Menten Summary

Enzymes are very efficient with high reaction rates when the substrate concentration is low but they can become saturated when the substrate concentration is high [16]. Competitive inhibition results 

FIGURE 8.11 A study of o-diphenol oxidase with catechol substrate including competitive (PHBA) and noncompetitive (phenylthiourea) inhibitors. (From Kimball, J., Enzyme kinetics, http / users.rcn.com/ jkimball.ma.ultranet/BiologyPages/E/EnzymeKinetics.html. With permission.) 

---

In summary, the simple Michaelis-Menten form of Equation (12.1) is usually sufficient for first-order reactions. It has two adjustable constants. Equation (12.4) is available for special cases where the reaction rate has an interior maximum or an inflection point. It has three adjustable constants after setting either 2 = 0 (inhibition) or k = 0 (activation). These forms are consistent with two adsorptions of the reactant species. They each require three constants. The general form of Equation (12.4) has four constants, which is a little excessive for a... 

The linear response range of the glucose sensors can be estimated from a Michaelis-Menten analysis of the glucose calibration curves. The apparent Michaelis-Menten constant KMapp can be determined from the electrochemical Eadie-Hofstee form of the Michaelis-Menten equation, i = i - KMapp(i/C), where i is the steady-state current, i is the maximum current, and C is the glucose concentration. A plot of i versus i/C (an electrochemical Eadie-Hofstee plot) produces a straight line, and provides both KMapp (-slope) and i (y-intercept). The apparent Michaelis-Menten constant characterizes the enzyme electrode, not the enzyme itself. It provides a measure of the substrate concentration range over which the electrode response is approximately linear. A summary of the KMapp values obtained from this analysis is shown in Table I. 

Ks is the dissociation constant for the enzyme substrate complex. It is important to remember that the Michaelis-Menten equation holds true not only for the mechanism as stated above, but for many different mechanisms that are not included in this treatment. In summary, ITm can be described as an apparent dissociation constant for all enzyme-bound species and, in all cases, it is the substrate concentration at which the enzyme operates at half-maximal velocity. 

Spreadsheet Summary The second exercise in Chapter 13 of Applications of Microsoft Excel in Analytical Chemistry involves enzyme catalysis. A linear transformation is made so that the Michaelis constant, K, and the maximum velocity, can be determined from a least-squares procedure. The nonlinear regression method is used with Excel s Solver to find these parameters by fitting them into the nonlinear Michaelis-Menten equation. 

In summary both presented methods are dealing with time-dependent substrate concentration data. While the first one ( initial rate method) uses differentiated values, the other approach uses integrated values. Both have in common that they are not suitable for analysing a reversible Michaelis-Menten mechanism. However, if the reaction conditions are obeying the conditions required for kinetic analysis via eqn (4.9) and (4.10), this method is highly recommended since it is most reliable and in practice very comfortable compared to the time-consuming initial rate experiments. All one has to do is to make sure that either sufficiently high substrate or enzyme/catalyst concentrations are applied. 

The mathematics of ligand-receptor interactions are beyond the scope of the cvurent article. Therefore, only important summary equations describing the bimolecular interaction of L with a single class of receptor are given below. These equations are analogous to the fundamental description of enzyme-substrate interactions first proposed by Michaelis and Menten, with the exception that L replaces the term for substrate, R replaces the enzyme, and LR substitutes for the enzyme-substrate complex. In binding reactions there is no term for product, since the binding of L to R does not result in the alteration of L. 

The theoretical description of electrocatalysis that takes into account electron and ion transfer and the transport process, the permeations of the substrates, and their combined involvement in the control over the overall kinetics has been elaborated by Albeiy and Hillman [312,313,373] and by Andrieux and Saveant [315], and a good summary can be found in [314]. Practically all of the possible cases have been considered, including Michaelis-Menten kinetics for enzyme catalysis. Inhibition, saturation, complex mediation, etc., have also been treated. The different situations have also been represented in diagrams. Based on the theoretical models, the respective forms of the Koutecky-Levich eqrration have been obtained, which make analyzing the resirlts of voltarrrmetry on stationary artd rotating disc electrodes a straightforward task. 

In summary, we found that NO inhibits O2 consumption in the normal perfused cat CB and can account for the unusual Michaelis-Menten kinetics that have been observed experimentally. Therefore, endogenous NO production can directly modulate O2 sensitivity as well as influencing many other physiological processes in the CB. 

In summary, for an enzyme model to be operative, a certain number of criteria, characteristic of enzyme catalysis, must be fulfilled, among which is substrate specificity—that is, selective differential binding. The enzymelike catalyst must also obey Michaelis-Menten kinetics (saturation behavior), lead to a rate enhancement, and show bi- and/or multifunctional catalysis (348). 

---