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Modelling atypical CYP3A4 kinetics: principles and pragmatism
ABB Archives of Biochemistry and Biophysics 433 (2005) 351–360 www.elsevier.com/locate/yabbi
Modelling atypical CYP3A4 kinetics: principles and pragmatism J. Brian Houston*, Aleksandra Galetin* Centre for Applied Pharmacokinetic Research, School of Pharmacy and Pharmaceutical Sciences, University of Manchester, Oxford Road, Manchester, Ml3 9PL, United Kingdom Received 12 August 2004 Available online 7 October 2004
Abstract The Michaelis–Menten model, and the existence of a single active site for the interaction of substrate with drug metabolizing enzyme, adequately describes a substantial number of in vitro metabolite kinetic data sets for both clearance and inhibition determination. However, in an increasing number of cases (involving most notably, but not exclusively, CYP3A4), atypical kinetic features are observed, e.g., auto- and heteroactivation; partial, cooperative, and substrate inhibition; concentration-dependent effector responses (activation/inhibition); limited substrate substitution and inhibitory reciprocity necessitating sub-group classification. The phenomena listed above cannot be readily interpreted using single active site models and the literature indicates that three types of approaches have been adopted. First the Ônaı¨veÕ approach of using the Michaelis–Menten model regardless of the kinetic behaviour, second the ÔempiricalÕ approach (e.g., employing the Hill or uncompetitive inhibition equations to model homotropic phenomena of sigmoidicity and substrate inhibition, respectively) and finally, the ÔmechanisticÕ approach. The later includes multisite kinetic models derived using the same rapid equilibrium/steady-state assumptions as the single-site model. These models indicate that 2 or 3 binding sites exist for a given CYP3A4 substrate and/or effector. Multisite kinetic models share common features, depending on the substrate kinetics and the nature of the effector response observed in vitro, which allow a generic model to be proposed. Thus although more complex than the other two approaches, they show more utility and can be comprehensively applied in relatively simple versions that can be readily generated from generic model. Multisite kinetic features, observed in isolated hepatocytes as well as in microsomes from hepatic tissue and heterologous expression systems, may be evident in substrate depletion–time profiles as well as in metabolite formation rates. Failure to adequately account for multisite kinetic phenomena will compromise any attempts to predict human drug clearance and drug–drug interaction potential from in vitro data. 2004 Elsevier Inc. All rights reserved. Keywords: CYP3A4; Atypical kinetics; Multisite kinetics
Background and scope For many years the Michaelis–Menten model, and the existence of a single active site for the interaction of substrate with drug metabolising enzyme, has been used to describe in vitro kinetic data for both clearance and inhibition determination. However, it has become increasingly common that atypical (non-Michaelis– Menten) kinetic features are observed. The phenomena *
Corresponding authors. Fax: +44 161 275 8349 (J.B. Houston). E-mail addresses: [email protected] (J.B. Houston), [email protected] (A. Galetin). 0003-9861/$ - see front matter 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.abb.2004.09.010
of auto- and heteroactivation; partial, cooperative, and substrate inhibition; concentration-dependent effector responses (activation/inhibition); limited substrate substitution; and inhibitory reciprocity, cannot be readily interpreted using single active site models. The most notable, but not the sole, drug metabolising enzyme associated with atypical kinetics is CYP3A4. The finding that a number of CYP3A4 substrates do not conform to the expected competitive type of interaction indicates the existence of, and interaction between, several binding sites on the enzyme. The large CYP3A4 active site may allow the simultaneous presence of multiple molecules (at least two) and the exact binding
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conformations appear to depend on the substrates involved, their relative concentration, and affinity for the enzyme. Various atypical effects can result, which may be either positive or negative in nature, and can be rationalised by multisite occupation by more than one molecule of the same substrate (homotropy), or interactions involving two or more different substrates (heterotropy). Homotropic effects represent alterations in either binding affinity or rate of product formation after the binding of a second molecule of the same substrate to the enzyme active site. As a net effect, CYP activity is either increased in a substrate concentration-dependent manner (sigmoidal kinetic profiles defined as autoactivation or positive homotropy) [1,2] or decreased (convex kinetic profiles defined as substrate inhibition or negative homotropy) [3,4]. The complexity of effects is increased for heterotropic interactions involving two different substrates [5–7]. In this case, in contrast to the expected simple competitive inhibition, a modifier can cause either activation or inhibition affecting binding affinity of a substrate or the rate of its metabolism by a particular CYP, or even both activation and inhibition. This scenario further increases in complexity when there are substrate-dependent [8,9] and/or pathway-differential effects [10,11]. Thus, heterotropic characteristics result in a limited ability to extrapolate in vitro data from one substrate to another and a lack of inhibitory reciprocity. Lack of mutual competitive inhibition, as observed in aflatoxin Bl-a-naphthoflavone [2], testosteronediazepam [7], and testosterone-7-benzyloxyquinoline interactions [12], favours the existence of a distinct effector-binding site. Site-directed mutagenesis studies have indicated that in case of CYP3A4 substrate and effector-binding sites are separate, but closely linked and the residues involved in the binding of either substrate and/or effector depend on the molecules present [13,14]. ÔMetabolicÕ and ÔregulatoryÕ sites may differ for the same compound as proposed earlier for the CYP3A4 modifiers a-naphthoflavone [10] and quinidine [4]. Mechanistic analysis of a range of variable and substrate-dependent effects observed for CYP3A4 prototypical substrates, supports the hypothesis of distinct and preferential binding domains for each substrate subgroup with one mutual site for all subclasses of CYP3A4 substrates. The net effect of the interaction depends on the particular substrate(s) present at the active site, the possible overlap of their binding domains and the relative concentrations of both [11]. A recent report on the crystal structure of this enzyme [15] provides additional support for cooperativity due to the large size of the active site cavity identified proximal to the catalytic heme iron, consistent with the mechanistic models postulated. However, in another crystal structure study, Williams et al. [16] reported progesterone binding
at a peripheral binding domain rather than at the active site resulting in an insignificant conformational change in the CYP3A4 protein. Whether this later observation is an artefact of the crystallisation process or this site has an actual functional recognition role requires further exploration. A wide range of other biophysical methods also support the existence of multiple binding sites for CYP3A4, as well as other CYPs [17]. In this mini-review equal emphasis will be placed on practicalities and principles of modelling atypical CYP3A4 kinetics. Although several comprehensive reviews (e.g. [18–20]) provide a rigorous base for analysis of complex kinetics, there has been little emphasis on developing pragmatic approaches that allow routine analysis of the ÔatypicalÕ interaction of drugs with CYP3A4.
Approaches in modelling atypical kinetics The literature indicates that atypical kinetic in vitro data are generally analysed by three approaches— Ônaı¨veÕ, empirical, and mechanistic methods. Investigators using the first approach apply the Michaelis–Menten model regardless of the kinetic behaviour observed, ignoring any evidence of sigmoidicity or convexity in the rate-substrate concentration profile. Use of empirical models (e.g., Hill or uncompetitive inhibition equations for the analysis of the two homotropic types described above) represents a useful tool for the preliminary analysis of data. While convenient to perform, this approach provides no mechanistic information of the interactions between homotropic or heterotropic ligands (substrate and/or effector). One mechanistic approach is the use of multisite kinetic models, derived from the same rapid equilibrium/ steady-state principles as the single-site Michaelis–Menten model and allowing the simultaneous fit of multiple sets of data to a single equation [21]. Fig. 1A shows a kinetic model for CYP3A4 with two substrate-binding sites, the second substrate molecule binds cooperatively. Autoactivation (positive homotropy) may result in either increased binding affinity for a second substrate molecule (dissociation constant Ks changes by the factor a < 1), or changes in the effective catalytic rate constant (Kp) by the factor b from SES complex (b > 1). In contrast negative cooperativity is defined by changes in a or b in the opposite direction (a > 1, resulting in biphasic kinetic profile, b < 1 resulting in substrate inhibition). Biphasic-type of curves is less common for CYP3A4 than substrate inhibition [22]. The proposed model does not distinguish between the simultaneous binding of multiple molecules within a single active site and the binding of two molecules to two distinct binding sites. The interaction factors defined in the model shown in Fig. 1A are consistent with the two-site model described by Korzekwa et al. [5]; the difference being that the
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Fig. 1. Multisite kinetic equilibria models and their corresponding equations. (A) A kinetic model for an enzyme with two-substrate binding sites, the second substrate (S) molecule binds cooperatively. (B) A generic two-site model for CYP3A4 interactions. Interaction factors associated with the changes in binding affinity (Ks or Ki): a—homotropic cooperativity, d—heterotropic cooperativity, and aM—cooperative binding of modifier; interaction factors associated with the changes in catalytic rate constant (Kp): b (SES) and c (MES).
changes in the binding affinity and the catalytic efficiency for the single- (SE/ES) and two-substrate bound form (SES) are characterised by two Km and two Vmax values, but the ratio of these two Km or Vmax values corresponds to the a and b interaction factors, respectively. Additionally, the model of Shou et al. [1] has two binding sites within the CYP3A4 active site differing in steric hindrance, hydrophobic interaction, and electron characteristics; i.e., an orientation difference in binding of S to E (SE „ ES). However, the fit obtained from this kinetic model for diazepam, temazepam, and nordiazepam metabolism in human liver microsomes was in good agreement with the simpler equations [5,22], as they both describe the reduced binding affinity and lower catalytic capacity of ES complex compared to ESS (Km1 > Km2, Vmax1 < Vmax2). For heterotropic effects, the simultaneous presence of two different substrates at the active site and an increased number of enzyme species results in models that are relatively complex. Fig. 1B shows the generic version of the two-site model and the corresponding interaction factors associated with changes in either binding affinity (a, d) or rate of product formation (b, c). This model is versatile in that it can be applied for activation or inhibition and can be reduced or expanded in complexity depending upon
the ÔvisibilityÕ of certain features in the data. Other reductions in the model requirements regarding the inclusion of interaction factors will be illustrated later. A limitation of this approach lies in the difficulty in assigning a unique model to a particular data set. The final selection of a particular multisite model will be based on an assessment of a simultaneous fit to multiple data sets (at least 60 data points including replicates) involving various statistical, simulation, and modelling techniques. However, an element of subjectivity is always present and supporting, independent experimentation is particularly valuable. Overall although more complex, these two- (or three-site) models can be comprehensively applied in the prediction of either clearance or potential in vivo drug interactions from ÔatypicalÕ in vitro data, as summarised in the following sections.
