Kinetics of Allosteric Inhibition of Single Enzyme by Product Molecules

Single-molecule experiment probed the catalytic conversions of Amplex Red to resorufin by horseradish peroxidase in which the product molecules were found to act as the allosteric inhibitor for the individual enzyme. While broad distributions of the initial reaction velocities and the number of product molecules required to cease the reaction unraveled the underlying dynamic disorder in the reaction pathway, bulk experimental measurements established the particularity of noncompetitive inhibition of the enzyme species. In this work, to rationalize the observed phenomena, we present a stochastic kinetic model of the enzymatic reaction taking into account the inhibitions of the enzyme and enzyme-substrate complex in the circumstance of their structural fluctuations. Starting from a chemical master equation that can further be reduced into a set of ordinary differential equations for the case of single-enzyme kinetics, we derived an analytical expression for the turnover time distribution, the first moment of which yielded the mean turnover time. The inverse of the latter showed excellent agreement with the bulk data of the initial enzymatic velocities measured in the presence of varying inhibitor concentrations. This supports the observed nature of inhibition which we further confirmed by constructing double-reciprocal plots for the inhibited kinetics. In addition, we successfully recovered ensemble data from another experiment that redesigned the aforesaid single-molecule catalysis to investigate the effects of molecular crowders on reaction velocity; the latter was greatly alleviated with increasing the molecular weight of the crowders. On the other hand, the calculated randomness parameter, determined from the higher moment of the turnover time distribution, clearly inferred dynamic disorder in the catalytic turnovers. Our work under a unified framework provides a robust theoretical description for the experimental kinetic study and eradicates the necessity of assuming an alternative mode of inhibition in analyzing the data, not consistent with the experiments, considered earlier.