Enzymes Eadie-Hofstee equation

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. 

There are well-established methods for obtaining the type of inhibition and the value of the inhibition constants from initial-rate kinetics, often from linearized plots such as lineweaver-Burk, Eadie-Hofstee, or Hanes. As these procedures are covered very well by a range of basic textbooks on biochemistry and kinetics (see the list of Suggested Further Reading ) we will not repeat these procedures here. Instead, we will discuss the situation in which an enzyme reaction is followed over more than just the initial range of conversion. Towards this end, the rate equation,... 

In addition to being easier to fit than the hyperbolic Michaelis-Menten equation, Lineweaver-Burk graphs clearly show differences between types of enzyme inhibitors. This will be discussed in Section 4.5. However, Lineweaver-Burk equations have their own distinct issues. Nonlinear data, possibly indicating cooperative multiunit enzymes or allosteric effects, often seem nearly linear when graphed according to a Lineweaver-Burk equation. Said another way, the Lineweaver-Burk equation forces nonlinear data into a linear relationship. Variations of the Lineweaver-Burk equation that are not double reciprocal relationships include the Eadie-Hofstee equation7 (V vs. V7[S]) (Equation 4.14) and the Hanes-Woolf equation8 ([S]/V vs. [S]) (Equation 4.15). Both are... 

London, U.K.), and the data are plotted on an Eadie-Hofstee plot (see Fig. 22). It should be noted that, at times, nonlinear regression lines represent the data points on an Eadie-Hofstee plots very poorly because the data reflect the contribution from two kinetically distinct enzymes whereas the computer software attempts to fit all data to an equation appropriate for a single enzyme. A relatively high standard error associated with the estimate of Km suggests that the nonlinear regression did not fit the data very well, and it is possible that a two enzyme model or perhaps an atypical enzyme kinetics model needs to be selected. When Km values are estimated by extrapolating data beyond the concentration range... 

When the Eadie-Hofstee plot suggests the involvement of two kinetically distinct enzymes in the formation of a particular metabolite, the data should be fitted to a dual-enzyme model according to the following equation ... 

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. 

Competitive inhibitors do not change the value of Vmax> which is reached when sufficiently high concentrations of the substrate are present so as to completely displace the inhibitor. However, the affinity of the substrate for the enzyme appears to be decreased in the presence of a competitive inhibitor. This happens because the free enzyme E is not only in equilibrium with the enzyme-substrate complex E. S, but also with the enzyme-inhibitor complex E. L Competitive inhibitors increase the apparent of the substrate by a factor of (1 + The evaluation of the kinetics is again greatly facilitated by the conversion of Equation 17.15 into a linear form using Line-weaver-Burk, Eadie-Hofstee, or Hanes-Woolf plots, as shown in Fig. 17.7. 

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. 

For the Michaelis-Menten equation there are algebraic transformations, in addition to the Lineweaver-Burk equation, that yield straight line plots from enzyme kinetic data. One such plot is due to Eadie and Hofstee their equation takes the following form ... 

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