Modelling multisite kinetics Impact of ‘atypical’ kinetics on the prediction of clearance A recent FDA report [23] indicates that testosterone is the most commonly used in vitro CYP3A4 probe. It was employed in approximately 50% of reported studies,
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contrasting with the use of midazolam (15–20%), nifedipine, felodipine, and erythromycin (the later three less than 10% each) for in vitro estimation of CYP3A4 activity. However, the differential effects observed for various CYP3A4 substrates [8] have resulted in the recommendation of employing two or more CYP3A4 substrates [24,25]. Midazolam, testosterone, and nifedipine are most commonly used as representatives of the different CYP3A4 subgroups, particularly as they show distinctive kinetic properties namely, hyperbolic, sigmoidal, and substrate inhibition, respectively. Multisite analysis of the interaction profiles observed between these three CYP3A4 prototypes indicates the existence of one preferential binding domain for each of the CYP3A4 substrate subgroups. However, the inter-substrate group interactions strongly imply the existence of a mutual binding domain common to each of the three CYP3A4 substrate subclasses [11]. Testosterone is the prototypic substrate for positive cooperative behaviour as autoactivation have been demonstrated in various CYP3A4-expression systems [2,7,26], CYP3A5 [27], and human liver microsomes [28]. Although sigmodicity may not be obvious on first inspection of the data (see Fig. 2A), an Eadie–Hofstee plot clearly shows curvature (Fig. 2B). For drugs dis-
playing positive homotropic behaviour, clearance is dependent on the substrate concentration (Fig. 2C) and an underestimation of clearance will be obtained if a hyperbolic curve is forced through the data to obtain the parameters Vmax and Km to calculate CLint. The CLmax, the maximum clearance when the enzyme is fully activated, represents the alternative to CLint for scaling of in vitro data and is now commonly used in the scaling strategy [29]. This parameter can be calculated by either Hill equation estimates [22] or using two-site model as shown in Eq. (1). pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi V max ð1=aÞ 1 CLmax ¼ ð1Þ 2ð1 aÞ Ks a and Ks are calculated from untransformed data using the two-site model. The CLmax estimate derived from the two-site kinetic model [30], assumes the equivalence of two sites and therefore b is 2 (and Vmax is equivalent to 2Kp[E]t, where [E]t is the total enzyme concentration). Simulations using the two-site model [20] indicate that significant sigmoidicity (defined by low a values) results in a pronounced characteristic shape of the clearance plots as seen in Fig. 2D; in cases where a > 0.5 the clearance plot tends towards Michaelis–Menten kinetic behaviour.
Fig. 2. Positive cooperativity as exemplified by testosterone 6b-hydroxylation—(A) rate–substrate concentration profile, (B) Eadie–Hofstee plot, and (C) clearance plot. The effect of a (extent of sigmoidicity) on the clearance plots and maximum clearance is shown in (D).
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The value of a provides a clearer indication of the extent of cooperativity than the Hill number. The use of CLmax allows autoactivation to be incorporated into in vitro–in vivo scaling strategies. The consequence of CYP3A homotropy is a dependence of clearance on substrate concentrations well below the Ks value in the region corresponding to first order kinetics in the Michaelis–Menten model (see Fig. 2C). This has implications on clearance estimates from rapid screening of metabolic stability of new drug candidates. These are routinely carried out by monitoring parent drug depletion at one substrate concentration, often in the l lM region, based on the rationale that this concentration should be well below the (unknown) Km value. If consideration is not given to the phenomenon of autoactivation then clearance is likely to be underestimated. For example, diazepam metabolite kinetics shows marked sigmoidicity and its microsomal half-life at l lM is five times longer than at 100 lM reflecting the non-activated and fully activated clearance (see Fig. 3). For substrate inhibition, a substantial underestimation of Vmax will occur by merely ignoring the high concentration data points and forcing a hyperbolic curve through the remaining lower substrate concentration data points and the Km value will be poorly estimated. How precisely the clearance estimate will be altered by model misspecification will vary from case-to-case and will be dependent on the number and quality of the data points. Nifedipine is a prototypical substrate reported to show negative homotropy, defined by a b term of 0.36 [20]. The importance of heterotropic effects on clearance determination has yet to be fully assessed but as steroids and dietary flavones are the most documented activators this may contribute to interindividual differences commonly seen between liver donor microsomes. Testosterone has also been reported as heteroactivator of several CYP3A4 substrates (e.g., diazepam [7], carbamazepine [31]), causing an increased metabolism rate and alteration from sigmoidal to hyperbolic kinetic profile. Fig. 3
Fig. 3. Diazepam depletion–time profiles and metabolic stability in human liver microsomes: effect of substrate concentration and testosterone—2.5 lM (d) and 100 lM (j) diazepam, and 100 lM diazepam in the presence of 100 lM testosterone (m).
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illustrates the impact of testosterone on diazepam microsomal half-life. Impact of ‘atypical’ kinetic on the prediction of drug–drug interactions The potential of substrates and modifiers of CYP3A4 to show homo- and heterotropic cooperative effects confounds any straightforward in vitro–in vivo correlation. The incorporation of these phenomena in the assessment of potential in vivo drug–drug interactions from in vitro data is rare [24,25,32]. Whether such phenomena are apparent in vivo remains questionable, however the appropriate in vitro analysis is essential to ensure accurate quantitative estimates for prediction [29]. To explore the range of possible consequences of heterotropic interactions use of multiple substrates in vitro at various substrate concentrations is recommended [8]. When modelling inhibitions at multiple sites three possible changes need to be considered [11]: (a) alterations in binding affinity (homo- and heterotropic effects on Ks and Ki), (b) alterations in rate of metabolite formation (effect on Kp), and (c) the lack of reciprocity between competing binders. A systematic approach to explain various kinetic phenomena observed for CYP3A4 interactions (namely, auto- and heteroactivation; partial, cooperative, and substrate inhibition; concentration-dependent effector responses (activation/inhibition); limited substrate substitution and inhibitory reciprocity; pathway differential effects) and their link with particular multisite interaction factors has been provided in our previous publications [11,29]. The application of a generic two-site model [4] has been proposed as an approach to accommodate the range of ÔinhibitionÕ effects observed for CYP3A4. The interaction factors associated with changes in either binding affinity (a, d) or rate of product formation (b, c) may be included or excluded in the modelling depending on the complexity of substrate kinetics (hyperbolic, substrate inhibition or sigmoidal) and the changes observed in the presence of the modifier. This mechanistic approach allows the simultaneous fit of all the data covering the full range of modifier concentrations, in contrast to empirical methods (e.g., Hill plots) where individual fits are obtained for each specific concentration of modifier. Cooperative binding of the second molecule of the same modifier (homotropic cooperativity) is defined by the interaction factor aM (positive <1, negative cooperativity >1, as discussed). The effects of felodipine on both midazolam and testosterone provide good examples of positive cooperativity [11]. In the first case, there is a progressive increase in the 50% inhibitory concentration
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as substrate concentration increases with a marked increases in the steepness of the concentration–effect curve. In the later case, the 50% inhibitory concentration decreases with substrate concentration. In contrast, binding affinity alterations due to heterotropic effects and formation of a complex with two different substrate molecules (MES) are described by the interaction factor d. The net effect of the increased affinity (d < 1) can vary from either heteroactivation or inhibition depending on the corresponding changes in the catalytic rate in the presence of a modifier (cKp) as illustrated previously [20]. The opposite scenario (d > 1) characterises partial inhibition where inhibition is achieved at only one of the two catalytically active sites, as the affinity of a second inhibitor molecule for a binding site is decreased compared to the first (e.g., l 0 -OH midazolam inhibition by testosterone [11]). The interaction factors b and c are associated with alterations in the Kp, either as a result of binding of a second substrate molecule (SES, e.g., substrate inhibition, bKp < Kp) or a modifier molecule (MES, heteroactivation c > 1, inhibition c < 1). In many cases a modifier can act in a concentration-dependent manner, causing activation at low substrate concentrations and inhibition at higher concentrations, as exemplified by the effect of quinidine on midazolam [4]. This behaviour can be rationalised by a relatively low value of the interaction factor c (<2) and at low S concentrations the rank order of metabolite formation is SEM > ES/SES. However, at higher concentrations the competition of the modifier with the substrate at both sites causes inhibition. However, with large values of c (>2), the activation is more pronounced and occurs over a wider range of substrate concentrations, as illustrated in Fig. 4. The application of simple models for interactions involving substrates with positive (testosterone, diazepam) or negative (terfenadine, nifedipine) homotropic kinetic properties is particularly problematic and the misuse of a one-site model may lead to inaccurate esti-
mation of kinetic parameters and failure to identify important drug–drug interactions.
