Matrix-Based Activity Pattern Classification as a Novel Method for the Characterization of Enzyme Inhibitors Derived from High-Throughput Screening

Abstract

One of the central questions in the characterization of enzyme inhibitors is determining the mode of inhibition (MOI). Classically, this is done with a number of low-throughput methods in which inhibition models are fitted to the data. The ability to rapidly characterize the MOI for inhibitors arising from high-throughput screening in which hundreds to thousands of primary inhibitors may need to be characterized would greatly help in lead selection efforts. Here we describe a novel method for determining the MOI of a compound without the need for curve fitting of the enzyme inhibition data. We provide experimental data to demonstrate the utility of this new high-throughput MOI classification method based on nonparametric analysis of the activity derived from a small matrix of substrate and inhibitor concentrations (e.g., from a 4_S × 4_I matrix). Lists of inhibitors from four different enzyme assays are studied, and the results are compared with the previously described IC₅₀-shift method for MOI classification. The MOI results from this method are in good agreement with the known MOI and compare favorably with those from the IC₅₀-shift method. In addition, we discuss some advantages and limitations of the method and provide recommendations for utilization of this MOI classification method.

Keywords

mode of inhibition enzyme inhibitors inhibitor classification enzyme assays

Introduction

Currently, many drug discovery programs rely on screening massive chemical libraries against molecular targets with a biologically relevant assay in an effort to find novel chemotypes as entry points.^1,2 As the scale of such high-throughput screening (HTS) is generally very large (hundreds of thousands to millions of chemical substances screened), the number of active compounds (“hits”) resulting from screening efforts is also quite large, and therefore effective filtering of the large primary hit lists in a systematic manner to provide a “clean” and information-rich structure-activity profile is critical for effective hit-to-lead selection. In addition to routine confirmation testing and counterscreens to weed unwanted hits that occur for various reasons, including data variability (false-positives), assay technology interferences, and/or interaction with biological off-targets, early assessment of hits with the desired mode of action (MOA) and pharmacological properties is among the most important parameters in selecting chemical starting points for hit-to-lead optimization.

Enzymes and receptors still comprise the majority of biochemical and cellular targets in current lead discovery efforts. There are more than 300 marketed drugs that work by modulating the activity of an enzyme and many others by modulating the activity of a receptor.³ For instance, inhibitors with a novel MOA for protein kinases were initially discovered through screening efforts.^4-6 Understanding the mode of inhibition (MOI) of enzyme targets enables one to prioritize chemotypes for further optimization of inhibition specificity and potency.⁷ Because of the complexity and low throughput of the conventional MOI determination methodologies, for any large collection of enzymatic inhibitors identified from a screening campaign, the MOI information for these hits is not readily obtainable. To remove or alleviate such bottlenecks downstream of HTS (sometimes referred to as the postscreening dilemma) in the drug discovery process, a number of approaches and methodologies have been explored in recent years, including the use of high-throughput infrastructure (e.g., automation) to increase the scale of conventional MOI determination. For example, using robotics and instrumentation, a fully automated steady-state enzyme kinetic assay in compound profiling has been described for dipeptidyl peptidase IV, and the setup was capable of producing full mechanistic inhibition analysis in a timely fashion to support drug discovery.⁸ Chemoinformatic and computational tools are employed to prioritize the hit scaffolds based on in silico models and analysis.^9,10 In the case of assessing the MOI of CK2 kinase inhibitors identified from a screening effort, the binding mode of the inhibitors was determined via combining structure-activity relationships with a molecular docking procedure.⁵ There are other novel strategies and methodologies for enabling enzyme mechanism and MOA studies, such as combining molecular docking with in vitro studies to elucidate the inhibitory effects of herbal compounds on human cytochrome P450 1A¹¹ and a method in which the MOI can be determined using a fixed inhibitor concentration over a range of substrate concentrations.¹²

To increase the throughput in MOI characterization, a few high-throughput approaches have been explored recently.^12,13 Based on the conventional IC₅₀ shift under different substrate concentrations and the relationship of IC₅₀, substrate concentration, K_m and K_i, which has been described by in the Cheng and Prusoff equation,¹⁴ Wei et al.¹³ described a high-throughput MOI classification approach for evaluating hits from HTS. The MOI of large number of hits can be classified as competitive, uncompetitive, noncompetitive, or mixed mode by measuring the ratio of IC₅₀ values (or percentage inhibition) obtained at two separated substrate concentrations. In this method, the ratio (R) of two IC₅₀ values for an inhibitor under two selected substrate concentrations is calculated (where [S1] < [S2]; concentrations are chosen to bracket the known K_m value). In this case, R = IC₅₀^S2/IC₅₀^S1 = (1 + [S2]/K_m)/(1 + [S1]/K_m) for competitive inhibitors and R = IC₅₀^S2/IC₅₀^S1 = (1 + K_m/[S2])/(1 + K_m/[S1]) for uncompetitive inhibitors, and so forth. Using these R values and the standard deviation of their measurements as a guide, this higher throughput method was applied to analyze the MOI for more than 900 screening hits to distinguish compounds between competitive, noncompetitive, or mixed MOIs.¹² Such large-scale MOI profiling would be difficult to implement with conventional methods.

Although simple to apply, the IC₅₀-shift (R-value) method for MOI classification of a large number of hits also has some practical limitations. First, the approach is based on the IC₅₀ ratio under the two different substrate concentrations. To distinguish among all types of MOI reliably, the two substrate concentrations need to be sufficiently below and above the known K_m value so that the separation of R value (IC₅₀ shift) for the inhibitors is sufficiently large. In practice, this demands wide separation between high and low substrate concentrations, which sometimes is practically unattainable because of substrate solubility, signal strength, and linearity at these substrate concentrations. The assay signal at high and low substrate concentrations needs to be strong and sensitive enough to yield reliable IC₅₀ values. As well, individual curve fitting to the data at both testing substrate concentrations needs to be performed, which is generally time-consuming. Error accumulation both from measurement and curve fitting can sometimes be significantly large in the IC₅₀ ratio R. Lastly, and maybe more practically important, hits from screening tend to have a wide range of activity; some compounds have strong activity, but many have weak activity, and both very strong and weak hits often do not generate full concentration-response curves from which reliable IC₅₀ values can be determined in the chosen compound titration range. If no IC₅₀ value or only one IC₅₀ value is obtained from the concentration-response curves at the two selected substrate levels, it is not possible to calculate the R ratio and this limits the classification of their MOI.

