Analysis of Chemical Kinetics of Multistep Reactions by Mean Reaction Time

Abstract

Although methods to derive the rate equation from a kinetic model have been known for over a century, it remains mathematically challenging to derive the rate equation for complex reactions involving multiple steps, as the derivation requires a solution for simultaneous differential equations. Furthermore, the derived kinetic equations are often difficult to intuitively understand. Here, we report a radically different approach to analyze chemical kinetics using the mean reaction time, the average of the time required for the completion of a chemical reaction. This mathematical description of chemical kinetics provides an intuitive understanding of how individual steps in a multistep reaction contributes to the overall kinetics. We demonstrate here the step-by-step approach to derive the formula for the mean reaction time from kinetic models. Surprisingly, one can derive the formula for the mean reaction time without solving simultaneous differential equations or using a steady-state approximation. Being an ensemble-averaged value, the mean reaction time cannot describe the distribution of the reaction time of the individual chemical entities. However, the mean reaction time reveals invaluable insights on how the energy levels of the ground states and the transition states affect the kinetics of the multistep reaction. As proof of principle, we apply the mean reaction time to enzyme kinetics and demonstrate that one can readily derive the expressions of the kinetic parameters (kcat/KM and kcat) even without deriving the Michaelis–Menten equation.