Michaelis Eadie-Hofstee plot

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. 

Enzyme kinetics Michaelis constant, symbol iCm maximum velocity of an enzyme catalysed reaction, Vm DC inhibitor constant, symbol X Michaelis-Menten equation and graph in the absence and the presence of inhibitors. Lineweaver-Burke and Eadie-Hofstee plots. 

Pirrang, Liu, and Morehead [22] have elegandy demonstrated the application of saturation kinetics (Michaehs-Menten) to the rhodium(II)-mediated insertion reactions of a-diazo /9-keto esters and a-diazo /9-diketones. Their method used the Eadie-Hofstee plot of reaction velocity (v) versus v/[S] to give and K, the equilibrium constants for the catalytic process. However, they were unable to measure the Michaelis constant (fC ) for the insertion reactions of a-diazo esters because they proved to be too rapid. 

Figure 3.6 Evaluation of kinetic parameters in Michaelis-Menten equation (a) Lineweaver-Burk plot, (b) C /r versus plot, and (c) Eadie-Hofstee plot.

Eadie-Hofstee Plot Another rearrangement of the Michaelis-Menten equation gives... 

The deviation of the reaction rate 31, from the rectangular hyperbola which would be shown by a true Michaelis-Menten reaction law, is best illustrated by considering the data as represented by an Eadie-Hofstee plot. The original equation for the Michaelis-Menten or Monod kinetics ... 

Evaluate the Michaelis-Menten kinetic parameters by employing (a) the Langmuir plot, (b) the Lineweaver-Burk plot, (c) the Eadie-Hofstee plot, and (d) non-linear regression procedure. 

Equation 11.16 is analogous to the Michaelis-Menten equation and changing [I] affects the apparent Km parameter but has no effect on Vjnax- The competitive inhibitor effect is observed graphically in families of Eadie-Hofstee plots where the lines intersect at Vmax on the y-axis, Fig. 11.12. 

Alternatively, you can linearize the Michaelis-Menten equation by using an Eadie-Hofstee plot [23,24]. Here the reaction velocity, v, is plotted as a function of v/[S], as shown in Eq. (2.43). This approach is more robust against error-prone data than the Lineweaver-Burk plot, because it gives equal weight to data points in any range of [S] or v. The disadvantage here is that both the ordinate and the abscissa depend on v, so any experimental error will be present in both axes. 

Figure 22 Examples of enzyme kinetic plots used for determination of Km and Vmax for a normal and an allosteric enzyme Direct plot [(substrate) vs. initial rate of product formation] and various transformations of the direct plot (i.e., Eadie-Hofstee, Lineweaver-Burk, and/or Hill plots) are depicted for an enzyme exhibiting traditional Michaelis-Menten kinetics (coumarin 7-hydroxylation by CYP2A6) and one exhibiting allosteric substrate activation (testosterone 6(3-hydroxylation by CYP3A4/5). The latter exhibits an S-shaped direct plot and a hook -shaped Eadie-Hofstee plot such plots are frequently observed with CYP3A4 substrates. Km and Vmax are Michaelis-Menten kinetic constants for enzymes. K is a constant that incorporates the interaction with the two (or more) binding sites but that is not equal to the substrate concentration that results in half-maximal velocity, and the symbol n (the Hill coefficient) theoretically refers to the number of binding sites. See the sec. III.C.3 for additional details.

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. 

Based on the result from the IC50 determination, determination of additional kinetic parameters such as Ki and the inhibition mode are useful (variation of the substrate concentration e.g. Km/4 1 Km with time). Transformation of the Michaelis-Menten equation are used both for calculation the Ki value as well as for graphical depiction of the type of inhibition (e.g. direct plot ([rate]/[substrate], Dixon plot [l/rate]/[inhibitor], Linewaver-Burk plot [l/rate]/[l/substrate] or Eadie-Hofstee plot [rate]/[rate/substrate]). 

E-pH diagram -> Pourbaix diagram Eadie-Hofstee plot Michaelis-Menten kinetics... 

A preferable, alternative form of the Michaelis-Menten equation is that of the Eadie-Hofstee plot (Equation 17.13)... 

The parameters V and Km (the Michaelis constant) of the equation can be evaluated from the slope and intercept of a linear plot of nu-1 against [S]-1 (a Lineweaver-Burk plot) or from the slope and intercept of a linear plot of nu against h/[S] (Eadie-Hofstee plot). 

Another method to obtain estimates for Km and is the rearrangement of the Michaelis-Menten equation to a linear form. The estimation for the initial velocities, Vo, from progress curves is not a particularly reliable method. A better way to estimate Vn is by the integrated Michaelis-Menten equation (Cornish-Bowden, 1975). Nevertheless, the graphical methods are popular among enzymolo-gists. The three most common linear transformations of the Michaelis-Menten equation are the Lineweaver-Burk plot of 1/Vo vs. 1/[S] (sometimes called the double-reciprocal plot), the Eadie-Hofstee plot, i.e. v vs. vo/[S], and the Hanes plot, i.e., [SJ/vo vs. [S] (Fig. 9.3). 

Despite their appealing simplicity, these methods have serious limitations. The Lineweaver-Burk and Hanes plots are unreliable, e.g., the variation of the variance almost certainly results in an incorrect weighting, whereas in the Eadie-Hofstee plot Vo is present in both variables. The direct linear plot of Eisenthal and Cornish-Bowden (1974), for which the Michaelis-Menten equation is rearranged to relate to A , i.e., = Vo -f- Vo A ,/[S] is very simple but... 

