Thermodynamic analysis of energy coupling by determination of the Onsager phenomenological coefficients for a 3×3 system of coupled chemical reactions and transport in ATP synthesis and its mechanistic implications

The nonequilibrium coupled processes of oxidation and ATP synthesis in the fundamental process of oxidative phosphorylation (OXPHOS) are of vital importance in biosystems. These coupled chemical reaction and transport bioenergetic processes using the OXPHOS pathway meet >90% of the ATP demand in aerobic systems. On the basis of experimentally determined thermodynamic OXPHOS flux-force relationships and biochemical data for the ternary system of oxidation, ion transport, and ATP synthesis, the Onsager phenomenological coefficients have been computed, including an estimate of error. A new biothermokinetic theory of energy coupling has been formulated and on its basis the thermodynamic parameters, such as the overall degree of coupling, $q$ and the phenomenological stoichiometry, $Z$ of the coupled system have been evaluated. The amount of ATP produced per oxygen consumed, i.e. the actual, operating P/O ratio in the biosystem, the thermodynamic efficiency of the coupled reactions, $\eta$, and the Gibbs free energy dissipation, $\Phi$ have been calculated and shown to be in agreement with experimental data. At the concentration gradients of ADP and ATP prevailing under state 3 physiological conditions of OXPHOS that yield $V_{\max }$ rates of ATP synthesis, a maximum in $\Phi$ of $\sim 0.5J{\left(hmgprotein\right)}^{-1}$, corresponding to a thermodynamic efficiency of $\sim 60\%$ for oxidation on succinate, has been obtained. Novel mechanistic insights arising from the above have been discussed. This is the first report of a 3 × 3 system of coupled chemical reactions with transport in a biological context in which the phenomenological coefficients have been evaluated from experimental data.