In this article, we describe in detail a new approach for high-throughput MOI assessment for rapid classification of screening hits against targeted enzymes. The method is based on pattern classification of the inhibition activity surface from testing a small matrix covering different substrate and inhibitor concentrations. Our method neither involves curve fitting nor determination of IC₅₀ values. To demonstrate the practical value of this approach as a rapid and effective method with experimental data sets, we selected four enzymatic inhibitor case studies. In all cases, the compounds and enzyme assays were originally derived from screening efforts. In a few cases, we had some prior knowledge of the MOI profile of the testing compounds, but in other cases, we had no MOI information available at the time of testing. Those cases with prior MOI knowledge serve to compare and validate the results of our new MOI classification method, whereas those that do not have any prior knowledge act as a blinded study in which we can compare results from matrices with different dimensions (small and large matrix testing) as well as to the IC₅₀-shift method.¹³ We expand the study in one case to a large hit list containing 1363 compounds. The enzymes varied in class ranging from firefly luciferase (FLuc),¹⁵ an NS5 RNA dependent RNA polymerase (RdRp),¹⁶ as well as protein methyl transferases. The assay formats and readouts also varied and included both direct and indirect detection methods including fluorometric and matrix-assisted laser desorption/ionization (MALDI) mass spectrometry (MS) detection. After testing various (substrate x inhibitor) matrices, we applied the MOI classification algorithm based on the S-gradient signature (J value) to assign the MOI. The data illustrate the advantages and limitations of this new method, and we provide several recommendations for performing the analysis. The outcome of these case studies clearly demonstrates that this simple MOI classification scheme is effective for the rapid profiling and characterization of a large number of enzyme inhibitors derived from HTS. This enables prioritization of enzyme inhibitors for lead development based on the MOI.

Materials and Methods

Matrix-Based MOI Classification Method

The activity of an enzymatic reaction can be described by Michaelis-Menton reaction kinetics.¹⁷ The inhibition of an enzymatic reaction at different substrate and inhibitor conditions can be derived from the Cheng and Prusoff equation.¹⁴ Based on these fundamental enzymatic equations, the following formulae for the percentage inhibition by an inhibitor (Inh%) were derived for each of the MOIs for reversible inhibitors.

For competitive inhibitors:

I n h % = 100 \cdot \frac{[I]}{[I] + (1 + \frac{[S]}{K_{m}}) \cdot K_{i}}

For uncompetitive inhibitors:

I n h % = 100 \cdot \frac{[I]}{[I] + (1 + \frac{K_{m}}{[S]}) \cdot K_{i}}

For noncompetitive inhibitors:

I n h % = 100 \cdot \frac{[I]}{[I] + K_{i}}

For mixed inhibitors:

I n h % = 100 \cdot \frac{[I]}{[I] + (\frac{[S] + K_{m}}{\frac{[S]}{α} + K_{m}}) • K_{i}}

In the above formulae, the Inh% in top three cases can be determined by the substrate concentration [S], inhibitor concentration [I], and the corresponding constants for K_m and K_i. The K_m is the Michaelis-Menten constant for the substrate. Competitive inhibitors bind exclusively to the free enzyme with a dissociation constant K_i. Uncompetitive inhibitors bind exclusively to the enzyme-substrate complex with a dissociation constant K_i. Noncompetitive inhibition refers to an inhibitor that binds to the free enzyme and enzyme-substrate complex with equal potency. Equations (1), (2), and (3) illustrate the relationship between Inh% and the substrate and inhibitor presented ([S] and [I]) for inhibitors in an enzymatic reaction (with characteristic constants K_m, and K_i). Equation 4 describes mixed inhibition, which is modulated by the ratio of the Ki values for both the free enzyme and the enzyme-substrate complex (designated as α). Equation 4 reduces to pure inhibition modes at certain values of α: noncompetitive when α = 1, competitive when α >>1, and uncompetitive when α << 1. From these equations, the theoretical Inh% can be calculated at different inhibitor concentrations ([I]) at any given substrate concentration ([S]). Analyzing the inhibition at various [I] and [S] levels should allow not only the determination of the MOI (competitive, noncompetitive, uncompetitive, and mixed) but also, when the K_m is known, the K_i values for inhibitors.

Based on these equations, we propose a simple way to classify a large number of inhibitors and assign the MOI via the activity surface pattern of a small substrate x inhibitor matrix test at several selected concentrations. The approach is described as follows. Suppose an enzymatic assay is tested at m substrate levels (denoted S₁, S₂, . . . , S_m) and n inhibitor levels (denoted I₁, I₂, . . . , I_n), and the test conditions compose a m × n matrix. The corresponding Inh% values also make a m × n matrix. In the following description of this nonparametric approach, we use a 4_S × 4_I matrix to illustrate the method and a two-step procedure for a real test.

Step 1: Determine the Normalized S Gradient at Each I Level

In a 4_S × 4_I matrix test, at each I level, there are four levels of S (S₁ to S₄) and four corresponding Inh% values (obtained from test). This gives four Inh% activity gradients (one at each I) along the substrate levels (referred to as the S gradient). We considered the parameter to evaluate the S gradient at each I level.

Local S-Gradient Average ( J_l)

In this evaluation, the slope using every point-to-point activity data was used to estimate the activity surface gradient along the S dimension (in a logarithmic scale). We use the formula (X_i – X_j)/(logS_i – logS_j) to calculate the normalized activity change (i.e., slope) between data point X_i and X_j (where i, j are two data points in the four S levels test at the same I level, and X is Inh% value). The four S levels would generate a total of six local gradient values. The average gradient is obtained from simply taking the average of the six local gradient values, as shown below (n = 6 in this case). The average gradient (denoted J) is used because of its greater resistance to data outliers in a real matrix test.

J_{l} = \frac{1}{k} \cdot \frac{1}{n} \cdot \sum^{n} \frac{X i - X j}{\log S i - \log S j}

Global S-Slope (J_g)

Alternatively, a slope function is used to estimate the S gradient at each I level.

J_{g} = \frac{1}{k} \cdot \frac{\sum (X i - \bar{X}) \cdot (\log S i - \bar{\log S})}{\sum {(\log S i - \bar{\log S})}^{2}}

where X and logS with top bar notation are the corresponding mean values for the four data points along S at each I. In both Equation 5 and 6, the term 1/k in the J formulae is a constant modifier of J value for convenience of classification (see next section).

Step 2: Apply S-Gradient Signature for MOI Classification

From step 1, a small m × n matrix testing (such as 4_S × 4_I) would generate a set of J values (J1, J2, . . . , Jn), with each J_i being the S-gradient vales at inhibitor concentration Ii of the matrix testing. This set of J values is referred to as the S-gradient signature of the matrix test. Key features of this signature are used to classify the MOI of the inhibitor (more details are given in the next section).

