Michaelis constant interpretation

A more detailed examination shows that, in case of equilibrium approximation, the value of fCM corresponds to the inverse stability constant of the catalyst-substrate complex, whereas in the case of the steady-state approach the rate constant of the (irreversible) product formation is additionally included. As one cannot at first decide whether or not the equilibrium approximation is reasonable for a concrete system, care should be taken in interpreting KM-values as inverse stability constants. At best, the reciprocal of KM represents a lower limit of a stability constant In other words, the stability constant quantifying the preequilibrium can never be smaller than the reciprocal of the Michaelis constant, but can well be significantly higher. 

Interpretation of the reciprocals of the Michaelis constants allows the following conclusions to be made regarding hydrogenations under specified experimental conditions. In the case of the methyl and cyclohexyl ligand, the prevailing form of the catalyst in solution is the catalyst-substrate complex. However, for the other examples of first-order reactions, large Michaelis constants (or very... 

The inhibition can be interpreted as an increase of the Michaelis constant KM. In the case of uncompetitive inhibition (Fig. 9B), the binding of the substrate to the enzyme is not affected. However, the [ES] complex becomes inactive upon binding of the inhibitor Using Kj —> oo, the corresponding rate equation is... 

Fortunately, a usual assumption for applying the steady-state condition to mechanism (34) is that k2 k-1. This resolves the problem, because then the Michaelis constant can be interpreted as an ordinary single-step equilibrium constant and the binding volume as a simple association volume. 

The interpretation of the volume change of the catalytic step will then be the same as of AV0 in Eq. (42), and the volume change of the binding step will be derived from the Michaelis constant... 

There exists a large literature on enzyme polymorphism and species adaptation (91), but none of it can as yet be interpreted in stereochemical terms. The best-studied species is Drosophila melanogaster, in which the frequency of the two dominant alleles of alcohol dehydrogenase varies with latitude in several continents one of these alleles has a consistently lower Michaelis constant for alcohols than the other (92). The two enzymes have been found to differ by the single substitution of a lysine for... 

All model parameters were well estimated by the validation data set, except the Michaelis constant (Km), which had a relative difference of more than 200%. As might be guessed, one problem with this approach is the difficulty in interpreting the results When do two parameters differ sufficiently in their values so as to render the model invalid Also, if only one parameter is appreciably different, as in this case, does this mean the whole model is not valid Because the Michaelis constant was off by 200%, does this mean the whole model was not applicable to the validation data set In this instance, the authors concluded the pharmacokinetics of dutasteride were similar between the validation data set and index data set and then went on to explain away the difference in Michaelis constants between the data sets. 

We have already seen that when the rate of a reaction, V, is equal to half the maximum rate possible, V= V /2, then = [S]. One interpretation of the Michaelis constant, K, is that it equals the concentration of substrate at which 50% of the enzyme active sites are occupied by substrate. The Michaelis constant has the units of concentration. 

Before proceeding to a ReactLab based mechanistic analysis it is informative to briefly outline the classical approach to the quantitative analysis of this and similar basic enzyme mechanisms. The reader is referred to the many kinetics textbooks available for a more detailed description of these methods. The scheme in equation (5) was proposed by Michaelis and Menten in 1913 to aid in the interpretation of kinetic behaviour of enzyme-substrate reactions (Menten and Michaelis 1913). This model of the catalytic process was the basis for an analysis of measured initial rates (v) as a function of initial substrate concentration in order to determine the constants Km (The Michaelis constant) and Vmax that characterise the reaction. At low [S], v increases linearly, but as [S] increases the rise in v slows and ultimately reaches a limiting value Vmax-... 

The Michaelis constant corresponds to the substrate concentration where the enzyme works at only half the maximum possible rate, i.e., when half the active sites are occupied. can also be interpreted as follows If the rate coefficient of product formation ( 2) is much lower than k i, which is often the case, Eq. (19.6) simplifies to Kyi = k ilki. In this case, Zm represents the equilibrium constant of dissociation of the enzyme-substrate complex. It is therefore a measure of the substrate affinity of the enzyme where low values indicate a high affinily. Typical /sTm values lie between 10 and 10 mol... 

