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Contemporary chemical biology and drug discovery are increasingly focused on the discovery of inhibitory molecules that interact with enzyme targets in specific ways, such as allosteric or orthosteric binding. Hence, there is increasing interest in evaluating hit compounds from high-throughput diversity screening to determine their mode of interaction with the target. In this work, the common inhibition modalities are reviewed and clarified. The impact of substrate concentration, relative to substrate KM, for each common inhibition modality is also reviewed. The pattern of changes in IC50 that accompany increasing substrate concentration are shown to be diagnostic of specific inhibition modalities. Thus, replots of IC50 as a function of the ratio [S]/KM are recommended as a simple and rapid means of assessing inhibition modality. Finally, specific recommendations are offered for ideal experimental conditions for the determination of inhibition modality through the use of IC50 replots.
High-throughput screening (HTS) of large, diverse chemical libraries has become a mainstay of modern drug discovery and chemical biology research. HTS is commonly used to identify chemical starting points for the pharmacological inhibition of pathogenic target proteins. Enzymes hold a preeminent position among drug targets due to their roles in specific chemical reactions of pathogenic relevance and due to their susceptibility to inhibition by pharmacologically tractable, small molecules.
For example, an important consideration for HTS assays is to poise the substrate concentration ([S]) equal to the value of KM for that substrate, so that the ratio [S]/KM = 1. Under these conditions, the assay has an equal likelihood of identifying inhibitors of diverse modes of interaction with the target enzyme; hence, assays run under the condition of [S]/KM = 1 are said to be run under balanced conditions.
Subsequent to an HTS campaign, researchers assess the desirability of particular hit compounds by a number of criteria. Many of these criteria focus on the data reproducibility, chemical structure and other aspects of the chemical, and physical qualities of hit compounds; these are familiar to the HTS community. More recently, there has been growing interest in strategies that target enzymes and other targets by specific mechanisms of interaction. A number of groups, for example, are focused on allosteric binding as the modality of greatest interest. For other groups, orthosteric binding of inhibitors, within the enzyme active site, is strongly preferred. Still other groups seek to find inhibitors that interact directly with enzyme-bound substrate(s) through covalent and noncovalent mechanisms. Hence, a question that commonly arises during postscreening compound assessment is the mode of interaction (MOI) between the inhibitor and the target enzyme. The topic of MOI has been generally covered in the biochemical literature.
However, the application of inhibition modality assessment and practical approaches to defining optimal experimental conditions for post-HTS analysis have received more limited attention.
Hence, the goal of the present work is to review the common modes of inhibitor interactions with enzymes and like targets, and to provide methodologies for facile assessment of inhibition modality, for the benefit of the readership of this journal and the broader scientific community.
Inhibitor Interactions with Targets
Common inhibition modalities are defined by the affinity with which an inhibitor binds to the free form of the enzyme (E), or to the enzyme–substrate (ES) binary complex (or to species that form subsequent to the ES complex along the reaction coordinate of the enzyme), or to both. As seen in Figure 1, an inhibitor may bind to both the free enzyme (E) and the enzyme–substrate (ES) complex. The affinity of the inhibitor for the ES complex may differ from its affinity for E by the thermodynamic cooperativity factor α. Likewise, the affinity of substrate (S) for E and for the enzyme–inhibitor (EI) complex will be affected by the same factor α, to form the thermodynamic cycle illustrated in Figure 1. Thus, five modes of inhibitor interaction with a target enzyme may be defined, in most instances, based on the quantitative value of α: pure competitive, mixed competitive, noncompetitive, mixed uncompetitive, and pure uncompetitive. These terms are defined below and also shown in Figure 1. For bisubstrate enzymes that show significant cooperativity or anticooperativity at varying substrate concentrations, the determination of inhibitor modality requires more advanced methods.
Figure 1Thermodynamic cycle of enzyme interactions with substrate and inhibitor molecules and definitions of different inhibition modalities with respect to values of α, Ki, and αKi.