Assays for the Lysine Methyl Transferase EZH2

EZH2 HTRF assay

Europium conjugated anti-histone H3K27Me2 antibody was obtained from Cisbio (No. 61KC2KAE). Compounds were tested in eight concentrations in a twofold dilution series (20 µM to 0.15 µM final concentration in a 4 µL reaction). Assay-ready plates were prepared by dispensing 40 nL compound into each well of 384 Proxiplates (6008289, PerkinElmer, Waltham, MA) using Echo Liquid Handler (Labcyte Inc., Sunnyvale, CA). The substrate mixtures were prepared by mixing biotinylated H3K27Me0 peptide (21–44 aa on H3, from AnaSpec No. 64440-1, final reaction concentration 0.1 µM) and each of the four different S-adenosyl methionine (SAM; No. S018, AK Scientific, Union City, CA) concentrations (20 µM, 5.7 µM, 1.6 µM, 0.5 µM final concentration) in final 4 µL reaction volume). To set up the assay, 2 µL substrate mixture and 2 µL of PRC2 enzyme (50 nM final concentration, produced in house) were incubated in 1x assay buffer containing 20 mM Tris buffer, pH 8, 0.005% Triton X-100, and 0.5 mM DTT for 3 h at ambient temperature. Two microliters of detection reagent (1 nM anti-dimethyl-H3K27-Eu and 40 nM SA-APC) was added to each well to a final reaction volume 6 µL. The plates were then incubated for an additional 2.5 h at ambient temperature. The fluorescent outputs were detected using PHERAstar microplate reader (BMG LABTECH, Ortenberg, Germany) with a homogeneous time-resolved fluorescence filter (excitation 337 nm, emission at 665 nm and 620 nm).

EZH2-MALDI assay

Compounds were tested in eight concentrations with a twofold dilution series (20 µM to 0.78 µM final reaction concentration in 10 µL reaction). Five microliters of PRC2 enzyme (10 nM final concentration) and 5 µL of substrate (20 µM of SAM and seven doses of H3K27Me0 peptide starting from 20 µM to 300 nM in a 1:2 titration series) were incubated in 1x assay buffer (20 mM Tris, pH 8, 0.01% Tween, 0.5 mM DTT) for 4 h at ambient temperature. A total of 2.5 µL of stop reagent containing trifluoroacetic acid at a final 0.1% and H3K27Me3 (AnaSpec No. 64367-1), as positive internal control, at final concentration 0.5 µM) was added to the plate. The plates were stored at −20 °C before MALDI MS analysis. MALDI MS analysis was performed similarly as described below for a protein methyl transferase.

MALDI MS Analysis of a Protein Methyl Transferase (PMT) with Peptide Variation

For PMT assays, 6 nM enzyme was used in five separate reactions with variable amounts of substrate for the MOI study. SAM substrate concentrations were fixed at 20 µM for each of these reactions, and substrate was used in the following concentrations (4.5 µM, 1.5 µM, 0.5 µM, 0.167 µM, and 0.056 µM). Each reaction was performed in 20 mM HEPES, pH 8, with 0.002% CHAPS, 0.5 mM NaCl. These variable substrate reactions were used to generate concentration-response curves (CRCs) for 26 putative PMT inhibitors of various MOIs. To generate the CRCs for each of the five reactions, assay-ready plates were generated by depositing 100 nL of compound into a 384-well small-volume Greiner plate with concentrations ranging from 20 µM to 0.150 µM. The peptide substrates from the five distinct reactions were then plated into each of the different assay-ready plates, and the reaction was performed at room temperature for 2 h. To quench the reactions, trifluoroacetic acid at a final concentration of 0.1% was added to stop the enzyme and then the reaction plates were stored at −80 °C until read by the MALDI MS. To read the reaction plates, each plate was thawed, 300 nL of each reaction was spotted onto a stainless steel MALDI MS plate and dried, and then 300 nL of the MALDI matrix alpha-cyanohydroxycinnamic acid (CHCA) was added to the dried spots and allowed to dry. The dried reaction spots from each 384-well plate were analyzed by a Bruker Autoflex MALDI MS. Substrate and product peptides were detected by measuring the intensity of the two ions for every spot (1084.5 Da and 1098.5 Da, respectively) representing the Me0 and Me1 peptides after data were acquired using 1000 shots/spot. Ratios of total product intensity divided by the sum of the substrate and product intensities were calculated for all doses of compound as well as the neutral control (DMSO only) and the active control (pre-quenched enzyme) reactions. The percentage activity of the enzyme in each well was determined by taking the product/substrate ratios for each reaction (R) and comparing them to the ratios of the neutral controls (NC) and active controls (AC) in the following equation: percentage activity = (R – (NC – AC))/(NC + AC) × 100%.

MALDI mass spectrometry analysis of PMT with SAM variation

For PMT assays, 6 nM enzyme was used in five separate reactions with variable amounts of substrate for the MOI study. Peptide concentrations were fixed at 0.5 µM for each of these reactions, and SAM was varied in the following concentrations (8.3 µM, 2.8 µM, 0.92 µM, 0.31 µM, and 0.1 µM). Each reaction was performed in 20 mM HEPES, pH 8, with 0.002% CHAPS, 0.5 mM NaCl. These variable substrate reactions were used to generate concentration-response curves for 26 putative enzyme inhibitors of various MOIs. To generate the CRCs for each of the five reactions, assay-ready plates were generated by depositing 100 nL of compound into a 384-well small-volume Greiner plates with concentrations ranging from 20 µM to 0.150 µM. The five distinct reactions were then plated into each of the different assay-ready plates, and the reaction was performed at room temperature for 2 h. To quench the reactions, trifluoroacetic acid at a final concentration of 0.1% was added to stop the enzyme, and then the reaction plates were stored at −80 °C until read by the MALDI MS. To read the reaction plates, each plate was thawed, 300 nL of each reaction was spotted onto a stainless steel MALDI MS plate and dried, and then 300 nL of the MALDI matrix CHCA was added to the dried spots and allowed to dry. The dried reaction spots from each 384-well plate were analyzed by a Bruker Autoflex MALDI MS. PMT substrate and product peptides were detected by measuring the intensity of the two ions for every spot (1084.5 Da and 1098.5 Da) representing the Me0 and Me1 peptides after data were acquired using 1000 shots/spot. Ratios of total product intensity divided by the sum of the substrate and product intensities were calculated for all doses of compound as well as the neutral control (DMSO only) and the active control (prequenched enzyme) reactions. The percentage activity of the enzyme in each well was determined by taking the product/substrate ratios for each reaction (R) and comparing them to the ratios of the NC and AC in the following equation: percent activity = (R –(NC – AC))/(NC + AC) × 100%.

