Abstract
In the present study, we conducted a retrospective analysis of 343 in vitro experiments to ascertain whether observed (experimentally determined) values of Ki for reversible cytochrome P450 (P450) inhibition could be reliably predicted by dividing the corresponding IC50 values by two, based on the relationship (for competitive inhibition) in which Ki = IC50/2 when [S] (substrate concentration) = Km (Michaelis-Menten constant). Values of Ki and IC50 were determined under the following conditions: 1) the concentration of P450 marker substrate, [S], was equal to Km (for IC50 determinations) and spanned Km (for Ki determinations); 2) the substrate incubation time was short (5 minutes) to minimize metabolism-dependent inhibition and inhibitor depletion; and 3) the concentration of human liver microsomes was low (0.1 mg/ml or less) to maximize the unbound fraction of inhibitor. Under these conditions, predicted Ki values, based on IC50/2, correlated strongly with experimentally observed Ki determinations [r = 0.940; average fold error (AFE) = 1.10]. Of the 343 predicted Ki values, 316 (92%) were within a factor of 2 of the experimentally determined Ki values, and only one value fell outside a 3-fold range. In the case of noncompetitive inhibitors, Ki values predicted from IC50/2 values were overestimated by a factor of nearly 2 (AFE = 1.85; n = 13), which is to be expected because, for noncompetitive inhibition, Ki = IC50 (not IC50/2). The results suggest that, under appropriate experimental conditions with the substrate concentration equal to Km, values of Ki for direct, reversible inhibition can be reliably estimated from values of IC50/2.
Introduction
When an investigational drug is evaluated in vitro as a direct, reversible inhibitor of human liver cytochrome P450 (P450) enzymes based on the Food and Drug Administration’s (FDA’s) 2012 draft Guidance for Industry on drug interactions (http://www.fda.gov/downloads/Drugs/GuidanceComplianceRegulatoryInformation/Guidances/UCM292362.pdf), the need for a clinical drug interaction study is based on eq. 1:
(1)where [I] is the maximum total (bound + unbound) plasma concentration of drug at steady state (Cmax,ss), and Ki,unbound is the dissociation constant for the enzyme-inhibitor complex for direct, reversible inhibition based on the concentration of unbound drug in the in vitro test system. AUCR, the area under the plasma concentration-time curve (AUC) ratio, represents the fold increase in plasma AUC of a probe drug whose clearance is entirely determined by metabolism by the P450 enzyme inhibited by the investigational drug (i.e., fractional metabolism by an enzyme, or fm = 1.0) (Ito et al., 1998; Rodrigues et al., 2001). When other pathways contribute to clearance of the probe drug, such that fm < 1, the fold increase in plasma AUC of the probe drug in the presence of the inhibitory drug is given by eq. 2:
(2)A clinical drug interaction study is recommended for P450 enzymes other than CYP3A when the ratio R1 > 1.1 (where R1 = 1 + [I]/Ki,unbound). The same criteria apply to significant circulating metabolites, defined by the FDA as metabolites whose plasma AUC is ≥25% of the parent AUC following dosing to steady state with the maximum clinical dose. The European Medicines Agency’s (EMA’s) 2012 Guideline on the Investigation of Drug Interactions (http://www.ema.europa.eu/docs/en_GB/document_library/Scientific_guideline/2012/07/WC500129606.pdf) is based on a similar type of ratio and cutoff value, namely, [I]unbound/Ki,unbound ≥ 0.02, where Ki,unbound is as defined earlier and [I]unbound is the unbound (free) maximum concentration of drug in plasma (mean Cmax obtained following treatment with the highest recommended clinical dose). The EMA’s guideline also applies to significant circulating metabolites, defined as phase 1 metabolites whose plasma AUC is >25% of the parent drug and >10% of total circulating drug-derived material. To evaluate the potential for reversible inhibition of CYP3A enzymes in the intestine, the concentration of inhibitor in eq. 1 is defined as [I]gut = molar dose/250 ml. Values of [I]gut can greatly exceed values of [I] (total Cmax,ss); accordingly, the FDA’s cutoff value for inhibition of intestinal P450 enzymes is 11 (based on 1 + [I]gut/Ki,unbound). The corresponding EMA cutoff is 10 (based on [I]gut/Ki,unbound).