When α approaches infinity, the inhibitor binds exclusively to E and not to ES. Such a compound is referred to as a pure competitive inhibitor (with respect to the substrate, S; for enzymes that act on multiple substrates, competitive inhibition against one substrate may display any of a number of patterns with respect to the other substrate[s]). The inhibitor is termed competitive because both the inhibitor and the substrate compete for binding to the same form of the enzyme, E. (Note that while formally a pure competitive inhibitor displays an α value of infinity, in practice some researchers consider inhibitors to be competitive if the value of α exceeds 10.) One can also say that the inhibitor and substrate are mutually exclusive in their binding to E; that is, either S or I can bind to E, but the two ligands cannot bind to the same molecule of E simultaneously.
It is tempting to infer that competitive inhibitors share a common binding site with the substrate (i.e., the enzyme active site). In many cases, this inference turns out to be true. For example, many ATP competitive inhibitors of kinases bind within the ATP binding pocket of these enzymes. However, the term competitive inhibition is not synonymous with a common binding site for both ligands. In some cases, the inhibitor may bind to a distinct site on the enzyme that is in allosteric communication with the substrate binding pocket. In many cases, allosteric, substrate competitive compounds result in conformational changes to the enzyme that change the ability of the enzyme to bind substrate. This was the case, for example, for certain ATP competitive inhibitors of the kinesin spindle protein (KSP).
found that a series of inhibitors bound to KSP in a mutually exclusive manner (competitive) with the substrate ATP. The cumulative data from the generation of resistant cells by site-directed mutagenesis and photoaffinity labeling demonstrated that the inhibitors in this pharmacophore series were binding to a remote pocket that was connected to the ATP binding pocket by an alpha-helical segment of the protein. They proposed that compound binding at this allosteric site induced a conformational change, propagated along the alpha helix, resulting in changes to the ATP binding pocket that precluded ATP binding. Several years later, Yokoyama et al.
identified another ATP competitive inhibitor series and published a crystal structure showing these inhibitors bind between helices α4 and α6—the same site predicted by Luo et al. As anticipated, the ATP binding site is significantly disrupted by allosteric binding of these compounds (Fig. 2). The examples of these KSP inhibitors illustrate the need for caution in making inferences regarding inhibitor binding site on the basis of steady-state inhibitor modality alone.
Figure 2PVZB1194 (yellow), an allosteric, ATP competitive inhibitor of KSP, binds in a site between α4 and α6 and significantly disrupts the ATP binding site (green ribbon; PDB code 3WPN
When α > 1.0 and less than the cutoff for competitive behavior (i.e., ≥ 10), the inhibitor is said to be a mixed inhibitor with greater affinity for (i.e., preferential binding to) the free enzyme; some authors refer to such inhibitors as mixed competitive. In the case that α = 1.0, the inhibitor has equal affinity for the E and ES forms and is referred to as noncompetitive. On the other hand, when α < 1.0, the inhibitor preferentially binds to the ES complex and is said to be mixed uncompetitive (see next).
The terms mixed and noncompetitive inhibition indicate that the compound binds specifically and with some affinity to two distinct forms of the enzyme: the free enzyme, E, and the ES complex. It is incorrect to infer that mixed and noncompetitive inhibitors bind to two distinct sites on the enzyme, with a stoichiometry of two ligands bound per molecule of enzyme target.
As determined by the value of α, the inhibitor may show preferential binding (i.e., greater affinity) to one or the other form, or may display equal affinity for both E and ES. That such compounds may bind with some affinity to the ES form of the enzyme suggests that the recognition elements of binding for the inhibitor are not completely overlapping with those of the substrate, and therefore the substrate and inhibitor binding sites may be thought to be distinct. Again, some caution must be exercised in drawing too definitive a conclusion regarding binding site location from the steady-state kinetic data.
