Michaelis Lineweaver-Burk plot

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. ... 

According to this expression, a plot of 1/v, versus l/[SJo will yield a straight line if the data follow the Michaelis-Menten mechanism. This line has a slope given by Km/Vmax, a y intercept of 1/Vmax, and an x intercept of -1 fKm. This is also illustrated in Fig. 4-7. Again, this treatment is valid when Eq. (4-107) applies whether or not the catalyst is an enzyme. The Lineweaver-Burk plot, Fig. 4-lb, is convenient for visualization but statistically unreliable for data fitting the form in Eq. (4-107) should be used for numerical analysis. 

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 Lineweaver-Burk plot uses the reciprocal of the Michaelis-Menten equation in the form of the equation of a straight line, y = mx+ b, having the form shown in equation 2.3 ... 

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.

Lineweaver-Burk Plot Rearrangement of the Michaelis-Menten equation (Equation 3.28) gives [4]... 

It is very useful to transform the Michaelis-Menten equation into a linear form for analyzing data graphically and detecting deviations from the ideal behavior. One of the best known methods is the double-reciprocal or Lineweaver-Burk plot. Inverting both sides of equation 3.1 and substituting equation 3.2 gives the Lineweaver-Burk plot 4... 

The treatment of results will be described for L-dopa. The procedure for D-dopa is identical. Prepare a table of L-dopa concentration per assay (mmo-lar) vs. AA/mm. Convert all AA/mm units to p,moles/min as desenbed in part B. Prepare a Michaelis-Menten curve (jumoles/min vs. [S]) as in Figure E5.1 and a Lineweaver-Burk plot (1/p.mole/min vs 1/[S]) as in Figure E5.2. Alternatively, you may wish to use the direct linear plot. Estimate and V max from each graph. The intercept on the rate axis of the Lineweaver-Burk plot is equal to UVm3zr For example, if the line intersects the axis at 0.02, then Vmax = 1/0.02 or 50 panoles of product formed per minute. The line intersects the 1/[S] axis at a point equivalent to — /Ku. If the intersection point on the 1/[S] axis is —0.67, then AM = -1/ -0.067 = 15 p-molar. Repeat this procedure for the data obtained for D-dopa. Compare the KM and max va ues and explain any differences. 

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. 

Mass transfer can alter the observed kinetic parameter of enzyme reactions. Hints of this are provided by non-linear Lineweaver-Burk plots (or other linearization methods), non-linear Arrhenius plots, or differing Ku values for native and immobilized enzymes. Different expressions have been developed for the description of apparent Michaelis constants under the influence of external mass transfer limitations by Homby (1968) [Eq. (5.69)], Kobayashi (1971), [Eq. (5.70)], and Schuler (1972) [Eq. (5.71)]. 

Michaelis-Menten and Lineweaver-Burk plots can help classify an inhibitor, but successful drug development requires the ability to compare the effectiveness of one inhibitor to another based on results from an assay. Enzymes are typically compared based on one of two values K or IC5(). 

As a complement to question 1, plot the binding data of thiomuscimol in Michaelis-Menten (response versus [L]) format. Try to create a Lineweaver-Burk plot (1/response versus 1/[L]) and perform a linear regression on the data. What is the problem you encounter while making this graph Do your best to graph the data. From the best-fit line of the Lineweaver-Burk plot, determine Kt) and Enva. How well does Ku in this graph match the Ku you determined in... 

Kinetic studies of this reaction have shown that it obeys Michaelis-Menton kinetics as expressed by the Lineweaver-Burk plot, the Michaelis constant (KJ for this reaction at pH 7.0 and 37.5 °C being 2.86 x 10 4 M 24). Free lysine, Leuehs Poly-L-lysine, total hydrolyzates of thermal polylysine, and amino group-modified thermal polylysine are completely inactive. The activity of thermal polylysine depends on the degree of polymerization 24). 

Alternatively, you can linearize the Michaelis-Menten equation by using an Eadie-Hofstee plot [23,24]. Here the reaction velocity, v, is plotted as a function of v/[S], as shown in Eq. (2.43). This approach is more robust against error-prone data than the Lineweaver-Burk plot, because it gives equal weight to data points in any range of [S] or v. The disadvantage here is that both the ordinate and the abscissa depend on v, so any experimental error will be present in both axes. 

These hyperbolic equations are analogous to the Michaelis-Menten equation. Nonlinear regression is preferable to the method proposed in the 1960s by Kitz and Wilson, which necessitates a double-reciprocal linear transformation of the data (analogous to a Lineweaver-Burk plot) that can bias the estimates of /clnact and A). 

The dynamics were run for several concentrations of substrate and variations in the Pc values. Initial velocities of the reaction were recorded. The Michaelis-Menten model was observed and characteristic Lineweaver-Burk plots were found from the model. Systematic variation of the lipophilicity of substrates and products showed that a lower affinity between a substrate and water leads to more of the S —> P reaction at a common point along the reaction progress curve. This influence is greater than that of the affinity between the substrate and the enzyme. The study created a model in which the more lipophilic substrates are more reactive. The water-substrate affinity appears... 

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

The rate of hydrolysis of 3H-phenyl-cocaine in the presence and absence of each monoclonal antibody as a function of substrate concentration was determined. Production of radiolabeled benzoic acid at time points corresponding to < 5% reaction extent provided initial rates. A saturation kinetics and a linear Lineweaver-Burk plot for each artificial enzyme were plotted. The first-order rate constants (kcat) and Michaelis constants (Km) of selected antibodies are provided in Table 2. 

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... 

Fig. 2.—Graphical Determination of the Maximum Velocity, V, and the Michaelis Constant, K . [(o) v against [S] (f>) t) against[S], Lineweaver—Burk plot (c) a Line-weaver—Burk plot for competitive inhibition (d) a Lineweaver—Burk plot for noncompetitive inhibition.]...

From the Lineweaver-Burk plot, the data do conform to the Michaelis-Menton rate law and... 

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. 

To motivate the form of the experiments, note first that two parameters are properties of the organism the m and the a of the chemostat equations. One might postulate that the competitor with the largest m or the one with the smallest a should win the competition. Recall that m is the maximal growth rate and that a (the Michaelis-Menten constant) represents the half-saturation concentration (and so is an indicator of how well an organism thrives at low concentrations). Both of these quantities are obtainable in the laboratory by growing the organism (without a competitor) on the nutrient. (Hansen and Hubbell used a Lineweaver-Burk plot.)... 

Reaction velocities were determined at various concentrations of a-glycerophosphate and of phenyl phosphate at pH 5.5 and 37° with 0.1 M acetate as buffer and 0.001 M EDTA. A Lineweaver-Burk plot yielded a value of 7 mM for the Michaelis constant with a-glycerophos-phate as substrate and 0.9 mM with phenyl phosphate as buffer. It will be recalled that the corresponding values for human prostatic phosphatase were 3.1 mM and 0.15 mM according to Tsuboi and Hudson (T3). Nigam et al. (N3) had obtained a value of 0.75 mM for phenyl phosphate. In view of the experimental errors inherently involved in the determination of Michaelis constants leading frequently to coefiBcients... 

The Michaelis-Menten equation can be algebraically transformed into more useful way to plot the experimental data. Lineweaver and Burk have taken the reciprocal of both [S] and v of the Michaelis-Menten equation to give Double Reciprocal or Lineweaver-Burke Plot Need in form y = ax + b, so take reciprocals of both sides (Fig. 6.4) and have -... 

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