Fig. 4 Mechanism of action (MOA) and inhibition studies of ML119 (compound 1) with HePTP and HePTP mutants, (a) Progress curves of HePTP (6.25 nM) activity in the presence of different doses of compound 1 (0, 0.078,0.156,0.313,0.625,1.25 /jM) and 0.3 mM OMFP in 20 mM Bis-Tris, pH 6.0,150 mM NaCI, 1 mM DH, and 0.005 % Tween-20 in 20 /jL totai assay voiume in biack 384-weii microtiter plates. No time-dependent inhibition was observed as demonstrated by the linear progress curves of the HePTP phosphatase reaction, (b) Eadie-Hofstee plot of the Michaelis-Menten kinetic study with compound I.The HePTP-catalyzed hydrolysis of OMFP was assayed at room temperature in a 60 /jL 96-well format reaction system in 50 mM Bis-Tris, pH 6.0 assay buffer containing 1.7 mM DTT, 0.005 % Tween-20, and 5 % DMSO. Recombinant HePTP (5 nM) was preincubated with various fixed concentrations of inhibitor (0,0.1,0.2,0.4,0.8,1.6 /jM) for 10 min. The reaction was initiated by addition of various concentrations of substrate (0,12.5,25,50,100,200,400 pM) to the...

These are similar to the equations for the Langmuir, the Lineweaver-Burks, and the Eadie-Hofstee plots that were discussed earlier with the Michaelis-Menten kinetics. 

Which of these plots should be used To generally understand the behavior of enzymes, use the simple graph of initial velocity against substrate concentration. The linearized forms are useful for calculation of ATM and Fmax. The Lineweaver-Burke plot is useful for distinguishing between types of inhibition (Chapter 8). The Eadie-Hofstee plot is better than the Lineweaver-Burke plot at picking up deviations from the Michaelis-Menten equation. 

The Eadie-Hofstee plot does a betterjob than the Line-weaver-Burke plot in evenly distributing the data points over the entire substrate concentration range, and can be a useful visual technique for ascertaining whether enzyme kinetics are typical (as shown) or atypical (see Figure 8.18, B and G). The Michaelis-Menten approach basically assumes that enzymes present a single binding site to each substrate. Estimates of V x of drug... 

Figure 6.5. Eadie-Hofstee plot for Michaelis-Menten kinetics.

A Lineweaver-Burk plot ( ) indicates that with D-glucose as the substrate, the enzyme obeys Michaelis-Menten kinetics with a Km value of 3.2 + 0.08 mM and a Vmax of 126.0 + 0.02 micromol/mg protein/min (Figure 11). Similar results were obtained by the direct linear plot (88), Hanes and Woolf ( ) or Eadie-Hofstee plots (90). All the kinetic data reported here and subsequently, were based on the initial rates of hydrogen peroxide formation... 

FIGURE 4.4 Eadie-Hofstee plot of a reaction that follows Michaelis-Menten kinetics. Kinetic parameters are as defined previously. 

FIGURE 4.9 Eadie-Hofstee plots useful to diagnose the type of kinetics occurring in a reaction for (a) hyperbolic (Michaelis-Menen) kinetics, (b) Sigmoidal kinetics, (c) Biphasic kinetics with no saturation of second phase, and (d) Substrate inhibition kinetics. 

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. 

The apparent Tmav and were determined to be 42.5 nmol/min/mg protein and 180.0 p.M, respectively, indicating a high capacity with a moderate affinity reaction. To ensure the suitability and accuracy of the parameter determination provided by the nonlinear regression analyses, the traditional biochemical plots, such as Michaelis-Menten or Eadie-Hofstee plots, can be used (Fig. 13.2). 

A procedure which yields a more uniform distribution of the data on the straight line is that proposed by Hofstee (the Eadie-Hofstee plot). In this procedure the Michaelis-Menten equation, 2.41, is algebraically rearranged into ... 

Table II. Apparent Michaelis-Menten constants determined from electrochemical Eadie-Hofstee plots...

The cellular uptake process for taurocholate was found to be linear for at least the first four min for all substrate concentrations examined. The initial rate of uptake (Vq) was determined from linear regression analysis of the increase in taurocholate concentrations in the cell pellet with time (1-4 min). The regression correlation coefficient in all cases was greater than 0.95. Extrapolation of the Vq line to zero time yielded a positive intercept indicative of nonsaturable nonspecific binding such as adherence to the outer cell membrane. The derived values for Vq were combined within each age-group and substrate concentration. These values were then analyzed according to Michaelis-Menten kinetics using Lineweaver-Burk or Eadie-Hofstee plots to obtain and V gx (Dixon and Webb, 1964). 

Eadie-Hofstee plot Michaelis-Menten kinetics... 

Analysis This example demonstrated how to evaluate the parameters V m and Ky in the Michaelis-Menten rate law from enzymatic reaction data. Two techniques were used a Lineweaver-Burk plot and non-linear regression. It ras also shown how (he analysis could be carried out using Hanes-Woolf and Eadie-Hofstee plots. 

Hofstee plot A graphical method used in enzyme kinetics to obtain a straight line fiom experimental data. It involves forming aplotofV/SversusVinwhichSis the substrate concentration at which the velocity v is observed. The gradient of the line is equal to -K and the intercept on the y-axis is equal to the maximum velocity V. Also known as the Eadie-Hofstee plot, it is named after Canadian biochemist George Sharp Eadie (1895-1976) and B. H. J. Hofstee who developed the plot in 1942 and 1959, respectively. See michaelis-MENTEN KINETICS. 

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