Modelling testosterone interactions: three-site model Two distinct types of heterotropic interactions have been reported for testosterone where positive cooperativity either remains in the presence of the modifier or is eliminated. The loss of sigmoidicity at high concentrations of modifier (linear Eadie–Hofstee plots as normally seen for hyperbolic kinetics) occurs in the presence of midazolam, nifedipine, and felodipine. An analogous situation is observed for substrates showing substrate inhibition kinetic properties. When c is comparable to b, the rate of metabolite formation from IES complex (cKp) is analogous to SES (bKp) and the substrate inhibition trend remains. However, at high substrate and inhibitor concentrations a non-productive inhibitor complex dominates, changing the profile to a hyperbolic type as observed in the quinidine effect on nifedipine [20]. The opposite scenario where the sigmoidal properties of testosterone are unaffected by increasing inhibitor concentration, suggest that the inhibitor acts at a distinct effector site. This complex type of interaction requires a three-site model and has been observed for the effects of diazepam [7], quinidine, haloperidol [4], and azoles [33] on testosterone. CYP3A4 inhibition, as characterised by testosterone, results in changes in either binding affinity or Vmax or a combined effect, as summarised in Table 1. Each type of interaction can be defined by a particular multisite kinetic model with the appropriate interaction factors. The threesite model (Fig. 5A) applied for the testosterone interaction with azoles is the same as that used for the effect of progesterone or quinidine. All modifiers cause a change in the rate of product formation rather than the binding affinity (no alteration in the cooperative binding of testosterone—Fig. 5B). However, the significantly higher affinity of azoles for the binding site in comparison to either quinidine or progesterone, and ease of formation of the non-productive complexes (SEI, SESI) is evident from the respective Ki values (Table 1). In the cases where d is >1 (e.g., haloperidol), the affinity of the second inhibitor molecule is decreased in the presence of the first, consistent with negative cooperative effect, resulting in partial inhibition despite very high haloperidol concentrations.
Prediction of drug–drug interactions using multisite inhibition data Extending the [I]/Ki approach Fig. 4. Activation or inhibition: concentration-dependent differential effect of a modifier. Rate–substrate concentration curves corresponding to different values of the interaction factor c.
The most promising approach to quantitative prediction of drug–drug interactions from in vitro data is
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Table 1 Use of three-site kinetic models to describe testosterone interactions with various modifiers [4,11,33] Modifier
Vmax
Ks (lM)
aKs (lM)
d
Ki (lM)
Nifedipine Felodipine Midazolam
fl · 4–6
fl · 2.5–5
› · 40
<1 (0.04–0.014)
9.5 37 23
Quinidine Progesterone
fl·2
M
M or › · 2
1
99 110
Itraconazole Ketoconazole
fl · 6–10
M
M or › · 2
1
0.17 0.23
Haloperidol
M
›·3
M (a fl)
>1 (8.2)
37
Fig. 5. (A) Three-site kinetic model for an enzyme where substrate binds cooperatively in the presence or absence of inhibitor at a distinct site. (B) Eadie–Hofstee plots for the effect of quinidine on 6b-hydroxy testosterone formation at concentrations of 0, 5, 10, 50, and 100 lM of the modifier.
based on the ratio between the concentration of the inhibitor in vivo at the enzyme active site (I) and inhibition constant (Ki), assuming reversible single-site inhibition. The major assumptions for this in vitro–in vivo extrapolation are reversible Michaelis–Menten type of inhibition (competitive or non-competitive), applicability of the well-stirred liver model and linear pharmacokinetics for the drug. The metric for the degree of drug–drug interaction is the AUC ratio for the plasma concentration in the presence and absence of the inhibitor [24,34]. To assess the importance of cooperativity and predict changes in the in vivo plasma concentration–time profile from CYP3A4 in vitro data, an equation was derived based on the same rapid equilibrium/steady-state assumptions (Eq. (2)) as the single-site model [29]. In addition to [I]/Ki ratio, the two-site model equation also incorporates changes in the catalytic efficacy (c) and binding affinity (d) in the presence of the inhibitor. In cases when c/d = 1, two-site prediction equation will reduce to the simple relationship 1 + [I]/Ki.
AUC ratio ¼
2 ½I c½I 1þ 1þ Ki dK i
ð2Þ
I represents the in vivo inhibitor concentration (either [I]in is the input plasma concentration or [I]av is the average plasma concentration during the dosing interval [35], whereas Ki estimates are obtained applying the generic two-site model. Changes in both position and the shape of the DDI prediction curve according to the c/d ratio are shown in Fig. 6. Simulations were performed for the case of inhibition (reduced metabolite formation, c 6 0.5) with a range of different binding scenarios—from increased (d = 0.05) to decreased (d = 2) binding affinity of inhibitor in the presence of substrate. The analysis shows that the inclusion of CYP3A4 kinetic complexities (as the c/d ratio) into the prediction strategy provides explanations for certain false negative and reduces the over-estimation of true positive predictions. The relative c/d ratio is both substrate and inhibitor dependent.
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Fig. 6. Practical implications of CYP3A4 multisite kinetics in predicting drug–drug interactions from in vitro parameters. The effect of interaction factors (shown as the c/d ratio) on the relationship between AUC ratio and [I]/Ki ratio.
Substrate substitution—use of testosterone Given that testosterone is the most widely used in vitro measure of CYP3A4 activity it is important to know the extent to which the Ki values for this probe may be extrapolated to clinically used drugs. Although the nature of the three-site interactions with testosterone is complex, a drug–drug interaction prediction equation involving the interaction factors is not necessary when sigmoidicity is maintained in the presence of the inhibitor. Thus, in the case of several azole inhibitors the simple 1 + [I]/Ki relationship is appropriate. The utility of the testosterone Ki values for predicting drug–drug interaction via the AUC ratio was investigated using 16 reported CYP3A4 in vivo interactions [34]. A variety of drugs and the azole inhibitors, ketoconazole, fluconazole, and itraconazole, were involved in these studies covering a range of AUC ratios from 2
to 24. The use of [I]av and the unbound microsomal Ki was found to be the best predictor when corresponding inhibitor–substrate pairs were investigated both in vitro and in vivo [33]. In comparison to benzodiazepines, testosterone Ki values gave the best prediction for the interactions of cyclosporine and simvastatin, consistent with the principle of the substrate substitution within the same substrate subgroup, i.e., that the extrapolation from one CYP3A4 substrate to another is more realistic within the same prototypical subgroup. Interactions of benzodiazepines (midazolam, alprazolam, and triazolam) were either under-predicted (ketoconazole, fluconazole—up to 3.8-fold) or over-predicted (itraconazole— up to 5.5-fold) (Figs. 7A and B, respectively). However, the azoles represent a limited range of inhibitors and the general applicability of these findings requires further evaluation.
Fig. 7. Comparison of AUC ratios predicted and observed in vivo data for interactions of CYP3A4 substrates with (A) ketoconazole and (B) itraconazole. Predicted values were obtained by Monte Carlo simulations applying [I]av/Ki,u approach using Ki for testosterone (Table 1). In case of itraconazole, the contribution of the active metabolite (hydroxy-itraconazole) was included in the prediction as ð½Iav =K i;u ÞICZ þ ð½Iav =K i;u ÞHICZ0 where I and Ki values for the metabolite represent literature values [34]. Microsomal binding was assumed to be the same for the metabolite as for the parent. ALP, alprazolam; CYS, cyclosporine; MDZ, midazolam; NIS, nisoldipine; SV, simvastatin; TZ, triazolam; FEL, felodipine; and QUI, quinidine.
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Importance of atypical kinetics in vitro and in vivo The occurrence of atypical kinetics for CYP3A4 substrates, notably auto- and heteroactivation; partial, cooperative, and substrate inhibition; concentration-dependent effector responses (activation/inhibition); limited substrate substitution and inhibitory reciprocity, is well documented. It is also becoming realised that such atypical behaviour is not unique to CYP3A4 substrates. Cooperativity can occur in multiple steps of CYP-cycle dependent on the enzyme, substrate and the modifier involved. Protein–ligand, ligand–ligand, and protein–protein interactions can all contribute to the occurrence of these phenomena [36]. An increasing number of studies indicate this type of interactions with other human enzymes, namely CYP2C9 [37,38] and a range of UDP–glucuronosyltransferase [39–41]. The crystal structure of CYP2C9 and binding studies with S-warfarin provide an insight on the simultaneous binding of more than one molecule at the CYP2C9 active site [42], consistent with previously observed profiles with CYP3A4. In addition, recent site-directed mutagenesis studies suggest also multiple substrate binding orientations within the active site of CYP2C8 [43]. Many atypical kinetic phenomena previously first observed in microsomes have since been documented in intact hepatocytes. Several examples of auto- and heteroactivation in both fresh and cryopreserved human hepatocytes have been reported [6,44,45]. Therefore, the view that atypical kinetics is a microsomal artefact is no longer a tenable explanation. The number of in vivo demonstrations of atypical kinetics is still small [46,47]; however, considering the multi-factorial nature of in vivo drug disposition it is perhaps not surprising that atypical enzyme kinetic events are ÔhiddenÕ in many cases. However, what is clear is that the current use of in vitro studies to determine metabolic stability and inhibition potential is likely to continue. The major rationale for these activities is to extrapolate of in vitro findings to an in vivo context in the form of a mechanism-based prediction. Therefore, it is essential to fully understand the in vitro system to ensure that appropriate parameters are abstracted and subsequently integrated with other metrics to provide erudite and realistic prediction of in vivo pharmacokinetics.
