Modified Michaelis-Menten mechanism

Dai, L. S. (1979). On the existence, uniqueness and global asymptotic stability of the periodic solution of the modified Michaelis-Menten mechanism. J. Diff. Eqs., 31, 392-417. 

In direct analogy to the Michaelis-Menten mechanism for reaction of enzyme with a substrate, the inactivator, I, binds to the enzyme to produce an E l complex with a dissociation constant K. A first-order chemical reaction then produces the chemically reactive intermediate with a rate constant k. The activated species may either dissociate from the active site with a rate constant to yield product, P, or covalently modify the enzyme ( 4). The inactivation reaction should therefore be a time-dependent, pseudo-first-order process which displays saturation kinetics. This is verified by measuring the apparent rate constant for the loss of activity at several fixed concentrations of inactivator (Fig. lA). The rate constant for inactivation at infinite [I], itj act (a function of k2, k, and k4), and the Ki can be extracted from a double reciprocal plot of 1/Jfcobs versus 1/ 1 (Fig. IB) (Kitz and Wilson, 1962 Jung and Metcalf, 1975). A positive vertical... 

The mechanisms of enzyme inhibition fall into three main types, and they yield particular forms of modified Michaelis-Menten equations. These can be derived for single-substrate/single-product enzymic reactions using the steady-state analysis of Sec. 5.10, as follows. 

Based on the mechanisms of enzyme hydrolysis of starch and the diffusion processes of enzyme and the starch digestion products in the plastic matrix, the following assumptions were made (a) the diffusion of both the enzyme and the products in the plastic matrix obeys the Pick s first law, (b) the diffusion coefficient is constant throughout the matrix during the reaction, (c) the hydrolytic reactions take place only inside the hydrophobic plastic matrix, and (d) the reaction between the enzyme and the substrate is a modified Michaelis-Menten type and the product (P), will competitively inhibit the enzyme activity ... 

The reduction of the produced hydrogen peroxide at the RDE completes the CirrEjrr mechanism. Rate determining is the step (c). For steady-state conditions the following equation (modified Michaelis-Menten equation) holds... 

Many enzyme-catalyzed reactions are consistent with a modified version of the Michaelis-Menten mechanism, in which the release of product from the ES complex is also reversible with the step... 

Equation 8.4a gives the expression for the rate of formation of product by a modified version of the Michaelis-Menten mechanism in which the second step is also reversible. Derive the expression and find its limiting behavior for large and small concentrations of substrate. 

At this point, it usually becomes necessary to reexamine the arbitrary conditions under which the assay was made for the purposes of enzyme purification. In an enzyme system involving a single substrate (or in which a second reactant such as water is in large excess), the value of k may be found to be related to the substrate concentration according to the Michaelis-Menten mechanism as modified by Briggs and Haldane (2) ... 

Often, a predicted rate law does not quite agree with the experimental one. Reaction conditions that modify the form of the rate law predicted by the mechanism may lead to final agreement (see Section 15.16 in the text and also in this study guide for an example, the Michaelis-Menten mechanism). If complete exploration of conditions fails to reproduce the experimental result, the proposed reaction mechanism is rejected. 

The inactivation presents distinct kinetics as a function of modifying reagents and the modified groups involved (117). For the simple cases in which preequilibrium binding is followed by a slow chemical step, the inactivation scheme (Scheme 1.7) resembles that of the Michaelis-Menten mechanism. 

A kinetic model describing the HRP-catalyzed oxidation of PCP by H202 should account for the effects of the concentrations of HRP, PCP, and H202 on the reaction rate. To derive such an equation, a reaction mechanism involving saturation kinetics is proposed. Based on the reaction scheme described in Section 17.3.1, which implies that the catalytic cycle is irreversible, the three distinct reactions steps (Equations 17.2 to 17.4) are modified to include the formation of Michaelis-Menten complexes ... 

The simple theory outlined above has to be modified to account for the pH dependence of the catalytic parameters in mechanisms more complicated than the basic Michaelis-Menten. 

Many of the subsequent developments in enzyme kinetics share the same basic postulates of Michaelis-Menten kinetics. Although the mechanisms and equations may be different in detail, they all lead to rate laws that are linear functions of enzyme concentration and rational functions of the reactant and modifier concentrations. Hence, all these developments are based upon the same underlying formalism, which I shall refer to as the Michaelis-Menten Formalism. 

In addition to substrate concentration, two groups of compounds alter the rate of an enzymic reaction by specific mechanisms. Activators are compounds which combine with an enzyme or enzyme-substrate complex to effect an increase in activity without being modified by the enzyme. Inhibitors are compounds which decrease the rate of an enzyme-catalysed reaction. Inhibitors are divided into two categories irreversible and reversible inhibitors. Irreversible inhibition involves the covalent bonding of the inhibitor to a functional group at the active site or elsewhere on the enzyme. Because the effective concentration of the enzyme is progressively declining, irreversible inhibition cannot be analysed by Michaelis-Menten kinetics. 

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