Estimations of in vivo clearance and drug interaction risk of investigational drugs is commonly achieved by extrapolation from in vitro measurements of cytochrome P450 (P450) activity (Houston, 1994; Ito et al., 1998). The generally acknowledged prediction methodology is based on the assumption that P450-mediated reactions follow simple Michaelis-Menten kinetics. However, extensive in vitro evidence suggest that CYP3A4, the most abundant hepatic P450 involved in the metabolism of a majority of drugs (Benet et al., 1996a; Thummel and Wilkinson, 1998) does not always display Michaelis-Menten kinetics. The atypical kinetics observed with CYP3A4 include sigmoidal saturation curves (autoactivation), activation by effectors (heteroactivation), marker substrate-dependent effects on estimations of K_i values, nonmutual inhibition between substrates, and simultaneous metabolism of two different substrates without competitive inhibition (Shou et al., 1994; Ueng et al., 1997; Korzekwa et al., 1998; Kenworthy et al., 1999; Wang et al., 2000; Galetin et al., 2002). Such cooperative effects are not limited to liver microsomes and recombinant P450s, but have been observed also in intact human hepatocytes (Maenpaa et al., 1998; Witherow and Houston, 1999; Ngui et al., 2001). It is unknown to what extent an erroneous assumption of Michaelis-Menten kinetics affects the prediction accuracy of in vivo clearance and drug interaction risks.

Although theoretically a potential source of both drug interactions (due to heteroactivation) and unexpectedly high and nonlinear in vivo clearance (due to autoactivation or endogenous heteroactivators), few attempts have been made to assess the in vivo relevance of atypical P450 kinetics. In the neonatal rat, the in vitro heteroactivator flavone caused an immediate 3- to 5-fold increase in the P450-mediated formation of tritiated water from tritium-labeled zoxazolamine (Lasker et al., 1982, 1984). Similarly, in phenobarbital-pretreated rats, caffeine caused a more than 3-fold increase in levels of acetaminophen glutathione conjugate, a secondary metabolite of acetominophen (Lee et al., 1996). In rhesus monkey, the in vitro CYP3A4 heteroactivator quinidine decreased diclofenac steady-state plasma levels by half (Tang et al., 1999; Ngui et al., 2000, 2001). In human, a weak increase (10%) in apparent oral clearance of the CYP2C9 substrate flurbiprofen was observed after 7 days of dapsone treatment (Hutzler et al., 2001). The lack of attempts to quantitatively correlate observed in vivo effect and in vitro P450 heteroactivation potency, however, allows speculations of alternative causes for these observations.

In an attempt to further test the hypothesis of in vivo P450 heteroactivation in human, we have investigated the mechanism of the clinically observed drug interaction between the two antiepileptic drugs felbamate and carbamazepine. Addition of felbamate to carbamazepine monotherapy results in a decrease in carbamazepine plasma concentrations and a concomitant increase in the plasma concentration of the P450-mediated metabolite carbamazepine-10,11-epoxide (carbamazepine-ep) (Graves et al., 1989; Albani et al., 1991; Theodore et al., 1991; Wagner et al., 1993). This drug interaction was chosen for our study because it fulfills some important criteria for testing the hypothesis of in vivo heteroactivation. The mechanism of the increase in carbamazepine clearance by felbamate is unknown and is in theoretical accordance with the expected effect of in vivo heteroactivation, since the major metabolic pathway (carbamazepine-ep formation) is mediated predominantly by CYP3A4 (Kerr et al., 1994) (Fig. 1), and the fraction of carbamazepine metabolized via carbamazepine-ep, as estimated from a number of clinical reports (Eichelbaum et al., 1985; Sumi et al., 1987; Faigle and Feldmann, 1989; Robbins et al., 1990; Kerr et al., 1994) is high enough to expect heteroactivation of this pathway to yield a measurable change in carbamazepine steady-state plasma concentrations (Css_CBZ). Carbamazepine is a low extraction drug, assuring that in vivo metabolic clearance is dependent on P450 activity with little influence of blood flow. Felbamate is a weak inducer of rat P450s, and no evidence for induction of human P450s has been reported (Segelman et al., 1985; Swinyard et al., 1987). Plasma protein binding displacement of carbamazepine by felbamate (fraction unbound of felbamate: 0.75) could be excluded based on literature (Albani et al., 1991; Benet et al., 1996b). The in vivo effect has been quantified in several independent studies in human, allowing for evaluation of in vitro based predictions.

To clarify the role of heteroactivation in the in vivo interaction between felbamate and carbamazepine, a detailed in vitro characterization of the effect of felbamate on the major metabolic pathway of carbamazepine was performed with regard to its potential for P450 induction and to its effects on kinetics of formation of carbamazepine-ep and carbamazepine-trans-diol (carbamazepine-diol). A scaling methodology is presented for predicting the effect of heteroactivation on total clearance and on steady-state plasma concentrations (Css) of parent drug and metabolite, in order to explore quantitative relationships between in vitro heteroactivation and the pharmacokinetic effect observed in vivo.