Typically, inhibition of P450 enzymes is first evaluated in vitro by determining the concentration of investigational drug (or significant circulating metabolite) that causes 50% inhibition of P450 enzyme activity (IC50) with a selective P450 probe at a substrate concentration approximately equal to Km (Michaelis-Menten constant). Determining the mechanism of reversible inhibition (competitive, noncompetitive, mixed, or uncompetitive) and measuring the value of Ki requires an in vitro evaluation of the effects of multiple inhibitor concentrations versus multiple substrate concentrations, ideally with the former spanning Ki and the latter spanning Km. Determining values of IC50 and Ki based on the unbound concentration of inhibitor in the test system (typically human liver microsomes) requires knowledge of fuinc (the fraction of unbound drug in the microsomal incubation), which can be determined experimentally or estimated theoretically from the inhibitor’s logP or logD value and the concentration of microsomal protein (Austin et al.., 2002; Hallifax and Houston, 2006).
The relationship between Ki and values of IC50 determined when [S] (substrate concentration) = Km depends on the mechanism of inhibition, as summarized in Table 1 (Cheng and Prusoff, 1973; Brandt et al., 1987; Cer et al., 2009). In the case of noncompetitive inhibition, Ki = IC50. In the case of competitive and uncompetitive inhibition, Ki = IC50/2. In the case of mixed inhibition, Ki values range from IC50 to IC50/2. The FDA’s 2012 Guidance for Industry on drug interactions acknowledges that Ki values are often estimated from values of IC50/2, based on the conservative assumption that the mechanism of reversible inhibition is competitive in nature. In the present study, we conducted a retrospective analysis of 343 in vitro Ki determinations to investigate whether experimentally determined Ki values can, in fact, be reliably estimated from values of IC50/2 when IC50 values are determined under conditions of [S] ≈ Km.
Materials and Methods
Chemicals and Reagents.
The commercial sources of most substrates, metabolites, internal standards, and reagents have been described previously (Pearce et al., 1996; Paris et al., 2009; Parkinson et al., 2011). Efavirenz was purchased from U.S. Pharmacopeia (Rockville, MD). 8-Hydroxyefavirenz, 8-hydroxyefavirenz-d4 (internal standard), and 6α-hydroxypaclitaxel-d5 (internal standard) were purchased from Toronto Research Chemicals, Inc. (North York, Ontario, Canada). The following chemicals were purchased from Sigma-Aldrich (St. Louis, MO): coumarin, paclitaxel, bufuralol, 1′-hydroxybufuralol, chlorzoxazone, 6-hydroxychlorzoxazone, 6-hydroxychlorzoxazone-d2 (internal standard), nifedipine, and oxidized nifedipine. 7-Hydroxycoumarin was purchased from Cerilliant (Round Rock, TX). 6α-Hydroxypaclitaxel, 7-hydroxycoumarin-d5 (internal standard), and dehydronifedipine-d6 (internal standard) were purchased from SynFine Research (Richmond Hill, Ontario, Canada). 10-Deacetyltaxol (internal standard) was purchased from A.F. Hauser, Inc. Pharmaceutical (Valparaiso, IN).
Investigational Drugs.
A total of 132 investigational drugs and drug metabolites were examined during the course of P450 inhibition studies sponsored by numerous pharmaceutical companies in the United States, Europe, and Japan. Unfortunately, because they are proprietary compounds and for reasons of confidentiality, we are not at liberty to disclose the identity of the structures of these compounds. The compounds represent a set of structurally diverse, small drug molecules under development for several different therapeutic indications. The design of the experiments and the interpretation of the results of this study (a comparison of two endpoints of P450 inhibition) required neither knowledge of chemical structures nor physicochemical properties.
Test System.
Pooled human liver microsomes (n = 16 or 200; mixed gender) were prepared from nontransplantable livers and characterized at XenoTech, LLC (Lenexa, KS) as described previously (Pearce et al., 1996; Parkinson et al., 2004).
Incubation Conditions.
