Progress curves inhibitors

E I is a kinetic chimera Kj and kt are the constants characterizing the inactivation process kt is the first-order rate constant for inactivation at infinite inhibitor concentration and K, is the counterpart of the Michaelis constant. The k,/K, ratio is an index of the inhibitory potency. The parameters K, and k, are determined by analyzing the data obtained by using the incubation method or the progress curve method. In the incubation method, the pseudo-first-order constants /cobs are determined from the slopes of the semilogarithmic plots of remaining enzyme activity... 

The ratio kJK, is obtained as /cobs/[I] at low inhibitor concentrations. With efficient inhibitors, parameters Kr and kt can be obtained using the progress curve method in which the enzyme substrate competes with the inhibitor as described for example in Ref. 21. 

Figure 4.3 Product progress curves for an enzyme-catalyzed reaction in the absence (closed circles) and presence open circles) of an inhibitor at a concentration that reduces the reaction rate by 50%. Inset The initial velocity phase of these progress curves.

If the inhibition is found to be rapidly reversible, we must next determine if the approach to equilibrium for the enzyme-inhibitor complex is also rapid. As described in Chapter 4, some inhibitors bind slowly to their target enzymes, on a time scale that is long in comparision to the time scale of the reaction velocity measurement. The effect of such slow binding inhibition is to convert the linear progress curve seen in the absence of inhibitor to a curvilinear function (Figure 5.10). When nonlinear progress curves are observed in the presence of inhibitor, the analysis of... 

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.

If the inhibitor is found to bind rapidly (linear progress curves) and dissociate rapidly (rapid recovery of activity upon dilution) from its target enzyme, then one can proceed to analyze its inhibition modality and affinity by classical methods. The modes of reversible inhibition of enzymes were described in Chapter 3. In the next section of this chapter we will describe convenient methods for determining reversible inhibition modality of lead compounds and lead analogues during compound optimization (i.e., SAR) studies. 

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... 

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 6.5 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).

For compounds that conform to the mechanism of scheme C, an alternative method for defining inhibition modality is to measure progress curves (or preincubation effects vide supra) at varying inhibitor and substrate concentrations, and to then construct a double reciprocal plot of 1/v, as a function of l/[.Sj. Using the analysis methods and equations described in Chapter 3, one can then determine the modality of inhibition for the inhibitor encounter complex. Similarly, for inhibitors that conform to the mechanism of scheme B, a double reciprocal plot analysis of l/vs as a function of 1/[S] can be used to define inhibition modality. 

Addition of the L-732,531 FKBP binary complex to a calcineurin activity assay resulted in increasingly nonlinear progress curves with increasing binary complex concentration. The htting of the data to Equation (6.3) revealed an inhibitor concentration effect on v-, as well as on vs and obs, consistent with a two-step mechanism of inhibition as in scheme C of Figure 6.3. Salowe and Hermes analyzed the concentration-response effects of the binary complex on v, and determined an IC50 of 0.90 pM that, after correction for I.S I/A (assuming competitive inhibition), yielded a A) value for the inhibitor encounter complex of 625 nM. 

These practical approaches are by no means mutually exclusive, and attempts should be made to combine as many of these as possible to improve ones ability to experimentally measure the K-pp of tight binding inhibitors. Thus one should always work at the lowest enzyme concentration possible, and drive the substrate concentration as high as possible, when dealing with competitive inhibitors. A long preincubation step should be used before activity measurements, or the progress curves should be fitted to Equation (6.2) so that accurate determinations of the steady state velocity at each inhibitor concentration can be obtained. Finally, the concentration-response data should be fitted to Morrison s quadratic equation to obtain good estimates of the value of Arfpp. 

Inhibition of enzyme activity by a chemical species that binds slowly and is tight-binding as well has a low dissociation constant). Such inhibitors require special kinetic analysis . The most common method of obtaining the inhibition parameters is by nonlinear regression analysis of the progress curves. 

If protease inhibitors should be identified and characterized, the assay should be tested for signal stability and endpoint linearity in the next step. The progress curves recorded for substrate concentrations near or below the KM value should be linear for up to 2 h. Such signal stability is a prerequisite to run the assay with a pre-incubation time of 1 h for enzyme and inhibitor. This long pre-incubation is recommended to ensure also that the IC50 values for slowly binding inhibitors are correctly determined. An additional hour for the incubation of enzyme, inhibitor and substrate after this pre-incubation is recommended. 

Progress curves for a slow-binding or slow tight-binding inhibitor are described by general Equation 13, where Vq, Vj, and k represent, respectively, the initial... 

Equation 16. Figure 13 gives an example of a progress curve for a slow-binding inhibitor. For each curve with inhibitor present, there is an initial burst followed by a slower steady-state rate. 

Figure 17.13. Reaction progress curves in the presence of increasing concentrations of a slow-binding inhibitor.

The inhibitor could be displaced from Factor Xa by substrates and, based on steady-state assumptions, the dissociation constant for (19) was found to be 14 pM (87). However, the reaction progress curves indicated a slow-binding process, probably by mechanism B. Stopped-flow fluorescence studies, combined with kinetic analysis, showed that the isomerization step (E. I -I- E. I ) is unusually fast and that the formation of E I is, at least, partially rate limiting. 

ATP hydrolysis is non-linear with respect to time. This is not due to enzyme inactivation since progress curves, where the product of variable enzyme concentration and time is plotted against the amount of product, yield points that fall on a single line. This is a response expected if a competitive inhibition occurs during catalysis [80] and suggests an explanation for non-linearity since ADP is a competitive inhibitor with respect to ATP [19]. However, the presence of an ATP-generating system, which increases the rate of phosphate production by a factor of three, does not result in a linear rate [81]. 

Figure 2. Progressive curves of the reaction of thrombin, substrate and inhibitor(P552) at 25 °C. TTie solid lines are the fitting results by using eq 5 in the text,...

It is important to point out that while most of the burden and expertise for impact are borne by the proposing researcher, it is often the chemists on the overall drug discovery team that have the appropriate domain expertise to evaluate the competitive landscape. It is also important for the assay development team to review and verify the assay development and optimization data of the benchtop assay. Sometimes the fundamental assumptions made are faulty, for example that the steady-state conditions are not met for an enzyme assay (i.e., nonlinear progress curves with too high a level of substrate consumption), that endpoint measurements were taken when a progress curve had already plateaued (this is a surprisingly common error, whose impact has been analyzed) [see Fi f. 3 in [4] for simulation, discussion of reasons for nonlinearity with respect to substrate depletion, and workable off-linearity for HTS], or that substrate concentration-to-7Cm ratio is set inappropriately and so will not allow detection of the desired types of inhibitors... 

Fig. 3 (a) Buffer optimization for a pNPP colorimetric assay in 384-well format using p-nitrophenol detection. Activity of HePTP at a concentration of 50 nM was tested in the presence of 1.3 mM pNPP, 1 mM DTT, 0.005 % Tween-20, and various concentrations of Bis-Tris, pH 6.0, and NaCI, over a reaction time of 1 h. The optimal buffer under HTS conditions was 20 mM Bis-Tris, pH. 6.0,1 mM DTT, and 0.005 % Tween-20. The value for pNPP was 0.4 mM. The reaction demonstrated linearity of the progress curves over a period of 2 h. Enzymatic activity was proportional to enzyme concentration. Assay performance was confirmed using the general PTP inhibitor orthovanadate, the ICeo value of which was 150 (b) Buffer optimization for an OMFP... 

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