Materials and Methods

Materials. Felbamate, carbamazepine, carbamazepine-ep, β-NADP, isocitric acid, dl-isocitric dehydrogenase, dexamethasone, rifampicin, β-glucuronidase, sulfatase (type IV from limpets), dimethyl sulfoxide (DMSO), Hybri-Max, and Williams' E medium were obtained from Sigma-Aldrich (St. Louis, MO). Fungizone (amphotericin B), penicillin-streptomycin, l-glutamine and Superscript^II were purchased from Invitrogen (Paisley, Scotland). Insulin (Actrapid) was obtained from NovoNordisk A/S (Bagsvaerd, Denmark). Bio-Rad protein assay dye reagent concentrate was purchased from Bio-Rad (Hercules, CA). CYP3A4 and human acidic ribosomal phosphoprotein (huPO) primers, TaqMan probes and TaqMan Universal PCR master mix were obtained from Applied Biosystems (Foster City, CA). RNA STAT-60 was obtained from BioSite (Täby, Sweden). Trans-10,11-dihydro-10,11-dihydroxycarbamazepine (carbamazepine-diol) was a gift from Dr. Gunnel Tybring (Karolinska Institute, Stockholm, Sweden). Centrifree YM-30 ultrafiltration devices were purchased from Millipore Corporation (Bedford, MA). All other chemicals were analytical or HPLC grade. Previously characterized recombinant cytochromes P450 (rCYPs)1A2, 2C8, 2C9, 2C19, 2D6, and 3A4 were expressed in yeast and produced at AstraZeneca Biotech Laboratory (Södertälje, Sweden) (Masimirembwa et al., 1999). Human liver samples used for making human liver microsomes and fresh liver slices were excess material from partial surgical liver resections at Sahlgrenska University Hospital (Göteborg, Sweden). The local ethics committee approved the collection of all human tissue used in the study.

Preparation of human liver microsomes and fresh human liver slices. Human liver microsomes (HLM) (from a pool of four livers) were isolated from human livers by differential centrifugation (Raucy and Lasker, 1991).

Fresh human liver slices (approximately 8 mm ø, 300 μm in thickness) were prepared from individual human liver samples as previously described (Sohlenius-Sternbeck et al., 2000) with the exception that liver perfusion with ViaSpan (Belzer UW, NPBI B.V., The Netherlands) was performed after surgical removal.

P450 Enzyme Identification for Formation of Carbamazepine-ep. Recombinant CYPs 1A2, 2C8, 2C9, 2C19, 2D6, and 3A4 were individually incubated with 50 and 250 μM carbamazepine to estimate the importance of different isoforms in metabolizing therapeutic plasma concentrations (≤50 μM) of carbamazepine. P450s (200 pmol/ml) were preincubated with carbamazepine for 5 min at 37°C, and the reaction was started by the addition of prewarmed NADPH regenerating system. After 60 min, the reaction was stopped by the addition of ice-cold acetonitrile (40% of incubation volume). Final incubation conditions were 0.5% dimethyl formamide (DMF) from stock solution of drug, 0.1 M KPO₄ at pH 7.4, 1 mM NADP, 16 mM MgCl₂, 7.5 mM isocitric acid, and 1.2 U/ml isocitric acid dehydrogenase. A standard curve for carbamazepine-ep was generated by spiking a matrix identical to that of samples. Samples and standards were centrifuged and supernatants were analyzed for metabolite by HPLC-UV.

Effect of Felbamate on Carbamazepine-ep Formation in HLM and rCYP3A4. The effect of felbamate on the intrinsic formation clearance of carbamazepine-ep at different carbamazepine concentrations was characterized in human liver microsomes and rCYP3A4. Carbamazepine concentrations of 0, 10, 20, 30, 40, 50, 100, 150, 300, 600, 900, and 1200 μM were combined with 0, 100, 300, 500, and 1000 μM felbamate (HLM) or 0 and 500 μM felbamate (rCYP3A4). HLM were used at a concentration of 1 mg/ml, and rCYP concentration was 80 pmol/ml. Samples were performed in duplicates with a final DMF concentration of 0.5%. Reactions were preincubated, started with the addition of NADPH regenerating system, and stopped by the addition of acetonitrile, as described for P450 identification. Incubation time was 35 min. The reaction was assumed to be at steady-state level, since metabolism was <10% and linear with respect to time and protein or P450 concentration and because substrate concentrations were much greater than CYP3A4 concentration. A standard curve for carbamazepine-ep was generated by spiking an incubation matrix identical to that of samples. The data were fitted to the Hill equation (where ν is the velocity of the reaction, V_max is the maximum velocity of the reaction, S is the substrate concentration, n is the Hill coefficient, which is equal to the number of binding sites only if there is a high degree of cooperativity, and S₅₀ is the substrate concentration at half V_max and is equal to , where K′ is a composite constant of the dissociation constant and the interaction factors by which it is changed by cooperative binding) and to the two-site equation (Korzekwa et al., 1998), which is a modified version of the classical model for nonessential activation (Segel, 1975), derived for rapid equilibrium conditions, assuming two identical binding sites (where V_max1 and V_max2 are the maximum velocities from enzyme occupied with one or two substrate molecules, respectively, K_m1 and K_m2 are the affinity constants for the first and second substrate binding, respectively, when product formation is assumed to be much slower than the on/off rate of binding). No disappearance of carbamazepine-ep could be detected in human liver microsomes at the incubation conditions used (data not shown).