Assay for NS5 RNA-Dependent RNA Polymerase (RdRp) from Dengue Virus

The fluorescent alkaline phosphatase-coupled polymerase assay was performed as described by Smith et al.¹⁶ Briefly, the fluorescent-based assay consisted of two steps: a polymerase initiation/elongation reaction and a signal generation reaction. The nucleoside triphosphates (GTP, ATP, UTP) and ATTO-CTP are the substrates used by NS5 polymerase for incorporation into the growing RNA chain. Release of the by-product ATTO-pyrophosphate during the polymerization reaction is catalyzed by NS5 RdRp.¹⁸ The ATTO-PPi is subsequently hydrolyzed by calf intestinal alkaline phosphatase (CIP) to liberate free product whose fluorescence signal can be detected by excitation wavelength at 420 nm and emission wavelength at 560 nm. The assay used viral genome-derived RNA (576-nt in length, derived by in vitro transcription [IVT])¹⁶ as an RNA substrate template to enable DENV NS5 de novo initiation activity. The assay was set in a 4 uL reaction volume in 1536-well plate (Greiner BioOne, Kremsmünster, Austria) containing 100 nM RdRp enzyme, 20 µM ATP, 20 µM GTP, 20 µM UTP, and 5 µM ATTO-CTP with IVT RNA at 0.156-10x of K_M value, respectively. The assay buffer contained 20 mM Tris-HCl, pH 7.5, 10 mM KCl, 1 mM MgCl₂, 0.3 mM MnCl₂, 0.02% CHAPS, and 2 mM TCEP. Both enzyme and substrate mixtures were dissolved in assay buffer. Fluorescence from the coupled reaction using ATTO-CTP was used in the assay to track polymerase elongation. The RdRp enzyme was dispensed at 2 µL volume into each well, and then 100 nL inhibitors were acoustically added for preincubation for 15 min at 22 °C. The substrate mixture at 2 µL was dispensed to initiate the reactions. The incubation time for each IVT RNA concentration varied as follows: 120 min for 0.156x K_m, 90 min for 0.625x K_m, 60 min for 2.5x K_m, 30 min for 10x K_m. The apparent K_m for RNA in the assay was determined to be ~125 nM. The negative control consisted of RNA and nucleotides without the enzyme. The stop solution contained 20 nM CIP in AttoPhos buffer supplemented with 160 mM NaCl and 20 mM MgCl₂. The BioRaptr liquid dispenser (Beckman Coulter, Brea, CA) was used for all enzyme, substrate, and stop solution addition. The Echo liquid handler (Labcyte, Sunnyvale, CA) was used for compound addition. After stop solution addition, the plates were incubated at 22 °C for 60 min prior to fluorescence measurement on PHERAstar microplate reader (BMG Labtech). A total of 165 compounds were tested in duplicates as eight-point twofold serial dilution in the concentration range of 0.39 to 50 µM. The percentage inhibition of the compounds was calculated using the positive and negative controls. ATTO-CTP was custom made by Trilink; nucleotides ATP, GTP, and UTP were purchased from Sigma (St. Louis, MO); CIP was obtained from New England Biolab (Ipswich, MA), AttoPhos buffer was purchased from Promega (Madison, WI).

Assay for FLuc Enzyme Activity

The FLuc enzyme assay has been previously described in Thorne et al.¹⁵ The assay was performed in 1536-well white Greiner MB plates (Greiner BioOne). Three microliters of substrates (ATP kept at 0.01 mM and D-luciferin was varied) was dispensed, and then compounds were added using a 20 nL pintool. The reaction was then started by the addition of FLuc enzyme (Sigma Aldrich, cat. No. L9506) at a final concentration of 10 nM. The assay buffer contained 50 mM Tris acetate (pH 7.5), 13.3 mM Mg-acetate, 0.01 mM D-luciferin (Sigma Aldrich, cat. No. L9504), 0.01 mM ATP, 0.01% Tween-20, and 0.05% bovine serum albumin. Following incubation for 10 min at room temperature, the plates were read on a PerkinElmer Viewlux using 1x binning and 30 s of exposure. The percentage inhibition of the compounds was calculated using the full activity (positive) and no enzyme (negative, as 100% inhibited) controls.

Results and Discussion

For a matrix activity pattern based classification for MOI types, both parametric and nonparametric parameters can be considered. In theory, an algorithm to match the theoretical inhibition surface models provided with Equations 1 to 3 to a parametrically modeled inhibition surface of the testing matrix can be developed and then used to predict the MOI type by the best fit of the surface models. However, similar to the IC₅₀ ratio approach, individual surface-fitting routines (vs. curve-fitting routines in the IC₅₀ ratio approach) is needed for each matrix test. To develop surface models would require significant computing power and detailed information about the enzymatic reaction such as the Michaelis-Menten constant K_m. As well, in the IC₅₀ ratio method, two IC₅₀ values must be calculated at high and low [S]/Km values, and oftentimes, one of these values is not determinable, for example, a competitive inhibitor at high [S]/Km conditions may show only weak inhibition. Alternatively, a nonparametric classification approach could be simpler to perform and less sensitive to error propagation. Because of these potential merits, we chose to further explore the nonparametric approach for MOI classification trials.

Figure 1 shows Inh% surface pattern from the theoretical inhibition ( Fig. 1A ) and a more discrete Inh% plot of a 4_S × 4_I matrix ( Fig. 1B ), both derived directly from Equations 1 to 3. From Figure 1 , it can be seen that, even for a small m × n matrix testing (such as 4_S × 4_I), the Inh% surface pattern is very distinctive for each inhibition mode and a good representative of the theoretical surface pattern. It should be noted that for most enzymatic assays, the enzyme concentration present in the reaction compared with substrate and inhibitor concentrations is very low, and the product conversion is usually also low, so one can use the initial substrate and inhibitor concentrations to approximate the free concentration. Also we note here that -100% activity is defined as full inhibition, 100 Inh%.

Figure 1.

Dependence of percentage inhibition on substrate and inhibitor concentration. Plots representing a S versus I matrix test and the corresponding Inh% values. (A) Theoretical Inh% surface deduced from Equations 1 to 3 for the three modes of inhibition. C, competitive; NC, noncompetitive; UC, uncompetitive. The vertical axis is the Inh% value, and the two horizontal axes are substrate (S) and inhibitor concentrations (I). (B) Similar three-dimensional plots of Inh% values of a 4_{S ×} 4_I matrix. In these calculations, the four S concentrations were set at a 1:5 series (0.1x K_m, 0.5x K_m, 2.5x K_m, and 12.5x K_m), and four I concentrations were also set at a 1:5 series (0.1 µM, 0.5 µM, 2.5 µM, and 12.5 µM) with a hypothetical K_i value of 1.0 µM.

For this approach, we evaluated two strategies to calculate the normalized Inh% activity gradient along the substrate levels (i.e., S gradient), as described in the Materials and Methods section. We compared both the local gradient average (J_l) and global S-slope (J_g) in our approach. For all the cases tested, J_l and J_g always yielded very similar or almost identical values, with a Pearson correlation coefficient in the range of r = 0.999 (data not shown). Therefore, the two gradient methods should almost always give the same MOI classification results in practical applications. The global S-slope in reality is easier to calculate than local S-gradient average, and we therefore recommend using the global S-slope (J_g) for J calculation.

Key Features of S-Gradient Signature

From step 1 of the Materials and Methods section, the S gradient (J: J_l ≈ J_g) at any one specific I level is obtained. For a 4_S × 4_I matrix test, the four S-gradient values at the ordered four I levels (e.g., I level from high to low) is referred here to a S-gradient signature ( Fig. 2a ). This S-gradient signature contains the critical Inh% surface pattern information of the matrix test and forms the basis for MOI classification. Three features of the signature are used for the nonparametric MOI classification.

