On the dynamics of the irreversible Michaelis-Menten reaction mechanism

Abstract

The mass action kinetic model of the irreversible Michaelis-Menten reaction mechanism is mathematically intractable: an explicit analytical solution cannot be obtained. This difficulty is overcome by applying simplifying kinetic assumptions but a full understanding of their dynamic implications and applicability is not readily available. This paper shows how simple modal analysis can provide both a conceptually appealing insight into the reaction dynamics and justification of the commonly used quasi-steady-state and quasi-equilibrium assumptions. The key results are that the quasi-steady-state assumption is applicable when the initial enzyme concentration, e 0, is much smaller than the Michaelis constant, K m, or when the initial substrate concentration, s 0, is much greater than K m. These results show that the commonly accepted criterion e 0 < < s 0 is incomplete and should be decomposed into e 0 < < K m and K m << s 0. The quasi-equilibrium assumption is valid when e 0 ⪢⪢ K m and when the rate of product formation is much slower than reversion to the substrate from the intermediate state, or k 2 ⪢⪢ k −1. The important dimensionless parameter ratios characterizing the reaction dynamics are e 0/ K m, s 0/ K m and k 2/ k −1.