Microsomal Free Fraction of Carbamazepine. The free fraction of carbamazepine in the HLM incubation matrix and the effect of felbamate was investigated by ultrafiltration. Incubation matrix lacking NADP (final concentrations 1 mg/ml HLM, 16 mM MgCl₂, 7.5 mM isocitric acid, 1.2 U/ml isocitric acid dehydrogenase, and 0.1 M KPO₄, pH 7.4) was spiked in duplicates with carbamazepine (20, 50, and 100 μM) or felbamate (500 μM) and carbamazepine (20 μM) together, yielding a final DMF concentration of 0.5% in all samples. Samples were kept at 37°C for 35 min to mimic incubation conditions. Aliquots were removed to serve as total concentration controls before applying samples to ultrafiltration Centrifree YM-30 devices (30,000-kDa cut-off). After centrifugation at a fixed angle at 1,000g for 15 min, cold acetonitrile (40% of incubation volume) was added to filtrates and control aliquots. Samples were centrifuged and supernatants analyzed for carbamazepine by HPLC-UV. Values were corrected for binding of drug to filtration device (7%).

Effect of Felbamate on Carbamazepine-diol Formation in Fresh Human Liver Slices. Fresh liver slices were preincubated in 6-well plates for 20 min at 37°C in a humidified cell incubator with 95% air/5% CO₂ in 2 ml of Williams' E medium supplemented with 2 mM l-glutamine. After preincubation, the medium was removed and duplicate slices were incubated for 175 min in prewarmed medium spiked with 10 μM carbamazepine-ep and 0, 100, 300, or 500 μM felbamate, all being in the range of relevant in vivo plasma concentrations. Felbamate was soluble in the matrix at these concentrations as judged by linearity (10–1000 μM) of UV absorbance when analyzed by HPLC. Valproic acid at 1 mM was used as control for epoxide hydrolase inhibition since this concentration was reported as relevant to the in vivo concentration at which this compound causes inhibition of carbamazepine-diol formation in vivo (Pisani et al., 1988; Ogiso et al., 1990). Final organic solvent concentration was 0.25% DMSO. Reactions were stopped by snap-freezing the slice and incubation medium. Samples were kept at -20°C until thawed on ice and homogenized by ultrasonication (Branson Sonifier 250; G. Heineman, Schwäbish Gmünd, Germany). Protein concentration of each homogenate was estimated according to Bradford (1976). Since 10 to 30% of total carbamazepine-diol recovered in human urine is glucuronidated (Tomson et al., 1983), aliquots of the homogenates were treated with β-glucuronidase (∼1000 U/ml) and sulfatase (∼10 U/ml) at pH 5 for 8 h at 37°C in a shaking water bath. The reaction was stopped, and protein precipitated by boiling for 2 min, a treatment that did not affect stability of carbamazepine-ep or carbamazepine-diol (data not shown).

Carbamazepine-diol, isolated from the urine of an epileptic patient treated with carbamazepine (Tybring et al., 1981), was used to generate a standard curve in a sample identical matrix. Samples and standards were centrifuged, and supernatants were analyzed by HPLC-UV.

Analytical Conditions. Carbamazepine-ep was quantified using a modified version of that previously reported (Remmel et al., 1990). A mobile phase consisting of 65% 25 mM K₂HPO₄ at pH 6, 21% methanol, and 14% acetontrile was pumped at a flow rate of 1.3 ml/min through a Zorbax-SB-C₁₈ column (4.1 × 15 cm, 5 μm). The analyte was detected by UV at 214 nm. UV response was linear in the range of 7 to 714 pmol. Injection volumes of samples were adjusted accordingly. Interassay coefficient of variation was <10% in the concentration range studied.

Carbamazepine-diol and felbamate were quantified using a mobile phase consisting of 82% 10 mM K₂HPO₄ at pH 6 and 18% acetonitrile, and carbamazepine using a mobile phase consisting of 67% 10 mM K₂HPO₄ at pH 6 and 33% acetonitrile. The flow rate and column were as for carbamazepine-ep analysis. Detection was by UV at 214 nm (carbamazepine-diol and carbamazepine) or 204 nm (felbamate). Intra-assay coefficients of variation over the concentration ranges studied were <10% for carbamazepine-diol and carbamazepine and <3% for felbamate. All analysis was performed on a HP-1100 Chemstation (Hewlett Packard, Palo Alto, CA).

