Kitz-Wilson plot

A plot of 1/kobs vs. 1/[R] will be linear if the reaction obeys Equation 9. From the extrapolated intercepts and slope of such a Kitz-Wilson plot one readily can obtain values for k2 and KR. Figure 3 shows a theoretical Kitz-Wilson plot that indicates the values of slope and intercepts from which k2 and KR can be calculated. 

Figure 3. Kitz-Wilson plot for verifying affinity-labeling mechanism.

This effect can be reduced if affinity-labeling kinetic data are analyzed by other types of linear plots used by enzyme kineticists. Two which appear to be useful improvements over the Kitz-Wilson plot are analogs of the Eadie-Hofstee and the Eisenthal-Comish-Bowden plots (20,21). 

The effects of L on the appearance of the Kitz-Wilson plot is exactly analogous to the effect of an enzyme competitive inhibitor on a Line-weaver-Burk plot. 

Kl. Figure 3 compares Kitz-Wilson plots obtained plus and minus L. Of course the effects of L on affinity-labeling kinetics could also be analyzed quantitatively by Eadie-Hofstee or direct linear-type plots. 

Plot 1/ kobxrved versus 1/inhibitor concentration (Lineweaver-Burk plot). Kinia is calculated as the reciprocal of the y-intercept, and K, as the negative of the reciprocal of the -intercept. Alternatively, Plot the Kitz-Wilson plot of tm (calculated as 0.692/ kobserved) versus the reciprocal of the inhibitor concentration and estimate Ktaact as the y-intercept, and Kt as the reciprocal of the -intercept. 

FIGURE 4.12 Kitz-Wilson plot of the half-lives (rate constants) for mechanism-based inactivation at each inactivator concentration. 

From this plot the half-lives (rate constants) for the inactivation by each concentration of inactivator can be calculated from the slopes of the individual lines. These half-life values are then plotted along the y-axis versus 1/[I] plotted along the x-axis. This plot is also known as a Kitz-Wilson plot (Fig. 4.12). In the case of a saturation reaction, (i.e., at infinite inactivator concentration there is a finite half-life) the point where the plotted line intersects the y-axis is equal to 0.693/kinact where A inact is the rate of inactivation and represents a complex mixture of 2 3 and 4 (see Scheme 4.5). The dissociation constant for the enzyme-mechanism-based inactivator complex (Ki) can also be estimated from this plot as the x-intercept of the line represents —l/Ki (Fig. 4.12). 

Enzymologists will recognize the complete equivalence of the Kitz-Wilson and Lineweaver-Burk plots. This equivalence extends to the practical statistical problems characteristic of the Lineweaver-Burk plot. [These have been discussed by Segel (19) and Cornish-Bowden (20).]... 

They center on the effect of errors in measuring kohs at low values of fcobs these errors are amplified in the value of l/kobs. However, it is points farthest out on the Kitz-Wilson (or Lineweaver-Burk) plot— those corresponding to the lowest values of kohs—that most strongly influence the slope selected for the straight line that best fits the data. Thus, error in the estimation of KR is introduced. 

Comparing Equation 29 with Equation 9 shows that the two expressions for kobe differ only in the constants in the numerators of the right-hand sides. Both mechanisms predict first-order kinetics for the loss of site activity and identical dependence of the observed first-order rate constant, kobBy on the [R]. The similarity of Equations 9 and 29 demonstrates that the documentation of saturation kinetics as evidenced by linear Kitz-Wilson or Eadie-Hofstee plots or by the critria of the direct linear plot does not prove that true affinity labeling is involved necessarily in a site-inactivating reaction. 

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). 

To determine the Ki and kmact values, first a plot of the log of the enzyme activity versus time is constructed (Fig. 16a). The rate of inactivation is proportional to low concentrations of the inactivator, but becomes independent at high concentrations. In these cases, the inactivator reaches enzyme saturation (just as substrate saturation occurs during catalytic turnover). Once all of the enzyme molecules are in the E-I complex, the addition of more inactivator does not affect the rate of the inactivation reaction. The half-lives for inactivation (fi/2) at each inactivator concentration (lines a-e in Fig. 16a) are determined. The fi/2 at any inactivator concentration equals log 2/kina( t,appf in the limiting case of infinite inactivator concentration, fi/2 = 0.693/kiiiact (log 2 = 0.693). A replot of these half-lives versus the inverse of the inactivator concentration, referred to as a Kitz and Wilson replot, is constructed to obtain the K and kjuact values (Fig. 16b). 

In direct analogy to the Michaelis-Menten mechanism for reaction of enzyme with a substrate, the inactivator, I, binds to the enzyme to produce an E l complex with a dissociation constant K. A first-order chemical reaction then produces the chemically reactive intermediate with a rate constant k. The activated species may either dissociate from the active site with a rate constant to yield product, P, or covalently modify the enzyme ( 4). The inactivation reaction should therefore be a time-dependent, pseudo-first-order process which displays saturation kinetics. This is verified by measuring the apparent rate constant for the loss of activity at several fixed concentrations of inactivator (Fig. lA). The rate constant for inactivation at infinite [I], itj act (a function of k2, k, and k4), and the Ki can be extracted from a double reciprocal plot of 1/Jfcobs versus 1/ 1 (Fig. IB) (Kitz and Wilson, 1962 Jung and Metcalf, 1975). A positive vertical... 

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