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Research ArticleArticle

Progress Curve Mechanistic Modeling Approach for Assessing Time-Dependent Inhibition of CYP3A4

Howard J. Burt, Henry Pertinez, Carolina Säll, Claire Collins, Ruth Hyland, J. Brian Houston and Aleksandra Galetin
Drug Metabolism and Disposition September 2012, 40 (9) 1658-1667; DOI: https://doi.org/10.1124/dmd.112.046078

Abstract

A progress curve method for assessing time-dependent inhibition of CYP3A4 is based on simultaneous quantification of probe substrate metabolite and inhibitor concentrations during the experiment. Therefore, it may overcome some of the issues associated with the traditional two-step method and estimation of inactivation rate (kinact) and irreversible inhibition (KI) constants. In the current study, seven time-dependent inhibitors were investigated using a progress curve method and recombinant CYP3A4. A novel mechanistic modeling approach was applied to determine inhibition parameters using both inhibitor and probe metabolite data. Progress curves generated for clarithromycin, erythromycin, diltiazem, and N-desmethyldiltiazem were described well by the mechanistic mechanism-based inhibition (MBI) model. In contrast, mibefradil, ritonavir, and verapamil required extension of the model and inclusion of competitive inhibition term for the metabolite. In addition, this analysis indicated that verapamil itself causes minimal MBI, and the formation of inhibitory metabolites was responsible for the irreversible loss of CYP3A4 activity. The kinact and KI estimates determined in the current study were compared with literature data generated using the conventional two-step method. In the current study, the inactivation efficiency (kinact/KI) for clarithromycin, ritonavir, and erythromycin were up to 7-fold higher, whereas kinact/KI for mibefradil, N-desmethyldiltiazem, and diltiazem were, on average, 2- to 4.8-fold lower than previously reported estimates. Use of human liver microsomes instead of recombinant CYP3A4 resulted in 5-fold lower kinact/KI for erythromycin. In conclusion, the progress curve method has shown a greater mechanistic insight when determining kinetic parameters for MBI in addition to providing a more comprehensive experimental protocol.

Introduction

The time-dependent loss of drug-metabolizing enzyme activity is often attributed to two mechanisms, mechanism-based inhibition (MBI) by the parent molecule and the formation of inhibitory metabolites. MBI is characterized by a partial metabolism of an inhibitor to a form that inactivates the catalyzing enzyme without leaving the active site, causing irreversible or quasi-irreversible inhibition (Silverman, 1995). MBI of cytochrome P450 (P450) enzymes often results in clinically significant drug-drug interactions (DDIs), which has lead the pharmaceutical industry to devote significant resources to the identification and characterization of new chemical entities showing this property (Kalgutkar et al., 2007; Grimm et al., 2009). Often, the goal of in vitro characterization is to determine an inactivation rate constant (kinact) and irreversible inhibition constant (KI) that can be applied to the prediction of the magnitude of an in vivo DDI (Mayhew et al., 2000; Wang et al., 2004; Galetin et al., 2006, 2010; Obach et al., 2007; Rowland Yeo et al., 2011; Kenny et al., 2012).

The kinetic parameters kinact and KI are often determined using a traditional two-step assay whereby enzyme, cofactors, and several concentrations of inhibitor are preincubated before aliquots are removed at multiple time points and placed into a final incubation containing a probe substrate for the assessment of remaining enzyme activity (Silverman, 1995). There are two main assumptions of this assay: 1) that there is negligible metabolism of an inhibitor in the preincubation stage and 2) that negligible inactivation occurs in the final incubation stage. The effect of the latter can be reduced, but not removed, by including a significant (usually 1:10 or 1:20) dilution step between incubations and applying the probe substrate at a saturating concentration (Obach et al., 2007; Grimm et al., 2009). As shown by the reaction scheme for MBI (Fig. 1), a mechanism-based inhibitor is characterized as both a substrate and an inactivator of the enzyme it inhibits; hence, depletion of inhibitor during the preincubation may be significant. These assumptions can culminate in a significant bias in the parameter estimates from this assay (Yang et al., 2005). In addition, these assumptions are also likely to be linked to the sensitivity of this assay to experimental design, resulting in a significant interlaboratory variability in MBI parameter estimates across literature (Ghanbari et al., 2006).

Fig. 1.
Fig. 1.

Reaction scheme for the progress curve assay. The complete scheme represents MBI with product inhibition incorporated, whereas the scheme to the left of the dashed line represents the conventional MBI model. E, free active enzyme; I, mechanism-based inhibitor; EI, initial enzyme-inhibitor complex; EI′, activated enzyme-inhibitor complex; EIinact, inactivated enzyme; P, inhibitor metabolite; EP, enzyme-inhibitor product complex; S, probe substrate; ES, enzyme-substrate complex; M, substrate metabolite.

A progress curve analysis can be applied after an incubation in which concentration of all components (inhibitor, substrate, and corresponding metabolites) are monitored from time zero by LC-MS/MS, in conjunction with enzyme activity. This approach does not necessitate the experimental separation of inhibition step from the assessment of remaining enzyme activity, thus overcoming the associated assumption in the conventional two-step assay. Therefore, this method has the potential to provide more mechanistic insight into the mechanism-based inhibitor being characterized. The dilution step is not required, and a lower initial enzyme concentration can be used compared with most of the two-step dilution studies reported in the literature so far, reducing the impact of nonspecific drug binding. Although progress curve methods for the assessment of MBI have been described previously (Waley, 1980; Garcia-Canovas et al., 1989; Wimalasena and Haines, 1996), it is only recently that this method has been considered for characterization of MBI with respect to drug-metabolizing enzymes (Fairman et al., 2007; Salminen et al., 2011a,b). However, these initial studies using progress curve methods have applied data analysis designed more for the characterization of a slow, tight-binding inhibition rather than MBI. In addition, the concentration of inhibitor in these studies was either assumed to be static or time averaged over the incubation, thereby failing to fully overcome the remaining assumption of the two-step assay.