Sign of J: As shown in Figure 2a , the S-gradient signatures of the three types of MOI have different signs. Competitive inhibition (C) gives negative J values, and uncompetitive inhibition (UC) gives positive J values for the signature components. For noncompetitive inhibition (NC), the theoretical J values of its signature components are all zero. In practical cases, NC may likely give J ≠ 0 but instead will have very small positive or negative values, so the J value amplitude needs to be considered as well.

J value amplitude (gradient strength): In any practical test, as mentioned above, the three MOI types (i.e., C, UC, and NC) probably cannot be classified unambiguously by the sign of J alone, particularly for NC, which gives a very small J value (J ≈ 0), and its sign will be easily affected by any measurement variation. In the same vein, experimental data variation will always obscure the border lines for C or UC types of MOI from NC. In addition, there are likely many inhibitors that do not belong to any one pure type of MOI classification, for they behave as mixed-mode inhibitors. For these reasons, the strength of the gradient signature (J value amplitude) needs to be combined with its sign for the MOI classification. We defined a gradient strength indicator (J_max) for this purpose.

J_{m a x} = Max (| J |) .

J_max has the maximum amplitude of the S-gradient signature components. J_max is a key indicator in this MOI classification approach. A large J_max with a negative sign is indicative of substrate competitive MOI, whereas a large J_max with a positive sign is indicative of uncompetitive MOI. Very small J_max values may suggest either a noncompetitive MOI or in special cases other inhibition types (see next section and Table 1 ). The only challenge is when the matrix testing data contain severe outliers. To minimize the outlier interference, we have also developed an algorithm to extract J_max effectively in data sets with outliers.

J_max position (pattern of the signature and the corresponding Inh%): Even though the combination of J_max and sign can usually give a good indication of the MOI type, confusion may arise in certain special occasions. For example, when the J_max value is close to zero, this can indicate an inhibitor with either a noncompetitive MOI (NC) or simply superpotent (or very weak) inhibition behavior over the testing range. The clue to distinguish these more intriguing situations lies in the pattern of the signature components. An NC inhibitor will produce not only a very small J_max (i.e., J_max ≈ 0) but also corresponding X values (Inh%) that are well spread between high and low values in the signature at different I concentrations. In contrast, a very small J_max value with the corresponding X values (Inh%) that show either constantly high or constantly low values in the signature at different I concentrations may simply mean either a superpotent or very weak inhibitor. More intriguingly, when J_max resides at the highest (or lowest) I level, it also suggests competitive or uncompetitive MOIs (based on the sign), although J_max has a moderate value. Altogether, these S-gradient signature patterns, combined with the corresponding Inh% values in the series, can distinguish the MOI type reliably from the matrix test. For example, for a 4_S × 4_I matrix test four S-gradient values are calculated (one for each inhibitor concentration based on all four substrate levels), and the sign and maximum S-gradient value (J_max) are used to classify the MOI provided that the J_max value taken meets certain additional criteria aimed at flagging very weak or strong inhibitors, as illustrated in the details of Table 1 . However, as will be shown in the section below, ambiguity in MOI classification does sometimes occur when the Ji and X values change is not covered well by the test matrix.

Figure 2.

Diagrams of mode of inhibition (MOI) categorization based on the S-gradient signature (a) S-gradient signature (J values of the inhibitor levels in an ordered titration series) of a 4_{S ×} 4_I matrix as shown in Figure 1B . Note the three MOI types (C on left, NC, middle with J = 0 in amplitude, and UC on right) give very distinct S-gradient signature in J amplitude and sign. (b) A series of four inhibitors with different potency (K_i) and mechanisms and their corresponding signatures are shown. J values were obtained by Equations 1-3 and 6 from a 4_S × 4_I matrix. For simplicity, MOI categorization by the sign and amplitude of J_max were indicated.

Table 1.

MOI Nonparametric Classification Scheme.

S-Gradient Signature
J_max Value^a	J_max Sign^b	Other Feature	MOI^a	Note^b
J_max > 3	Negative		C
J_max > 3	Positive		UC
1 < J_max < 3	Negative	J_max at highest IWeak inhibition	C*^c	Weak inhibitor
	Positive	J_max at highest IWeak inhibition	UC*	Weak inhibitor
	Negative	J_max at lowest IStrong inhibition	C*	Strong inhibitor
	Positive	J_max at lowest IStrong inhibition	UC*	Strong inhibitor
	Negative	J_max at middle I levelsGood inhibition spread	Mixed C-NC	Mixed MOI
	Positive	J_max at middle I levels Good inhibition spread	Mixed NC-UC	Mixed MOI
J_max < 1	Negative, positive, or zero	Good inhibition spread	NC
		Inhibition constantly high or low	No prediction	Extremely potent or weak inhibition outside the matrix test range

MOI = mode of inhibition; C = competitive; NC = noncompetitive; UC = uncompetitive.

We use k = 5 for J calculation in Equations 4 and 5.

Based on full inhibition for X = −100%.

C* and UC* denote the C and UC prediction, respectively, as a likely MOI for weak or strong inhibitors.

MOI Classification

Table 1 summarizes the MOI nonparametric classification scheme we propose for characterizing the results from small matrix testing. The classification scheme uses the S-gradient features described and discussed above. The J_max value categorization was based on theoretical case tests and simulations from Equations 1 to 7 at various S, I, and K_i levels most relevant to practical test (vide infra). Figure 2b shows a further simplified diagram to visualize the MOI categorization based only on J_max and its sign. In general, mixed inhibitors with α values ~2 to 5 yielded intermediate J_max values yielding mixed NC/C classifications, whereas α values ~10 showed negative J_max values >3 yielding the classification as competitive. Similarly, uncompetitive inhibitors showed positive J_max > 3 for α values ~0.1 and mixed NC/UC classifications at α values ~0.2 to 0.5. It is worth noting that, for the convenience of J_max presentation, we use k = 5 in J calculation from Equations 5 and 6. The k constant is a modifier of the amplitude. The k value should be held constant so it does not affect the relative amplitude of J. However, this may affect the MOI classification stringency and sometimes can be adjusted slightly according to the experimental data variability and the desired stringency for the MOI classification.

Theoretical Simulations

Based on the calculated J and J_max data from Equations 6 and 7, respectively, we first conducted several theoretical test cases. It is important to demonstrate the effectiveness of the approach under different S and I concentrations as well as K_i ranges. In reality, however, the highest and lowest S and I concentrations can be limited by the substrate and inhibitor availability (e.g., solubility) and assay sensitivity. Sometimes only a certain range of [S] or [I] can be practically achieved. One would like to see if the matrix approach can effectively cover a wide range of inhibitor potencies, as when dealing with a large number of hits from HTS. The choice of [S] and [I] ranges should be driven by the K_M and K_i values with sufficient coverage above and below these values. In our first theoretical matrix (4_{S ×} 4_I) test case, we used both S and I in 1:3, 1:4, and 1:5 dilution series and K_i values from nanomolar to micromolar range.

