Rate law of mitochondrial respiration versus extramitochondrial ATP/ADP ratio

Rate equations describing the dependence of mitochondrial respiration or ATP formation on the extramitochondrial ATP/ADP ratio were derived from a simplified reaction scheme of oxidative phosphorylation. The equations include maximum velocities of (1) respiration, (2) ATP formation, and (3) other energy utilizing side reactions; apparent Michaelis constants for ATP and ADP; an apparent cooperativity coefficient; and in addition an apparent equilibrium constant which is equal to the ATP/ADP ratio at zero net formation of ATP in the resting state of mitochondria. The control characteristics described by the rate equation are in close agreement with curves that can be obtained from a much more complex mathematical model of phosphorylating mitochondria. The kinetic parameters of the equation can be estimated from experimental data by a nonlinear regression procedure. The results demonstrate a weak apparent cooperativity and a strong shift of the apparent affinity ratio for ATP and ADP towards ADP.