The current study describes a novel modeling approach for the analysis of the data generated by progress curve experiments. The mechanistic model developed allows simultaneous fitting of the data describing changes in inhibitor and probe substrate metabolite concentration with respect to time, accounting for all the processes occurring in the incubation system. This method has been applied to the characterization of time-dependent inhibition of CYP3A4 by seven inhibitors, namely clarithromycin, erythromycin, diltiazem, N-desmethyldiltiazem, verapamil, mibefradil, and ritonavir. In addition, parameter estimates obtained by progress curve were compared with those reported in the literature by the conventional two-step method.

Materials and Methods

Chemicals.

Diltiazem, mibefradil, verapamil, quinidine, ketoconazole, dextromethorphan, dl-isocitric acid, β-NADP, and isocitric dehydrogenase were purchased from Sigma-Aldrich (Poole, Dorset, UK). Clarithromycin was purchased from Synfine Research (Richmond Hill, ON, Canada). Ritonavir was purchased from Sequoia Research Products (Pangbourne, Berkshire, UK). Erythromycin was purchased from Acros Organics (Fisher Scientific UK, Loughborough, Leicestershire, UK). N-Desmethyldiltiazem was purchased from Toronto Research Chemicals Inc. (North York, ON, Canada). 3-Hydroxyquinidine was purchased from Ultrafine Ltd. (Manchester, UK). Methanol and magnesium chloride were obtained from BDH Laboratory Supplies (VWR International, Lutterworth, Leicestershire, UK). All other reagents were of analytical grade. Recombinant human CYP3A4 expressed with cytochrome P450 oxidoreductase in baculovirus-infected insect cells (Supersomes) were purchased from BD Gentest (Woburn, MA). Pooled human liver microsomes (HLMs) (mixed gender, 50 donors; BD Gentest) characterized for CYP3A4 content were kindly donated by Pfizer Ltd. (Sandwich, UK).

Progress Curve Assay in Recombinant CYP3A4.

Progress curves were obtained for the CYP3A4 inhibitors clarithromycin, erythromycin, diltiazem, N-desmethyldiltiazem, verapamil, mibefradil, and ritonavir. In addition, ketoconazole was included as an example of a CYP3A4 inhibitor where inhibition does not occur in a time-dependent manner. Quinidine 3-hydroxylation was used as the probe reaction for CYP3A4 activity. Profiles of metabolite formation kinetics were obtained in both recombinant CYP3A4 and HLMs under linear conditions; the resulting Km and kcat parameters are shown in Supplemental Fig. S1. Quinidine was selected because other commonly used CYP3A4 probes (midazolam, felodipine, and alprazolam) failed to display linear formation of metabolites over the time course of the progress curve incubation (40 min) and exhibited substrate inhibition (e.g., nifedipine) or sigmoidal kinetics (e.g., testosterone) (Galetin et al., 2003). Therefore, quinidine, as a low-clearance compound following standard Michaelis-Menten kinetics, seemed more suitable. The contribution of quinidine N-oxidation was considered negligible because quinidine clearance via 3-hydroxylation has been reported to be 15-fold greater than N-oxidation in vivo (Nielsen et al., 1995). All assays were performed in duplicate, and concentrations of organic solvent did not exceed 1% v/v in the incubations.

Progress curve incubations had a total volume of 1.5 ml and consisted of (final concentrations in parentheses) inhibitor (seven concentrations), CYP3A4 probe quinidine (50 μM), recombinant CYP3A4 (20 pmol/ml for mibefradil and ritonavir, 50 pmol/ml for all other inhibitors), and an NADPH-regenerating system containing NADP+ (1 mM), isocitric acid (7.5 mM), magnesium chloride (10 mM), and isocitric dehydrogenase (1 unit/ml), made up in 0.1 M phosphate buffer, pH 7.4. Recombinant CYP3A4 concentrations of 20 and 50 pmol/ml corresponded to protein concentrations of approximately 0.03 and 0.073 mg/ml according to the supplier's characterization. An inhibitor-free control incubation was also included to confirm linearity of quinidine 3-hydroxylation. Inhibitor concentration ranges were as follows: clarithromycin, 1 to 500 μM; erythromycin, 0.5 to 200 μM; diltiazem, 0.5 to 100 μM; N-desmethyldiltiazem, 1 to 200 μM; verapamil, 0.3 to 300 μM; mibefradil, 0.01 to 5 μM; ritonavir, 0.01 to 5 μM; and ketoconazole, 0.01 to 2 μM.

Preliminary mixtures contained all constituents minus recombinant CYP3A4 in a 96-well plate, prewarmed to 37°C in a shaking plate incubator. The progress curves were then initiated by the addition of recombinant CYP3A4 at time zero. A time zero sample was immediately taken by removing a 100 μl aliquot of each incubation mixture into 100 μl of dextromethorphan internal standard solution in ice-cold methanol. Subsequent samples were taken in the same manner at 12 time points up to 40 min. Once all time points were taken, samples were centrifuged at 1000g for 10 min. The supernatant of each well was removed and analyzed for 3-hydroxyquinidine and the corresponding inhibitor by LC-MS/MS.

