On the Dynamics of the Irreversible Michaelis-menten Reaction Mechanism

The mass action kinetic model of the irreversible Michael&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 quasisteady-state and quasi-equilibrium assumptions. The key results are that the quasi-steady-state assumption is applicable when the initial enzyme concentration, e,, concentration, sO, is much smaller than the Michaelis constant, K,, or when the initial substrate is much greater than K,.These results show that the commonly accepted criterion e, < s0 is incomplete and should be decomposed into e, < K, and K, 6 s,,. The quasi-equilibrium assumption is valid when e0 % K, and when the rate of product formation is much slower than reversion to the substrate from the intermediate state, or kZ + k1. The important dimensionless parameter ratios characterizing the reaction dynamics are e,/K,, so/K, and k,/k _ 1