Lineweaver

The equilibrium constants obtained using the metal-ion induced shift in the UV-vis absorption spectrum are in excellent agreement with the results of the Lineweaver-Burke analysis of the rate constants at different catalyst concentrations. For the copper(II)ion catalysed reaction of 2.4a with 2.5 the latter method gives a value for of 432 versus 425 using the spectroscopic method. 

In a Lineweaver-Burke analysis Mk pp is plotted as a function of l/[catalyst]. The intercept of this plot on the y-axis provides the value of Vk-yA, whereas the intercept on the x-axis yields the value for 1/K,z. 

A plot of 1/v versus 1/[S], which is called a double reciprocal, or Lineweaver-Burk plot, is a straight line with a slope of Km/Vmax) a y-intercept of 1/Vmax> and an x-intercept of-l/Km (Figure 13.11). 

The three reversible mechanisms for enzyme inhibition are distinguished by observing how changing the inhibitor s concentration affects the relationship between the rate of reaction and the concentration of substrate. As shown in figure 13.13, when kinetic data are displayed as a Lineweaver-Burk plot, it is possible to determine which mechanism is in effect. 

Effect of the concentration of inhibitor on the Lineweaver-Burk plots for (a) competitive inhibition, (b) noncompetitive inhibition, and (c) uncompetitive inhibition. The inhibitor s concentration increases in the direction shown by the arrows. 

Lineweaver-Burk plot a graphical means for evaluating enzyme kinetics, (p. 638)... 

Equation 1-111 is known as the Lineweaver-Burk or reciprocal plot. If the data fit this model, a plot of l/V versus 1/Cg will he linear with a slope K /V x intercept l/V x-... 

Lineweaver-Burk Plot (Rate of reaction m. s/kmol)... 

Equation 11-17 is refeiTed to as a Lineweaver-Burk equation involving separate dependent and independent variables 1/v and 1/Cg, respeetively. Equation 11-17 ean be further rearranged to give... 

Equation 11-18 is referred to as the Eadie-Hofstee equation, where V is plotted against v/C . However, both of these equations are sub-jeeted to large eiTors. Equation 11-18 in partieular eontains tlie measured variable v in both eoordinates, whieh is subjeeted to the largest errors. Eigures 11-2 and 11-3 show plots of Lineweaver-Burk and Eadie-Hofstee equations, respeetively. 

Using the developed eomputer program PROGl, the model equation 1/Y = A + B 1/X represents the Lineweaver-Burk plot represented by Equation 11-17 as ... 

Figure 11-5 shows the Lineweaver-Burk plot of 1/v versus 1/Cj,. 

Figure 11-5. Double reoiprooal (Lineweaver-Burk) plot to determine and kg...

Competitive and non-eompetitive inhibitions are easily distinguishable from the Lineweaver-Burk plot. In the ease of eompetitive inhibitors, the intereept on tlie 1/Cg axis inereases while tlie intereept of tlie 1/v axis remains unehanged by the addition of the inhibitor. Conversely, with a non-eompetitive inhibitor, only the 1/v axis intereept inereases. The effeet of eompetitive inhibitors ean be reversed by inereasing the substrate eoneentration. Where the enzyme or the enzyme substrate eomplex is made inaetive, a non-eompetitive inhibitor deereases of the enzyme, but remains eonstant. 

Lineweaver-Burk plot Method of analyzing kinetic data (growth rates of enzyme catalyzed reactions) in linear form using a double reciprocal plot of rate versus substrate concentration. 

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. ... 

Because of the hyperbolic shape of versus [S] plots, Vmax only be determined from an extrapolation of the asymptotic approach of v to some limiting value as [S] increases indefinitely (Figure 14.7) and is derived from that value of [S] giving v= V(nax/2. However, several rearrangements of the Michaelis-Menten equation transform it into a straight-line equation. The best known of these is the Lineweaver-Burk double-reciprocal plot ... 

FIGURE 14.9 The Lineweaver-Burk double-reciprocal plot, depicting extrapolations that allow the determination of the and 31-intercepts and slope. 

FIGURE 14.13 Lineweaver-Bnrk plot of competitive inhibition, showing lines for no I, [I], and 2[I]. Note that when [S] is infinitely large (1/[S] = 0), Enax the same, whether I is present or not. In the presence of I, the negative 3c-intercept = —l/fCjil + U-]/Ki). 

Pure noncompetitive inhibition occurs if Ki = Ki. This situation is relatively uncommon the Lineweaver-Burk plot for such an instance is given in Eigure 14.15. Note that K is unchanged by I (the x-intercept remains the same, with or without I). Note also that Tmax decreases. A similar pattern is seen if the amount of enzyme in the experiment is decreased. Thus, it is as if I lowered [E],... 

FIGURE 14.16 Lineweaver-Burk plot of mixed noncompetitive inhibition. Note that both intercepts and the slope change in the presence of I. (a) When Ki is less than Ki (b) when Ki is greater than Ki. ... 

Both classes of single-displacement reactions are characterized by lines that intersect to the left of the 1/v axis in Lineweaver-Burk doublereciprocal plots (Figure 14.18). 

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. 

Write the Lineweaver-Burk (double-reciprocal) equivalent of this equation, and from it calculate algebraic expressions for (a) the slope (b) the y-intercepts and (c) the horizontal and vertical coor-... 

First draw both Lineweaver-Burk plots and Hanes-Woolf plots for the following a Monod-Wyman-Changeux allosteric K enzyme system, showing separate curves for the kinetic response in (1) the absence of any effectors (2) the presence of allosteric activator A and (3) the presence of allosteric inhibitor I. Then draw a similar set of curves for a Monod-Wyman-Changeux allosteric Uenzyme system. 

This is referred to as a double reciprocal or lineweaver Burk plot. From this linear plot, Kd = slope/intercept and the 1 /intercept = Bmax. Finally, a linear plot can be achieved with... 

The competitive and non-competitive inhibitors are easily distinguished in a Lineweaver-Burk plot. The competitive inhibitor intercepts on the Mv axis whereas the non-competitive inhibitor intercepts on the 1/5 axis. The reaction of inhibitors with substrate can be assumed as a parallel reaction while the undesired product is formed along with desired product. The reactions are shown as ... 

Plot both sets of data as a Lineweaver-Burk plot for competitive inhibition (see Fig. 

Fig. E 5.1. Competitive inhibition based on the Lineweaver-Burk model.

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