Erythromycin Progress Curve Assay in HLMs.

For erythromycin, progress curves were also obtained using pooled HLMs. The CYP3A4 content of the 50 donor pool used in the current study had been previously determined by the supplier as 138 pmol CYP3A4/mg protein, which is consistent with the population average of 111 pmol CYP3A4/mg protein (Rostami-Hodjegan and Tucker, 2007). Progress curves were obtained using the same method as above, maintaining a final CYP3A4 concentration of 50 pmol/ml (0.36 mg protein/ml).

LC-MS/MS Analysis.

The supernatant of samples from incubations with an initial inhibitor concentration <5 μM could be analyzed directly by LC-MS/MS, whereas in the cases when initial inhibitor concentration was >5 μM, aliquots were diluted into an equivalent matrix to prevent saturation of the detector.

Compound separation was achieved using a Luna C18 3 μm 50 × 4.6 mm column (Phenomenex, Torrance, CA) maintained at 40°C in an Alliance 2795 HT LC system (Waters, Milford, MA). An initial mobile-phase composition of 90:10 water/methanol (v/v) and 1 mM ammonium acetate was maintained for 1 min before a gradient was run to 65% of 90:10:0.05 methanol/water/formic acid (v/v) and 35% of 90:10 methanol/water (v/v) and 1 mM ammonium acetate at 4 min, after which starting conditions were returned to at 5 min. For the analysis of ritonavir, an alternative high-performance liquid chromatography gradient was used to aid compound separation. In this case, an initial mobile-phase composition of 50% 90:10 water/methanol (v/v) and 1 mM ammonium acetate and 50% 90:10:0.05 water/methanol/formic acid (v/v) was maintained for 1 min before a gradient was run to 100% of 90:10:0.05 methanol/water/formic acid (v/v) at 3 min. These conditions were maintained for 1 min, after which starting conditions were returned to at 5 min. A flow rate of 1 ml/min was maintained, of which 0.25 ml/min was sent to a Micromass Quattro Ultima triple quadrupole mass spectrometer (Waters) with an atmospheric pressure electrospray ion source. MS/MS analysis used a desolvation gas (nitrogen) flow rate of 600 l/h, a cone gas (nitrogen) flow rate of 150 l/h, a collision gas (argon) pressure of 2 × 10−3 mbar, and a source temperature of 125°C. Using the positive ion mode, protonated ions were formed using a capillary voltage of 3.5 kV and cone energies shown in Table 1. Product ions formed in argon with collision energy and mass transition values shown in Table 1 were quantified using Micromass QuanLynx 4.1 software.

View this table:
TABLE 1

LC-MS/MS conditions for the selected compounds and metabolites with details on the mass transitions

Data Analysis.

Progress curves were analyzed by simultaneous nonlinear least-squares regression of probe metabolite (3-hydroxyquinidine) and inhibitor concentration data using MATLAB (version 7.8; MathWorks, Inc., Natick, MA). In addition, all experiments for each inhibitor (i.e., multiple starting concentrations of inhibitor) were analyzed simultaneously. The total number of data points simultaneously fitted ranged between 275 and 336, depending on the inhibitor. Before this analysis, the fraction of substrate and inhibitor unbound in the incubation (fuinc) was estimated using algorithms based on compound lipophilicity and protein concentration (Hallifax and Houston, 2006). For the two inhibitors with greatest nonspecific binding potential (mibefradil and ritonavir), equilibrium dialysis experiments have previously been performed at three different protein concentrations (Gertz et al., 2008). These data were then extrapolated to the protein concentrations used in the current study using eq. 1. Embedded Image where Ka is the microsomal binding affinity (obtained by nonlinear regression) and C is the microsomal protein concentration. If the estimated fuinc was <90%, data were corrected to represent unbound concentration. This was found to only be the case for mibefradil progress curves (fuinc = 0.63) and erythromycin progress curves in HLMs (fuinc = 0.83).

Differential eqs. 2 to 4 describe the changes in active enzyme, inhibitor, substrate, and substrate metabolite over time, respectively. This mechanistic MBI model was adapted from Yang et al. (2007) and implemented in MATLAB (MathWorks, Inc.); the model is based on the conventional reaction scheme for MBI illustrated in Fig. 1. Embedded Image Embedded Image Embedded Image where [E]t, [I]t, [M]t, and [S]t are the concentrations of active enzyme, inhibitor, substrate metabolite, and substrate, respectively, at time t; kinact, KI, and Ki are the maximum inactivation rate constant, irreversible inhibition constant, and reversible inhibition constant, respectively; kcat,I is the turnover number for the inhibitor; and kcat,S and Km,S are the turnover number and Michaelis-Menten constant for the substrate, respectively.

In cases where the initial fitting using eqs. 2 to 4 produced a poor result (assessed by diagnostic plots and objective function value), the model was extended to incorporate product inhibition from the inhibitor metabolite (see Fig. 1). In this case, eqs. 5 to 8 were applied, and the model is referred to as an extended mechanistic MBI model. Embedded Image Embedded Image Embedded Image Embedded Image where [P]t is the concentration of the inhibitor metabolite at time t and KiP is the inhibition constant for the inhibitor metabolite. Other parameters are as defined previously (eqs. 2–4).

