The effect of futile chemical cycles on chemical-to-mechanical energy conversion in interacting motor protein systems

We consider the non-equilibrium steady-state conversion of chemical to mechanical energy in motor protein systems with protein–protein interactions. Our approach combines a two-dimensional chemomechanical coupling model with a simple exclusion process. The chemomechanical model explicitly includes both chemical and mechanical degrees of freedom to describe not only coupled chemomechanical transitions but also uncoupled transitions, such as futile chemical cycles, that lead to energy loss. The simple exclusion process describes strong repulsive protein–protein interactions in the mechanical degree of freedom and these interactions have implications for the chemical degree of freedom via the chemomechanical coupling. Using the combined chemomechanical exclusion model, we determine the efficiency of energy conversion as a function of motor density and chemical driving force. We show that as motor density increases, mechanical motion is blocked, losses due to futile chemical cycles increase, and the efficiency of chemical-to-mechanical energy conversion is reduced.