Biochemical Engineering Fundamentals. Part 1 - Bailey J., Ollis D. 1989

Kinetics of Enzyme-Catalyzed Reactions
Determination of Rate Constants for the Elementary Steps of an Enzymatic Reaction

In Section 3.2.2, we discussed various graphical Methods for determining the parameters v_max and K_m in the Michaelis–Menten Equation. As the Briggs–Haldane analysis shows, these parameters are determined by the rate constants of the elementary reaction steps k₁, k_-1, and k₂. At the same time, it follows from equations (3.10) and (3.11) that knowing the parameters K_m and v_max is not sufficient to determine the rates of individual reaction steps. To estimate the latter, we obviously need to find other independent relationships between the rate constants of the elementary steps and experimental data.

Such more fundamental kinetic parameters are of interest for at least two reasons. First, they provide a deeper insight into the actual processes occurring during enzyme-catalyzed reactions. For example, we can find out how rapidly the substrate interacts with the enzyme and compare these values with The rate of the reverse process, the dissociation of the ES complex. Second, as we have already seen, the simplifications underlying the Michaelis–Menten equation are reasonably valid only at relatively low enzyme concentrations. If this condition is not met, studying The kinetics of an enzymatic reaction is possible only by taking into account the material balance data for s, p, and (es), which in turn requires knowing the rate constants of the individual reaction steps k₁, k_-1, and k₂. For these reasons, it seems appropriate to discuss here the experimental methods for determining these parameters and the results obtained using such methods.

In the pre-steady-state kinetics method, the primary focus is on the short period (about 1 s or less) immediately after THE START OF the reaction, when the quasi-steady-state approximation is not yet applicable. During this period, the Substrate Concentration changes insignificantly, allowing an approximate solution of the material balance equations for (es) and p. Comparing the relationship between p and t obtained in this way with experimental data, along with the determined values of v_max and K_m, provides all the information necessary to calculate k₁, k_-1, and k₂. The experimental basis of this method is the stopped-flow technique, developed and refined by B. Chance and co-workers. According to this technique, enzyme and substrate solutions are rapidly mixed in a spectrophotometer cuvette; the spectrophotometric method allows monitoring Changes in the concentrations of reactants and products occurring within a few milliseconds.

Relaxation methods, developed and widely used by Eigen and co-workers, make it possible to study reactions that are completed within a few nanoseconds. There are several variants of this method, but they are all based on THE PRINCIPLE OF perturbing the equilibrium (or steady-state) condition of the reaction mixture by artificially inducing a step-change in certain reaction conditions, such as Temperature, pressure, or electric field strength. The subsequent response of the reaction system to this change is continuously recorded. As shown schematically in Fig. 3.13, the response to a step-change in reaction conditions is nothing other than a transition to a new, near-equilibrium or steady state.