There are examples of noncompetitive inhibitors that bind within the enzyme active site, where substrate normally binds. This can occur for a number of reasons, as reviewed by Copeland
For example, with enzymes that act on macromolecular substrates, the recognition elements for substrate binding may be external to the catalytic active site.
In such cases, the binding of a small-molecule inhibitor to the catalytic active site may not preclude binding of a macromolecular substrate (driven by a recognition element elsewhere on the enzyme), but will block catalysis. This is found to be the case, for example, with many active site-directed protease inhibitors.
One often finds that such compounds display competitive inhibition in assays conducted with short peptides as substrate, for which most of the recognition elements of binding are within or proximal to the enzyme active site. When, however, these same compounds are studied in assays that utilize full-length proteins as substrate—which may gain significant binding energy through recognition elements external to the enzyme active site (i.e., exosite interactions)—one finds that the compounds now display noncompetitive inhibition (Fig. 3; see Copeland
Human Alpha-Thrombin Inhibition by the Highly Selective Compounds N-Ethoxycarbonyl-D-Phe-Pro-Alpha-azaLys p-Nitrophenyl Ester and N-Carbobenzoxy-Pro-Alpha-azaLys p-Nitrophenyl Ester: A Kinetic, Thermodynamic and X-Ray Crystallographic Study.
When the inhibitor exclusively binds to the ES complex, with no affinity for E (i.e., when Ki approaches infinity, but α << 1.0), it is referred to as pure uncompetitive inhibition. In practice, some researchers consider any compound for which α < 0.1 to be uncompetitive. The exclusivity of compound binding to the ES complex may be due to a conformational change of the enzyme upon substrate binding, which creates or modifies a neomorphic pocket for inhibitor interactions. In other cases, direct interactions may occur between the substrate and inhibitor molecules that enhance inhibitor binding. This was the case, for example, with the PRMT5 inhibitor series described by Chan-Penebre et al.
These compounds formed a ternary complex between PRMT5, its substrate S-adenosylmethionine (SAM), and the inhibitors. Crystallographic analysis demonstrated that an aryl group on the inhibitor formed a key π-cation interaction with the partially charged methyl group of the substrate SAM, or with the methyl group of the SAM-mimetic, sinefugin (Fig. 4). When, however, the product S-adenosylhomocyteine (lacking the critical methyl group) was bound within the SAM binding pocket, the affinity of the inhibitors was markedly reduced.
Figure 4The π-cation interaction (dashed line) between the SAM methyl group and the tetrahydroisoquinoline (THIQ) moiety of EPZ015666 in the PRMT5-SAM-EPZ015666 ternary complex is important for inhibitor binding to the ES complex (PDB code = 4X61; PRMT5 shown in grey; SAM and EPZ015666 shown in green). The positions of the inhibitor and product SAH in the PRMT5-SAH-EPZ015666 ternary complex (PDB code = 4X61; SAH and EPZ015666 shown in cyan) are comparable to the ES complex, but the affinity for the inhibitor to the EP complex is reduced by ~200-fold in the absence of the SAM methyl group.
Traditionally, inhibition modality has been determined by analysis of the impact of inhibitor concentration on the steady-state parameters of the enzymatic reaction, KM, kcat, and kcat/KM.
In 1973, Cheng and Prusoff used steady-state enzyme kinetic analysis to derive equations for the IC50 (the concentration of inhibitor yielding half-maximal inhibition of the target enzyme) as a function of substrate concentration ([S]), substrate KM, inhibitor concentration ([I]), Ki, and α. The equations derived by Cheng and Prusoff
Relationship between the Inhibition Constant (K1) and the Concentration of Inhibitor Which Causes 50 Per Cent Inhibition (I50) of an Enzymatic Reaction.
define distinct behaviors for the changes in IC50 of an inhibitor at varying values of [S] for different inhibition modalities. These equations, when recast in terms of the ratio [S]/KM, may be used to define diagnostic curve patterns for different inhibition modalities, when data are replotted as IC50 as a function of [S]/KM. Such replots provide a simple and rapid means of determining inhibition modality for multiple compounds during post-HTS hit analysis. This topic has been described, for example, by Copeland.