References [1] M. Shou, Q. Mei, W. Ettore Jr., R. Dai, T. Baillie, T.H. Rushmore, Biochem. J. 340 (1999) 845–853. [2] Y.-F. Ueng, T. Kuwabara, Y.-J. Chun, F.P. Guengerich, Biochemistry 36 (1997) 370–381. [3] Y. Lin, P. Lu, C. Tang, Q. Mei, G. Sandig, A.D. Rodrigues, T.H. Rushmore, M. Shou, Drug. Metab. Dispos. 29 (2001) 368– 374.
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[4] A. Galetin, S.E. Clarke, J.B. Houston, Drug Metab. Dispos. 30 (2002) 1512–1522. [5] K.R. Korzekwa, N. Krishnamachary, M. Shou, A. Ogai, R.A. Parise, A.E. Rettie, F.J. Gonzalez, T.S. Tracy, Biochemistry 37 (1998) 4137–4147. [6] J.S. Ngui, W. Tang, R.A. Stearns, M. Shou, R.R. Miller, Y. Zhang, J.H. Lin, T.A. Baillie, Drug Metab. Dispos. 28 (2000) 1043–1050. [7] K.E. Kenworthy, S.E. Clarke, J. Andrews, J.B. Houston, Drug Metab. Dispos. 29 (2001) 1–8. [8] K.E. Kenworthy, J.C. Bloomer, S.E. Clarke, J.B. Houston, Br. J. Clin. Pharmacol. 48 (1999) 716–727. [9] D.M. Stresser, A.P. Blanchard, S.D. Turner, J.C.L. Erve, A.A. Dandeneau, V.P. Miller, C.L. Crespi, Drug Metab. Dispos. 28 (2000) 1440–1448. [10] M. Shou, R. Dai, D. Cui, K.R. Korzekwa, T.A. Baillie, T.H. Rushmore, J. Biol. Chem. 276 (2001) 2256–2262. [11] A. Galetin, S.E. Clarke, J.B. Houston, Drug Metab. Dispos. 31 (2003) 1108–1116. [12] P. Lu, Y. Lin, A.D. Rodrigues, T.H. Rushmore, T.A. Baillie, M. Shou, Drug Metab. Dispos. 29 (2001) 1473–1479. [13] T.L. Domanski, Y.-A. HE, K.K. Khan, F. Roussel, Q. Wang, J.R. Halpert, Biochemistry 40 (2001) 10150–10160. [14] Y.A. He, F. Roussel, J.R. Halpert, Arch. Biochem. Biophys. 409 (2003) 92–101. [15] J.K. Yano, M.R. Wester, G.A. Schoch, K.J. Griffin, C.D. Stout, E.F. Johnson, J. Biol. Chem. 275 (2004) 38091–38094. [16] P.A. Williams, J. Cosme, D. Matak Vinkovic, A. Ward, A.C. Angove, P.J. Day, C. Vonrhein, I.J. Tickle, H. Jhoti, Science 30 (2004) 683–686. [17] M.-Y. Yoon, P.A. Campbell, W.M. Atkins, Drug Metab. Rev. 36 (2004) 219–230. [18] M. Shou, Y. Lin, P. Lu, C. Tang, Q. Mei, D. Cui, W. Tang, J.S. Ngui, C.C. Lin, R. Singh, B.K. Wong, J.A. Yergey, J.H. Lin, P.G. Pearson, T.A. Baillie, A.D. Rodrigues, T.H. Rushmore, Curr. Drug Metab. 2 (2001) 17–36. [19] K. Korzekwa, in: A.D. Rodrigues (Ed.), Drug–Drug Interactions, Marcel Dekker, New York, 2002, pp. 33–54. [20] J.B. Houston, K.E. Kenworthy, A. Galetin, in: M. Fisher, J. Lee, S. Obach (Eds.), Drug Metabolizing Enzymes: Cytochrome P450 and Other Enzymes in Drug Discovery and Development, Fontis Media, Lausanne, 2003, pp. 211–254. [21] I.H. Segel, in: Enzyme Kinetics: Behaviour and Analysis of Rapid Equilibrium and Steady State Enzyme Systems, Wiley, New York, 1975. [22] J.B. Houston, K.E. Kenworthy, Drug Metab. Dispos. 28 (2000) 246–254. [23] R. Yuan, S. Madani, X.-X. Wei, K. Reynolds, S.-M. Huang, Drug Metab. Dispos. 30 (2002) 1311–1319. [24] G.T. Tucker, J.B. Houston, S.-M. Huang, Br. J. Clin. Pharmacol. 48 (2001) 716–727. [25] T.D. Bjornsson, J.T. Callaghan, H.J. Einolf, V. Fischer, et al., Drug Metab. Dispos. 31 (2003) 815–832. [26] G.R. Harlow, J.R. Halpert, Proc. Natl. Acad. Sci. 95 (1998) 6636– 6641. [27] K.C. Patki, L.L. von Moltke, D.J. Greenblatt, Drug Metab. Dispos. 31 (2003) 938–944. [28] C.A. Lee, S.H. Kadwell, T.A. Kost, C.J. Serabjit-Singh, Arch. Biochem. Biophys. 319 (1995) 157–167. [29] J.B. Houston, A. Galetin, Drug Metab. Rev. 35 (2003) 393– 415. [30] A. Galetin, C. Brown, D. Hallifax, K. Ito, J.B. Houston, Drug Metab. Dispos. 32 (2004) in press. [31] N. Torimoto, I. Ishii, M. Hata, H. Nakamura, H. Imada, N. Ariyoshi, S. Ohmori, T. Igarashi, M. Kitada, Biochemistry 42 (2003) 15068–15077. [32] J.H. Lin, Curr. Drug Metab. 1 (2001) 305–331.
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[33] A. Galetin, J.B. Houston, Drug Metab. Rev. 35 (Suppl. 2) (2003) 103. [34] K. Ito, H.S. Brown, J.B. Houston, Br. J. Clin. Pharmacol. 57 (2004) 473–486. [35] S. Kanamitsu, K. Ito, Y. Sugiyama, Pharm. Res. 17 (2000) 336– 343. [36] W.M. Atkins, Drug Discov. Today 9 (2004) 478–484. [37] J.M. Hutzler, M.C. Wienkers, J.L. Wahlstrom, T.J. Carlson, T.S. Tracy, Arch. Biochem. Biophys. 410 (2003) 16–24. [38] A.-C. Egnell, C. Eriksson, N. Albertson, J.B. Houston, S. Boyer, J. Pharmacol. Exp. Ther. 307 (2003) 878–887. [39] J.A. Williams, B.J. Ring, V.E. Cantrell, K. Campanelle, D.R. Jones, S.D. Hall, S.A. Wrighton, Drug Metab. Dispos. 30 (2001) 1266–1273. [40] A.N. Stone, P.I. Mackenzie, A. Galetin, J.B. Houston, J.O. Miners, Drug Metab. Dispos. 31 (2003) 1086–1089.
[41] V. Uchaipichat, P.I. Mackenzie, X.-H. Guo, D. Gardner-Stephen, A. Galetin, J.B. Houston, J.O. Miners, Drug Metab. Dispos. 32 (2004) 413–423. [42] P.A. Williams, J. Cosme, A. Ward, H.C. Angove, D. Matak Vinkovic, H. Jhoti, Nature 424 (2003) 464–468. [43] O. Kerdpin, D.J. Elliot, S.L. Boye, D.J. Birkett, K. Yoovathaworn, J.O. Miners, Biochemistry 43 (2004) 7834–7842. [44] J. Ma¨enpa¨a¨, S.D. Hall, B.J. Ring, C.C. Strom, S.A. Wrighton, Pharmacogenetics 8 (1998) 137–155. [45] H.C. Rawden, A. Tindall, D. Hallifax, J.B. Houston, Drug Metab. Rev. 33 (Suppl 1) (2001) 420. [46] W. Tang, R.A. Stearns, G.Y. Kwei, S.A. Iliff, R.R. Miller, M.A. Egan, N.X. Yu, D.C. Dean, S. Kumar, M. Shou, J.H. Lin, T.A. Baillie, J. Pharmacol. Exp. Ther. 291 (1999) 1068–1074. [47] A.-C. Egnell, J.B. Houston, S. Boyer, J. Pharmacol. Exp. Ther. 305 (2003) 1251–1262.