Progress curves for ketoconazole were fitted using a simplified model assuming competitive inhibition and static concentration of enzyme, as shown in eqs. 9 and 10.

Embedded Image Embedded Image

Values for quinidine Km (23.7 and 121 μM in recombinant CYP3A4 and HLMs, respectively) and kcat (2.26 and 5.61 min−1 in recombinant CYP3A4 and HLMs, respectively) determined in a separate experiment (Supplemental Fig. 1) were used as input parameters and were not estimated by the fitting procedure. The differential equations for each inhibition component were solved using the standard numerical ordinary differential equation solver function ODE45 in MATLAB (MathWorks, Inc.). The MATLAB lsqnonlin function was used for optimization of parameters by minimizing a weighted objective function based on the sum of squared errors (eq. 11). Embedded Image where [M]obs and [I]obs represent observed concentrations of substrate metabolite and inhibitor, respectively, and [M]pred and [I]pred are the corresponding predicted concentrations of substrate metabolite and inhibitor, respectively. Goodness of fit and performance of different models was assessed by diagnostic plots (predicted vs. observed concentration of inhibitor or metabolite) and Akaike information criterion. Standard errors calculated by the method of Landaw and DiStefano (1984) were used to assess the quality of the parameter estimates.

Determination of Inhibitor Intrinsic Clearance.

Inhibitor intrinsic clearance was determined independently of the inhibition parameter estimation using the method described previously (Gertz et al., 2011). A first-order decay equation was fitted to the depletion profile at each inhibitor concentration to determine the initial depletion rate constant k (GraFit 6.0.12; Erithacus Software, Horley, Surrey, UK). In the case of biphasic depletion, only the initial log-linear phase was considered. Unbound intrinsic clearance (CLint,u) at each concentration was determined using eq. 12 and was normalized for enzyme concentration to obtain units of μl · min−1 · pmol P450−1. Embedded Image where V is the incubation volume. Finally, to facilitate comparison between inhibitors, unbound intrinsic clearance at an infinitesimal concentration (CLint,u(C = 0)) was determined by plotting CLint,u against a range of inhibitor concentrations and fitting using eq. 13 (Gertz et al., 2011). Embedded Image where C is the concentration of inhibitor.

Comparison of Parameters from Progress Curve and Two-Step Methods.

The kinact and KI estimates obtained using the progress curve method in the current study were compared with those obtained by the traditional two-step method. A database of kinact and KI estimates for time-dependent inhibitors of CYP3A4 characterized by the two-step method was collated from literature. Further details of this database are provided in Supplemental Table S1. This comparison was made using parameter estimates from the same in vitro system (i.e., recombinant human CYP3A4). For KI estimates, a correction for the fraction of inhibitor unbound in the incubation was made using algorithms based on compound lipophilicity and protein concentration reported in the study (Hallifax and Houston, 2006). Geometric mean fold difference was used as a measure of the bias in parameter estimates between methods and was obtained using eq. 14.

Embedded Image

In addition to the comparison of methods with a recombinant CYP3A4 in vitro system, progress curve data for erythromycin in HLMs from the current study were compared with kinact and KI from literature studies using the two-step method in HLMs.

Determination of Mibefradil kinact and KI Using the Two-Step Method.

In the absence of literature kinact and KI values for mibefradil in a recombinant enzyme system using the two-step method, these parameters were generated in house using several probe substrates. Preincubations contained 120 μl of recombinant CYP3A4 (final concentration, 600 pmol CYP3A4/ml or 0.66 mg protein/ml) and 200 μl of an NADPH-regenerating system in 0.1 M phosphate buffer, pH 7.4, consisting of (final concentration in preincubation) NADP+ (1 mM), isocitric acid (7.5 mM), magnesium chloride (10 mM), and isocitric dehydrogenase (0.8 units/ml). These were made up to 390 μl with phosphate buffer and placed in a shaking waterbath at 37°C for 5 min before preincubation was initiated by the addition of a 10 μl mibefradil solution, achieving final concentrations of 0.5, 0.75, 1, 2, 3, and 5 μM and an inhibitor-free control.

At time points of 0, 0.5, 1, 2, 5, and 10 min, a 25-μl aliquot of the preincubation was removed and placed into a final incubation (1:20 dilution). Prewarmed final incubation tubes contained 250 μl of NADPH-regenerating system and 10 μl of midazolam, testosterone, or quinidine at final concentrations of 100, 250, and 500 μM, respectively, made up to 475 μl with phosphate buffer. Final incubations were terminated after 2.5, 3.5, and 5.5 min for midazolam, testosterone, and quinidine as probe substrates, respectively, by the addition of 500 μl of diazepam internal standard (2 μM) in ice-cold acetonitrile. The assay was performed in duplicate. Concentrations of organic solvent (methanol or acetonitrile) in which inhibitor was dissolved did not exceed 1% v/v in the incubations. Probe metabolism linearity had been confirmed by previous linearity studies.

After termination of all final incubations, the tubes were thoroughly vortex mixed and centrifuged at 12,100g for 10 min. The supernatant of each microtube was removed and analyzed for 1′-hydroxy and 4-hydroxymidazolam, 6β-hydroxy testosterone, or 3-hydroxyquinidine. The metabolite formation rate at each preincubation time point was expressed as the natural logarithm of the percentage of inhibitor-free control. A profile at each inhibitor concentration was constructed, from which the slope of the initial linear inhibition portion (first 2 min) was determined by linear regression, representing the rate of inactivation (kobs) kinact and KI were determined by fitting eq. 15 to data using nonlinear regression analysis (GraFit 6.0.12; Erithacus Software). KI estimates were corrected for fuinc, which was obtained using the same experimental data used to correct mibefradil progress curve assays.