Investigation of CYP3A4 Induction Potential of Felbamate. Fresh human liver slices (n = 4 individuals) were preincubated in 6-well plates for 1 h at 37°C in a humidified cell incubator with 95% air/5% CO₂ in 2 ml of Williams' E medium supplemented with 2 mM l-glutamine, 2.5 μg/ml fungizone, 0.1 μM insulin, penicillin-streptomycin (1 μg/ml), and 0.1 μM dexamethasone. Dexamethasone was added from a stock in ethanol yielding a final ethanol concentration of 0.1%. After preincubation, the medium was removed and duplicate slices were individually incubated with medium spiked with 25 μM of the positive control rifampicin, or 0, 50, 250, or 500 μM felbamate. Felbamate was soluble in the matrix at these concentrations as judged by linearity (10–1000 μM) of UV absorbance when analyzed by HPLC. Drugs were added to the incubation medium from stocks in DMSO yielding a final DMSO concentration of 1%. The spiked medium was changed every 24 h during which minimal clearance of felbamate occurred, as judged by HPLC analysis of spiked (50 μM) aliquots before and after incubation (not shown). The experiment was ended after 72 h by transferring slices from the incubation medium to RNA Stat-60 and snap-freezing. Samples were kept at -80°C pending RNA isolation.

Samples were thawed on ice and homogenized using a Polytron PT 1200 CL (Kinematica, Basel, Switzerland). Total mRNA was isolated according to instructions from the RNA-Stat-60 manufacturer. Chromosomal DNA was removed by treating samples with RQ1 RNase-free DNase (Promega, Madison, WI) following the suppliers instructions. Reverse transcription was performed using Superscript first strand synthesis system (Invitrogen). Subsequent real time PCR for cDNA quantification was carried out using TaqMan universal PCR master mix and Taqman probes and an ABI PRISM 7700 sequence detector with Sequence Detector v 1.7 software (Applied Biosystems, Foster City, CA) as previously described (Engman et al., 2001; Westlind et al., 2001). Briefly, this method uses the addition of a sequence-specific quenched fluorescent Taqman probe to the traditional PCR set-up. The original amount of mRNA in the sample is proportional to the fluorescence emitted upon cleavage of the specific cDNA annealing probe, through the 5′ exo-nuclease activity of the Taq polymerase (Holland et al., 1991). VIC was used as the 5′ reporter fluorochrome and tetramethylrhodamine (TAMRA) was used as the 3′ quencher fluorochrome. Simultaneous quantification of the housekeeping gene human acidic ribosomal phosphoprotein (huPO) allowed for normalization between samples. A standard curve for CYP3A4 cDNA was constructed to ensure linearity in the concentration range studied. Experimental conditions had been priorly optimized to achieve the same efficiency for huPO cDNA as for target cDNA. The CYP3A4 forward primer sequence was 5′-CATTCCTCATCCCAATTCTTGAAGT -3′, the CYP3A4 reverser primer sequence was 5′-CCACTCGGTGCTTTTGTGTATCT-3′, and the CYP3A4 probe sequence was 5′-VIC-CGAGGCGACTTTCTTTCATCCTTTTTACAGATTTTC-TAMRA-3′, all spanning exon junctions, thus preventing amplification of genomic DNA (Engman et al., 2001).

The relative fold increase in mRNA in samples compared with controls was calculated using the comparative C_T method (Heid et al., 1996). Each sample from four individual human livers was analyzed once in triplicate. Results were analyzed for statistical significance by setting the average value of duplicate control samples from each liver to 1 and performing a post hoc Dunnett's t test analysis of variance (SPSS 10.1).

In Vitro-in Vivo Correlation. Following chronic, oral administration, average plasma steady-state concentrations of carbamazepine (Css_CBZ) and carbamazepine-ep (Css_CBZ-ep) can be estimated by eqs. 3 and 4 (Houston, 1986), where fa is the fraction of carbamazepine absorbed, F_HCBZ is the fraction of carbamazepine escaping first pass metabolism, D is the dose, τ is the dosing interval, CLtot_CBZ is the total in vivo elimination clearance of carbamazepine, fm is the fraction of drug converted to the metabolite, F_HCBZ-ep is the fraction of epoxide escaping immediate further metabolism before reaching the systemic circulation and CLtot_CBZ-ep is the total elimination clearance of carbamazepine-ep. For a primary metabolite, the average steady-state concentration is the result of the sum of the metabolite formed systemically and that formed by first-pass metabolism (Houston 1986). Since carbamazepine does not undergo first-pass metabolism (F_Hcbz = 1) (Faigle and Feldmann, 1989), it follows that: Parameters D and τ are unchanged by felbamate treatment. It is assumed that felbamate does not affect the complete absorption of carbamazepine (fa = 1) (Faigle and Feldmann, 1989), since it is considered unlikely that heteroactivation would cause first pass metabolism of a completely absorbed low extraction drug. The value of F_HCBZ-ep is unknown and was regarded unaffected by felbamate by the same reasoning, since carbamazepine-ep is also a low clearance drug (Graves et al., 1989). Considering further that CLtot_CBZ can be expressed as where fm is the fraction of carbamazepine metabolized via the carbamazepine-ep pathway, with subscripts “control” and “FBM” defining absence and presence of felbamate coadministration, respectively. Since the change in CLtot_CBZ-ep can be approximated to the change in carbamazepine-diol formation, since the fraction of carbamazepine-ep metabolized to carbamazepine-diol is close to 1 (Theodore et al., 1991), it follows that the effect of felbamate treatment on Css_CBZ-ep and Css_CBZ can be expressed as It can be shown (see Appendix) that if the magnitude of clearance through alternative pathways is assumed unaffected by felbamate, then With “FI” denoting fractional increase, where FICLf_CBZ-ep is the fractional increase in predicted in vivo formation clearance of carbamazepine-ep, which is defined as

