Derivable Equations and Issues Often Ignored in the Original Michaelis-Menten Mathematical Formalism

Background: There has been recent shift from the core issue of Michaelian kinetics to issues regarding various kinds of quasi-steady-state assumptions. Derivable equations with which to determine reverse rate constant for the dissociation of enzyme-substrate complex (ES) is given less attention.

Objectives: The objectives of this research are: 1) to derive other equations from differential equations whose evaluation leads to MM equation and 2) quantify based on derived equations the kinetic parameters given less attention and duration of catalytic events.

Methods: A major theoretical research and experimentation using Bernfeld method.

Results and Discussion: The durations for ES dissociation (ESD) into free substrate, S and enzyme, E were much shorter than the duration of ESD into E and product, P in 3 minutes duration of assay with low [S]; it was the shortest and longest in 3 and 5 minutes durations respectively with high [S]. The durations of ESD into E and P was shortest in 3 minutes duration of assay with high [S]. The values of reverse rate constant, k-1 for ESD into S and E in 3 minutes duration of assay with high [S] was » the rate constant, k2 for product formation and they are much higher than in other duration of assay.

Conclusion: The equations for the determination of the durations of various events, in a given catalytic cycle were derived. The various time regimes for each event and the rate constant for the dissociation of the ES can be graphically and calculationally determined as the case may be. Substrate concentration regime and duration of assay affects rate constants.