Embedded Image

Results

Progress Curve Method in Recombinant CYP3A4.

Progress curves were successfully generated for seven time-dependent inhibitors of CYP3A4 using quinidine 3-hydroxylation as the CYP3A4 probe reaction. Final parameter estimates from the fitting procedure are shown in Table 2. Progress curves for clarithromycin, erythromycin, diltiazem, and N-desmethyldiltiazem were described well using the mechanistic MBI model (eqs. 2–4). An example of the progress curves obtained for erythromycin and 3-hydroxyquinidine, together with corresponding diagnostic plots of observed vs. predicted concentrations of substrate metabolite and inhibitor, is illustrated in Fig. 2. Progress curves and diagnostic plots for other inhibitors are shown in Supplemental Figs. S2 and S3, respectively.

View this table:
TABLE 2

Progress curve parameter estimates obtained in recombinant CYP3A4 with quinidine as the probe substrate for seven time-dependent inhibitors using a mechanistic MBI model

The percentage of CV is shown in parentheses.

Fig. 2.
Fig. 2.

Progress curve data for 3-hydroxyquinidine (A) and erythromycin (B). Dashed lines were obtained by simultaneous fitting of the mechanistic MBI model to the data. C and D represent comparison of predicted vs. observed probe metabolite (3-hydroxyquinidine) and inhibitor concentrations.

Progress curves for mibefradil, ritonavir, and verapamil were poorly described using the standard mechanistic MBI model. The fitting for these compounds exhibited an underestimation of inhibitor clearance and overestimation of the rate of inactivation at mid-range concentrations. For these inhibitors, incorporation of a reversible interaction between active enzyme and the product of inhibitor metabolism (as opposed to inhibitor inactivation) resulted in significant improvements to the fitting and reduction in the Akaike information criterion value. This extended mechanistic MBI model is represented by eqs. 5 to 8 and is shown schematically in Fig. 1. An example of simultaneous fitting of progress curve profiles with the mechanistic and extended mechanistic MBI model (incorporating also product inhibition) is shown in Fig. 3 for mibefradil. Progress curves obtained for this inhibitor over a range of concentrations using the extended mechanistic MBI model and corresponding diagnostic plots are shown in Fig. 4.

Fig. 3.
Fig. 3.

Example of the effect of product inhibition on progress curve fitting for mibefradil. ▵, probe metabolite; ○, inhibitor unbound concentrations (n = 2). The solid and dashed lines represent the results of simultaneous fitting with and without a product inhibition component included in the mechanistic MBI model, respectively.

Fig. 4.
Fig. 4.

Progress curve data for 3-hydroxyquinidine (A) and mibefradil (B). Dashed lines were obtained by simultaneous fitting of the extended mechanistic MBI model to the data. C and D represent comparison of predicted versus observed probe metabolite (3-hydroxyquinidine) and inhibitor concentrations.

In the case of verapamil, the extended mechanistic MBI model produced a good fit to progress curve data; however, a very low kinact estimate (<0.001 min−1) was obtained, suggesting the absence of MBI. The model was reduced to a product inhibition only model, resulting in a fit of comparable quality (<20% difference in minimum objective function value); the parameter estimates are shown in Table 2. These findings indicate that in the case of verapamil, rapid turnover to a potent inhibitory metabolite is largely responsible for the time-dependent aspect of CYP3A4 inhibition seen for verapamil, rather than MBI from the parent compound.

Final kinact estimates ranged from 0.028 to 0.55 min−1 for diltiazem and ritonavir, respectively, whereas KI,unbound estimates ranged 31-fold with ritonavir and erythromycin being at the lower and higher end of the range (Table 2). The rank order for inactivation efficiency (kinact/KI) for the inhibitors in this study was ritonavir > mibefradil > N-desmethlydiltiazem > erythromycin > clarithromycin > diltiazem > verapamil (no MBI from parent). For the reversible inhibitor ketoconazole, a competitive inhibition model incorporating the depletion of inhibitor described the progress curves well, with a resulting Ki of 0.007 μM, which is at the lower end of the reported ketoconazole Ki values in the recombinant system and generally lower than estimates from HLMs (Greenblatt et al., 2010).

Determination of Inhibitor Intrinsic Clearance.

To investigate a link between inhibitor clearance and product inhibition, unbound intrinsic clearance estimates were determined independently of inhibition parameter estimation for all seven inhibitors. Ritonavir and mibefradil showed substantial depletion through the course of the experiment, and the unbound intrinsic clearances for these inhibitors were 96- and 49-fold higher than for verapamil, respectively (Fig. 5). Although lower than ritonavir and mibefradil, verapamil intrinsic clearance was still approximately 3-fold greater compared with the remaining inhibitors in the dataset (0.18–0.52 μl · min−1 · pmol P450−1 for clarithromycin and diltiazem, respectively). This clear distinction between inhibitors in the extent of their metabolism indicated a link between inhibitor clearance and the requirement for product inhibition to be incorporated into the mechanistic model for the analysis of progress curve data. As expected, the more rapid metabolism associated with mibefradil, ritonavir, and verapamil was also reflected in the estimations of the kcat and Ki parameters for these compounds (Table 2).

