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K_IIV, AN IN VIVO PARAMETER FOR PREDICTING THE MAGNITUDE OF A DRUG INTERACTION ARISING FROM COMPETITIVE ENZYME INHIBITION

Department of Medicinal Chemistry (J.M.N., K.L.K., R.H.L., W.F.T.), School of Pharmacy, University of Washington, Seattle, Washington and Department of Medicine (R.A.O.), Santa Clara Valley Medical Center, San Jose, California

(Received January 7, 2003; Accepted April 22, 2003)

	Abstract

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The goal of the study was to test the assumption that a competitive inhibition constant determined in vivo, K_iiv, like its corresponding in vitro counterpart, K_i, is independent of inhibitor concentration. Inhibition of the CYP2C9-dependent formation of (S)-7-hydroxywarfarin from (S)-warfarin was measured in seven healthy subjects at three different doses of fluconazole. Prothrombin time measurements showed increasing anticoagulant activity with increasing fluconazole dose. The pharmacokinetic parameters calculated from the (S)- and (R)-warfarin plasma levels were consistent with previous studies. Fluconazole reduced the clearance of (S)-warfarin to a greater extent than that of (R)-warfarin. The decrease in clearance of both warfarin enantiomers was fluconazole dose-dependent. The formation of (S)-7-hydroxywarfarin was inhibited by 31, 55, and 77% at the 100, 200, and 300 mg daily doses of fluconazole, respectively. K_iiv, values calculated from these data based on plasma fluconazole levels at each dose and data from earlier work at 400-mg daily doses of fluconazole were 30.7 ± 23.7, 19.6 ± 3.8, 17.9 ± 7.5, and 19.8 ± 3.5 µM, respectively. These results confirm the hypothesis that K_iiv is independent of inhibitor concentration.

The implicit assumption of the guidance and indeed of all in vitro–in vivo correlations is that the qualitative behaviors of the P450s are largely independent of their external biochemical environments. Thus, the same P450 should form the same primary metabolites from a given substrate and an inhibitor should inhibit the same enzymes, both in vitro and in vivo (Wrighton et al., 1993; Houston, 1994; Rodrigues, 1994; Ball et al., 1995; Houston and Carlile, 1997; Iwatsubo et al., 1997; Rodrigues and Wong, 1997; Ito et al., 1998). The assumption is essential because without it, in vitro–in vivo correlations would not be possible. Accumulated evidence suggests that in general it does hold, at least qualitatively. Quantitatively, the picture is much less clear and often problematic.

Of the possible in vitro kinetic inhibition parameters that might be used to predict the magnitude of an in vivo drug interaction resulting from competitive inhibition, the in vitro K_i is particularly useful. It is a constant that can be readily determined.² Moreover, it is a constant that is largely independent of substrate identity and one that can be used to predict enzyme behavior over a large range of substrate and enzyme concentrations.

However, even competitive inhibition, the simplest of cases, is subject to at least three potential problems that can result in significant differences in the in vitro and in vivo properties of an enzyme. First, equal nominal concentrations of inhibitor in plasma or microsomes do not guarantee equal concentrations of the inhibitor at the active site of the enzyme in the in vivo and in vitro environments. Active uptake or differences in lipid solubility and/or protein binding properties in the immediate vicinity of the enzyme could foster differences in concentrations (von Moltke et al., 1994; Obach, 1996; Iwatsubo et al., 1997; Yamano et al., 1999). Second, differences between the two environments in factors such as pH, ionic strength or solvent could perturb enzyme activity. Different pHs or ionic strengths can alter active site water content, conformational architecture, and/or reactivity by modulating environmental charge (Schrag and Weinkers, 2000). The common solvents used to dissolve inhibitor in in vitro experiments can have differential effects on the measured enzyme kinetic parameters (Busby et al., 1999; Tang et al., 2000; Easterbrook et al., 2001). Third, a metabolite of the inhibitor, rather than the inhibitor itself, could be the primary species inhibiting the enzyme. Although significant metabolite inhibition is probably uncommon, it does happen (He et al., 1995; Schmider et al., 1999). When it does, it can easily be missed because the time frame of microsomal experiments are often insufficient to produce the levels of metabolite generated in vivo and thereby produce the magnitude of inhibition seen in vivo. The overall effect of these three problems in general is to render a given concentration of the inhibitor to be more potent in vivo than it is in vitro. This is particularly true with highly lipid soluble inhibitors.

