Lineweaver-Burke graph

Figure 2.8a and b illustrate the effects of a competitive and a non-competitive inhibitor on the Lineweaver-Burke graph. Note the changes in the slope of the lines in the presence of the inhibitor and how this affects values for Km and V/m[Pg.43]

Figure 2.8 (a) Effect of a competitiveinhibitor on the. Lineweaver-Burke graph, (b) Effect of a noncompetitive inhibitor on the Lineweaver-Burke graph... 

The effects of these classes of inhibitors on Lineweaver-Burk kinetics are shown in Figures 1-8-7 and 1-8-8. Notice that on a Lineweaver-Burk graph, inhibitors always lie above the control on the right side of the y-axis. A line below the control might represent the addition of an activator. 

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... 

Figures 4.12, 4.14, and 4.17 are Lineweaver-Burk graphs of competitive, noncompetitive, and uncompetitive reversible inhibitors. Sketch three Michaelis-Menten graphs showing an enzyme with and without one of the three types of inhibitors. Clearly label the important parts of each graph. 

The activities of free and immobilized invertase for various substrate concentrations are plotted in a Lineweaver-Burk graph, from which Vmax and Km values were calculated (Fig. 9). The Km of free enzyme was 40.3 mM, while the apparent Km was 38.2 mM for the immobilized one. These similar Km values for both forms indicate that enzyme-substract interaction is not substantially altered after immobilization. However, the Vmax for immobilized invertase (0.0489 U/mL) was 35% higher than the Vmax for soluble invertase (0.0320 U/mL). Such a difference could be explained by the predominance of supramolecular aggregates (hexamer, octamer forms) guaranteed under the conditions of the immobilization assay. 

Intercepts of Lineweaver—Burk Graphs in the Presence of Inhibitor... 

As already oudined, inhibition is essentially complete when caused by reagents that react with sulfhydryl groups (for example, p-chloro-mercuribenzoate, p-mercuribenzoate, o-iodosobenzoate, L-ascorbic acid silver, cupric, and mercuric ions iodine, and ferricyanide) this inactivation can be reversed to some extent by hydrogen sulfide and by cysteine. Lineweaver—Burk graphs have shown that the action of L-ascorbic acid is noncompetitive, and L-ascorbic acid acting in the presence of cupric ions probably causes formation of an inactive cuprous-enzyme. The action of p-chloromercuribenzoate on barley beta-amylase has been shown to be a competitive inhibition. In contrast, the soya-bean p-chloromercuribenzoate inhibition is noncompetitive, and the extent of inhibition is inversely related to the concentration of acetate ion. The latter exhibits a protective effect, and there... 

Of the six curves labeled in the Lineweaver-Burk graph below, three represent the effects of 0 mM, 5 mM, and 15 mM of a competitive inhibitor on a hypothetical enzyme. Which of the curves most likely represents the 15-mM concentration of the competitive inhibitor ... 

FIGURE 14.18 Single-displacement bisubstrate mechanism. Double-reciprocal plots of the rates observed with different fixed concentrations of one substrate (B here) are graphed versus a series of concentrations of A. Note that, in these Lineweaver-Burk plots for singledisplacement bisubstrate mechanisms, the lines intersect to the left of the 1/v 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. 

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. 

Use the data in Table 2.2 to plot Michaelis-Menten, Lineweaver-Burke and Eadie-Hofstee graphs to determine Km and Vm DC values. Answers are given at the end of the chapter. 

Test your IT skills. Try creating Excel spreadsheets based on the Michaelis-Menten equation (Equation 2.9) and its variants (Equations 2.10 and 2.11). Insert into your spreadsheets your own values for JCm, Vmax, [S], [I] and A) and use Excel to plot Michaelis-Menten, Lineweaver-Burke and Eadie-Hofstee graphs. 

Historically, data have been transformed to facilitate plotting on linear plots such as Lineweaver-Burk (1/y versus 1/[S]), Hanes-Woolf ([S]/y versus [S]), or Eadie-Hofstee (v/[S] versus y). However, with the present availability of affordable nonlinear regression and graphing software packages such as GraphPad Prism,... 