Fig. 5.
Fig. 5.

Unbound intrinsic clearance determined by mechanistic model independently of inhibition parameter estimation for ritonavir (RIT), mibefradil (MIB), verapamil (VER), diltiazem (DIL), erythromycin (ERY), N-desmethyldiltiazem (N-desDIL), and clarithromycin (CLA).

Mibefradil Two-Step Assay in Recombinant CYP3A4.

Parameter estimates obtained for mibefradil using the two-step assay with recombinant CYP3A4 are shown in Table 3. A 2.5-fold difference was observed in the kinact value depending on the probe used, with quinidine resulting in highest estimates; variation in unbound KI values was less than 2-fold between the probes used.

View this table:
TABLE 3

Parameter estimates for mibefradil obtained using the two-step approach with recombinant CYP3A using different probe substrates

The percentage of CV is shown in parentheses.

Comparison of Parameters from Progress Curve and Two-Step Methods.

Estimates of kinact and KI obtained using the progress curve method were compared with those collated from literature in which the two-step method was used. To minimize any potential intersystem bias, only two-step data obtained using recombinant CYP3A4 were included in this analysis. For the seven inhibitors in this study, 24 sets of two-step method parameters were collated from nine studies (Supplemental Table S1).

Figure 6 shows a comparison of parameter estimates from both methods, in which multiple data points for each inhibitor represent multiple literature two-step assay data available for comparison. Estimates of kinact obtained from the progress curve method were within an order of magnitude of estimates obtained using the two-step method for all inhibitors (Fig. 6A). Across inhibitors, a 2.2-fold higher value was observed for the two-step method estimates compared with the progress curve. In particular, kinact for mibefradil and N-desmethyldiltiazem were, on average, 4- and 7-fold higher using the two-step method, respectively. However, a large range in the two-step method estimates was apparent for some inhibitors for which multiple data were available for comparison. For example, clarithromycin (n = 2), erythromycin (n = 10), and diltiazem (n = 3) showed 6-, 8-, and 9-fold ranges in the two-step method kinact estimates, respectively. The choice of probe substrate may, to some extent, be a contributing factor to this variability, as in the above example, either testosterone (n = 9), midazolam (n = 4), or triazolam (n = 2) were used.

Fig. 6.
Fig. 6.

Comparison of kinact (A) and KI, unbound (B) estimates obtained using the progress curve method in the current study and those obtained using the two-step method from literature for ritonavir (RIT), mibefradil (MIB), verapamil (VER), diltiazem (DIL), erythromycin (ERY), N-desmethyldiltiazem (N-desDIL), and clarithromycin (CLA). All data were obtained using recombinant CYP3A4 and corrected for fuinc. Verapamil is absent from this plot because kinact and KI were not apparent using the progress curve method.

A comparison of KI, unbound between methods is shown in Fig. 6B. For all inhibitors (with the exception of erythromycin), KI estimates from both methods were within an order of magnitude of one another and were, on average, 3.3-fold lower using the progress curve method. As with kinact, a large (21-fold) range was apparent for estimates of erythromycin KI reported in the literature using the conventional two-step method; however, the overall trend was for a 9-fold higher value using the two-step method for this inhibitor. No strong trend in values for inactivation efficiency (kinact/KI) between methods was apparent. The greatest overall difference was seen for erythromycin with a 7-fold higher kinact/KI using the progress curve method, whereas for mibefradil, diltiazem, and N-desmethyldiltiazem, kinact/KI were 1.9-, 2.6-, and 4.8-fold lower using the progress curve method, respectively.

Erythromycin Progress Curve Assay in HLMs.

In addition to the recombinant system, erythromycin progress curve data were also generated in HLMs. A good fit was obtained for the erythromycin progress curves using HLMs and the mechanistic MBI model (eqs. 2–4); resulting parameter estimates are shown in Table 2. Estimates of kinact and KI in HLMs were 1.8-fold lower and 2.8-fold higher, respectively, than estimates generated using recombinant CYP3A4, leading to a 5-fold lower value of inactivation efficiency in HLMs.

The differences in erythromycin kinact and KI estimates in recombinant CYP3A4 and HLMs using the progress curve method were compared with intersystem differences reported in literature for the parameters obtained by the conventional two-step method. A database of studies in which time-dependent inhibitors of CYP3A4 have been characterized in both recombinant CYP3A4 and HLMs using the two-step method has been described previously (Houston and Galetin, 2010). This database contained six published studies with 19 sets of parameters for 16 inhibitors. Within this database, a 1.7-fold lower and 2.5-fold higher value for kinact and KI, respectively, was evident for parameters estimated in HLMs compared with recombinant CYP3A4. Accounting for the same degree of intersystem bias in progress curve erythromycin parameters generated in recombinant CYP3A4 resulted in the kinact and KI values comparable to the parameters obtained experimentally in HLMs.

Erythromycin progress curve parameters obtained with HLMs were also compared with 12 sets of parameters determined using the two-step method with HLMs from literature sources (Kanamitsu et al., 2000; Yamano et al., 2001; Dai et al., 2003; Ito et al., 2003; McConn et al., 2004; Zhao et al., 2005; Polasek and Miners, 2006; Obach et al., 2007; Rowland Yeo et al., 2011). Whereas kinact estimates were highly variable across literature studies, the central tendency did not indicate a difference between methods for this parameter (Fig. 7). However, KI estimates determined using the progress curve method seemed lower than those determined using the two-step method by a factor of approximately 10-fold, resulting in kinact/KI values using the progress curve method being higher to a similar degree (Fig. 7).