Modelling atypical CYP3A4 kinetics: principles and pragmatism J. Brian Houston*, Aleksandra Galetin* Centre for Applied Pharmacokinetic Research, School of Pharmacy and Pharmaceutical Sciences, University of Manchester, Oxford Road, Manchester, Ml3 9PL, United Kingdom Received 12 August 2004 Available online 7 October 2004
Abstract The Michaelis–Menten model, and the existence of a single active site for the interaction of substrate with drug metabolizing enzyme, adequately describes a substantial number of in vitro metabolite kinetic data sets for both clearance and inhibition determination. However, in an increasing number of cases (involving most notably, but not exclusively, CYP3A4), atypical kinetic features are observed, e.g., auto- and heteroactivation; partial, cooperative, and substrate inhibition; concentration-dependent effector responses (activation/inhibition); limited substrate substitution and inhibitory reciprocity necessitating sub-group classification. The phenomena listed above cannot be readily interpreted using single active site models and the literature indicates that three types of approaches have been adopted. First the Ônaı¨veÕ approach of using the Michaelis–Menten model regardless of the kinetic behaviour, second the ÔempiricalÕ approach (e.g., employing the Hill or uncompetitive inhibition equations to model homotropic phenomena of sigmoidicity and substrate inhibition, respectively) and finally, the ÔmechanisticÕ approach. The later includes multisite kinetic models derived using the same rapid equilibrium/steady-state assumptions as the single-site model. These models indicate that 2 or 3 binding sites exist for a given CYP3A4 substrate and/or effector. Multisite kinetic models share common features, depending on the substrate kinetics and the nature of the effector response observed in vitro, which allow a generic model to be proposed. Thus although more complex than the other two approaches, they show more utility and can be comprehensively applied in relatively simple versions that can be readily generated from generic model. Multisite kinetic features, observed in isolated hepatocytes as well as in microsomes from hepatic tissue and heterologous expression systems, may be evident in substrate depletion–time profiles as well as in metabolite formation rates. Failure to adequately account for multisite kinetic phenomena will compromise any attempts to predict human drug clearance and drug–drug interaction potential from in vitro data. 2004 Elsevier Inc. All rights reserved. Keywords: CYP3A4; Atypical kinetics; Multisite kinetics
Background and scope For many years the Michaelis–Menten model, and the existence of a single active site for the interaction of substrate with drug metabolising enzyme, has been used to describe in vitro kinetic data for both clearance and inhibition determination. However, it has become increasingly common that atypical (non-Michaelis– Menten) kinetic features are observed. The phenomena *
Corresponding authors. Fax: +44 161 275 8349 (J.B. Houston). E-mail addresses: [email protected] (J.B. Houston), [email protected] (A. Galetin). 0003-9861/$ - see front matter 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.abb.2004.09.010
of auto- and heteroactivation; partial, cooperative, and substrate inhibition; concentration-dependent effector responses (activation/inhibition); limited substrate substitution; and inhibitory reciprocity, cannot be readily interpreted using single active site models. The most notable, but not the sole, drug metabolising enzyme associated with atypical kinetics is CYP3A4. The finding that a number of CYP3A4 substrates do not conform to the expected competitive type of interaction indicates the existence of, and interaction between, several binding sites on the enzyme. The large CYP3A4 active site may allow the simultaneous presence of multiple molecules (at least two) and the exact binding
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conformations appear to depend on the substrates involved, their relative concentration, and affinity for the enzyme. Various atypical effects can result, which may be either positive or negative in nature, and can be rationalised by multisite occupation by more than one molecule of the same substrate (homotropy), or interactions involving two or more different substrates (heterotropy). Homotropic effects represent alterations in either binding affinity or rate of product formation after the binding of a second molecule of the same substrate to the enzyme active site. As a net effect, CYP activity is either increased in a substrate concentration-dependent manner (sigmoidal kinetic profiles defined as autoactivation or positive homotropy) [1,2] or decreased (convex kinetic profiles defined as substrate inhibition or negative homotropy) [3,4]. The complexity of effects is increased for heterotropic interactions involving two different substrates [5–7]. In this case, in contrast to the expected simple competitive inhibition, a modifier can cause either activation or inhibition affecting binding affinity of a substrate or the rate of its metabolism by a particular CYP, or even both activation and inhibition. This scenario further increases in complexity when there are substrate-dependent [8,9] and/or pathway-differential effects [10,11]. Thus, heterotropic characteristics result in a limited ability to extrapolate in vitro data from one substrate to another and a lack of inhibitory reciprocity. Lack of mutual competitive inhibition, as observed in aflatoxin Bl-a-naphthoflavone [2], testosteronediazepam [7], and testosterone-7-benzyloxyquinoline interactions [12], favours the existence of a distinct effector-binding site. Site-directed mutagenesis studies have indicated that in case of CYP3A4 substrate and effector-binding sites are separate, but closely linked and the residues involved in the binding of either substrate and/or effector depend on the molecules present [13,14]. ÔMetabolicÕ and ÔregulatoryÕ sites may differ for the same compound as proposed earlier for the CYP3A4 modifiers a-naphthoflavone [10] and quinidine [4]. Mechanistic analysis of a range of variable and substrate-dependent effects observed for CYP3A4 prototypical substrates, supports the hypothesis of distinct and preferential binding domains for each substrate subgroup with one mutual site for all subclasses of CYP3A4 substrates. The net effect of the interaction depends on the particular substrate(s) present at the active site, the possible overlap of their binding domains and the relative concentrations of both [11]. A recent report on the crystal structure of this enzyme [15] provides additional support for cooperativity due to the large size of the active site cavity identified proximal to the catalytic heme iron, consistent with the mechanistic models postulated. However, in another crystal structure study, Williams et al. [16] reported progesterone binding
at a peripheral binding domain rather than at the active site resulting in an insignificant conformational change in the CYP3A4 protein. Whether this later observation is an artefact of the crystallisation process or this site has an actual functional recognition role requires further exploration. A wide range of other biophysical methods also support the existence of multiple binding sites for CYP3A4, as well as other CYPs [17]. In this mini-review equal emphasis will be placed on practicalities and principles of modelling atypical CYP3A4 kinetics. Although several comprehensive reviews (e.g. [18–20]) provide a rigorous base for analysis of complex kinetics, there has been little emphasis on developing pragmatic approaches that allow routine analysis of the ÔatypicalÕ interaction of drugs with CYP3A4.
Approaches in modelling atypical kinetics The literature indicates that atypical kinetic in vitro data are generally analysed by three approaches— Ônaı¨veÕ, empirical, and mechanistic methods. Investigators using the first approach apply the Michaelis–Menten model regardless of the kinetic behaviour observed, ignoring any evidence of sigmoidicity or convexity in the rate-substrate concentration profile. Use of empirical models (e.g., Hill or uncompetitive inhibition equations for the analysis of the two homotropic types described above) represents a useful tool for the preliminary analysis of data. While convenient to perform, this approach provides no mechanistic information of the interactions between homotropic or heterotropic ligands (substrate and/or effector). One mechanistic approach is the use of multisite kinetic models, derived from the same rapid equilibrium/ steady-state principles as the single-site Michaelis–Menten model and allowing the simultaneous fit of multiple sets of data to a single equation [21]. Fig. 1A shows a kinetic model for CYP3A4 with two substrate-binding sites, the second substrate molecule binds cooperatively. Autoactivation (positive homotropy) may result in either increased binding affinity for a second substrate molecule (dissociation constant Ks changes by the factor a < 1), or changes in the effective catalytic rate constant (Kp) by the factor b from SES complex (b > 1). In contrast negative cooperativity is defined by changes in a or b in the opposite direction (a > 1, resulting in biphasic kinetic profile, b < 1 resulting in substrate inhibition). Biphasic-type of curves is less common for CYP3A4 than substrate inhibition [22]. The proposed model does not distinguish between the simultaneous binding of multiple molecules within a single active site and the binding of two molecules to two distinct binding sites. The interaction factors defined in the model shown in Fig. 1A are consistent with the two-site model described by Korzekwa et al. [5]; the difference being that the
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Fig. 1. Multisite kinetic equilibria models and their corresponding equations. (A) A kinetic model for an enzyme with two-substrate binding sites, the second substrate (S) molecule binds cooperatively. (B) A generic two-site model for CYP3A4 interactions. Interaction factors associated with the changes in binding affinity (Ks or Ki): a—homotropic cooperativity, d—heterotropic cooperativity, and aM—cooperative binding of modifier; interaction factors associated with the changes in catalytic rate constant (Kp): b (SES) and c (MES).
changes in the binding affinity and the catalytic efficiency for the single- (SE/ES) and two-substrate bound form (SES) are characterised by two Km and two Vmax values, but the ratio of these two Km or Vmax values corresponds to the a and b interaction factors, respectively. Additionally, the model of Shou et al. [1] has two binding sites within the CYP3A4 active site differing in steric hindrance, hydrophobic interaction, and electron characteristics; i.e., an orientation difference in binding of S to E (SE „ ES). However, the fit obtained from this kinetic model for diazepam, temazepam, and nordiazepam metabolism in human liver microsomes was in good agreement with the simpler equations [5,22], as they both describe the reduced binding affinity and lower catalytic capacity of ES complex compared to ESS (Km1 > Km2, Vmax1 < Vmax2). For heterotropic effects, the simultaneous presence of two different substrates at the active site and an increased number of enzyme species results in models that are relatively complex. Fig. 1B shows the generic version of the two-site model and the corresponding interaction factors associated with changes in either binding affinity (a, d) or rate of product formation (b, c). This model is versatile in that it can be applied for activation or inhibition and can be reduced or expanded in complexity depending upon
the ÔvisibilityÕ of certain features in the data. Other reductions in the model requirements regarding the inclusion of interaction factors will be illustrated later. A limitation of this approach lies in the difficulty in assigning a unique model to a particular data set. The final selection of a particular multisite model will be based on an assessment of a simultaneous fit to multiple data sets (at least 60 data points including replicates) involving various statistical, simulation, and modelling techniques. However, an element of subjectivity is always present and supporting, independent experimentation is particularly valuable. Overall although more complex, these two- (or three-site) models can be comprehensively applied in the prediction of either clearance or potential in vivo drug interactions from ÔatypicalÕ in vitro data, as summarised in the following sections.