Ki and IC50 values were determined in accordance with recommendations in the FDA and EMA guidance documents and consensus papers (Tucker et al., 2001; Bjornsson et al., 2003). All experiments were performed under the following conditions: 1) the concentration of P450 marker substrate was approximately equal to Km for IC50 determinations and spanned Km for Ki determinations (i.e., [S] ranged from 0.25 times Km to 10 times Km, solubility permitting); 2) the substrate incubation time was 5 minutes to minimize metabolism-dependent inhibition and inhibitor depletion; and 3) the concentration of human liver microsomes was 0.1 mg/ml or less to maximize the unbound inhibitor concentration.
In general, incubations were conducted at 37°C in 200- or 400-µl incubation mixtures containing potassium phosphate buffer (50 mM, pH 7.4), MgCl2 (3 mM), EDTA (1 mM), NADPH-generating system, and human liver microsomes. Most of the P450 reactions examined have been described in detail elsewhere (Paris et al., 2009; Parkinson et al., 2011). The P450 substrates, analytes (metabolites measured), internal standards, and microsomal protein concentration for all of the P450 reactions examined are summarized in Supplemental Table 1.
Analytical Methods.
All metabolites and their internal standards (usually isotopically labeled metabolites) were measured with validated liquid chromatography–tandem mass spectrometry methods on AB Sciex (Framingham, MA) API 2000, 3000, or 4000 mass spectrometers with Shimadzu (Kyoto, Japan) high-performance liquid chromatography pumps and autosampler systems according to methods described previously (Paris et al., 2009; Parkinson et al., 2011). Peak areas for all metabolites were integrated with an AB Sciex Analyst data system, and metabolites were quantified by reference to a standard calibration curve based on back-calculation of a weighted (1/x), linear, least-squares regression.
Data Processing.
IC50 data were processed with one of two validated software packages, Galileo- Laboratory Information Management System (Galileo version 3.3; Thermo Fisher Scientific Inc., Grand Island, NY) or XLfit (version 3.0.5; ID Business Solutions Ltd., Guildford, Surrey, UK), which is used within a customized software program (DI IC50 LCMS Template version 2.0.3) for Microsoft Excel Office 2000 (version 9.0; Microsoft Inc., Redmond, WA). Both software programs use a Levenberg-Marquardt algorithm (Levenberg, 1944; Marquardt, 1963), also known as a damped least-squares algorithm, to fit a nonlinear regression (sigmoidal) curve to IC50 data based on the following equation:
(3)where Min = zero (no inhibition) and Max = 100 (complete inhibition). In XLfit, the terms Min and Max are called background and range, respectively. Both software programs have been validated for their ability to calculate IC50 values only when they lie within the actual range of inhibitor concentrations tested. In other words, none of the IC50 values reported here was extrapolated from data that fell above or below the highest or lowest concentration of inhibitor, respectively.
The data for Ki determinations were processed with one of two comparable methods. The first method used Microsoft Excel to calculate rates of metabolite formation, which were imported into GraFit (Erithacus Software Ltd., Horley, Surrey, UK) to perform nonlinear regression according to the Michaelis-Menten equations associated with each type of direct inhibition. The second method used a Galileo Laboratory Information Management System (Thermo Scientific, Waltham, MA) with Crystal Reports-SAP Business Objects (SAP, Newtown Square, PA). The data (i.e., reaction rates at all concentrations of inhibitor at all concentrations of P450 marker substrates) were fitted to the Michaelis-Menten equations for competitive, noncompetitive, uncompetitive, and mixed (competitive-noncompetitive) inhibition (see Table 1) by nonlinear regression analysis. The goodness of fit to each of the four inhibition equations was determined by χ2 analysis (with lower values indicating better fit) or by comparison of Akaike information criterion values (with higher values indicating better fit), which provided an initial basis for identifying the mechanism of inhibition. Eadie-Hofstee plots (rate versus rate/[S]) were inspected visually. At times, the nonlinear regression lines did not correlate well with the data points depicted on the Eadie-Hofstee plot, and visual inspection of the kinetic plots was necessary to deduce the mechanism of inhibition. Both methods of data processing are validated to calculate Ki values only when they lie within the range of inhibitor concentrations tested.
Statistical Analysis.