Due to the lack of an appropriate enzyme kinetic model for heteroactivation, in which parameters bear a clear relation to clearance, quantitave prediction of in vivo CLf_{CBZ-epcontrol} and CLf_CBZ-epFBM was performed from in vitro data of each carbamazepine-felbamate combination, for an extended range of relevant in vivo carbamazepine concentrations (10–100 μM) and for all felbamate concentrations used (100–1000 μM; observed C_max in vivo: 660 ± 110 μM) (Sachdeo et al., 1997). Predictions were made from in vitro intrinsic carbamazepine-ep formation clearance in HLM based on a hepatic microsomal recovery factor of 40 mg/g of liver and the well stirred model (Pang and Rowland, 1977) (eq 9), taking into account both microsomal and plasma free fraction of carbamazepine where CLf_in vivo is the predicted in vivo formation clearance, Q is the hepatic blood flow, Clf_int is the whole liver in vitro intrinsic formation clearance, fu_mic and fu_plasma are the free fractions of carbamazepine in the microsomal incubation matrix and plasma, respectively.

The magnitude of fm_control for chronic oral administration was approximated to 0.6, based on calculations from literature data (yielding values of 0.4–0.7 for single dosing, increasing to up to 0.85 for chronic dosing) (Eichelbaum et al., 1985; Sumi et al., 1987; Faigle and Feldmann, 1989; Robbins et al., 1990; Kerr et al., 1994). The magnitude of fm_control was assumed constant over the range of carbamazepine concentrations, regardless of any autoactivation, due to difficulties in assigning which carbamazepine concentration to consider as the control value corresponding to literature fm_control.

Due to probable nonlinearity in the studies on felbamate inhibition of carbamazepine-diol formation in liver slices (due to long incubation times) these data were not scaled to an absolute in vivo formation clearance value. Instead it was assumed that the low clearance of carbamazepine-ep (Benet et al., 1996b) allows the approximation that CLtot_CBZ-ep is independent of hepatic blood flow and proportional to in vitro CLf_CBZ-diol × fu_plasma. Since fu_plasma is not changed by felbamate (Albani et al., 1991), the in vivo ratio of CLtot_{CBZ-epcontrol}/CLtot_CBZ-epFBM was quantitatively estimated from the ratio of the amount of carbamazepine-diol formed in human liver slices in the absence or presence of felbamate.

It can be shown that the plasma Css ratio of carbamazepine-ep to carbamazepine-diol is determined only by the elimination clearances of both metabolites (Wagner et al., 1993). Assuming that felbamate does not affect the glucuronidation and/or renal excretion of carbamazepine-diol, and that CLtot_CBZ-ep = CLf_CBZ-diol as described above, then which can be estimated by inhibition data in human liver slices, as described above. Furthermore, from eqs. 3 and 4 and the above-defined assumptions, it follows that: of which all parameters can be estimated as described above. These relationships were used for further evaluation of the success of in vitro-in vivo correlation.

Meta-Analysis of Clinical Studies on the Effect of Felbamate on Css_CBZ. To estimate a quantitative population mean of the percent change of Css_CBZ caused by felbamate coadministration, a total of eight reports, some overlapping, were found and considered for a meta-analysis. Three studies (Fuerst et al., 1988; Leppik et al., 1991; Wagner et al., 1991) were excluded due to confounding events associated with the coadministration of a third drug with P450-inducing properties. Due to the crossover design in one of the remaining reports (Wilensky et al., 1985; Graves et al., 1989; Albani et al., 1991; Theodore et al., 1991; Wagner et al., 1993) a total of eight comparisons (n = 4–34 subjects) of Css_CBZ with or without coadministration of felbamate were included in the meta-analysis.

The following random effects model was used for investigation of the population mean and the average study deviation from it where ŷ_i is the observed average percent change in Css_CBZ caused by felbamate in study number i; y_i is the true percent change in each study; where τ_i is the variance of the mean in study number i, μ is the population mean, and where Ω is the between study variance, so that √Ω is the average deviation from the population mean.

