Michaelis-Menten kinetics 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.

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 ... 

Fig. S.51. Eadie-Hofstee type plot showing departure from Michaelis-Menten kinetics due to external diffusion limitation...

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. 

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.

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... 

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. 

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. 

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 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... 

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. 

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 ... 

---