Hofstee plot

For the Eadie-Hofstee plot, both coordinates contain rates that are subjected to the greatest error, as indicated in Figure E.2.3. 

Eadie-Hofstee plot, 111 Electrode, 14, 15, 72, 73, 75-80 Electrodialysis, 351, 353-356, 393 Elemental composition, 228-230 Embden-Myerhof-Pamas pathway (EMP), 3, 207, 244-251... 

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. 

The Scatchard plot is bound free (/i/ L, y-axis) vs. bound (B, x-axis) (the Eadie-Hofstee plot is bound vs. bound/free). If this equation is applicable (i.e., the binding represents a simple bimolecular... 

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. 

Methods of plotting data obtained from enzyme catalyzed reactions, (a) Lineweaver-Burk plot, (b) Eadie or Hofstee plot, (c) Hanes plot. 

An alternative method known as the Hofstee plot uses the Michaeiis equation in the form... 

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. 

More accurate means of determining Km and Vmax are offered by either the Lineweaver-Burke (double reciprocal) plot or the Eadie-Hofstee plot (Figure 2.7). 

Figure 2.7 (a) Lineweaver-Burke plot (b) Eadie-Hofstee plot... 

Purification. One main peak was observed with detection at 405 nm, when purified lignin peroxidase was analyzed by Mono Q chromatography. The retention time of the main peak was 11.8 min and its area was 98.9% of the total peak area. Possibly the enzyme solution contains, however, two isoenzymes which have very similar properties. The Kj of the purified lignin peroxidase for veratryl alcohol was 139 on the basis of Eadie-Hofstee plot. 

In addition to the Lineweaver-Burk plot (see p.92), the Eadie-Hofstee plot is also commonly used. In this case, the velocity v is plotted against v /[A]. In this type of plot, Vmax corresponds to the intersection of the approximation lines with the v axis, while Km is derived from the gradient of the lines. Competitive and non-competitive inhibitors are also easily distinguishable in the Eadie-Hofstee plot. As mentioned earlier, competitive inhibitors only influence Km, and not Vmax- The lines obtained in the absence and presence of an inhibitor therefore intersect on the ordinate. Non-competitive inhibitors produce lines that have the same slope (llower level. Another type of inhibitor, not shown here, in which Vmax and lselective binding of the inhibitor to the EA complex. 

A graphical procedure " for plotting enzyme initial rate data as v versus v/[S] (also known as the Woolf-Au-gustinsson-Hofstee plot), where the initial velocity v is the so-called (y)-axis variable and v divided by the initial substrate concentration [S] is the so-called (v)-axis variable, such that the vertical-axis intercept equals Vmax, the slope equals and the horizontal-axis intercept is V IK... 

See Double-Reciprocal Plot Hanes Plot Direct Linear Plot Dixon Plot Dixon-Webb Plot Eadie-Hofstee Plot Substrate Concentration Range Frieden Protocol Fromm Protocol Point-of-Convergence Method Dal-ziel Phi Relationships Scatchard Plots Hill 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 7.7 Eadie-Hofstee plot for the hydrolysis of triethyl orthoformate in 1, pH 11,100 mM K2CO3,50 C, using NPr4 as a competitive inhibitor.

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

While the point for [S] = 0 and v = 0 cannot be plotted, the ratio v / [S] approaches Vma JKm as v approaches zero. Notice the distribution of the points in Fig. 9-4. Substrate concentrations were chosen such that the increase in velocity from point to point is more or less constant, a desirable experimental situation. The points on the Eadie-Hofstee plot are also nearly evenly distributed, but those of the Lineweaver-Burk plot are compressed at one end. (However, if the substrate concentrations for successive points are selected in the ratios 1,1 / 3,1/ 5,1/ 7, and 1/9, the spacing will be uniform on the Lineweaver-Burk plot.) A second advantage of the Eadie-Hofstee plot is that the entire range of possible substrate concentration from near zero to infinity can be fitted onto a single plot. 

Figure 9-4 The Eadie-Hofstee plot of v / [S] against v. The slope is -1/K, the intercept on the vertical axis is Vlnax/Km and that on the horizontal axis is Vmax.

Figure 9-6 Reciprocal plots used to analyze kinetics of two-substrate enzymes. (A) Plot of 1 / against 1 / [A] for a series of different concentrations of the second substrate B. (B) A secondary plot in which the intercepts from graph A are plotted against 1/ [B], (C) Secondary plot in which the slopes from graph A have been plotted against 1 / [B]. The figures have been drawn for the case that Kmp = 10 3 M, Kun, = 2 Km, and K B = KeqAKmB (Eq. 9-46) = KmJ 200 and [A] and [B] are in emits of moles per liter. Eadie-Hofstee plots of v / [A] vs vf at constant [B] can also be used as the primary plots. The student can easily convert Eq. 9-44 to the proper form analogous to Eq. 9-21.

Figure 9-10 Effect of a competitive inhibitor on the Eadie-Hofstee plot (top) and on a double reciprocal plot (bottom). The apparent Km (Eq. 9-59) is increased by increasing [ I ], but E.naxis unchanged.

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