Michaelis-Menten plots

FIGURE 6.51 Determination of Vmax and Km for ATP. A Michaelis-Menten plot of PKA phosphorylation of labeled peptide substrate was used to determine Vmax and Km in the presence and absence of three concentrations of inhibitor H-89. 

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 effect of the inhibitor has resulted in a loss of the cooperative effect normally seen in allosteric enzymes so the graph looks like a simple Michaelis-Menten plot. 

The rhodium dimer has two Lewis acidic sites and thus the catalyst could coordinate to two substrate molecules under saturation kinetics, which would make the Michaelis-Menten plots complicated. This does not happen and the second site becomes less acidic once the other site is occupied by the substrate. What does happen, though, is that other Lewis bases compete with the substrate, as might be expected. The ligand dissociation reaction may be part of the rate equation of the process. Coordination of one Lewis base reduces already the activity of the catalyst. The solvent of choice is often anhydrous dichloromethane. The polar group may also be part of one of the substrates and in this instance one cannot avoid inhibition. 

A hyperbolic Michaelis-Menten plot for a simple unireactant enzyme system... 

Figure 6.5 Michaelis-Menten plot of the arbitrary reaction rate (v) over the ClAA concentration (s).

Michaelis-Menten plot for an enzyme-catalyzed reaction. From Biochemistry, 3rd ed., p. 377, by C. Mathews, K. van Holde, and K. Ahern, Benjamin/ Cummings, Redwood City, CA, 2000. 

Most of the acceptors, such as maltose, isomaltose, and methyl a-D-glucopy-ranoside, were apparent competitive inhibitors for dextransucrase, as determined by Lineweaver-Burke or Hanes-Woolf plots103 however, when higher sucrose concentrations were used in a Michaelis-Menten plot, the inhibition was not reversed for methyl a-D-glucopyranoside as it should have been for a competitive inhibitor.103 It was concluded that the acceptors were being bound at a site that was separate and distinct from the sucrose binding-sites. 

Figure 7.21. Ideal Michaelis-Menten plots showing the relationship between rate of NH4 transformation, V, and substrate (S) concentration.

The experimental data in Figure 7.26 show normal and linearized competitive Michaelis-Menten plots of Rb+ uptake by plant roots. The data clearly demonstrate... 

Figure 7.26. Normal and linearized Michaelis-Menten plots describing rubidium (Rb+) uptake by plant roots under three different concentrations of K+ (competitive process) (from Epstein and Hagen, 1952, with permission).

If the Michaelis-Menten plot is extrapolated to infinitely high substrate concentrations, the extrapolated rate is equal to Vmax. 

Before the availability of computers, the determination of X jyj and V values required algebraic manipulation of the basic Michaelis-Menten equation. Because Vis approached asymptotically (see Figure 8,11). it is impossible to obtain a definitive value from a typical Michaelis-Menten plot. Because X jyj is the concentration of substrate at V 2, it is likewise impossible to determine an accurate value of K jy[. However, can be accurately determined if the... 

The influence the competitive inhibitor has on the Michaelis-Menten plot and on its double reciprocal linear transformation, as well as the evaluation of K is given in Fig.9.3. An example of the practical importance of competitive inhibition in EIA will be discussed in Section 10.1.3.5. 

PROBLEM 6.2 Consider the Michaelis-Menten plot illustrated in Figure 6.5). Identify the following points on the curve max b. Km Solution a. Vmax is the maximum rate the enzyme can attain. Further increases in substrate concentration do not increase the rate. b. Km = [S] at VmJ2... 

Michaelis-Menten Plot of Uninhibited Enzyme Activity Versus Competitive inhibition. 

Using a Michaelis-Menten plot, determine Km for the uninhibited reaction and the inhibited reaction. 

A plot of this type is sometimes called a Michaelis-Menten plot. At low s strate concentration, (S). 

Fig. 2 Assays with the purified XlnD on pNP-x, ran at 37 °C in 50 mM citrate buifer at pH 4.8 a reaction rate vs substrate concentration and b Michaelis-Menten plots of data from assays with varying initial D-xylose concentrations...

Biochemical Plots Several methods are readily applied to the determination of kinetic parameters and Tmax)- Traditionally, these terms are determined using the classic biochemical plots, particularly those transformed from the well-known Michaelis-Menten plot, for example, Lineweaver-Burk and Eadie-Hofstee plots (Li et ah, 1995 Nakajima et ah, 2002 Nnane et ah, 2003 Yamamoto et ah, 2003). 

FIGURE 13.2 Biochemical plots for the enz5me kinetic characterizations of biotransformation, (a) Direct concentration-rate or Michaelis-Menten plot (b), Eadie-Hofstee plot (c), double-reciprocal or Lineweaver-Burk plot. The Michaelis-Menten plot (a), typically exhibiting hyperbolic saturation, is fundamental to the demonstration of the effects of substrate concentration on the rates of metabolism, or metabolite formation. Here, the rates at 1 mM were excluded for the parameter estimation because of the potential for substrate inhibition. Eadie-Hofstee (b) and Lineweaver-Burk (c) plots are frequently used to analyze kinetic data. Eadie-Hofstee plots are preferred for determining the apparent values of and Umax- The data points in Lineweaver-Burk plots tend to be unevenly distributed and thus potentially lead to unreliable reciprocals of lower metabolic rates (1 /V) these lower rates, however, dictate the linear regression curves. In contrast, the data points in Eadie-Hofstee plot are usually homogeneously distributed, and thus tend to be more accurate. 

FIGURE 13.3 Determination of the potential involvements of multiple enz5mes in a biotransformation pathway using the common biochemical plots. As shown by the plots, (a) Michaelis-Menten plot (b) Eadie-Hofstee plot and (c) Lineweaver-Burk plot, at least two enzjmatic components (El and E2) are responsible for the substrate s biotransformation one high affinity and low capacity, and the other low affinity and high capacity. Of the three plots shown, the Eadie-Hofstee plot most apparently demonstrates the biphasic kinetics due to either multiple enzymes or possibly the deviations from Michaelis-Menten kinetics, that is, homotropic cooperation. 

Computational Approach Computational nonlinear regression analysis, in which the data points in the Michaelis-Menten plots are directly fitted, is the preferred approach for analysis of metabolic kinetic data. Such an approach should be utilized as often as possible, given its unbiased nature. Regression analyses for the determination of and Ymax, or CLim (or Kjoj Vmax) 0 described below, for the SigmaPlot (Version 9.0, Syst Inc.) software. 

Biphasic kinetics should preferably be analyzed using such a computational approach. The above mathematic model can be revised to comprise two independent hyperbolic components y = axj(b + v) + cxj d + x). Here a and b are, respectively, Vmax and for one kinetic component, and c and d are those for the other, respectively. After the raw data (5 and V), used for the construction of the Michaelis-Menten plot shown in Fig. 13.3, were processed using SigmaPlot, following the procedure as described, the results for the nonlinear regression analyses were generated, they are summarized in Table 13.5. Of the... 

V/S is in essence the slope of the pseudolinear portion of the Michaelis-Menten plot. 

A generalized Michaelis-Menten plot depicting the rate (v ) versus concentration of substrate or reactant (IRJ). At higher concentrations, the rate approaches a maximum value (v) due to saturation of the enzyme. At v/2, [RJ = K, the binding constant of enzyme for substrate. 

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