The Optimal Efficiency and the Economic Degrees of Coupling of Oxidative Phosphorylation

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Abstract
A phenomenological theory considering the output characteristics of oxidative phosphorylation has been worked out by adopting the formalism of linear nonequilibrium thermodynamics. The linearity of oxidative phosphorylation in the range of the output forces of practical interest has been experimentally verified. The efficiency of oxidative phosphorylation is zero if either a load with a zero conductance (open-circuited situation) or a load with an infinite conductance (short-circuited situation) is attached to oxidative phosphorylation. In between these extreme conductances there exists a finite load conductance permitting oxidative phosphorylation to operate with optimal efficiency. The necessary and sufficient condition for optimal efficiency was found to be L33/L11=√1−q2 where L11 is the phenomenological conductance of phosphorylation, L33 the phenomenological conductance of the load and q the degree of coupling of oxidative phosphorylation driven by respiration. This condition was called conductance matching. Under the condition of conductance matching, four output functions of oxidative phosphorylation of practical interest were optimized. A maximal net rate of oxidative phosphorylation occurs at a degree of coupling qf= 0.78. A maximal output power of oxidative phosphorylation, i.e. net rate times established phosphate potential, results at qp= 0.91. The maximization of the function net rate times efficiency yielded an economic degree of coupling qecp= 0.95 for maximal ATP flow. Finally, maximization of the function output power times efficiency led to a degree of coupling qecp= 0.97. This last function simultaneously maximizes net rate of ATP production, developed phosphate potential and efficiency and reflects therefore the most economic solution to the output problem under the condition of conductance matching. In isolated rat livers perfused in a metabolic resting state, the condition of conductance matching is fulfilled. In addition, the degree of coupling of oxidative phosphorylation under these conditions corresponds to the economic degree of coupling qecp.

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