Modelling multisite kinetics Impact of ‘atypical’ kinetics on the prediction of clearance A recent FDA report [23] indicates that testosterone is the most commonly used in vitro CYP3A4 probe. It was employed in approximately 50% of reported studies,
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contrasting with the use of midazolam (15–20%), nifedipine, felodipine, and erythromycin (the later three less than 10% each) for in vitro estimation of CYP3A4 activity. However, the differential effects observed for various CYP3A4 substrates [8] have resulted in the recommendation of employing two or more CYP3A4 substrates [24,25]. Midazolam, testosterone, and nifedipine are most commonly used as representatives of the different CYP3A4 subgroups, particularly as they show distinctive kinetic properties namely, hyperbolic, sigmoidal, and substrate inhibition, respectively. Multisite analysis of the interaction profiles observed between these three CYP3A4 prototypes indicates the existence of one preferential binding domain for each of the CYP3A4 substrate subgroups. However, the inter-substrate group interactions strongly imply the existence of a mutual binding domain common to each of the three CYP3A4 substrate subclasses [11]. Testosterone is the prototypic substrate for positive cooperative behaviour as autoactivation have been demonstrated in various CYP3A4-expression systems [2,7,26], CYP3A5 [27], and human liver microsomes [28]. Although sigmodicity may not be obvious on first inspection of the data (see Fig. 2A), an Eadie–Hofstee plot clearly shows curvature (Fig. 2B). For drugs dis-
playing positive homotropic behaviour, clearance is dependent on the substrate concentration (Fig. 2C) and an underestimation of clearance will be obtained if a hyperbolic curve is forced through the data to obtain the parameters Vmax and Km to calculate CLint. The CLmax, the maximum clearance when the enzyme is fully activated, represents the alternative to CLint for scaling of in vitro data and is now commonly used in the scaling strategy [29]. This parameter can be calculated by either Hill equation estimates [22] or using two-site model as shown in Eq. (1). pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi V max ð1=aÞ 1 CLmax ¼ ð1Þ 2ð1 aÞ Ks a and Ks are calculated from untransformed data using the two-site model. The CLmax estimate derived from the two-site kinetic model [30], assumes the equivalence of two sites and therefore b is 2 (and Vmax is equivalent to 2Kp[E]t, where [E]t is the total enzyme concentration). Simulations using the two-site model [20] indicate that significant sigmoidicity (defined by low a values) results in a pronounced characteristic shape of the clearance plots as seen in Fig. 2D; in cases where a > 0.5 the clearance plot tends towards Michaelis–Menten kinetic behaviour.
Fig. 2. Positive cooperativity as exemplified by testosterone 6b-hydroxylation—(A) rate–substrate concentration profile, (B) Eadie–Hofstee plot, and (C) clearance plot. The effect of a (extent of sigmoidicity) on the clearance plots and maximum clearance is shown in (D).
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The value of a provides a clearer indication of the extent of cooperativity than the Hill number. The use of CLmax allows autoactivation to be incorporated into in vitro–in vivo scaling strategies. The consequence of CYP3A homotropy is a dependence of clearance on substrate concentrations well below the Ks value in the region corresponding to first order kinetics in the Michaelis–Menten model (see Fig. 2C). This has implications on clearance estimates from rapid screening of metabolic stability of new drug candidates. These are routinely carried out by monitoring parent drug depletion at one substrate concentration, often in the l lM region, based on the rationale that this concentration should be well below the (unknown) Km value. If consideration is not given to the phenomenon of autoactivation then clearance is likely to be underestimated. For example, diazepam metabolite kinetics shows marked sigmoidicity and its microsomal half-life at l lM is five times longer than at 100 lM reflecting the non-activated and fully activated clearance (see Fig. 3). For substrate inhibition, a substantial underestimation of Vmax will occur by merely ignoring the high concentration data points and forcing a hyperbolic curve through the remaining lower substrate concentration data points and the Km value will be poorly estimated. How precisely the clearance estimate will be altered by model misspecification will vary from case-to-case and will be dependent on the number and quality of the data points. Nifedipine is a prototypical substrate reported to show negative homotropy, defined by a b term of 0.36 [20]. The importance of heterotropic effects on clearance determination has yet to be fully assessed but as steroids and dietary flavones are the most documented activators this may contribute to interindividual differences commonly seen between liver donor microsomes. Testosterone has also been reported as heteroactivator of several CYP3A4 substrates (e.g., diazepam [7], carbamazepine [31]), causing an increased metabolism rate and alteration from sigmoidal to hyperbolic kinetic profile. Fig. 3
Fig. 3. Diazepam depletion–time profiles and metabolic stability in human liver microsomes: effect of substrate concentration and testosterone—2.5 lM (d) and 100 lM (j) diazepam, and 100 lM diazepam in the presence of 100 lM testosterone (m).
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illustrates the impact of testosterone on diazepam microsomal half-life. Impact of ‘atypical’ kinetic on the prediction of drug–drug interactions The potential of substrates and modifiers of CYP3A4 to show homo- and heterotropic cooperative effects confounds any straightforward in vitro–in vivo correlation. The incorporation of these phenomena in the assessment of potential in vivo drug–drug interactions from in vitro data is rare [24,25,32]. Whether such phenomena are apparent in vivo remains questionable, however the appropriate in vitro analysis is essential to ensure accurate quantitative estimates for prediction [29]. To explore the range of possible consequences of heterotropic interactions use of multiple substrates in vitro at various substrate concentrations is recommended [8]. When modelling inhibitions at multiple sites three possible changes need to be considered [11]: (a) alterations in binding affinity (homo- and heterotropic effects on Ks and Ki), (b) alterations in rate of metabolite formation (effect on Kp), and (c) the lack of reciprocity between competing binders. A systematic approach to explain various kinetic phenomena observed for CYP3A4 interactions (namely, auto- and heteroactivation; partial, cooperative, and substrate inhibition; concentration-dependent effector responses (activation/inhibition); limited substrate substitution and inhibitory reciprocity; pathway differential effects) and their link with particular multisite interaction factors has been provided in our previous publications [11,29]. The application of a generic two-site model [4] has been proposed as an approach to accommodate the range of ÔinhibitionÕ effects observed for CYP3A4. The interaction factors associated with changes in either binding affinity (a, d) or rate of product formation (b, c) may be included or excluded in the modelling depending on the complexity of substrate kinetics (hyperbolic, substrate inhibition or sigmoidal) and the changes observed in the presence of the modifier. This mechanistic approach allows the simultaneous fit of all the data covering the full range of modifier concentrations, in contrast to empirical methods (e.g., Hill plots) where individual fits are obtained for each specific concentration of modifier. Cooperative binding of the second molecule of the same modifier (homotropic cooperativity) is defined by the interaction factor aM (positive <1, negative cooperativity >1, as discussed). The effects of felodipine on both midazolam and testosterone provide good examples of positive cooperativity [11]. In the first case, there is a progressive increase in the 50% inhibitory concentration
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as substrate concentration increases with a marked increases in the steepness of the concentration–effect curve. In the later case, the 50% inhibitory concentration decreases with substrate concentration. In contrast, binding affinity alterations due to heterotropic effects and formation of a complex with two different substrate molecules (MES) are described by the interaction factor d. The net effect of the increased affinity (d < 1) can vary from either heteroactivation or inhibition depending on the corresponding changes in the catalytic rate in the presence of a modifier (cKp) as illustrated previously [20]. The opposite scenario (d > 1) characterises partial inhibition where inhibition is achieved at only one of the two catalytically active sites, as the affinity of a second inhibitor molecule for a binding site is decreased compared to the first (e.g., l 0 -OH midazolam inhibition by testosterone [11]). The interaction factors b and c are associated with alterations in the Kp, either as a result of binding of a second substrate molecule (SES, e.g., substrate inhibition, bKp < Kp) or a modifier molecule (MES, heteroactivation c > 1, inhibition c < 1). In many cases a modifier can act in a concentration-dependent manner, causing activation at low substrate concentrations and inhibition at higher concentrations, as exemplified by the effect of quinidine on midazolam [4]. This behaviour can be rationalised by a relatively low value of the interaction factor c (<2) and at low S concentrations the rank order of metabolite formation is SEM > ES/SES. However, at higher concentrations the competition of the modifier with the substrate at both sites causes inhibition. However, with large values of c (>2), the activation is more pronounced and occurs over a wider range of substrate concentrations, as illustrated in Fig. 4. The application of simple models for interactions involving substrates with positive (testosterone, diazepam) or negative (terfenadine, nifedipine) homotropic kinetic properties is particularly problematic and the misuse of a one-site model may lead to inaccurate esti-
mation of kinetic parameters and failure to identify important drug–drug interactions.