The accuracy of the prediction of observed Ki values from values of IC50/2 was assessed by determining the average fold error (AFE) according to eq. 4 (Obach et al., 1997). This method is based on absolute values of the logarithm of the ratio of predicted-to-observed values, meaning that all negative values are converted to positive values so that, for example, values 50% less and 100% more than the observed value both represent a 2-fold error. An AFE value of 1 represents a perfect prediction.
(4)The precision of the prediction was assessed by calculating the root mean square error (RMSE) according to eq. 5 (Sheiner and Beal, 1981):
(5)The normalized RMSE (NRMSE; expressed as a percentage) was calculated as follows:
(6)In all cases, the observed Ki is the experimentally determined value, and the predicted Ki corresponds to IC50/2.
Results
The nine P450 enzymes and 14 marker substrates examined in the current study, and the distribution of the types of reversible inhibition (i.e., competitive, noncompetitive, mixed, and uncompetitive inhibition) observed in vitro with human liver microsomes are summarized in Fig. 1 and Table 2. The inhibitors were 132 structurally diverse investigational drugs, some of which were examined as reversible inhibitors of more than one P450 enzyme (data not shown). The correlations between the 343 observed (experimentally determined) Ki values and those predicted from the corresponding values of IC50/2 (when [S] ≈ Km) are shown in Fig. 2 and Table 3. The correlations between observed and predicted Ki values as a function of the mechanism of P450 inhibition are shown in Fig. 3. The ratios of the observed-to-predicted Ki values as a function of the mechanism of P450 inhibition are shown in Fig. 4 and Table 3. Measures of the accuracy (AFE) and precision (RMSE and NRMSE) of predicting Ki values from IC50/2 when [S] ≈ Km are shown in Figs. 2 and 3, and summarized in Table 3.
Discussion
A total of 343 Ki values for reversible inhibition of various P450 enzymes was determined experimentally (from studies with multiple inhibitor concentrations versus multiple substrate concentrations) with 132 structurally diverse investigational drugs (some of which were examined with more than one P450 enzyme) after determining IC50 values in human liver microsomes under conditions where [S] ≈ Km. Table 2 shows the distribution of the four mechanisms of reversible inhibition for the 343 Ki determinations. The compounds were predominantly (∼95%) mixed (n = 217) or competitive (n = 108) P450 inhibitors; however, noncompetitive inhibitors (n = 13) and uncompetitive inhibitors (n = 5) were also represented in the data set. The distribution of P450 enzymes analyzed as well as the marker substrates used are shown in Fig. 1 and Table 2. For the seven drug-metabolizing P450 enzymes listed in the FDA and EMA guidance documents on drug interactions, the number of Ki determinations ranged from 21 (CYP1A2) to 94 (CYP3A4/5). Relatively few Ki values were determined with CYP2A6 (n = 6) and CYP2E1 (n = 2). Four P450 enzymes (CYP2B6, 2C8, 2D6, and 3A4/5) were assayed with more than one substrate.
The correlation between the observed (experimentally determined) Ki values and the predicted Ki values (from IC50/2) for the entire data set is shown in Fig. 2. The experimentally determined Ki values ranged 200,000-fold from 9 nM to 1.9 mM. Overall, predicted values of Ki (based on IC50/2) correlated well (r = 0.940) with observed values of Ki, and the prediction was both accurate (AFE = 1.10) and precise (RMSE = 64.2; NRMSE = 3.38%).
When the data were segregated by inhibition type, the observed and predicted Ki values were highly correlated for all four types of inhibition (r values ranged from 0.926 to 0.994), as shown in Table 3 and Fig. 3. Values of IC50/2 served as accurate predictors of observed Ki values for competitive inhibition (AFE = 1.10) and uncompetitive inhibition (AFE = 1.24). This was as expected because, in theory, Ki should equal IC50/2 for these types of inhibition (Table 1). Values of IC50/2 also accurately predicted Ki values for mixed inhibition (AFE = 1.07), where, in theory, Ki values can range from IC50 to IC50/2 (Table 1). However, IC50/2 was a less accurate predictor of Ki values for noncompetitive inhibition. In this case, the AFE value of 1.85 indicates that the prediction was off by a factor of nearly 2, which is consistent with the equation in Table 1, indicating that, for noncompetitive inhibition, Ki = IC50, not IC50/2. Omitting the 13 Ki values for noncompetitive inhibition (where theoretically Ki = IC50 and not IC50/2) resulted in a negligible improvement in overall AFE; the value decreased from 1.10 to 1.08, and NRMSE decreased slightly from 3.38 to 3.34%, as shown in Table 3.
