We show that the rate at which electrons pass through the respiratory chain in mitochondria and respiring prokaryotic cells is described by the product of three terms, one describing electron donation, one acceptance, and a third, the thermodynamic drive. We apply the theory of nonequilibrium thermodynamics in the context of the chemiosmotic model of proton translocation and energy conservation. This approach leads to a closed-form expression that predicts steady-state electron flux as a function of chemical conditions and the proton motive force across the mitochondrial inner membrane or prokaryotic cytoplasmic membrane. The rate expression, derived considering reverse and forward electron flow, is the first to account for both thermodynamic and kinetic controls on the respiration rate. The expression can be simplified under specific conditions to give rate laws of various forms familiar in cellular physiology and microbial ecology. The expression explains the nonlinear dependence of flux on electrical potential gradient, its hyperbolic dependence on substrate concentration, and the inhibiting effects of reaction products. It provides a theoretical basis for investigating life under unusual conditions, such as microbial respiration in alkaline waters.
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