Below, we reintroduce the method for the intended readership of this journal and provide practical recommendations for experimental methods that allow the most effective data ranges to be used for this purpose.
Mathematical Treatment
For any two ligands, I and J, that bind to a common target, E, it can be shown that the apparent affinity constant for ligand I (IC50i) is affected by the presence of J by the following equation:
where [J] is the concentration of ligand J, Ki and Kj are the equilibrium dissociation constants for ligands I and J, respectively, and α is a thermodynamic cooperativity term that describes any cooperative or anticooperative interactions between the binding of I and J to E. Equation 1 is valid for any type of target (enzymes, receptors, etc.) and binding partners (i.e., ligands). When the term α approaches infinity, the two ligands cannot bind simultaneously to the same molecule of target. Hence, in this case ligands I and J can be said to bind to E in a mutually exclusive or competitive manner. As discussed above, the competitive or mutually exclusive binding of two distinct ligands is sometimes thought to indicate that the two ligands share a common binding site on the target, but this is not necessarily the case. The two ligands may, indeed, share a common binding site, or each may bind to separate binding sites that are somehow in allosteric communication with one another.
Suppose that the target of interest is an enzyme and that ligand I represents an inhibitor of enzymatic activity and ligand J is the substrate of enzymatic action. In this special case, we would replace the terms [J] and Kj by the terms [S] and KS. If, however, the experimental conditions involve steady-state turnover of the enzyme (e.g., an enzyme activity assay), the term KS must be further replaced by the steady-state Michaelis constant, KM. Making these substitutions, eq 1 can be recast as follows:
(2)
If we divide the numerator and denominator by Ki, we obtain
(3)
Equation 3 is identical to the Cheng–Prusoff equation
Relationship between the Inhibition Constant (K1) and the Concentration of Inhibitor Which Causes 50 Per Cent Inhibition (I50) of an Enzymatic Reaction.
for mixed-type inhibition, which is valid for all forms of inhibition modality.
For the purposes of diagnosing inhibitor modality, a replot of IC50 as a function of the ratio of substrate concentration to the KM for that substrate ([S]/KM) is of most general utility. Hence, recasting eq 1 in terms of the ratio [S]/KM as the independent variable is what is desired. Dividing the numerator and denominator of eq 3 by KM, we obtain the following:
(4)
or
(5)
When α = 1 (noncompetitive inhibition), this equation reduces to the simple equality IC50 = Ki.
As α approaches infinity (i.e., pure competitive inhibition), this equation reduces to the following:
(6)
Multiplying the numerator and denominator of eq 6 by Ki yields the following:
(7)
When Ki approaches infinity, but αKi is finite (i.e., pure uncompetitive inhibition), eq 5 reduces to the following:
(8)
Multiplying the numerator and denominator by (KM/[S]) yields
(9)
Then multiplying the numerator and denominator by αKI yields
(10)
Diagnostic Value of Replots
If one measures the IC50 of an inhibitor at multiple values of [S]/KM and replots the IC50 as a function of [S]/KM, the pattern of the data provides a clear indication of the modality of inhibitor interaction with the target.
From eq 7, we find that for a pure competitive inhibitor, the replot will yield an ascending linear function of IC50 with respect to [S]/KM, with both slope and y intercept equal to the Ki of the compound (Fig. 5A).
Figure 5Simulated replots of IC50 as a function of [S]/KM for different inhibition modalities. For each graph, the data simulations used the idealized combinations of [I] and [S]/KM as recommended in the text. (A) Pure competitive inhibition. (B) Pure uncompetitive inhibition. (C) Noncompetitive inhibition. (D) Mixed inhibition with α = 0.1 (closed circles), 0.3 (open circles), 1.0 (closed triangles), 2.0 (open squares), and 3.0 (closed squares).