ŷ_i was estimated from reported values of Css_CBZ when coadministered with felbamate (Css_CBZFBM) and the corresponding Css_CBZ without felbamate coadministration (Css_CBZcontrol) and their respective distributions. Reported Css values were trough (minimum) concentrations. For each study, 1000 data points each of Css_CBZFBM and Css_CBZcontrol were randomly generated (S-Plus 2000), assuming normal distribution since variations were reported as standard deviations. To avoid overestimation of variation and to more closely mimic the physiologic condition that no increase in Css_CBZ has ever been reported for felbamate coadministration, the random generation of Css_CBZcontrol values was restricted so that Css_CBZFBM/Css_CBZcontrol ≤ 1.1. The allowance of a 10% increase was based on an approximate average of reported coefficients of variation in analytical assays used to measure the plasma Css_CBZ.

Although the randomly generated ŷ_i showed a slightly tailed distribution toward lower values, this was not considered enough evidence to assume a distribution other than normal for μ. Gamma distribution was assumed for σ_i. τ_i was estimated for each study as (S.D.)²/n, where S.D. is the standard deviation of the randomly generated percent change in Css, and n is the number of individuals. A non-informative prior was used, and stationary distribution was equivalent to posterior distribution before sampling was initiated.

Using the median and the precision of median instead of mean and precision of mean due to the slightly tailed distribution of ŷ_i yielded no significant difference in results (data not shown). The analysis was performed in Winbugs 13 (as available on http://www.mrc-bsu.cam.ac.uk/bugs).

Results

In Vitro Effect of Felbamate on Carbamazepine Metabolism. The capability of a panel of drug-metabolizing P450s to metabolize carbamazepine to carbamazepine-ep from two different carbamazepine concentrations (50 and 250 μM) is shown in Fig. 2. Even at 250 μM carbamazepine, well above plasma concentrations of this drug, the activity of CYP3A4 was more than 20-fold higher than that of CYP2C8, at equimolar amounts of P450.

Formation of carbamazepine-ep displayed sigmoidal kinetics in HLM, characteristic of autoactivation (Fig. 3, A and B). Sigmoidicity was less evident in rCYP3A4 as judged by visual inspection and by a lower Hill coefficient (Fig. 3, C and D; Table 1). Consistent with the atypical characteristics of the kinetics in rCYP3A4, the data were not well described by the Michaelis-Menten equation (not shown). Parameter estimates from fitting carbamazepine-ep formation in HLM and rCYP3A4 to eqs. 1 and 2 in the presence and absence of felbamate are given in Table 1. Addition of 1 mM felbamate slightly decreased sigmoidicity in HLM as judged by visual inspection and by changes in the Hill coefficient (Table 1).

Felbamate heteroactivates carbamazepine-ep formation in HLM (Fig. 3, A, B, and E) and rCYP3A4 (Fig. 3, C, D, and F) at relevant in vivo concentrations of both drugs (felbamate C_max: 660 ± 110 μM (Sachdeo et al., 1997); concentrations shown to give drug interaction in vivo: [felbamate] 90–315 μM and [carbamazepine] 15–70 μM) (Wilensky et al., 1985; Graves et al., 1989; Theodore et al., 1989; Albani et al., 1991; Theodore et al., 1991; Wagner et al., 1993). Heteroactivation is most evident at low substrate concentrations, resulting in a doubling in activity when combining the highest felbamate concentration (1 mM) and the lowest carbamazepine concentration (10 μM). The degree of heteroactivation at the same felbamate concentration is similar between HLM and rCYP3A4 (Fig. 3, E and F). The free microsomal fraction of carbamazepine was 0.98, and this value was not affected by felbamate (data not shown).

CYP3A4 is not significantly induced by felbamate (50–500 μM), as measured by the ratio of rCYP3A4/huPO mRNA in human liver slices compared with that in DMSO-treated controls (significance limit set at p < 0.05). The positive control (rifampicin 25 μM) did induce CYP3A4 (Fig. 4).

Felbamate inhibits the formation of carbamazepine-diol from a therapeutic concentration of carbamazepine-ep (10 μM) in human liver slices in a concentration-dependent manner (Fig. 5). Between 10 and 30% of the carbamazepine-diol was further conjugated in human liver slices, which is consistent with that reported in human volunteers (Tomson et al., 1983) (data not shown).

Meta-Analysis of in Vivo Effect of Felbamate on Css_CBZ. The results of the random generation of the percent change in Css_CBZ caused by felbamate coadministration in each individual case is shown in Fig. 6. Applying the random effects model yielded a global mean of 24.0% decrease (95% confidence interval 27.5–20.6%) with an average study deviation from the global mean of 1.5%. Resulting individual estimations of y_i (the estimated true percent change in each study after applying the random effects model) are shown in Fig. 6.

Quantitative in Vitro-in Vivo Correlation of the Felbamate-Carbamazepine Drug Interaction. As a consequence of autoactivation, the predicted clearance of carbamazepine [based on HLM data and using the well stirred model, assuming the fraction metabolized is 0.4 for a single dose of carbamazepine (Faigle and Feldmann, 1989)] ranges from 0.18 ml/min/kg at 10 μM carbamazepine to a maximum clearance (CL_max) of 0.53 ml/min/kg at a concentration of 300 μM, well above therapeutic carbamazepine plasma concentrations (Fig. 7).

