Weakly-coupled models for motor enzyme function

Abstract

In strongly-coupled models for motor enzyme function, such as the original Huxley (1957) model for muscle, ATP binding and subsequent hydrolysis are required for the detachment and reattachment of every force-producing cross-bridge. In weakly-coupled models, cross-bridges can be 'mechanically detached' without ATP binding when they have been pushed far beyond their free energy minimum and have accumulated so much strain that the attached state is less stable than the detached state. Weakly-coupled models assume that these mechanically detached cross-bridges can rejoin the pool of detached molecules that can reattach as force-producing cross-bridges, without going through an ATP hydrolysis cycle. This paper bases this assumption on a thermodynamically rigorous model for interaction between a motor enzyme molecule and binding sites on a cytoskeletal protein filament, equivalent to other examples of ligand binding interactions. It attempts to identify more clearly the features that must be added to the idea of ligand binding equilibrium to simulate a weakly-coupled motor enzyme model. Models that assume a vectorial conformational change and a longitudinal series elastic element appear to be incompatible with the assumptions of weakly-coupled cross-bridge models. A stochastic computational method has been used to examine the properties of these models. The computations have examined the behaviour of a model containing a four-state ATPase cycle, but the model is computationally a nine-state model because a force-generating attached state is allowed to equilibrate with different detached states at negative and at positive distortions, and because three adjacent sites are considered as possible attachment sites for each of the two attached states of the ATPase cycle.