For a pure uncompetitive inhibitor, the replot will appear as a descending curvilinear function, conforming to the form of eq 10 (Fig. 5B). The situations of pure competitive and pure uncompetitive inhibition correspond to the limiting values of the thermodynamic cooperativity term, α.
As described earlier, an α value of unity corresponds to the situation in which the inhibitor binds with equal affinity to the free enzyme and the enzyme–substrate complex. This results in a linear, horizontal replot of IC50 as a function of [S]/KM (Fig. 5C).
When the value of α is greater than 1 but finite, the inhibitor binds to the free enzyme with greater affinity than it does to the ES complex. Such inhibitors display ascending, curvilinear replots of IC50 as a function of [S]/KM, with the degree of curvature being a function of the value of α. In contrast, when an inhibitor displays greater affinity for the ES complex than for the free enzyme, the value of α will be less than 1. In this case, the inhibitor will display a descending, curvilinear replot, again with the degree of curvature being a function of α (Fig. 5D).
The various patterns of replots for different values of α are illustrated in Figure 5. The distinct shapes of these plots make it quite simple and rapid to distinguish between competitive, noncompetitive, and uncompetitive modalities of inhibition. For inhibitors that display differential affinity for the free enzyme and ES complex, the ability to quantify the values of Ki, α, and αKi will depend on the range of [S]/KM values sampled and the number and quality of data points collected. This point is developed further in the next section.
Recommendations for Experimental Measurement of IC50 as a Function of [S]/KM
Reflecting on the forms of eqs 7 and 10, we find that when [S] = KM, the IC50 measured for any inhibition modality will deviate from the true equilibrium dissociation constant (Ki or αKi) by only twofold or less. This is the mathematical basis for the balanced assay conditions that have been recommended for HTS.
If we assume that the HTS assay was run under such balanced conditions, one method to obtain a quick sense of inhibition mode would be to determine the IC50 of selected hits at [S] = KM and [S] = 10KM conditions. This can be quickly performed in high throughput, along with other follow-up assays, typically performed to remove nonproductive compounds that interfere with the assay or are pharmacologically untenable. Competitive inhibitors should display an increase in IC50 of about 5.5-fold when the [S] = 10KM data are compared with that for balanced conditions. Uncompetitive inhibitors, in contrast, will show about a twofold decrease in IC50 at the higher substrate concentration. Noncompetitive and mixed inhibitors will show little shift in IC50 under these two conditions. Such experiments can give a quick but crude assessment of likely inhibitor modality assuming the signal-to-noise window within the assay and other statistical considerations provide the researcher the ability to measure these differences in the IC50. Once the number of desired hits has been reduced, additional experiments to further understand inhibitor modality can be performed. Copeland has previously suggested using a combination of three inhibitor concentrations (plus control experiments with no inhibitor) under eight different [S]/KM conditions ranging from [S] = 0.08KM to 10KM.
These conditions are adequate for an initial assessment of inhibition modality. However, with the more common use of 96-, 384-, and 1536-well plates for screening, a more robust combination of conditions, described below, can be easily accommodated by most laboratories today.
