Eadie-Hofstee plot analysis

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. 

For a plot of l/rQ versus l/(S)o, called a Lineweaver-Bmk plot, the intercept determines 2(E)o and can then be determined from the slope. For a plot of ro/(S)o versus r, called an Eadie-Hofstee plot, the slope determines and A 2(E)o can then be determined from the intercept. The classic plot is the Lineweaver-Burk plot, which has the advantage of displaying the variables separately on different axes. However, the Eadie-Hofstee plot has some practical advantages as demonstrated by a statistical comparison of several different methods of data analysis. ... 

This equation shows that a plot of R versus R/[S] should result in a line that has a slope of — Ki and an intercept of fe2[E],. A plot of this type is known as an Eadie—Hofstee plot, and it is illustrated graphically in Figure 6.7. The methods of data analysis that are based on Eqs. (6.29) and (6.33) are called single reciprocal methods. 

A crucial point in evaluating uptake data for amino acids is whether this uptake is mediated by a low-affinity system alone, or by a low- and a high-affinity system, i.e., if the uptake is mediated by one or two transport carriers. Shank and Campbell (1984) calculated the K , and Vmax values with the Pennzyme computer program (Kohn et al., 1979). This program uses a weighted nonlinear regression analysis, and Eadie-Hofstee plots are used to evaluate the presence of a two-carrier transport system. Figure 1... 

In the graphical analysis of initial rate data, it is pradent to use all three plots shown in Figs. 3 and 4. The direct plot of versus [A] wiU show directly the influence of substrate concentration on initial rate of reaction. The two linear plots should be used together, because the Lineweaver-Burk plot serves to visualize the influence of low concentrations whereas the Hanes plot serves to visualize the influence of high concentrations of substrates. The third plot, the Eadie-Hofstee plot, is useful in detecting exceptionally bad measurements (Section 3.11). 

Enzyme-catalyzed reactions are sometimes analyzed by use of the Eadie-Hofsteeplot, in which i>/[S] ) is plotted against t>. (a) Using the simple Michaehs-Menten mechanism, derive a relation between t>/[S] and V. (b) Discuss how the values of and are obtained from analysis of the Eadie-Hofstee plot, (c) Determine the Michaehs constant and the maximum velocity of the reaction from Exercise 8.14 by using an Eadie-Hofstee plot to analyze the data. 

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). 

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. 

Equation 7.3.31 gives rise to what is known as an Eadie or Hofstee plot, while equation 7.3.32 gives rise to a Hanes plot. The Eadie plot has the advantage of spreading the points out more evenly and of determining K and J ax separately. The three types of plots are shown schematically in Figure 7.4. The Lineweaver-Burk and Eadie plots are the ones used most frequently in data analysis. 

When the incorporation of [ H]NAD into TCA insoluble products was measured as a function of NAD concentration in permeabilised LI 210 cells, a pronouncedly biphasic plot was obtained (Fig. 1). This data was analysed using a Hofstee-Eadie transformation (v vs v/s) and was shown to divide quite clearly into two data sets, corresponding to NAD concentrations above and below 10 juM. The kinetic constants calculated from this analysis are shown in Table 1. Below 10 ijM the reaction has a of 9.45 (jM whereas above 10 juM the is 29.9 ijM. 

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