Enzyme kinetic data, treatments

Enzyme kinetics. Data for reactions that follow the Michaelis-Menten equation are sometimes analyzed by a plot of v,/tA]o versus l/[A]o. This treatment is known as an Eadie-Hofstee plot. Following the style of Fig. 4-7b, sketch this function and label its features. 

Cleland and Mannervik have described least squares programs and procedures for treating enzyme kinetic data. The interested reader will also wish to consult numerous articles in vols. 210 and 259 in Methods in Enzy-mology (L. Brand M. L. Johnson, eds.) dealing with numerical computer methods for statistical treatment of kinetic and equilibrium data. 

F29. Frieden, C., Treatment of enzyme kinetic data. I. The effect of modifiers on the kinetic parameters of single substrate enzymes. J. Biol, Chem. 239, 3522-3531 (1964). 

Kinetic treatments Enzyme kinetic data are treated according to two assumptions ... 

Although the steady state treatment is the preferred approach for analyzing enzyme kinetic data, the applications of both kinetic treatments in general enzyme reactions will be considered. 

The steady-state kinetic treatment of random reactions is complex and gives rise to rate equations of higher order in substrate and product terms. For kinetic treatment of random reactions that display the Michaelis-Menten (i.e. hyperbolic velocity-substrate relationship) or linear (linearly transformed kinetic plots) kinetic behavior, the quasi-equilibrium assumption is commonly made to analyze enzyme kinetic data. 

The treatment of enzyme kinetics in this book is radically different from the traditional way in which this topic is usually covered. In this book, I have tried to stress the understanding of how models are arrived at, what their Umitations are, and how they can be used in a practical fashion to analyze enzyme kinetic data. With the advent of computers, linear transformations of models have become unnecessary—this book does away with Unear transformations of enzyme kinetic models, stressing the use of nonUnear regression techniques. Linear transformations are not required to carry out analysis of enzyme kinetic data. In this book, I develop new ways of analyzing kinetic data, particularly in the study of pH effects on catalytic activity and multisubstrate enzymes. Since a large proportion of traditional enzyme kinetics used to deal with linearization of data, removing these has both decreased the amount of information that must be acquired and allowed for the development of a deeper understanding of the models used. This, in turn, will increase the efficacy of their use. 

Two other general ways of treating micellar kinetic data should be noted. Piszkiewicz (1977) used equations similar to the Hill equation of enzyme kinetics to fit variations of rate constants and surfactant concentration. This treatment differs from that of Menger and Portnoy (1967) in that it emphasizes cooperative effects due to substrate-micelle interactions. These interactions are probably very important at surfactant concentrations close to the cmc because solutes may promote micellization or bind to submicellar aggregates. Thus, eqn (1) and others like it do not fit the data for dilute surfactant, especially when reactants are hydrophobic and can promote micellization. 

Rigorous treatments of enzyme kinetics are complex. The following discussions require several assumptions in order to fit the data to simplified models. While these models have their limitations, they often provide useful information about an enzyme s action on a specific substrate. 

Although our discussion thus far has been concerned with enzymatic methods, an analogous treatment for ordinary catalysis gives rate laws that are similar in form to those for enzymes. These expressions often reduce to the first-order case for ease of data treatment, and many examples of kinetic-catalytic methods are found in the literature. ... 

The quantitative treatment of kinetic data is based on the pseudophase separation approach, i.e. the assumption that the aggregate constitutes a (pseudo)phase separated from the bulk solution where it is dispersed. Some of the equations below are reminiscent of the well-known Michaelis- Menten equation of enzyme kinetics [101]. This formal similarity has led many authors to draw a parallel between micelle and enzyme catalysis. However, the analogy is limited because most enzymatic reactions are studied with the substrate in a large excess over the enzyme. Even for systems showing a real catalytic behavior of micelles and/or vesicles, the above assumption of the aggregate as a pseudophase does not allow operation with excess substrate. The condition... 