The Lineweaver-Burk equation is a reciprocal form of the Michaelis-Menten equation. The same data graphed in this way yield a straight line as shown in Figure 1-8-6. The actual data are represented by the portion of the graph to the right of the y-axis, but the line is extrapolated into the Idt quadrant to determine its intercept with the x-axis. The intercept of the line with the x-axis gives the value of The intercept of the line with the y-axis gives the value of... 

The x-coordinate axis for a graph of Cartesian coordinates [x,y or [x, f(x)] or the x-value for any [x,y] ordered pair. This corresponds to the [Substrate Concentration]-axis in v versus [S] plots or the ll[Substrate Concentra-fton]-axis in so-called double-reciprocal or Lineweaver-Burk plots. 

Kinetic analysis of tyrosinase and calculation of constants will be described using graphical analysis by the Michaelis-Menten equation, Lineweaver-Burk equation, or the direct linear curve. Procedures for preparing these graphs are described below. Alternatively, students may use available computer software to graph data and calculate kinetic constants. Recommended enzyme kinetic computer software packages include Enzyme... 

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. A/i/min. Convert all AA/mm units to /xmoles/min as described in part B. Prepare a Michaehs-Menten curve (/xmoles/min vs. [S]) as in Figure E5.1 and a Lineweaver-Burk plot (l//xmole/min vs. 1/[S]) as in Figure E5.2. Alternatively, you may wish to use the direct linear plot. Estimate Ku and Vmax from each graph. The intercept on the rate axis of the Lineweaver-Burk plot is equal to 1/V-. For example, if the line intersects the axis at 0.02,... 

This expression indicates that a plot of 1/v versus 1/[S] fits a straight line with a slope of Km/Vmax (fig. 7.9). Such a plot is known as a Lineweaver-Burk, or double-reciprocal, plot. The intercept of the line on the ordinate occurs at 1/v = 1/Vmax, and the intercept on the abscissa occurs at 1/[S] = -1 IKm. Vmax and Km thus can be determined readily from the graph. 

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... 

Repeat Question 11, but graph the data as a linear, double reciprocal plot in the spirit of the Lineweaver-Burk equation (see Chapter 4). Plot l/ATm vs. 1 /(N/nt) and perform a linear regression to determine the best-fit line (Equation 4.a). The x-intercept corresponds to the KD of the DNA-netropsin complex. The KD value from this method should be more accurate than the estimation in Question 11. 

Graphing these values gives a Lineweaver-Burk plot. From the best straight line through the data, the intercept on the horizontal axis = — 1/Km and the intercept on the vertical axis = 1/Umax. From these values, we can calculate Km and Umax ... 

Using the Living Graphs for Equation 6-30 and the Lineweaver-Burk equation in Box 6-1, create Lineweaver-Burk (double-reciprocal) plots for all the cases in (a) and (b). When a = 2.0, does the x intercept move to the right or to the left If a = 2.0 and a = 3.0, does the x intercept move to the right or to the left ... 

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)]. 

For each of the four types of enzyme inhibition given in Table 9.1, derive the Lineweaver-Burk equations and draw archetypal graphs. 

To derive the Lineweaver-Burk equations, we proceed by simply taking the reciprocals of each side of the equations expressing v0 as a function of [S]0 in Table 9-1. The corresponding graphs of l/u0 versus l/[S]o have varying slopes, intercepts, or both as [I] is varied. Pure noncompetitive inhibition shows lines... 

Prepare a plot of l/V0 versus l/[ONPG] (a Lineweaver-Burk plot) using the data obtained from tubes 2 to 6. Compare the x-intercept and y-intercept of this graph with those obtained in the absence of inhibitor (to determine Km and Umax). Are they the same What type of inhibition does methyl-/3,D-galactopyranoside display toward /3-galactosidase Can you calculate an inhibition constant (K ) for this inhibitor (remember that the methyl-/3,D-galactopyra-noside stock solution was at a concentration of 750 mM) ... 

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