The predicted percent changes in in vivo Css_CBZ and Css_CBZ-ep caused by felbamate CYP3A4 heteroactivation and epoxide hydrolase inhibition are shown in comparison with in vivo values in Fig. 8 and Fig. 9. The predicted decrease in Css_CBZ caused by CYP3A4 heteroactivation ranges from 6.6% to 37%, depending on the particular combination of carbamazepine and felbamate concentrations. The predicted effect of heteroactivation alone on the fraction metabolized to carbamazepine-ep is relatively small, ranging from 4.4 to 24.5%.

The ratio Css_CBZ-ep/Css_CBZ is predicted to change by 20 to 47% in the range of 100 to 300 μM felbamate, which is in accordance with reported changes in vivo (25–40% increase at plasma concentrations of 85–252 μM felbamate) (Albani et al., 1991; Wagner et al., 1993). Similarly, the predicted change in Css_CBZ-ep/Css_CBZ-diol (34–125% in the range of 100 to 300 μM felbamate) is comparable to that reported in vivo (70–120% at 85–252 μM felbamate) (Albani et al., 1991; Wagner et al., 1993).

Discussion

Atypical kinetics of CYP3A4 are commonly observed in vitro. Results from enzyme kinetic studies on wild-type and active-site mutants suggest that this is a result of cooperative binding of two or more substrates and/or effector molecules in the large CYP3A4 active site, possibly with presence of additional allosteric sites (Shou et al., 1994; Ueng et al., 1997; Korzekwa et al., 1998; Domanski et al., 2000; Hosea et al., 2000; Kenworthy et al., 2001; Galetin et al., 2002). Although direct evidence for the mechanism of ligand interaction at the CYP3A4 active site must await successful CYP3A4 crystallization studies, the potential effects and relevance of activation on human pharmacokinetics can be addressed now.

In this study, we have investigated whether the drug interaction between felbamate and carbamazepine observed in epileptic patients is due to a heteroactivating effect of felbamate on CYP3A4. We show the lack of a significant effect on CYP3A4 mRNA levels in fresh human liver slices (Fig. 4) by felbamate at concentrations relevant to those giving rise to a significant interaction in vivo. It has been shown previously that felbamate does not displace carbamazepine, carbamazepine-ep, or carbamazepine-diol from plasma proteins (Albani et al.,1991), thus excluding a confounding factor. We confirm earlier reports that CYP3A4 and CYP2C8 are capable of carbamazepine-ep formation (Kerr et al., 1994) (Fig. 2). However, taking into account the low relative contribution of CYP2C8 even at carbamazepine concentrations well above those in plasma, as well as the relative P450 isoform abundance in liver (Thummel and Wilkinson, 1998), our results suggest that CYP3A4 is the only isoform significantly contributing to carbamazepine-ep formation in the clinical situation.

We confirm the atypical nature of carbamazepine-ep formation in HLM and rCYP3A4 (Kerr et al., 1994; Ueng et al., 1997; Korzekwa et al., 1998) (Fig. 3, A–D). Consistently, parameter estimates from the two-site equation (Korzekwa et al., 1998) suggest that binding of the first carbamazepine molecule increases the affinity for binding of the second molecule (K_m1 > K_m2), in both HLM and rCYP3A4. The low values and high estimate errors for V_max1 suggest carbamazepine-ep formation takes place only from doubly occupied enzyme, as has been previously suggested (Korzekwa et al., 1998). In contrast, for rCYP3A4, V_max1 > V_max2, suggesting substrate inhibition at high substrate concentrations, which is confirmed by the nature of the Eadie-Hofstee plot (Fig. 3D). The reason for the inconsistency in kinetic profile between HLM and recombinant CYP3A4 is unclear. It cannot be explained solely by contribution of several isoforms in the HLM, since the sigmoidicity occurs at low substrate concentrations, where CYP3A4 is the only isoform capable of producing measurable amounts of carbamazepine-ep. It is, however, possible that any substrate inhibition of CYP3A4 would be disguised in HLM by the contribution of other isoforms at high substrate concentrations, and that sigmoidicity in rCYP3A4 would have been observed if analytical limitations had allowed the monitoring of product formation from lower substrate concentrations. The inconsistency in kinetic profile between different sources of P450s has been reported earlier for carbamazepine and for other CYP3A4 substrates (Houston and Kenworthy, 2000) and calls for further investigation.