The stability of proteins can be viewed from kinetic as well as from thermodynamic considerations. Here we give the thermodynamic description and note that the kinetic description would be equivalent in view of the thermodynamic basis of the classical transition state theory. An example of the treatment of kinetic data of the stability of enzymes is given by Weemaes et al. [78]. 

Should one use the Hill plot in practice to examine the initial velocity behavior of enzymes Because infinite cooperativity is assumed to be the basis of the Hill treatment, only rapidly equilibrating systems are suitable for the Hill analysis. However, enzyme systems displaying steady-state kinetic behavior will not satisfy this requirement for this reason, one must avoid the use of kinetic data in any application of the Hill equation to steady-state enzyme systems. 

Enzyme kinetics the mathematical treatment of enzyme-catalysed reactions. A great deal of information about reaction mechanisms can be obtained from kinetic experiments and evaluation of the data... 

A most satisfactory treatment of kinetic data is the direct linear plot of Eisenthal and Cornish Bowden (1974). Axes are drawn with -S on the abscissa and V on the ordinate, but instead of making the usual hyperbolic plot of S/v (see Enzyme kinetics), corresponding points (each reading of -S and its related v value) are joined by straight lines. The point of intersection of this family of lines gives the values of V and K . Mathematically, this plot corresponds to a rearrangement of the general equation = v + vK ,/... 

The initial rate assumption is one of the most powerful and widely used assumptions in the kinetic characterization of enzyme action. The proper choice of reaction conditions that satisfy the initial rate assumption is itself a challenge, but once conditions are established for initial rate measurements, the kinetic treatment of an enzyme s rate behavior becomes much more tractablek In reporting initial rate data, investigators would be well advised to provide the following information ... 

There are methods used Lo study enzymes other than those of chemical instrumental analysis, such as chromatography, that have already been mentioned. Many enzymes can be crystallized, and their structure investigated by x-ray or electron diffraction methods. Studies of the kinetics of enzyme-catalyzed reactions often yield useful data, much of this work being based on the Michaelis-Menten treatment. Basic to this approach is the concept (hat the action of enzymes depends upon the formation by the enzyme and substrate molecules of a complex, which has a definite, though transient, existence, and then decomposes into the products, of the reaction. Note that this point of view was the basis of the discussion of the specilicity of the active sites discussed abuve. 

In the presence of PPi, known to bind strongly to the enzyme active site (Section III,E), there was a weak protective effect. The experimental points fell in the shaded area of Fig. 6, and the data were analyzed with equations developed by Scrutton and Utter (45). The results of this treatment led to the conclusion that TNBS can react with both free enzyme and enzyme-PPi complex to cause catalytic inactivation the differences are only quantitative (45). Either TNBS can displace PP, from an active site lysine or TNBS modifies a different lysine, apart from the active site, and the presence of PPi on the enzyme partially protects against TNBS inactivation by some indirect mechanism. Unfortunately, as discussed above, this issue cannot be settled with these kinetic analyses. Furthermore, because all of the enzyme lysines are to some extent reactive with TNBS (Fig. 5), the single super-reactive lysine whose modification leads to inactivation cannot be isolated and identified, as, for example, in a particular peptide fragment. A variety of interpretations are possible, as discussed elsewhere (45). 

Crude estimates of the affinities of the enzyme for other compounds have been made by study of their capacity to inhibit hydrolysis of PPi. If the observed inhibition is assumed to be competitive, a simplified kinetic treatment yields the inhibition constants (Ki" values) listed in Table VI (54). The data indicate that several of the compounds whose hydrolysis is not catalyzed (Section III,D) are nevertheless bound weakly to the enzyme (e.g., ADP, methylene-bis-phosphonate). There is also very weak binding of Pi( the product of the enzymic reaction [Eq. 

A good example of the range of parameters available from flow calorimetric data can be found from the study of enzyme/substrate systems. The kinetic nature of enzyme systems has been previously described by Michaelis and Menten. In the treatment discussed here, the parameters sought are the enthalpy, rate constant, Michaelis constant and the enzyme activity. The following example describes a study on the well-known enzyme substrate system, urea/urease. 

---