The ratios of observed-to-predicted Ki values are shown in Fig. 4 and summarized in Table 3. Of the 343 predicted Ki values, 316 (92%) were within a factor of 2 of the experimentally determined Ki value. Two predicted values were less than 0.5 (but not less than 0.33) and 25 values were greater than 2, only one of which was greater than 3. In other words, of the 343 predicted Ki values, 316 were within a factor of 2 and 342 were within a factor of 3, meaning only one value fell outside a 3-fold range (the actual value was 3.41). A preliminary account of this work included a second case in which the predicted Ki value was more than 3-fold greater than the experimentally determined Ki value (Haupt et al., 2011). However, in this case, the initial IC50 value was below the lowest concentration of inhibitor tested, and an interpolated IC50 value was used in the analysis. This observation underscores the importance of predicting Ki values only when the IC50 value falls within the range of inhibitor concentrations tested.
It is important to note that other experimental conditions can affect the measured values of IC50 and the kinetic constants Km and Ki (Obach, 1996, 1997, and 1999; McLure et al., 2000; Austin et al., 2002; Di Marco et al., 2003; Margolis and Obach, 2003; Hallifax and Houston, 2006; Howgate et al., 2006; Brown et al., 2007a,b; Ogilvie et al., 2011; Parkinson et al., 2011). In this study, all Ki and IC50 values were determined at 0.1 mg microsomal protein/ml or less with a short substrate incubation time (5 minutes) to minimize metabolic loss of the inhibitory drug, to reduce the possibility of metabolism-dependent inhibition, and to maximize the concentration of unbound inhibitor. Membrane partitioning [commonly but erroneously called nonspecific binding (Nagar and Korzekwa, 2012)] decreases the unbound concentration of inhibitor, but this effect can be corrected by measuring or calculating fuinc (Austin et al., 2002; Hallifax and Houston, 2006) and expressing the inhibition constant as Ki,unbound, now recommended by both the FDA and EMA. This same approach can be applied to measurements of Ki based on IC50/2. It should be noted that, in the current study, IC50 and Ki values for a given P450 enzyme were determined under identical experimental conditions (i.e., the same concentration of microsomal protein), such that values of fuinc were the same for predicted and observed Ki determinations. Accordingly, correcting for fuinc would have had no effect on estimates of the ratio of the prediction-to-observed Ki values or the accuracy and precision of predicting Ki values from IC50/2.
Although the experimentally determined Ki values varied approximately 200,000-fold, most of them (240 of 343) fell between 1 and 25 µM (with 61 greater than 25 µM and 42 less than 1 µM). In the majority of cases (287 of 343 determinations), the initial IC50 value was 50 µM or less (hence, the predicted Ki value was 25 µM or less), suggesting that the decision to measure Ki values was biased toward those cases in which the initial IC50 determination suggested relatively strong P450 inhibition. There were 37 cases in which the initial IC50 was greater than 100 µM (i.e., the inhibition was relatively weak). It might be expected that, in these cases, the decision to perform a Ki determination was biased toward CYP3A4/5 because of its intestinal location, where the relevant inhibitor concentration is molar dose/250 ml, not plasma Cmax,ss. However, of the 37 cases of weak inhibition, Ki values were determined for a wide variety of P450 enzymes: 13 for CYP3A4/5, 6 for CYP2C9, 6 for CYP2C19, 5 for CYP2D6, 3 for CYP2B6, 2 for CYP1A2, 1 for CYP2A6, and 1 for CYP2C8. Therefore, CYP3A4/5 represented only 35% of the cases in which Ki was determined when the initial IC50 was greater than 100 µM.
