Slow binding inhibitors

1 DETERMINING kobs THE RATE CONSTANT FOR ONSET OF INHIBITION 

The hallmark of slow binding inhibition is that the degree of inhibition at a fixed concentration of compound will vary over time, as equilibrium is slowly established between the free and enzyme-bound forms of the compound. Often the establishment of enzyme-inhibitor equilibrium is manifested over the time course of the enzyme activity assay, and this leads to a curvature of the reaction progress curve over a time scale where the uninhibited reaction progress curve is linear. We saw 

Evaluation of Enzyme Inhibitors in Drug Discovery, by Robert A. Copeland ISBN 0-471-68696-4 Copyright 2005 by John Wiley Sons, Inc. 

Enzyme Inhibitor Apparent k (M-V1) Apparent koS (s-1) Dissociation Half-life 

Cytidine deaminase Cytidine phosphinamide analogue 8.3 x 103 7.8 x 10 6 25 hours 

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Slow-binding inhibitors operate by one of two mechanisms. Either the inhibitor binds slowly in an initial step, or the initial binding step occurs quickly, followed by a slow rearrangement of the E-I complex. 

Figure 5.10 Progress curves for an enzyme in the absence (open circles) and presence (closed circles) of an slow-binding inhibitor. See Chapter 6 for more details on this form of inhibition.

Figure 6.1 Typical progress curve for an enzyme reaction in the presence of a slow binding inhibitor. The initial (v,) and steady state (vs) velocities are defined by the slope values in the early and late stages of the progress curve, respectively, as indicated by the dashed lines.

Figure 6.2 Effect of preincubation time with inhibitor on the steady state velocity of an enzymatic reaction for a very slow binding inhibitor. (A) Preincubation time dependence of velocity in the presence of a slow binding inhibitor that conforms to the single-step binding mechanism of scheme B of Figure 6.3. (B) Preincubation time dependence of velocity in the presence of a slow binding inhibitor that conforms to the two-step binding mechanism of scheme C of Figure 6.3. Note that in panel B both the initial velocity (y-intercept values) and steady state velocity are affected by the presence of inhibitor in a concentration-dependent fashion.

Figure 6.5 Concentratioin esponse plot of inhibition by a slow binding inhibitor that conforms to scheme B of Figure 6.3. The progress curves of Figure 6.4A were fitted to Equation (6.1). The values of vs thus obtained were used together with die velocity of the uninhibited reaction (v0) to calculate the fractional activity (vs/v0) at each inhibitor concentration. The value of Kf9 is then obtained as the midpoint (i.e., die IC50) of die isotherm curve, by fitting die data as described by Equation (6.8).

In the mechanism illustrated by scheme B, significant inhibition is only realized after equilibrium is achieved. Hence the value of vs (in Equations 6.1 and 6.2) would not be expected to vary with inhibitor concentration, and should in fact be similar to the initial velocity value in the absence of inhibitor (i.e., v, = v0, where v0 is the steady state velocity in the absence of inhibitor). This invariance of v, with inhibitor concentration is a distinguishing feature of the mechanism summarized in scheme B (Morrison, 1982). The value of vs, on the other hand, should vary with inhibitor concentration according to a standard isotherm equation (Figure 6.5). Thus the IC50 (which is equivalent to Kfv) of a slow binding inhibitor that conforms to the mechanism of scheme B can be determined from a plot of vjv0 as a function of [/]. 

Figure 6.7 Concentratiom-esponse plots for the initial (A) and final (B) inhibited states of an enzyme reaction inhibited by a slow binding inhibitor that conforms to die mechanism of scheme C of Figure 6.3. The values of Vj and vs at each inhibitor concentration were obtained by fitting the data in Figure 6.6Ato Equation (6.1). These were then used to calculate the fractional velocity (Vj/v0 in panel A and vs/v0 in panel B), and die data in panels A and B were fit to Equations (6.8) and (6.9) to obtain estimates of Kf99 and Kf 9, respectively.

Note that for very slow binding inhibitors that are studied by varying preincubation time, the fits of the exponential decay curves to Equation (6.4) provide values for both V, and kohs for each inhibitor concentration. The values of v, at each inhibitor concentration represent the v-intercepts of the best fit to Equation (6.4), and these can be used in conjunction with Equation (6.8) to obtain an independent estimate of... 

Figure 6.8 Replot of kobs as a function of inhibitor concentration for a slow binding inhibitor that conforms to the mechanism of scheme C of Figure 6.3 when the value of k6 is too small to estimate from the y-intercept of the data fit.

Determining Inhibition Modality for Slow Binding Inhibitors 153... 

DETERMINING INHIBITION MODALITY FOR SLOW BINDING INHIBITORS... 

As stated above, the vast majority of slow binding inhibitors that have been reported in the literature are active-site directed, hence competitive inhibitors. Nevertheless, there is no theoretical reason why noncompetitive or uncompetitive inhibitors could not also display slow binding behavior. Thus, to convert the apparent values of K,... 

The inhibition modality for a slow binding inhibitor is easily determined from the effects of substrate concentration on the value of k0bs at any fixed inhibitor concentration (Tian and Tsou, 1982 Copeland, 2000). For a competitive inhibitor the value of fcobs will diminish hyperbolically with increasing substrate concentration according to Equation (6.15) ... 

Figure 6.9 Effect of substrate concentration (relative to KM) on the value of kAs at a fixed concentration of a slow binding inhibitor that is competitive (closed circles), uncompetitive (open circles), or noncompetitive (a = 1, closed squares) with respect to the varied substrate.

Some Examples of Pharmacologically Interesting Slow Binding Inhibitors 157... 

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