Non-Steady State Analysis of Enzyme Kinetics in Real Time Elucidates Substrate Association and Dissociation Rates: Demonstration with Analysis of Firefly Luciferase Mutants.

Firefly luciferase has been widely used in biotechnology and biophotonics due to photon emission during enzymatic activity. In the past, the effect of amino acid substitutions (mutants) on the enzymatic activity of firefly luciferase has been characterized by the Michaelis constant, K. The K is obtained by plotting the maximum relative luminescence units (RLU) detected for several concentrations of the substrate (luciferin or luciferyl-adenylate). The maximum RLU is used because the assay begins to violate the quasi-steady state approximation when RLU decays as a function of time. However, mutations also affect the time to reach and decay from the maximum RLU. These effects are not captured when calculating the K. To understand changes in the RLU kinetics of firefly luciferase mutants, we used a Michaelis-Menten model with the non-steady state approximation. In this model, we do not assume that the amount of enzyme-substrate complex is at equilibrium throughout the course of the experiment. We found that one of the two mutants analyzed in this study decreases not only the dissociation rate ( k) but also the association rate ( k) of luciferyl-adenylate, suggesting the narrowing of the structural pocket containing the catalytic amino acids. Furthermore, comparative analysis of the nearly complete oxidation of luciferyl-adenylate with wild-type and mutant firefly luciferase reveals that the total amount of photons emitted with the mutant is 50-fold larger than that with the wild type, on average. These two results together indicate that the slow supply of luciferyl-adenylate to the enzyme increases the total number of photons emitted from the substrate, luciferyl-adenylate. Analysis with the non-steady state approximation model is generally applicable when enzymatic production kinetics are monitored in real time.