Supplementary Figure S1 shows the plots of S-gradient signatures of a 4_{S ×} 4_I matrix at 1:5 dilution series. The J_max values over most of the S, I, and K_i levels give a value <–3 for competitive, >3 for uncompetitive, and of course zero for noncompetitive inhibitors, with few exceptions where the K_i values are either very large or very small—corresponding to very weak or very potent inhibitors (e.g., the rightmost case in Suppl. Fig. S1). These results indicate that under practical S and I testing conditions, an inhibitor with pure competitive, noncompetitive, or uncompetitive inhibition modes will be classified effectively by this simple J_max classification scheme. However, for very weak inhibitors, for instance, K_i = 30 µM, representing a very weak inhibitor, the J_max value falls in 1 < J_max < 3. As seen in Table 1 , J_max values in the range of 1 < J_max < 3 with a negative sign could be inhibitors with either “mixed” MOI or competitive MOIs with either “weak” or “strong” potency, which can be further distinguished by the S-gradient signature patterns (J_max position in the signature). This is based on the fact that a weak inhibitor will always have J_max at the highest level of I (Suppl. Fig. S1). This can be further confirmed with the percentage of inhibition (X) value: A weak inhibitor may show inhibition only at the highest [I]. In a similar vein, a “strong” inhibitor always has J_max at the lowest concentration of I and shows mostly strong inhibition across the I levels with partial inhibition even at the lowest I concentration. On the other hand, a “mixed” type inhibitor also has values of 1 < J_max < 3 but the %Inh values clearly show a dependence on I concentration and the J_max position is not likely at either the highest or lowest I concentrations, which clearly distinguishes this from either weak or strong inhibitors. Altogether, the parameters noted in Table 1 can be used to classify the MOI from the experimental matrix testing approach.

Matrix Test Data Analysis and MOI Prediction

The matrix test data were analyzed using the following steps. First, the activity data were normalized with a conventional plate-based method using the positive and negative controls on the test plate to convert the activity into percentage inhibition (Inh%) values. Then, the matrix data set was directly plugged into an Excel worksheet calculation containing a calculation template to convert the matrix Inh% values at each and every inhibitor concentration into the S gradient (J value) and simultaneously apply the classification algorithm for MOI prediction of each compound tested. The MOI classification algorithm is based on the calculations for the global J values (J_g) and a set of modified classification criteria. For example, to obtain a more indicative J_max and to make this value more experimental error resistant (i.e., outlier resistant), J_max was further defined in the S-gradient signature as the J with maximum absolute value within 20% to 80% average Inh% range. To further reduce outlier interference in the test data, we found it was usually very helpful to first remove any obvious outliers by either an outlier filter or simply having a quick visual inspection of the matrix Inh% data and excluding any data points that were clearly an outlier to the surrounding data sets. This can be done in a program such as Spotfire, and some examples are given in this article. To flag a hit as “too weak” or “too potent” (i.e., outside the matrix test prediction range), we used average Inh% <20 Inh% at the highest inhibitor concentration and average Inh% >80 Inh% (plus with lowest Inh% >90% of average Inh% at the lowest inhibitor concentration) as the criteria, respectively. In addition, a matrix data set was flagged as noisy data if the average Inh% from the inhibitor titration series failed to show a clear decreasing trend with decreasing inhibitor concentrations. For comparison, data analysis with the IC₅₀ shift method (aka R-ratio) was conducted essentially the same way as previously described by Wei et al.¹³

Experimental Case 1: Tests of Two Different Methyl Transferase Enzymes with Inhibitors of Known and Unknown MOI

As a first case, we tested two different methyl transferase assays, each with a small number of inhibitors with both known and unknown MOIs. The enzymes have two substrates: a histone-derived peptide substrate providing methylation sites and SAM as the methyl donor. For each methyl transferase assay, we performed a titration series in the matrix test for each of the two substrates. We also used this case for evaluation of different dimensions of the M_{S ×} N_I matrix in the MOI classification. At first, we tested 42 compounds in the methyl transferase EZH2 biochemical assay using the PRC2 complex.¹⁹ Two of the inhibitors, dubbed here as B-268 and B-920, have their MOI known: B-268 is a proprietary known competitive inhibitor for the histone peptide substrate, whereas B-920 is a known SAM competitive inhibitor. For the peptide substrate titration, we used a 5_S × 8_I matrix test, and for SAM, we used a 4_S × 8_I matrix test. After normalization of the raw data to Inh%, the data were subdivided into several smaller matrices and evaluated with this matrix MOI classification method by the J values (we consistently used J_g in the MOI analysis and the same for other case studies in this work). We evaluated one 5_S × 8_I, two distinct 4_S × 8_I, and four distinct 4_S × 4_I matrices from the peptide titration matrix test and one 4_S × 8_I and two distinct 4_S × 4_I matrices from the SAM titration matrix test. The results clearly show that for the same inhibitor, different matrices tend to generate similar (many are the same) MOI predictions for each substrate. Occasionally, a different MOI prediction is obtained by using different matrices; in most of these occasions, the discrepancy was caused by data variations and outliers or because the J_max value was at the borderline of the classification criteria for some of the matrix test results. Importantly, both of the two known inhibitors have their MOI classified correctly by this method (Suppl. Table S1). Namely, the MOI of B-268 (also labeled as compound No. 3 in Suppl. Table S2) was classified unanimously as “competitive” for peptide substrate by all six different matrices evaluated, and B-920 (also labeled as compound No. 15 in Suppl. Table S2) was classified unanimously as SAM competitive inhibitor by all three different matrices used. As also shown in Supplementary Table S1, these two compounds showed some evidence of competitive behavior against the peptide substrate as well, but the MOI prediction was less consistent for the peptide substrate, indicating there is no strong MOI tendency when tested against the other substrate. As well, 29 of the 42 tested compounds generated good signal and could have their MOI classified with most of the matrices employed, and overall, there is high consistency of the MOI prediction among the matrices (see Suppl. Table S2.).

