Kinetics and Efficiency of Energy-Transducing Enzymes

Complexes I to IV, with the exception of Complex II, are redox-driven proton pumps that convert redox energy of oxygen reduction to proton gradient across the mitochondrial or bacterial membrane; in turn, the created electrochemical gradient drives the adenosine triphosphate synthesis in the cells by utilizing complex V of the chain. Here we address a general question of the efficiency of such enzymes, considering them as molecular machines that couple endergonic and exergonic reactions and converting one form of free energy into another. One well-known example of the efficiency is given by Carnot's theorem for heat engines. Here we extend the concept to respiratory enzymes and specifically focus on the proton pumping by Complex I of the respiratory chain, nicotinamide adenine dinucleotide dehydrogenase. To discuss the efficiency issues, we develop a model of enzyme kinetics, which generalizes the Michaelis-Menten model. Our model includes several substrates and products and, in general, can be considered as Generalized Michaelis-Menten Kinetic model. The model might be useful for describing complex enzyme kinetics, regardless of the efficiency issues that are addressed in this paper.