Fig. 7.
Fig. 7.

Box plot comparison of erythromycin parameter estimates obtained using the progress curve method with HLMs in the current study with those available in literature using the two-step method in this in vitro system (n = 12).

Discussion

In the current study, irreversible inhibition of CYP3A4 was characterized for seven compounds using a novel progress curve method. A comprehensive mechanistic model was developed allowing simultaneous assessment of both reversible and time-dependent inhibitory effects, in addition to considering metabolism of the inhibitor and the probe substrate (Figs. 2⇑–4). This dynamic model represented substantial improvement over the conventional two-step method and highlighted the potential for providing greater insight into the mechanisms by which such inhibitors operate. Progress curve data for both the probe metabolite and inhibitor were described well by a standard mechanistic MBI model in the case of clarithromycin, erythromycin, diltiazem, and N-desmethyldiltiazem. In contrast, mibefradil, ritonavir, and verapamil required modification of the model to account for the competitive inhibition term for inhibitor metabolite.

The inhibition parameters determined in the current study were compared with 24 sets of estimates obtained mainly from literature using the two-step method and a recombinant CYP3A4 system. These comparisons were hampered by the large interlaboratory variation (up to 9- and 21-fold for kinact and KI, respectively) observed in the two-step method parameters. With the exception of verapamil, the overall trend was toward a lower kinact and KI using the progress curve method, leading to an increase in inactivation efficiency (kinact/KI) of <2-fold. Trends were inhibitor specific, as the erythromycin kinact/KI was, on average, 7-fold higher with the progress method but 1.9- and 4.8-fold lower with mibefradil and diltiazem, respectively.

In the case of verapamil, the use of the extended mechanistic MBI model resulted in a very low kinact estimate (<0.001min−1), suggesting that the irreversible inhibition effect of verapamil is caused via formation of inhibitory metabolites. Verapamil and its two N-dealkylated metabolites, norverapamil and N-dealkylverapamil, have been reported to form metabolite intermediate complexes (MICs) when incubated with CYP3A4 (Ma et al., 2000; Wang et al., 2004). The results of the current study suggest that whereas MIC formation has been identified during incubations, the irreversible inhibition effect occurs almost entirely via verapamil metabolites and not the parent compound.

Recently, NADPH-dependent heme destruction was identified as the primary mechanism of CYP3A4 MBI by mibefradil, rather than MIC or covalent adduct formation (Foti et al., 2011). Mibefradil is metabolized via two main pathways in man: CYP3A4-mediated oxidation and hydrolysis of its ester side chain. The desmethoxy metabolite of mibefradil has been shown to inhibit CYP3A4, although to a lesser degree than mibefradil (Bui et al., 2008; Foti et al., 2011). Findings in the current study suggest that the products of CYP3A4-mediated oxidation of mibefradil also play a contributory role to its time-dependent inhibition of CYP3A4.

Ritonavir is known to undergo CYP3A4-mediated metabolism (Kumar et al., 1996), but the inhibitory potential of the resulting metabolites is not well characterized. Although most studies consider ritonavir to inhibit CYP3A4 purely via MBI (Kempf et al., 1997; Ma et al., 2000; Lim et al., 2005; Kalgutkar et al., 2007), a rapid tight binding of ritonavir to CYP3A4 heme in the absence of NADPH has been identified, in addition to MBI (Sevrioukova and Poulos, 2010). In the current study, although the fitting to ritonavir progress curve data was significantly improved when the mechanistic MBI model was extended to include product inhibition, the residual error for probe metabolite data was higher than for the other inhibitors investigated, especially at higher ritonavir concentrations (Supplemental Figs. S2 and S3). Therefore, further refinement of the inhibition model may be necessary for this compound, especially given the known complexity of interactions associated with ritonavir. It is acknowledged that in an intact hepatocyte system, ritonavir causes a complex combination of induction and inhibition effects on CYP3A4 and P-glycoprotein, all of which may contribute to in vivo DDI (Kirby et al., 2012).

MIC-forming secondary and tertiary amines often undergo sequential metabolism to species that also form MIC with the same enzyme (e.g., clarithromycin, erythromycin, diltiazem, and N-desmethyldiltiazem) (Ohmori et al., 1993; Mayhew et al., 2000; Zhao et al., 2007; Zhang et al., 2009; Hanson et al., 2010). However, despite this, only in the cases of mibefradil, ritonavir, and verapamil was incorporation of the metabolite effects required in the data analysis, most likely because of a balance of faster metabolism of these compounds and the apparent potency of their metabolites (Fig. 4). For the lower clearance compounds, although the inhibitory metabolites may have been formed, their concentrations are unlikely to have been high enough to exert a significant effect on CYP3A4 activity in the current setting. In addition, parameter estimation for mibefradil, ritonavir, and verapamil suggests that the product of inhibitor metabolism is, in fact, a more potent inhibitor of CYP3A4 than the parent drug, with the inhibition constant for the metabolite (KiP) being 9- to 19-fold lower than the time-dependent inhibition constant (KI). Further explanation of the mechanism of inhibition by the products of inhibitor metabolism was not possible because of the lack of authentic standards for the respective metabolites. However, it would be feasible to include such data in parameter estimation in the future, allowing further refinement of the model.