To expand on this case, we tested a PMT and performed a large 5_S × 12_I matrix test with 26 inhibitors. Among these inhibitors, nine are previously known to be competitive for a histone peptide substrate and uncompetitive for SAM from previous conventional MOI studies, with the rest of the inhibitors with unknown MOI but suspected to have similar behavior as the nine known inhibitors. Likewise, either the peptide substrate or SAM was varied in the matrix tests. After normalization of the raw data to Inh%, the data were subdivided into several smaller matrices including various iterations of 4_S × 6_I, 4_S × 4_I, 3_S × 6_I, and 3_S × 4_I combinations, and the J values were used to classify the MOIs (see Suppl. Table S3). The results of the MOI classification showed that all 26 tested compounds are competitive with the peptide substrate when analyzed using the 5_S × 12_I matrix data set. Also, most (all except one compound, i.e., compound 20 in Suppl. Table S3) of these were classified to have a MOI that is uncompetitive with SAM. From the assay performance point of view, we observed that the peptide titration data set had higher data quality (lower data variability) than that from the SAM titration experiment. This fact was also reflected in that the MOI classification from SAM titration data showed overall more variable than those from the peptide titration data among the different matrices listed in Supplementary Table S3. Using those from the 5_S× 12_I titration matrix (the largest matrix data set) as a standard MOI for comparison, we see that all of the nine inhibitors with known MOI were classified as competitive for the peptide substrate. As well, seven of the nine were classified correctly as uncompetitive for SAM, with the other two (compounds No. 1 and 16 in Suppl. Table S3) classified as the related UC/NC mixed MOI for SAM. Again, this may also have something to do with a high degree of data variability in SAM titration experiment. Therefore, all of these nine inhibitors were classified correctly or as having very similar MOIs for both substrates. As expected, the rest of the “unknown” inhibitors have similar MOIs as these nine inhibitors, except one (compound 20), which showed competitive behavior for both substrates. Furthermore, it can be seen that all the evaluated subdimensional matrices (i.e., 4_S × 6_I, 4_S × 4_I, 3_S × 6_I, and 3_S × 4_I matrices) have >80% consistency with the 5_S × 12_I matrix MOI prediction for peptide titration data. For SAM titration, because of the lower test data quality, the 4_S × 6_I and one 4_S × 4_I matrices gave >80% consistency, whereas the 3_S × 6_I, 3_S × 4_I, and the other 4_S × 4_I, matrices gave only 58% to 77% consistency. However, when the MOI predictions were not the same between the matrices, disagreements were usually small and the MOIs were still similar (i.e., between any particular MOI and the related mixed mode). Again, on most of these occasions, the discrepancy was caused by larger data variations, strong outliers, or because the analyzed J_max value was at the borderline of the classification criteria. Consistent with expectations, as the dimension of the M_S × N_I matrix becomes smaller, the analysis tends to yield higher mixed modes and more variation in the MOI prediction. This tendency seems also to hold in other case studies (vide infra). Therefore, the matrix dimension, which ties to the titration ranges of the substrate and inhibitor, affects the consistency of the classification results. This is similar to how the number of critical data points affects curve-fitting results in a typical CRC analysis. These results support that, given a test data set of reasonably high quality (i.e., low data variation), one can judiciously select the titration series. We observed that a titration matrix size as small as either 4_S × 6_I or 4_S × 4_I can be used to quite reliably classify the MOI.

Experimental Case 2: Test of High-Throughput MOI Determination for Dengue NS5 RdRp Inhibitors

To test the matrix-based MOI analysis against a list of inhibitors derived directly from an HTS campaign, we performed a 4_S × 8_I matrix test of 165 inhibitors in a biochemical RdRP assay.¹⁶ We evaluated the MOI prediction with three matrices—4_S × 8_I and two distinct 4_S × 4_I matrices (details in Suppl. Table S4)—and the results showed that the three matrices yielded very similar MOI prediction for these inhibitors. Figure 3 shows the heat maps of Inh% data for the list of uncompetitive, noncompetitive, and the one competitive compound from one of the 4_S × 4_I matrix analyses. Also, example CRCs for the full eight-point titration series are shown in Figure 3 , which shows visually that the MOI prediction agrees well with the observed shift in titration curves for different substrate concentrations, supporting primarily the validity of the MOI prediction results. To further validate the matrix MOI classification results, we performed a direct comparison of the J_max value from this analysis (note that the J_max value is one major factor, but not the only factor, for MOI prediction in our method) to the IC₅₀ shift method (R value, for MOI prediction) previously described,¹³ and the result is shown in Figure 4 . It is quite obvious that the two metrics give overall very similar MOI predictions for most of the inhibitors. The J_max (from a 4_S × 4_I matrix analysis) and R values (from the two eight-point CRCs at highest and lowest substrate concentrations, as suggested by the originally described method) correlated well (r = 0.826). It can also be seen that inhibitors with the UC and UC/NC mixed modes have the most difference in MOI prediction by the two metrics: the R value tends to predict more inhibitors as UC/NC mixed modes (130) with 10 compounds classified as UC and 23 classified as NC. The J_max values classify the majority either as UC (75) or UC/NC mixed (75) and 11 as NC. It should be noted that this disagreement could be due in part to the data sets used in the evaluation (i.e., 4S × 4_I vs. 2_S × 8_I) containing different levels of data variations. It is known that Dengue RdDP polymerase switches between a rigid “closed” form for initiation and a more flexible “open” form for elongation,²⁰ which may provide a mechanism for uncompetitive inhibitors, but more follow-up work will have to be done to confirm this hypothesis. There was one competitive compound consistently found by both methods. This compound is an analog of the aminoglycoside gentamicin, likely competing by binding to the RNA substrate.²¹

Figure 3.

Representative data from the RdDp inhibitor testing. (a) Top: Heat map of the results from matrix testing at four inhibitor and four substrate concentrations using concentrations of 25, 6.25, 1.56, and 0.39 µM of inhibitor and 1200, 300, 75, and 18.75 nM of RNA substrate for compounds classified as UC (uncompetitive) inhibitors and several representative concentration-response curves (CRCs; bottom). (b) Top: Heat map of the results from same matrix testing for compounds classified as mixed inhibitors and representative CRCs. (c) Top: Heat map of the results from the same matrix testing of the only competitive inhibitor identified from the same matrix testing as noted above and the CRC.

Figure 4.

Comparison of the IC₅₀ shift method to the matrix S-gradient signature determination for mode of inhibition (MOI) classification for the Dengue RdDp inhibitors. For the IC₅₀ shift method, the data from the 1200 nM and 18.75 nM RNA substrate concentrations were taken. For matrix S-gradient signature determination, 25, 6.25, 1.56, and 0.39 µM of inhibitor and 1200, 300, 75, and 18.75 nM of RNA substrate was used for the matrix. (a) Histogram of the MOI classifications for the IC₅₀ shift method. (b) Histogram of the MOI classifications for the matrix S-gradient signature determination. (c) Plot of the Jg values (J_max) versus the IC₅₀ shift ratio (R); data are colored by the MOI obtained from the J_max values. Grids show the cutoffs used to determine the MOIs from the J_max values (horizontal lines) and the IC₅₀ shift (R values, vertical lines, MOI regions labeled on top of the graph). Annotations are C = competitive, NC = noncompetitive, UC = uncompetitive, M = mixed. Note the IC₅₀ shift method did not distinguish between mixed uncompetitive (M_UC-NC) and mixed competitive (M_C-NC). ND = not determinable.