Data simulations of combinations of inhibitor and substrate concentrations lead to the following recommendations. First, the IC50 of a test compound should be determined under balanced conditions. Once this is well established, a 10-point titration of compound should be used for subsequent experiments, which represents a 3-fold dilution scheme from 1000- to 0.03-fold the IC50 of balanced conditions. Additionally, duplicate experiments should be performed at each value of [S]/KM in the absence of compound (i.e., zero inhibitor controls). This scheme would thus require 12 wells of a multiwell plate for each [S]/KM condition to be explored. This 12-well compound titration should be performed at eight values of [S]/KM, conforming to a threefold dilution scheme from 30[S]/KM to 0.01[S]/KM, as illustrated in Figure 6. The range of inhibitor and substrate concentrations may need to be modified to account for any chemical, physical, or technical limitations of the experiment. In some cases, DMSO tolerability of the assay or solubility limits of the reagents may limit the range of inhibitor or substrate concentrations that can be practically used. In other cases, the signal-to-noise ratio at reagent titration extremes may be limiting, resulting in high variability between IC50 replicates, and negatively impact the confidence of the researcher in data analysis and interpretation. Additionally, all of the assay conditions should be consistent with steady-state conditions of enzyme turnover, and one may find that some of the extreme values of [S]/KM are inconsistent with steady-state turnover for a practical assay time course. These and other practical factors may require the researcher to modify the above-recommended ideal range of [I] and [S]/KM for specific assays. Nevertheless, the range of inhibitor concentrations recommended above provides sufficient data points for curve fitting and takes into account the potential changes in concentration–response behavior that may be evoked by different inhibition modalities as [S]/KM is varied. Likewise, the range of [S]/KM values recommended provides the greatest discriminatory power possible for the determination of the α value and, from that, the diagnosis of inhibition modality.
Figure 6Scheme for inhibition modality determination by measuring concentration–response data for a compound at multiple values of [S]/KM. This scheme represents the idealized combination of inhibitor concentrations and [S]/KM values arrayed in a 96-well format. Plates with 384- or 1536-well formats may be used to obtain replicate data using the same scheme. This scheme is presented for illustrative purposes; to avoid potential edge effects, a randomized layout of this scheme is possible with certain liquid handling capabilities.
As stated in the introduction, there is increasing interest within the research community in pursuing inhibitors of specified modality (e.g., allosteric inhibitors) for chemical biology and drug discovery purposes. The number of compounds that can or should be tested in these types of experiments, as well as the location of these assays within the validation funnel, will differ depending on the size of the screen, the effectiveness of filter assays, liquid handling capabilities, and the importance of inhibitor modality to the target of interest. Additionally, knowledge of the inhibition modality of a compound informs experimental conditions for subsequent analyses and further validation. For example, if a compound is known to be uncompetitive with substrate, it would be pointless to pursue x-ray crystallography, surface plasmon resonance, or other biophysical studies in the absence of substrate. The enzymology concepts and schemes presented here may be of value to researchers of varied backgrounds interested in identifying and studying target inhibitors of a specified modality from large-scale screening efforts or smaller, focused hit-finding investigations.
Descriptions of common modes of inhibitor interactions with enzyme targets have been provided, and caveats have been clearly presented to caution against inferring details of inhibitor binding site locations exclusively on the basis of different inhibition modalities. The utility of IC50 replots as a function of [S]/KM is recommended as a facile and accurate means of assessing inhibition modality for multiple compounds that may be of interest as hits from HTS campaigns. The diagnostic patterns in such replots, expected for each inhibition modality, has been described. Specific recommendations for experimental conditions for data collection, aimed at constructing these replots, have also been offered. These recommendations reflect ideal conditions for generating replots. Clearly, each system of enzyme assay, inhibitors, and other assay components will present unique experimental limitations; thus, the reader will need to adapt the scheme presented here to account for such limitations. Finally, it is worth noting that while the focus of the present work has been on enzyme targets, the general approach presented here is applicable, with modifications, to any target system and its interacting ligands.
Acknowledgments
The authors would like to thank William P. Janzen for helpful discussions.
Declaration of Conflicting Interests
The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding
The authors received no financial support for the research, authorship, and/or publication of this article.
Relationship between the Inhibition Constant (K1) and the Concentration of Inhibitor Which Causes 50 Per Cent Inhibition (I50) of an Enzymatic Reaction.
Human Alpha-Thrombin Inhibition by the Highly Selective Compounds N-Ethoxycarbonyl-D-Phe-Pro-Alpha-azaLys p-Nitrophenyl Ester and N-Carbobenzoxy-Pro-Alpha-azaLys p-Nitrophenyl Ester: A Kinetic, Thermodynamic and X-Ray Crystallographic Study.
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