Torque-coupled thermodynamic model for F_{o}F_{1}-ATPase

F_{o}F_{1}-ATPase is a motor protein complex that utilizes transmembrane ion flow to drive the synthesis of adenosine triphosphate (ATP) from adenosine diphosphate (ADP) and phosphate (Pi). While many theoretical models have been proposed to account for its rotary activity, most of them focus on the F_{o} or F_{1} portions separately rather than the complex as a whole. Here, we propose a simple but new torque-coupled thermodynamic model of F_{o}F_{1}-ATPase. Solving this model at steady state, we find that the monotonic variation of each portion's efficiency becomes much more robust over a wide range of parameters when the F_{o} and F_{1} portions are coupled together, as compared to cases when they are considered separately. Furthermore, the coupled model predicts the dependence of each portion's kinetic behavior on the parameters of the other. Specifically, the power and efficiency of the F_{1} portion are quite sensitive to the proton gradient across the membrane, while those of the F_{o} portion as well as the related Michaelis constants for proton concentrations respond insensitively to concentration changes in the reactants of ATP synthesis. The physiological proton gradient across the membrane in the F_{o} portion is also shown to be optimal for the Michaelis constants of ADP and phosphate in the F_{1} portion during ATP synthesis. Together, our coupled model is able to predict key dynamic and thermodynamic features of the F_{o}F_{1}-ATPase in vivo semiquantitatively, and suggests that such coupling approach could be further applied to other biophysical systems.