Two (completely) rate-limiting steps in one metabolic pathway? The resolution of a paradox using bacteriorhodopsin liposomes and the control theory

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Abstract
Proton pumping by bacteriorhodopsin and chargecompensating ion movement can both and simultaneously behave as the rate-limiting step in light-driven proton uptake into bacteriorhodopsin liposomes. This apparently excessive control exerted on the net proton influx is possible because of the negative (−1) ‘control coefficient” of the net proton influx with respect to the proton leaks. Furthermore, the property of bacteriorhodopsin that it is inhibited by the membrane potential is responsible for the transfer of part of the control on the net proton influx from the first, irreversible, step in the pathway (i.e. bacteriorhodopsin) to the second, reversible, step (i.e., charge-compensating ion movement).