Modelling testosterone interactions: three-site model Two distinct types of heterotropic interactions have been reported for testosterone where positive cooperativity either remains in the presence of the modifier or is eliminated. The loss of sigmoidicity at high concentrations of modifier (linear Eadie–Hofstee plots as normally seen for hyperbolic kinetics) occurs in the presence of midazolam, nifedipine, and felodipine. An analogous situation is observed for substrates showing substrate inhibition kinetic properties. When c is comparable to b, the rate of metabolite formation from IES complex (cKp) is analogous to SES (bKp) and the substrate inhibition trend remains. However, at high substrate and inhibitor concentrations a non-productive inhibitor complex dominates, changing the profile to a hyperbolic type as observed in the quinidine effect on nifedipine [20]. The opposite scenario where the sigmoidal properties of testosterone are unaffected by increasing inhibitor concentration, suggest that the inhibitor acts at a distinct effector site. This complex type of interaction requires a three-site model and has been observed for the effects of diazepam [7], quinidine, haloperidol [4], and azoles [33] on testosterone. CYP3A4 inhibition, as characterised by testosterone, results in changes in either binding affinity or Vmax or a combined effect, as summarised in Table 1. Each type of interaction can be defined by a particular multisite kinetic model with the appropriate interaction factors. The threesite model (Fig. 5A) applied for the testosterone interaction with azoles is the same as that used for the effect of progesterone or quinidine. All modifiers cause a change in the rate of product formation rather than the binding affinity (no alteration in the cooperative binding of testosterone—Fig. 5B). However, the significantly higher affinity of azoles for the binding site in comparison to either quinidine or progesterone, and ease of formation of the non-productive complexes (SEI, SESI) is evident from the respective Ki values (Table 1). In the cases where d is >1 (e.g., haloperidol), the affinity of the second inhibitor molecule is decreased in the presence of the first, consistent with negative cooperative effect, resulting in partial inhibition despite very high haloperidol concentrations.
Prediction of drug–drug interactions using multisite inhibition data Extending the [I]/Ki approach Fig. 4. Activation or inhibition: concentration-dependent differential effect of a modifier. Rate–substrate concentration curves corresponding to different values of the interaction factor c.
The most promising approach to quantitative prediction of drug–drug interactions from in vitro data is
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357
Table 1 Use of three-site kinetic models to describe testosterone interactions with various modifiers [4,11,33] Modifier
Vmax
Ks (lM)
aKs (lM)
d
Ki (lM)
Nifedipine Felodipine Midazolam
fl · 4–6
fl · 2.5–5
› · 40
<1 (0.04–0.014)
9.5 37 23
Quinidine Progesterone
fl·2
M
M or › · 2
1
99 110
Itraconazole Ketoconazole
fl · 6–10
M
M or › · 2
1
0.17 0.23
Haloperidol
M
›·3
M (a fl)
>1 (8.2)
37
Fig. 5. (A) Three-site kinetic model for an enzyme where substrate binds cooperatively in the presence or absence of inhibitor at a distinct site. (B) Eadie–Hofstee plots for the effect of quinidine on 6b-hydroxy testosterone formation at concentrations of 0, 5, 10, 50, and 100 lM of the modifier.
based on the ratio between the concentration of the inhibitor in vivo at the enzyme active site (I) and inhibition constant (Ki), assuming reversible single-site inhibition. The major assumptions for this in vitro–in vivo extrapolation are reversible Michaelis–Menten type of inhibition (competitive or non-competitive), applicability of the well-stirred liver model and linear pharmacokinetics for the drug. The metric for the degree of drug–drug interaction is the AUC ratio for the plasma concentration in the presence and absence of the inhibitor [24,34]. To assess the importance of cooperativity and predict changes in the in vivo plasma concentration–time profile from CYP3A4 in vitro data, an equation was derived based on the same rapid equilibrium/steady-state assumptions (Eq. (2)) as the single-site model [29]. In addition to [I]/Ki ratio, the two-site model equation also incorporates changes in the catalytic efficacy (c) and binding affinity (d) in the presence of the inhibitor. In cases when c/d = 1, two-site prediction equation will reduce to the simple relationship 1 + [I]/Ki.
AUC ratio ¼
2 ½I c½I 1þ 1þ Ki dK i
ð2Þ
I represents the in vivo inhibitor concentration (either [I]in is the input plasma concentration or [I]av is the average plasma concentration during the dosing interval [35], whereas Ki estimates are obtained applying the generic two-site model. Changes in both position and the shape of the DDI prediction curve according to the c/d ratio are shown in Fig. 6. Simulations were performed for the case of inhibition (reduced metabolite formation, c 6 0.5) with a range of different binding scenarios—from increased (d = 0.05) to decreased (d = 2) binding affinity of inhibitor in the presence of substrate. The analysis shows that the inclusion of CYP3A4 kinetic complexities (as the c/d ratio) into the prediction strategy provides explanations for certain false negative and reduces the over-estimation of true positive predictions. The relative c/d ratio is both substrate and inhibitor dependent.
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Fig. 6. Practical implications of CYP3A4 multisite kinetics in predicting drug–drug interactions from in vitro parameters. The effect of interaction factors (shown as the c/d ratio) on the relationship between AUC ratio and [I]/Ki ratio.
Substrate substitution—use of testosterone Given that testosterone is the most widely used in vitro measure of CYP3A4 activity it is important to know the extent to which the Ki values for this probe may be extrapolated to clinically used drugs. Although the nature of the three-site interactions with testosterone is complex, a drug–drug interaction prediction equation involving the interaction factors is not necessary when sigmoidicity is maintained in the presence of the inhibitor. Thus, in the case of several azole inhibitors the simple 1 + [I]/Ki relationship is appropriate. The utility of the testosterone Ki values for predicting drug–drug interaction via the AUC ratio was investigated using 16 reported CYP3A4 in vivo interactions [34]. A variety of drugs and the azole inhibitors, ketoconazole, fluconazole, and itraconazole, were involved in these studies covering a range of AUC ratios from 2
to 24. The use of [I]av and the unbound microsomal Ki was found to be the best predictor when corresponding inhibitor–substrate pairs were investigated both in vitro and in vivo [33]. In comparison to benzodiazepines, testosterone Ki values gave the best prediction for the interactions of cyclosporine and simvastatin, consistent with the principle of the substrate substitution within the same substrate subgroup, i.e., that the extrapolation from one CYP3A4 substrate to another is more realistic within the same prototypical subgroup. Interactions of benzodiazepines (midazolam, alprazolam, and triazolam) were either under-predicted (ketoconazole, fluconazole—up to 3.8-fold) or over-predicted (itraconazole— up to 5.5-fold) (Figs. 7A and B, respectively). However, the azoles represent a limited range of inhibitors and the general applicability of these findings requires further evaluation.
Fig. 7. Comparison of AUC ratios predicted and observed in vivo data for interactions of CYP3A4 substrates with (A) ketoconazole and (B) itraconazole. Predicted values were obtained by Monte Carlo simulations applying [I]av/Ki,u approach using Ki for testosterone (Table 1). In case of itraconazole, the contribution of the active metabolite (hydroxy-itraconazole) was included in the prediction as ð½Iav =K i;u ÞICZ þ ð½Iav =K i;u ÞHICZ0 where I and Ki values for the metabolite represent literature values [34]. Microsomal binding was assumed to be the same for the metabolite as for the parent. ALP, alprazolam; CYS, cyclosporine; MDZ, midazolam; NIS, nisoldipine; SV, simvastatin; TZ, triazolam; FEL, felodipine; and QUI, quinidine.
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Importance of atypical kinetics in vitro and in vivo The occurrence of atypical kinetics for CYP3A4 substrates, notably auto- and heteroactivation; partial, cooperative, and substrate inhibition; concentration-dependent effector responses (activation/inhibition); limited substrate substitution and inhibitory reciprocity, is well documented. It is also becoming realised that such atypical behaviour is not unique to CYP3A4 substrates. Cooperativity can occur in multiple steps of CYP-cycle dependent on the enzyme, substrate and the modifier involved. Protein–ligand, ligand–ligand, and protein–protein interactions can all contribute to the occurrence of these phenomena [36]. An increasing number of studies indicate this type of interactions with other human enzymes, namely CYP2C9 [37,38] and a range of UDP–glucuronosyltransferase [39–41]. The crystal structure of CYP2C9 and binding studies with S-warfarin provide an insight on the simultaneous binding of more than one molecule at the CYP2C9 active site [42], consistent with previously observed profiles with CYP3A4. In addition, recent site-directed mutagenesis studies suggest also multiple substrate binding orientations within the active site of CYP2C8 [43]. Many atypical kinetic phenomena previously first observed in microsomes have since been documented in intact hepatocytes. Several examples of auto- and heteroactivation in both fresh and cryopreserved human hepatocytes have been reported [6,44,45]. Therefore, the view that atypical kinetics is a microsomal artefact is no longer a tenable explanation. The number of in vivo demonstrations of atypical kinetics is still small [46,47]; however, considering the multi-factorial nature of in vivo drug disposition it is perhaps not surprising that atypical enzyme kinetic events are ÔhiddenÕ in many cases. However, what is clear is that the current use of in vitro studies to determine metabolic stability and inhibition potential is likely to continue. The major rationale for these activities is to extrapolate of in vitro findings to an in vivo context in the form of a mechanism-based prediction. Therefore, it is essential to fully understand the in vitro system to ensure that appropriate parameters are abstracted and subsequently integrated with other metrics to provide erudite and realistic prediction of in vivo pharmacokinetics.