Michaelis constant can be easily interpreted as the concentration of substrate where the rate of the reaction is half of its maximum. This is, at this concentration, half of the enzyme molecules bind the substrate and, thus, it should be independent of the enzyme concentration. However, this is a rather simplistic conclusion because it considers that all enzymes strictly follow the Michaeiis-Menten behavior over a wide range of experimental conditions. If not, the fCm is likely to equal a much more complex relationship between the different rate constants involved. The clear dependence between Vmax and enzyme concentration enables a direct way for the estimation of enzyme concentration (see Figure 5B). This is the case of many clinical determinations targeting key enzymes for diagnostic purposes or the basis of many other assays, e.g., immunoassays, where enzymes are used as reporters or tracers for easy and sensitive transduction of noncatalytic interactions. 

The only study that has not been consistent with the proposed random mechanism has been that of Viebrock 47). He used an impure rat liver preparation that likely was the basic isozyme based on the Michaelis constants observed. The results of that study were interpreted as being consistent with an ordered mechanism in which GTP, IMP, and aspartate add in that order with release of GDP, Pi, and adenylosuccinate in that order. This mechanism is clearly ruled out by the data of Ogawa et al. 49) who show inhibition patterns for AMP and GDP in which these compounds were competitive versus IMP and GTP, respectively, and noncompetitive relative to the other two substrates. 

Equation 11-15 is known as the Michaelis-Menten equation. It represents the kinetics of many simple enzyme-catalyzed reactions, which involve a single substrate. The interpretation of as an equilibrium constant is not universally valid, since the assumption that the reversible reaction as a fast equilibrium process often does not apply. 

The interpretations of Michaelis and Menten were refined and extended in 1925 by Briggs and Haldane, by assuming the concentration of the enzyme-substrate complex ES quickly reaches a constant value in such a dynamic system. That is, ES is formed as rapidly from E + S as it disappears by its two possible fates dissociation to regenerate E + S, and reaction to form E + P. This assumption is termed the steady-state assumption and is expressed as... 

Finally, a feedback mechanism has often been used to explain observed (negative and positive) deviations from the Scatchard type plots or nonunity slopes of the nonsaturated portion of the logarithmic Michaelis-Menten plots (e.g. [209]). When no artifacts are present (cf. [197,198]), deviations can indeed be interpreted to indicate that the intrinsic stability or dissociation rate constants vary with the number of occupied transport sites. Nonetheless, several other physical explanations, including multiple carriers, non 1 1 binding, carrier aggregation, etc. must also be considered. 

The electron transfer from cytochrome c to O2 catalyzed by cytochrome c oxidase was studied with initial steady state kinetics, following the absorbance decrease at 550 nm due to the oxidation of ferrocyto-chrome c in the presence of catalytic amounts of cytochrome c oxidase (Minnart, 1961 Errede ci a/., 1976 Ferguson-Miller ei a/., 1976). Oxidation of cytochrome c oxidase is a first-order reaction with respect to ferrocytochrome c concentration. Thus initial velocity can be determined quite accurately from the first-order rate constant multiplied by the initial concentration of ferrocytochrome c. The initial velocity depends on the substrate (ferrocytochrome c) concentration following the Michaelis-Menten equation (Minnart, 1961). Furthermore, a second catalytic site was found by careful examination of the enzyme reaction at low substrate concentration (Ferguson-Miller et al., 1976). The Km value was about two orders of magnitude smaller than that of the enzyme reaction previously found. The multiphasic enzyme kinetic behavior could be interpreted by a single catalytic site model (Speck et al., 1984). However, this model also requires two cytochrome c sites, catalytic and noncatalytic. 

When accurate data can be obtained over a range of both concentrations and temperatures, it is possible from the Michaelis-Menton model to obtain data on the first-order rate constant kz and the constant Km = kz + kz)/ki and their apparent activation energies Ez and Unfortunately, most of the values quoted in the literature for the activation energies of enzyme-catalyzed reactions are derived from the use of overly simple first-order equations to describe the reaction. Consequently these values are a composite of Kmj kzy and the other constants in the Michaelis-Menton equation and cannot be used for interpretive purposes. Where the constants have been separated it is found that the values of Ez are low and of order of magnitude of 5 to 15 Kcal/mole. It is of interest to note that enzyme preparations from different biological sources, which may show different specific activity for a given reaction, have very nearly the same temperature coefficient for their specific rate constants. ... 

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