Experimental Case 3: Example High-Throughput MOI Determination: Firefly Luciferase Inhibitors

Because the S-gradient matrix method does not require any individual curve fitting as required by the IC₅₀ shift method, one can easily apply this method to any large number of compounds. To examine the MOI classification in a high-throughput mode, we chose to test a series of 1363 FLuc inhibitors that had been previously identified in a screen of the NIBR compound collection aimed at identifying compounds that might interfere with this commonly used reporter enzyme.²² For MOI determination, these compounds were arrayed as a quantitative HTS (qHTS) format within 1536-well plates and 12 plates were screened, with each plate representing a different inhibitor concentration. The set of qHTS plates was then screened at four different concentrations of the substrate D-luciferin in a biochemical assay measuring FLuc enzyme activity.²² The data were then broken down to 4_S × 8_I and two 4_S × 4_I matrices (Suppl. Table S5), and the J_g values were used to determine the MOI. Example heat maps and CRCs are shown in Supplementary Figure S2. Overall, this set of inhibitors was found to be enriched with luciferin competitive inhibitors, with 37 noncompetitive inhibitors and no uncompetitive inhibitors. The mixed inhibition mode found was mixed NC/C, and no inhibitors with mixed NC/UC MOIs were identified (Suppl. Fig. S2). These MOIs for FLuc inhibitors with respect to D-luciferin substrate are consistent with the known binding modes of FLuc inhibitors as most of these are known to bind to the D-luciferin pocket.¹⁵ As well, potent compounds with MOIs classified as either NC or mixed NC/C often contained an oxadiazole core and an aryl m-carboxylate moiety. These compounds are similar to the known potent FLuc inhibitor PTC124, which forms an adenylate in the presence of ATP, leading to a multisubstrate adduct inhibitor that binds with sub-nM potency through filling both the D-luciferin and ATP pockets.^15,23

A comparison of the FLuc inhibitor MOIs classified from the IC₅₀ shift ratio (R value) to that derived from J_max in the current S-gradient matrix method is shown in Supplementary Figure S3. In this case, most of the compounds have predicted MOIs (Suppl. Fig. S3a, b), except 11 compounds, which were not determinable because of weak inhibition signal in CRCs even at the highest inhibitor concentration using the IC₅₀ shift method. Using the R value, the majority of the compounds (nearly 1000 compounds) are characterized as mixed MOI, and these are mostly found to be mixed C/NC MOI based on J_max values (Suppl. Fig S3b, c). Twenty-six compounds were classified as NC by R value, and these are found as either C/NC (22 compounds), or in four cases, the MOI was not determinable because of noisy data in the matrix MOI. Although the majority of the inhibitors were classified to be the same or at least similar MOIs between the two methods, it should also be noted that a few inhibitors were classified with very different MOIs. For example, one uncompetitive inhibitor was classified using the R ratio value but was classified as a competitive inhibitor using the J_max value. Examination of the CRCs for this compound shows that at the highest substrate concentration, a very shallow parametric curve is fitted to the data, resulting in an IC₅₀ of approximately 1 µM at the highest tested substrate concentration, but this drops to approximately 10 µM at lower substrate concentrations (Suppl. Fig. S3d). This curve-fitting bias, therefore, led to the UC classification by the R value method and illustrates how inspection of all the curve-fitting routines is required for the R value method. However, the J_max value correctly determines the MOI as competitive by not depending on the curve-fitting bias. Overall, comparative results from this case and the previous cases support that this matrix S-gradient method performs as well or even better in the accuracy of MOI classification compared with the IC₅₀ shift method.

Some Important Considerations

This study supports that robust MOI classification can be achieved from nonparametric analysis of activity values derived from a small matrix testing of substrate and inhibitor concentrations. A few recommendations are suggested when implementing this method. For assays with reasonably good data quality and low data variability, the method performs well at smaller test matrices such as 4_S × 4_I, allowing these to be employed for high-throughput assays. In this case, the number of data points collected is the same as the 2_S × 8_I employed in the IC₅₀-shift method but without the need for curve fitting. Of course, for assays in which reagents are readily available and low cost, larger 4_S × 6_I or 4_S × 8_I matrices could be employed followed by applying the same nonparametric analysis procedure. In every case presented here, because of either data variation or the presence of very strong or weak inhibitors, we found a small subset of compounds whose MOI could not be determined. Therefore, it is important to have checks of the %Inh values at low and high inhibitor concentrations over the tested substrate concentration range. Our analysis takes into consideration both weak or superpotent activity by initially examining the inhibition values at low and high inhibitor concentration to prevent generation of erroneous J values. As well, the J_max values should be qualified by considering if the S-gradient signature spans a meaningful activity range. For example, we considered J_max values only if the S-gradient spanned an average of 20% to 80% Inh%. The choice of substrate and inhibitor concentrations is also important, and we found that using a relatively broad range (e.g., covering >100-fold range in concentration) was usually optimal. We used a constant value of k = 5 for the MOI classifications described here, which proved adequate in providing accurate MOI classification based on the amplitude of J values we measured. However, this value can be modified depending on the data variation and assay bias. Overall, one big advantage of the current method is that once a format is judiciously chosen for the matrix testing, the MOI classification could be accurately determined by simply pasting the normalized data into the Excel calculation and classification worksheet. This method provides a rapid and simple procedure for assessing the MOI of large number of compounds arising from screening efforts.

We summarize the overall process of applying the S-gradient signature J with experimental data from matrix testing for MOI classification as illustrated in Figure 5 . The process consists of the following three steps: (1) design of the M_S × N_I matrix (i.e., selection of the substrate and inhibitor range and dilution series), (2) test of the matrix activity to obtain the corresponding Inh% data matrix after normalization of the activity, and (3) calculation of the S-gradient signature (J) and applying the classification algorithm for MOI prediction of each compound tested. For a 4_S × 4_I matrix specifically, compounds are arrayed at four concentrations and then tested at four different substrate concentrations. The compound dilution series can be arrayed in four adjacent wells (intraplate dilution series). Alternatively, a qHTS format²⁴ (i.e., an interplate dilution series) can be applied, and the qHTS set is then screened at four substrate concentrations, as was done for our FLuc case study. Following the assay, the data are normalized by the positive and negative controls on the plates to calculate the Inh% (note in the convention used in this article, complete inhibition is defined as −100%). J values are calculated at the four substrate levels for each compound, and then the MOIs are classified via an algorithm based on the S-gradient signature (J values). This method should also be applicable to binding assays in which ligand and inhibitor concentrations are varied to determine the mechanism of inhibitor binding. In practice, the solubility, background fluorescence, liquid-handling precision, and the possibility of substrate inhibition will affect the test data and thus the classification accuracy. These interfering factors should be taken note of whenever possible no matter which method of MOI determination is employed.

Figure 5.

Process for matrix-based experimental testing, data analysis, and S-gradient signature classification for different modes of inhibition (MOIs). An example test of 4_S × 4_I was performed in the enzyme assays, and example heat maps representing the Inh% values are shown for various patterns. S-gradient signature classification bins the data either as C (competitive), UC (uncompetitive), NC (noncompetitive), or mixed (C/NC or UC/NC). Noisy data as well as very weak or very potent compounds are also correctly identified for which the MOI was not determinable (ND).

Footnotes

Acknowledgements

The authors wish to acknowledge the insightful inputs from Dr. Hanspeter Gubler (Novartis) for this study. We would also like to thank Drs. Guy Herr, Zinger Yang, and John Lin for helpful inputs during the initial discussion. The authors also thank Ms. Pei-I Ho for her technical support in the FLuc assay and testing and Drs. William Hill and Timothy Benson for their support of the study.

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.

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