 ATP synthesis reversible-balance concentration ratio

For tight coupling of n downhill protons to m synthesized ATP per cycle, reversible balance gives $\Delta G_{\mathrm{hyd}}=(n/m)F\Delta p$ with a negative signed driving proton-motive force. Inserting $\Delta G_{\mathrm{hyd}}=\Delta G_{\mathrm{hyd}}^{\circ }+RT\ln (a_{\mathrm{ADP}}{a}_P/a_{\mathrm{ATP}})$ determines a concentration-ratio threshold. Finite net synthesis requires a driving margin, so balance alone does not specify the ratio in a working cell.