <0.033 Hz this behavior was rever sed: the rapid cycling cross-bridge distribution changed little, effectivel y functioning as a constant force generator, while the latch bridge bond di stribution changed substantially and dominated the stiffness and hysteresis . The analysis showed the dissociation of force/length hysteresis and cross -bridge cycling rates when strain amplitude exceeds 3%; that is, there is o nly a weak coupling between net external mechanical work and the ATP consum ption required for cycling cross-bridges during the oscillatory steady stat e. Although these results are specific to airway smooth muscle, the approac h generalizes to other smooth muscles subjected to cyclic length fluctuatio ns.