Contrary to the inconsistency in kinetic profile for carbamazepine-ep formation in the absence of effector, felbamate heteroactivated carbamazepine-ep formation in both HLM and rCYP3A4. Inhibition of further metabolism of carbamazepine-ep by felbamate was excluded as a reason for the increase in carbamazepine-ep levels, since no disappearance of carbamazepine-ep could be detected in human liver microsomes under the incubation conditions used (data not shown). The heteroactivating effect of felbamate was modeled by estimating the change in apparent constants of the velocity equations attempting to describe the carbamazepine-CYP3A4 interaction (Table 1). The results suggest that in both HLM and rCYP3A4, felbamate increases the affinity for binding of the first carbamazepine molecule (decrease in Km₁) and increases the rate of product formation when two substrate molecules bind the enzyme (increase in V_max2). The decrease in Km₁ suggests that at higher effector concentrations than what was used here, the enzyme would be in an activated state at such low substrate concentrations that Michaelis-Menten-like kinetics would be observed, as is common for potent heteroactivators (Ueng et al., 1997; Houston and Kenworthy, 2000). No conclusion can be drawn regarding the binding site of felbamate based on the parameter estimates. If felbamate binds to the hypothesized nonproductive carbamazepine binding site to increase the affinity and catalytic efficiency of the productive site, a decrease in carbamazepine affinity of this site would be expected at high effector concentrations due to competition. A more complex model taking into account that the asymmetric structure of CYP3A4 requires the assumption of structural difference between binding sites would be needed to test this hypothesis. The low heteroactivation potency of felbamate, however, excludes any meaningful conclusions to be drawn from more complex models. It cannot be excluded, based on current empirical data, that felbamate increases P450 activity without binding directly to the CYP3A4, but by affecting other components of the catalytic cycle.

We propose a scaling methodology where in vitro heteroactivaton can be extrapolated to in vivo effect on Css, despite lack of mechanistic knowledge, provided that drug concentrations at the active site can be estimated to allow selection of appropriate concentrations for in vitro investigation. In this case, we have assumed that there is no active transport of drug in or out of the hepatocyte, and that concentrations at the active site can be estimated by those in plasma.

Due to autoactivation, carbamazepine clearance is predicted to be concentration-dependent (Fig. 7). The slight underestimation is within the error range resulting from uncertainty in the scaling process and fraction metabolized via the carbamazepine-ep. Although there is some evidence of dose-dependent carbamazepine clearance after single dosing (Cotter et al., 1977; Bertilsson et al., 1986), the role of autoactivation has not been investigated. In the case of chronic administration, any autoactivation would be expected to be disguised by the effect of carbamazepine on CYP3A4 induction.

For heteroactivation, eqs. 5, 6, and 7 predict that the in vivo change in Css of a chronically administered low extraction drug and its metabolite will be dependent on the fraction metabolized through the affected pathway in the absence of the heteroactivator. Thus, only for a very minor metabolite (low fm_control), will the change in metabolite Css approach the magnitude of the heteroactivating effect on formation clearance, whereas the effect on the parent drug Css will be low, unless the activator is potent enough to make a sufficiently large change in the quantitative importance of the pathway to alter total clearance. If fm_control is high, heteroactivation will effect the steady-state level of parent drug more than that of the metabolite.

Applying the proposed methodology to the felbamate-carbamazepine interaction, shows that in vitro heteroactivation of CYP3A4-mediated carbamazepine-ep formation at concentrations relevant to those giving rise to the in vivo drug interaction (felbamate concentration 90–315 μM, carbamazepine concentration 15–70 μM) (Wilensky et al., 1985; Graves et al., 1989; Theodore et al., 1989, 1991; Albani et al., 1991; Wagner et al., 1993) quantitatively corresponds to the decrease in Css_CBZ seen in vivo, as estimated by the result of the meta-analysis (Fig. 8). A slight underestimation of the effect would be expected since the relative abundance of CYP3A4 in human liver microsomes is probably lower than that in vivo after chronic carbamazepine administration. Based on eqs. 6 and 7, the effect of heteroactivation on Css_CBZ-ep is expected to be small. However, when taking into account also the inhibitory effect of felbamate on further metabolism of the carbamazepine-ep to carbamazepine-diol, the in vivo effect of felbamate on Css_CBZ-ep is predicted to be in the range of that reported (Fig. 9). The correspondence of in vitro derived data with in vivo Css_CBZ-ep/Css_CBZ and Css_CBZ-ep/Css_CBZ-diol ratios further validates the correspondence to the in vivo situation.

Using a well documented drug-drug interaction as a tool, we have shown for the first time that a clinical interaction can be quantitatively explained by careful characterization of an in vitro P450 activation event. The data presented here indicate that isolated in vitro human cytochrome P450 systems can be used to quantitatively characterize potential drug-drug interactions arising from cooperative binding of concomitantly administered drugs and that such in vitro activation events appear to have clinical pharmacokinetic consequences. This raises the question of whether P450 activation studies should be routinely carried out alongside the now-common P450 inhibition studies required in drug discovery.

Appendix: Derivation of Relationship Describing Effect of Heteroactivation on Fraction Metabolized

By definition where fm_activation is the fraction of drug converted to the metabolite when the pathway is activated, CLf_{metactivation} is the in vivo formation clearance of metabolite when activated, and CL_{otheractivation} is the in vivo clearance through other pathways when the activator is added. Defining the fractional change in in vivo formation clearance (FICLf_met) as where CLf_metcontrol is the formation clearance without activation, the following relationship holds. Assuming that CL_{otheractivation} = CL_othercontrol = (1 - fm_control) × CLtot_control where CLtot_control is the total clearance without activation, fm_activation can be expressed as Further, since then Dividing all functions by CLtot_control gives from which it follows that