References [1] M. Shou, Q. Mei, W. Ettore Jr., R. Dai, T. Baillie, T.H. Rushmore, Biochem. J. 340 (1999) 845–853. [2] Y.-F. Ueng, T. Kuwabara, Y.-J. Chun, F.P. Guengerich, Biochemistry 36 (1997) 370–381. [3] Y. Lin, P. Lu, C. Tang, Q. Mei, G. Sandig, A.D. Rodrigues, T.H. Rushmore, M. Shou, Drug. Metab. Dispos. 29 (2001) 368– 374.
359
[4] A. Galetin, S.E. Clarke, J.B. Houston, Drug Metab. Dispos. 30 (2002) 1512–1522. [5] K.R. Korzekwa, N. Krishnamachary, M. Shou, A. Ogai, R.A. Parise, A.E. Rettie, F.J. Gonzalez, T.S. Tracy, Biochemistry 37 (1998) 4137–4147. [6] J.S. Ngui, W. Tang, R.A. Stearns, M. Shou, R.R. Miller, Y. Zhang, J.H. Lin, T.A. Baillie, Drug Metab. Dispos. 28 (2000) 1043–1050. [7] K.E. Kenworthy, S.E. Clarke, J. Andrews, J.B. Houston, Drug Metab. Dispos. 29 (2001) 1–8. [8] K.E. Kenworthy, J.C. Bloomer, S.E. Clarke, J.B. Houston, Br. J. Clin. Pharmacol. 48 (1999) 716–727. [9] D.M. Stresser, A.P. Blanchard, S.D. Turner, J.C.L. Erve, A.A. Dandeneau, V.P. Miller, C.L. Crespi, Drug Metab. Dispos. 28 (2000) 1440–1448. [10] M. Shou, R. Dai, D. Cui, K.R. Korzekwa, T.A. Baillie, T.H. Rushmore, J. Biol. Chem. 276 (2001) 2256–2262. [11] A. Galetin, S.E. Clarke, J.B. Houston, Drug Metab. Dispos. 31 (2003) 1108–1116. [12] P. Lu, Y. Lin, A.D. Rodrigues, T.H. Rushmore, T.A. Baillie, M. Shou, Drug Metab. Dispos. 29 (2001) 1473–1479. [13] T.L. Domanski, Y.-A. HE, K.K. Khan, F. Roussel, Q. Wang, J.R. Halpert, Biochemistry 40 (2001) 10150–10160. [14] Y.A. He, F. Roussel, J.R. Halpert, Arch. Biochem. Biophys. 409 (2003) 92–101. [15] J.K. Yano, M.R. Wester, G.A. Schoch, K.J. Griffin, C.D. Stout, E.F. Johnson, J. Biol. Chem. 275 (2004) 38091–38094. [16] P.A. Williams, J. Cosme, D. Matak Vinkovic, A. Ward, A.C. Angove, P.J. Day, C. Vonrhein, I.J. Tickle, H. Jhoti, Science 30 (2004) 683–686. [17] M.-Y. Yoon, P.A. Campbell, W.M. Atkins, Drug Metab. Rev. 36 (2004) 219–230. [18] M. Shou, Y. Lin, P. Lu, C. Tang, Q. Mei, D. Cui, W. Tang, J.S. Ngui, C.C. Lin, R. Singh, B.K. Wong, J.A. Yergey, J.H. Lin, P.G. Pearson, T.A. Baillie, A.D. Rodrigues, T.H. Rushmore, Curr. Drug Metab. 2 (2001) 17–36. [19] K. Korzekwa, in: A.D. Rodrigues (Ed.), Drug–Drug Interactions, Marcel Dekker, New York, 2002, pp. 33–54. [20] J.B. Houston, K.E. Kenworthy, A. Galetin, in: M. Fisher, J. Lee, S. Obach (Eds.), Drug Metabolizing Enzymes: Cytochrome P450 and Other Enzymes in Drug Discovery and Development, Fontis Media, Lausanne, 2003, pp. 211–254. [21] I.H. Segel, in: Enzyme Kinetics: Behaviour and Analysis of Rapid Equilibrium and Steady State Enzyme Systems, Wiley, New York, 1975. [22] J.B. Houston, K.E. Kenworthy, Drug Metab. Dispos. 28 (2000) 246–254. [23] R. Yuan, S. Madani, X.-X. Wei, K. Reynolds, S.-M. Huang, Drug Metab. Dispos. 30 (2002) 1311–1319. [24] G.T. Tucker, J.B. Houston, S.-M. Huang, Br. J. Clin. Pharmacol. 48 (2001) 716–727. [25] T.D. Bjornsson, J.T. Callaghan, H.J. Einolf, V. Fischer, et al., Drug Metab. Dispos. 31 (2003) 815–832. [26] G.R. Harlow, J.R. Halpert, Proc. Natl. Acad. Sci. 95 (1998) 6636– 6641. [27] K.C. Patki, L.L. von Moltke, D.J. Greenblatt, Drug Metab. Dispos. 31 (2003) 938–944. [28] C.A. Lee, S.H. Kadwell, T.A. Kost, C.J. Serabjit-Singh, Arch. Biochem. Biophys. 319 (1995) 157–167. [29] J.B. Houston, A. Galetin, Drug Metab. Rev. 35 (2003) 393– 415. [30] A. Galetin, C. Brown, D. Hallifax, K. Ito, J.B. Houston, Drug Metab. Dispos. 32 (2004) in press. [31] N. Torimoto, I. Ishii, M. Hata, H. Nakamura, H. Imada, N. Ariyoshi, S. Ohmori, T. Igarashi, M. Kitada, Biochemistry 42 (2003) 15068–15077. [32] J.H. Lin, Curr. Drug Metab. 1 (2001) 305–331.
360
J.B. Houston, A. Galetin / Archives of Biochemistry and Biophysics 433 (2005) 351–360
[33] A. Galetin, J.B. Houston, Drug Metab. Rev. 35 (Suppl. 2) (2003) 103. [34] K. Ito, H.S. Brown, J.B. Houston, Br. J. Clin. Pharmacol. 57 (2004) 473–486. [35] S. Kanamitsu, K. Ito, Y. Sugiyama, Pharm. Res. 17 (2000) 336– 343. [36] W.M. Atkins, Drug Discov. Today 9 (2004) 478–484. [37] J.M. Hutzler, M.C. Wienkers, J.L. Wahlstrom, T.J. Carlson, T.S. Tracy, Arch. Biochem. Biophys. 410 (2003) 16–24. [38] A.-C. Egnell, C. Eriksson, N. Albertson, J.B. Houston, S. Boyer, J. Pharmacol. Exp. Ther. 307 (2003) 878–887. [39] J.A. Williams, B.J. Ring, V.E. Cantrell, K. Campanelle, D.R. Jones, S.D. Hall, S.A. Wrighton, Drug Metab. Dispos. 30 (2001) 1266–1273. [40] A.N. Stone, P.I. Mackenzie, A. Galetin, J.B. Houston, J.O. Miners, Drug Metab. Dispos. 31 (2003) 1086–1089.
[41] V. Uchaipichat, P.I. Mackenzie, X.-H. Guo, D. Gardner-Stephen, A. Galetin, J.B. Houston, J.O. Miners, Drug Metab. Dispos. 32 (2004) 413–423. [42] P.A. Williams, J. Cosme, A. Ward, H.C. Angove, D. Matak Vinkovic, H. Jhoti, Nature 424 (2003) 464–468. [43] O. Kerdpin, D.J. Elliot, S.L. Boye, D.J. Birkett, K. Yoovathaworn, J.O. Miners, Biochemistry 43 (2004) 7834–7842. [44] J. Ma¨enpa¨a¨, S.D. Hall, B.J. Ring, C.C. Strom, S.A. Wrighton, Pharmacogenetics 8 (1998) 137–155. [45] H.C. Rawden, A. Tindall, D. Hallifax, J.B. Houston, Drug Metab. Rev. 33 (Suppl 1) (2001) 420. [46] W. Tang, R.A. Stearns, G.Y. Kwei, S.A. Iliff, R.R. Miller, M.A. Egan, N.X. Yu, D.C. Dean, S. Kumar, M. Shou, J.H. Lin, T.A. Baillie, J. Pharmacol. Exp. Ther. 291 (1999) 1068–1074. [47] A.-C. Egnell, J.B. Houston, S. Boyer, J. Pharmacol. Exp. Ther. 305 (2003) 1251–1262.