Lineweaver-Burk plots Michaelis-Menten kinetics

Lineweaver-Burk plot - Michaelis-Menten kinetics Lingane, James J. 

The Michaelis-Menten equation is, like Eq. (3-146), a rectangular hyperbola, and it can be cast into three linear plotting forms. The double-reciprocal form, Eq. (3-152), is called the Lineweaver-Burk plot in enzyme kinetics. ... 

In our previous work [63], we studied the hydrolysis kinetics of lipase from Mucor javanicus in a modified Lewis cell (Fig. 4). Initial hydrolysis reaction rates (uri) were measured in the presence of lipase in the aqueous phase (borate buffer). Initial substrate (trilinolein) concentration (TLj) in the organic phase (octane) was between 0.05 and 8 mM. The presence of the interface with octane enhances hydrolysis [37]. Lineweaver-Burk plots of the kinetics curve (1/Uj.] = f( /TL)) gave straight lines, demonstrating that the hydrolysis reaction shows the expected kinetic behavior (Michaelis-Menten). Excess substrate results in reaction inhibition. Apparent parameters of the Michaelis equation were determined from the curve l/urj = f /TL) and substrate inhibition was determined from the curve 1/Uj.] =f(TL) ... 

The reaction rates as a function of hydroperoxide concentration in the presence of reduced selenosubtilisin can be described by the Michaelis-Menten equation. The apparent Ac at anf Aa values at 60 pH t-butyl hydroperoxide are 430 min and 160 mM, respectively.Lineweaver-Burk plots of the kinetic data at several thiol concentrations gave parallel lines, indicating the involvement of covalent intermediates in the reaction. A possible kinetic mechanism consistent with all the data is shown in Equation 5. 

Fig. 39.17. Schematic illustration of Michaelis-Menten kinetics in the absence of an inhibitor (solid line) and in the presence of a competitive inhibitor (dashed line), (a) Plot of initial rate (or velocity) V against amount (or concentration) of substrate X. Note that the two curves tend to the same horizontal asymptote for large values of X. (b) Lineweaver-Burk linearized plot of 1/V against l/X. Note that the two lines intersect at a common intercept on the vertical axis.

Characteristically, within certain concentration limits, if a chemical is absorbed by passive diffusion, then the concentration of toxicant in the gut and the rate of absorption are linearly related. However, if absorption is mediated by active transport, the relationship between concentration and rate of absorption conforms to Michaelis-Menten kinetics and a Lineweaver-Burk plot (i.e., reciprocal of rate of absorption plotted against reciprocal of concentration), which graphs as a straight line. 

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.

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.

Regulatory enzymes are usually identified by the deviation of their kinetics from Michaelis-Menten kinetics plots of velocity versus substrate concentration can be a sigmoidal curve or a modified hyperbola [Fig. 9-7(o)]. If these curves are plotted in the double-reciprocal (Lineweaver-Burk) form, nonlinear graphs are obtained [Fig. 9-7(6)]. 

Henderson-Hasselbalch equation lahn-Teller effect Lee-Yang-Parr method Lineweaver-Burk method Mark-Houwink plot Meerwein-Ponndorf theory Michaelis-Menten kinetics Stem-Volmer plot van t Hoff-Le Bel theory Wolff-Kishner theory Young-Laplace equation Ziegler-Natta-type catalyst... 

When the substrate concentration is large, the reaction rate is dependent on the substrate concentration. This represents zero-order kinetic behavior. When the concentration is very low, then the kinetics may be represented by first-order kinetic behavior. At Jr = Jrmax/2, the value of the Michaelis constant KM is obtained as S. The Michaelis-Menten equation can be linearized, and the Lineweaver-Burk plot (Figure 8.3) is obtained from the following form... 

Treatment of Kinetic Data. Analysis of Michaelis-Menten kinetics is greatly facilitated by a linear representation of the data. Converting the Michaelis-Menten Equation 17.10 into Equation 17.12 leads to the popular Lineweaver-Burk plot. 

The answer is b. (Murray, pp 48-73. Scriver, pp 4571-4636. Sack, pp 3-17. Wilson, pp 287-317.) When an enzyme obeys classic Michaelis-Menten kinetics as seen in the figure presented in question 154, the Michaelis constant (Km) and the maximal rate (V ax) can be readily derived. By plotting a reciprocal of the Michaelis-Menten equation, a straight-line Lineweaver-Burk plot is produced. The y intercept is l/Vmax, while the x intercept is —l/K . Thus, a reciprocal of these absolute values yields Vjnax and Kn. 

Michaelis-Menten Kinetics Lineweaver-Burk Plots Enzyme Inhibition... 

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. 

Henderson—Hasselbalch equation Jahn—Teller effect Lineweaver—Burk method Mark-Houwink plot Meerwein—Ponndorf theory Michaelis—Menten kinetics Stern—Volmer plot van t Hoff—Le Bel theory Wolff—Kishner theory Young—Laplace equation Ziegler—Natta-type catalyst... 

D23.4 Refer to eqns 23.26 and 23.27, which are the analogues of the Michaelis-Menten and Lineweaver-Burk equations (23.21 and 23,22), as well as to Figure 23.13, There are three major modes of inhibition that give rise to distinctly different kinetic behavior (Figure 23.13), In competitive inhibition the inhibitor binds only to the active site of the enzyme and thereby inhibits the attachment of the substrate. This condition corresponds to a > 1 and a = 1 (because ESI does not form). The slope of the Lineweaver-Burk plot increases by a factor of a relative to the slope for data on the uninhibited enzyme (a = a = I), The y-intercept does not change as a result of competitive inhibition, In uncompetitive inhibition, the inhibitor binds to a site of the enzyme that is removed from the active site, but only if the substrate is already present. The inhibition occurs because ESI reduces the concentration of ES, the active type of the complex, In this case a = 1 (because El does not form) and or > 1. The y-intercepl of the Lineweaver-Burk plot increases by a factor of a relative to they-intercept for data on the uninhibited enzyme, but the slope does not change. In non-competitive inhibition, the inhibitor binds to a site other than the active site, and its presence reduces the ability of the substrate to bind to the active site. Inhibition occurs at both the E and ES sites. This condition corresponds to a > I and a > I. Both the slope and y-intercept... 

Figure 4.9-3 A Lineweaver-Burk plot for determining Michaelis-Menten kinetic parameters for ibuprofen esterification using a lipase in SCCO2 according to Scheme 4.9-1 [22].

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 4.2 Lineweaver-Burk (double-reciprocal) plot of a reaction that follows Michaelis-Menten kinetics. Kinetic parameters are as defined previously. 

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. 

Figure 15.7 Lineweaver-Burke plot to estimate the fundamental pharmacokinetic parameters of a drug that exhibits nonlinear kinetics. Km, Michaelis-Menten constant V ax, maximum velocity.

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