Two rules of enzyme kinetics for reversible Michaelis‐Menten mechanisms

Abstract

In a Michaelis-Menten type reversible enzyme reaction (one substrate, one product) the rapid equilibrium kinetics in one direction excludes rapid equilibrium in the reverse direction. If rapid equilibrium functions in any direction, in the reverse reaction van Slyke type 'kinetic constant' appears in the rate equation independently of whether steady state is reached in finite time or the final equilibrium is attained at t = m. If the reaction proceeds in one direction with rapid equilibrium and in the reverse direction with steady-state kinetics, the thermodynamic equilibrium of the reaction determines that a higher equilibrium concentration of product (or substrate) can be reached only with steady-state kinetics.Let us consider a reversible Michaelis-Menten type mechanism [1,2], where a single product is formed through a single enzyme-substrate complex from a single substrate (scheme 1). E+S -where E stands for enzyme, S for substrate and P for product. The kl and k-2 are second order, k-t and kz first order rate constants. In this case, considering the initial velocity conditions in both directions:where KM,S and KM,p are the Michaelis constants of the substrate and product, respectively. If k2 < k_, in the forward reaction, the rapid equilibrium kinetics holds. Consequently in this case

Global Regression Using the Explicit Solution of Michaelis‐Menten Kinetics Employing Lambert's W Function: High Robustness of Parameter Estimates

“…Other enzymes such as isomerases or dehydrogenases, however, work reversibly; they can be started by substrates as well as products and, finally, attain an equilibrium state. Their kinetics is more complicated, and it remains to be shown whether Lambert's W function is useful in these situations …”

Optimal temperature policy for immobilized enzyme packed bed reactor performing reversible Michaelis–Menten kinetics using the disjoint policy

“…At this special case the complex concentration, C ES , starts from 0 and when t ® ¥, C ES approaches a constant value. This means that the reversible Michaelis±Menten reaction follows steady state mechanism in both forward and reverse directions and approach equilibrium asymptotically as t ® ¥ (Keleti, 1986). On the other hand, if K p ¹ K s , then the reaction follows steady state kinetics in forward direction but not in the reverse one (Keleti, 1986).…”

“…This means that the reversible Michaelis±Menten reaction follows steady state mechanism in both forward and reverse directions and approach equilibrium asymptotically as t ® ¥ (Keleti, 1986). On the other hand, if K p ¹ K s , then the reaction follows steady state kinetics in forward direction but not in the reverse one (Keleti, 1986). Recently, enzyme deactivation with substrate protection is proposed and validated experimentally for a speci®c case of immobilized glucose isomerase (Chen and Wu, 1987;Houng et al, 1993).…”

Dynamic modeling of biochemical reactions with application to signal transduction: principles and tools using Mathematica

“…The above models are essentially of the Michaelis-Menten type (Keleti, 1986) with C LR playing the role of the enzyme and G that of the substrate. From a quantitative point of view a difference arises: in enzyme kinetics the usual assumption is that the number of enzyme molecules is relatively low; here this is just the opposite.…”

“…Although this procedure seems to be not well-founded from a mathematical point of view, it can be supported by the theory of singular perturbations, see references inÉrdi and Tóth (1989), Keleti (1986), Turányi and Tóth (1992) or Zachár (1998). We do not investigate this model further; it is intended as an introduction to the line of thought which lies behind the reaction rates of the rational type found in the next example.…”