Although advances in LC-MS/MS have allowed use of lower protein concentration in the predilution step (Nishiya et al., 2009; Rowland Yeo et al., 2011), most of the two-step studies reported in the literature have used a high enzyme concentration in the preincubation to facilitate a significant dilution into the final incubation. Under these conditions, the assumption of E≪I can be compromised, and rapid metabolite production, which is not accounted for in the data analysis process, may lead to significant bias in parameter estimates. The identification of inhibition arising from a metabolite is often achieved by performing a two-step assay at several enzyme concentrations, with a correlation between the degree of time-dependent inhibition and protein concentration indicating an effect from the formed metabolite. This method was previously performed to assess the impact of sequential metabolism on diltiazem CYP3A4 inhibition (Zhao et al., 2007) and can be followed by a separate two-step assay for such metabolites to assess the relative metabolite/parent inhibition potency (Zhang et al., 2009; Hanson et al., 2010).

The advantage of the progress curve method described in the current study is that it equates to a stoichiometric representation of the entire in vitro system under investigation. This should allow for a more accurate determination of kinetic parameters specific to the parent compound while providing further insight into the mechanism of inhibition. In addition, because aspects such as enzyme concentration and substrate kinetics (Km and Vmax) are input parameters for the data analysis, interlaboratory variability in parameter estimates may be reduced. Further investigation is required to determine the ability of this method to quantitatively characterize the inhibition by metabolites. The lower enzyme concentration used in the progress curve method may limit the identification of metabolite effects for inhibitors with a moderate or low degree of metabolism, as exemplified by the lack of effect from the inhibitory metabolites of clarithromycin, erythromycin, diltiazem, and N-desmethyldiltiazem in the current study. Given the choice of models available to mechanistically describe the inhibition processes, the data analysis step described in the current study is more subjective than the two-step method. Our recommendation would be to perform the initial analysis with the standard mechanistic MBI model, which can be subsequently extended (as in the case of product inhibition) or reduced (as in cases when a parameter has minimal impact) as appropriate.

The progress curves in the current study were initially obtained using recombinant CYP3A4 to simplify the modeling to a single enzyme system. Erythromycin was investigated further by applying the progress curve method in HLMs, because its metabolism can be attributed exclusively to CYP3A4 (Watkins et al., 1989; Rivory et al., 2001); therefore, no alteration to the mechanistic MBI model was required. The progress curves generated for erythromycin using HLMs resulted in estimates of inactivation efficiency (kinact/KI) 5-fold lower than those generated using recombinant CYP3A4, which is in agreement with general intersystem differences seen for parameters obtained by the conventional two-step method assay (Houston and Galetin, 2010). When compared with literature studies with erythromycin using the two-step method, progress curve data in both recombinant CYP3A4 (Fig. 5) and HLMs (Fig. 7) found comparable kinact values but a trend toward a 10-fold lower KI estimate using the progress curve method. Therefore, it is clear that the progress curve method indicates greater inhibition potency for erythromycin; however, overall results using a recombinant CYP3A4 system do not support this trend.

In conclusion, this study has described a novel progress curve technique and corresponding mechanistic model for the characterization of time-dependent inhibition of CYP3A4. This method has shown potential in providing a greater insight into the mechanism of irreversible inhibition, especially for moderate to high-turnover inhibitors with inhibitory metabolites. The proposed mechanistic MBI model allowed simultaneous assessment of P450 inhibition and metabolism of both the inhibitor and probe substrate, generating a number of important input in vitro data for the prediction of these types of drug-drug interactions using physiologically based modeling approaches.

Authorship Contributions

Participated in research design: Burt, Collins, Houston, Hyland, and Galetin.

Conducted experiments: Burt and Säll.

Performed data analysis: Burt and Pertinez.

Wrote or contributed to the writing of the manuscript: Burt, Houston, and Galetin.

Acknowledgments

We thank Sue Murby for assistance with the LC-MS/MS analysis and Drs. Maurice Dickins and David Fairman (Pfizer, Sandwich, UK) for contribution to discussions about this project.

Footnotes

  • This work was supported by Pfizer Pharmacokinetics, Dynamics, and Metabolism at Department (Sandwich, UK) within the Centre for Applied Pharmacokinetic Research at the University of Manchester.

  • Article, publication date, and citation information can be found at http://dmd.aspetjournals.org.

    http://dx.doi.org/10.1124/dmd.112.046078.

  • ↵Embedded Image The online version of this article (available at http://dmd.aspetjournals.org) contains supplemental material.

  • ABBREVIATIONS:

    MBI
    mechanism-based inhibition
    DDI
    drug-drug interaction
    P450
    cytochrome P450
    HLMs
    human liver microsomes
    fuinc
    fraction unbound in incubation
    MIC
    metabolite intermediate complex
    Km
    Michaelis-Menten constant
    kinact
    inactivation rate constant
    KI
    irreversible inhibition constant
    Ki
    reversible inhibition constant
    LC-MS/MS
    liquid chromatography-tandem mass spectrometry.

  • Received April 5, 2012.
  • Accepted May 23, 2012.

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PROGRESS CURVE ASSESSMENT OF TIME-DEPENDENT INHIBITION

Howard J. Burt, Henry Pertinez, Carolina Säll, Claire Collins, Ruth Hyland, J. Brian Houston and Aleksandra Galetin
Drug Metabolism and Disposition September 1, 2012, 40 (9) 1658-1667; DOI: https://doi.org/10.1124/dmd.112.046078
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