Master equation approach to single oligomeric enzyme catalysis: mechanically controlled further catalysis

Motivated by the single molecule enzymatic experiments, we have provided a master equation description of enzyme catalysis in a chemiostatic condition for an immobilized oligomeric molecule with many equivalent active sites. The random attachment and detachment of substrate molecules on the various active sites of the oligomeric enzyme is studied in terms of the classical parameters of the Michaelis-Menten type process. In the limit of single molecule process, the master equation approach gives the result of waiting time distribution. On the other hand, for a large number of equivalent active sites or a few numbers of active sites with large Michaelis constant, the master equation gives a Poisson distribution in the nonequilibrium steady state. For the oligomeric enzyme, the net rate of the reaction in the nonequilibrium steady state is multiplied by the number of active sites which is further enhanced by more than two orders of magnitude with the application of external force of 10-100 pN through the techniques of atomic force microscopy. Substrate flux and reaction rate constants have interesting consequences on the dynamics and at nonequilibrium steady state which can be the controlling factors for macroscopic biochemical processes.