Coupled enzyme systems in a vesicular membrane: oxidative phosphorylation as an example.

We consider a small vesicle whose membrane transports a ligand L into the vesicle through enzymatic units of type A and transports L out of the vesicle through units of type B. Oxidative phosphorylation in mitochondria provides an example, in which L is H+. The kinetics of the two membrane systems (A and B) are coupled through the concentration of L in the vesicle. This interdependence causes the combined membrane system (A plus B) to simulate a single system whenever the net ligand transport into the vesicle is zero. For example, in oxidative phosphorylation, it was thought for some time that ATP was synthesized by the respiratory chain system (via an "active intermediate"). We give the simplest possible analyses of this kind of coupled system, which is very common, by using two-state enzymes for both A and B above. A numerical example is included that illustrates respiratory control in a qualitative way: although the respiratory chain flux by itself does not depend on ADP concentration, the steady-state flux of the coupled systems (respiratory chain and reverse ATPase) does depend on ADP concentration through the interior ligand (H+) concentration.