Interestingly, uncompetitive inhibition, characterized by a decrease in both Vmax and Km, was observed only when nifedipine was the substrate. Of the 10 assays performed with nifedipine, 5 exhibited uncompetitive inhibition. The CYP3A substrates used in the current study, midazolam, testosterone, and nifedipine, are thought to bind to three distinct regions within the substrate-binding site and exhibit distinct enzyme kinetics characterized by hyperbolic (typical Michaelis-Menten) kinetics in the case of midazolam, substrate activation (sigmoidal kinetics due to homotropic cooperativity) in the case of testosterone, and substrate inhibition in the case of nifedipine. The high prevalence of uncompetitive inhibition observed with nifedipine, which suggests some inhibitors bind to the CYP3A-nifedipine (enzyme-substrate) complex, is consistent with previous studies documenting the so-called stand-alone properties of nifedipine as a CYP3A4/5 substrate (Kenworthy et al., 1999; Wang et al., 2000; Galetin et al., 2002, 2003; Foti et al., 2010).
Overall, our analysis of 343 determinations supports theoretical considerations (Table 1) that, when determined under in vitro conditions of low protein concentration, short substrate incubation time, and [S] ≈ Km, values of IC50/2 provide an accurate prediction (generally within a factor of 2) of experimentally determined Ki values for all types of reversible, direct inhibition of P450 enzymes. In the case of noncompetitive inhibitors, values of Ki estimated from IC50/2 were off by a factor of ∼2 (AFE = 1.85), which is consistent with theoretical considerations (Table 1). However, noncompetitive inhibitors accounted for a relatively low percentage (∼4%) of the types of inhibition observed (13 of 343 determinations). In conclusion, the results of our analysis suggest that, under appropriate experimental conditions, Ki values for direct, reversible inhibition can be reliably, albeit somewhat conservatively, estimated from values of IC50/2.
The following excerpt is from the FDA’s Guidance for Industry on drug interactions (from footnote 2 on page 21): “For a drug that is a reversible inhibitor, R = 1+[I]/Ki. Ki is the unbound inhibition constant determined in vitro. Sometimes inhibitor concentration causing 50% inhibition (IC50) is determined, and Ki can be calculated as IC50/2 by assuming competitive inhibition.” The results of our analysis suggest that measuring IC50 is sufficient to estimate Ki for the purpose of evaluating the potential of an investigational drug to cause clinically relevant P450 inhibition, with two stipulations. First, IC50 is determined under appropriate experimental conditions, as described in the previous paragraph. Second, the Ki value estimated from IC50/2 is corrected for the fraction of unbound drug in the test system, such that Ki,u is estimated from (IC50/2)⋅fuinc, where fuinc is determined experimentally or calculated from log P (in the case of nonionic and basic drugs) or log D7.4 (in the case of acidic and zwitterionic drugs), as described by Austin et al. (2002) and Hallifax and Houston (2006).
Acknowledgments
The authors thank the Analytical Sciences and Enzyme Inhibition departments at XenoTech LLC for technical assistance.
Authorship Contributions
Participated in research design: Kazmi, Ogilvie, Buckley, Paris, A. Parkinson.
Conducted experiments: Haupt, Smith, Leatherman.
Performed data analysis: Haupt, Kazmi, Ogilvie, Buckley, Paris, O. Parkinson, A. Parkinson.
Wrote or contributed to the writing of the manuscript: Haupt, Kazmi, Ogilvie, Buckley, O. Parkinson, Paris, A. Parkinson.
Footnotes
- Received July 28, 2015.
- Accepted September 8, 2015.
Parts of this work were previously presented at the following meeting: Haupt L, Kazmi F, Ogilvie B, Buckley D, Smith B, Leatherman S, and Parkinson A (2011) Can Ki values for direct inhibition of CYP enzymes be reliably estimated from IC50 values? Seventeenth North American Regional ISSX Meeting; 2011 Oct 16–20; Atlanta, GA.
↵This article has supplemental material available at dmd.aspetjournals.org.
Abbreviations
- AFE
- average fold error
- AUC
- area under the plasma concentration-time curve
- EMA
- European Medicines Agency
- FDA
- U.S. Food and Drug Administration
- NRMSE
- normalized root mean square error
- P450
- cytochrome P450
- RMSE
- root mean square error
- Copyright © 2015 by The American Society for Pharmacology and Experimental Therapeutics