Despite these problems, the ability to predict drug interactions is a goal clearly worth pursuing. But, recognizing that greater understanding is required before the problems associated with using an in vitro K_i as a predictor of inhibition in vivo can be completely and systematically solved a more direct approach might be useful in the interim. Determination of the in vivo K_i, K_iiv, of an inhibitor represents such an approach, at least for interactions governed by competitive enzyme inhibition (Kunze and Trager, 1996).

Theoretically, K_i and K_iiv should be identical (Kunze and Trager, 1996). Any difference in their measured values should be a reflection of differences encountered by the inhibitor in the in vitro and in vivo environments as discussed above. Of the two constants, K_i more accurately measures the molecular interaction of the inhibitor with the enzyme. In contrast K_iiv is a direct experimental measure of the actual in vivo effectiveness of the inhibitor. That is, K_iiv unlike K_i automatically incorporates into its value the effects of factors such as differences in active site inhibitor concentration, environmental differences, and/or inhibitor metabolism. Thus, K_iiv should be a powerful and practical parameter for predicting an interaction providing that certain underlying assumptions can be confirmed. A major assumption is that K_iiv, like K_i, is independent of inhibitor concentration. Although not addressed directly, two recent in vivo metabolic studies from our laboratory with an inhibitor for two different P450s (CYP1A2 and CYP2C19) indicate that K_iiv is indeed independent of inhibitor concentration (Yao et al., 2001, 2003). The present study was undertaken with yet another inhibitor (fluconazole) and enzyme (CYP2C9) to further establish the concentration independence of K_iiv by directly testing this assumption.

	Materials and Methods

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Chemicals and Materials. Pseudoracemic warfarin containing equal amounts of (S)-4'-deuterowarfarin and unlabeled (R)-warfarin was prepared for oral dosing as described previously (Heimark et al., 1992). Pentadeuteriophenyl analogs of warfarin and warfarin metabolites were prepared as described previously (Heimark et al., 1985). Fluconazole was obtained as a gift from Pfizer Inc. (New York, NY). -(2,4-Dichlorophenyl)-1H-imidazole-1-ethanol was purchased from Janssen Pharmaceutica (New Brunswick, NJ).

Clinical Protocol. Seven, healthy, paid male volunteers of ages 21 to 35 served as study subjects in a protocol of an open label, one-sequence, 4-period crossover design. After being carefully informed of the nature and risk of the study, all the volunteers signed written consent forms in accordance with all conditions required by federal regulations and by the institutional review board of the Santa Clara Valley Medical Center of San Jose, CA. None of the subjects had taken any drug for the preceding two months, and each served as his own control. Complete blood counts and panel-20 blood tests were performed on all subjects before and after all periods.

The study was divided into two phases, warfarin alone, the control phase (first period), or warfarin combined with fluconazole, the interaction phase (second, third, and fourth periods). For the control phase, each subject received a 500-mg capacity gelatin capsule containing pseudoracemic warfarin, 0.75 mg/kg [37.5 mg/kg each of (R)- and (S)-warfarin], mixed in lactose. The capsule was ingested with a full glass of water 2 h before breakfast. No additional food or liquid was ingested before breakfast. Blood samples (12 ml) were obtained by venipuncture just before warfarin ingestion and at 2, 6, 24, 48, 72, 96, 120, 144, 168, 192, 216, 240 h after ingestion. Each blood sample was mixed in a glass tube with citrate buffer in a ratio of 9:1. The buffer was prepared by mixing solutions of sodium citrate, 0.1 mol/l, and citric acid, 0.1 mol/l in a ratio of 3:2. After addition of the citrate, each blood sample was centrifuged at 2000 rpm for 30 min at 4°C, the plasma removed and divided into two portions (3 ml each). Subsequently, one plasma portion, after addition of the internal standard pentadeuteriowarfarin (final concentration, 1 µg/ml), was used to determine (R)- and (S)-warfarin concentration. The second plasma portion was used for a prothrombin time determination. Both plasma portions were stored at -20°C until workup for analysis.

After a 4-week wash out and rest period, the second phase was begun. Fluconazole was administered on three separate occasions in daily doses of 200 (2 tablets, second period followed by a 4-week wash out), 100 (1 tablet, third period followed by a 4-week wash out), and finally 300 mg (3 tablets, fourth period). In each period the fluconazole dose was administered before breakfast beginning 7 days before administration of a single dose of pseudoracemic warfarin, 0.75 mg/kg [37.5 mg/kg each of (R)- and (S)-warfarin], and continuing for an additional 11 days. Zero hour blood samples (12 ml) were obtained by venipuncture just before fluconazole administration (day 1) and again just before warfarin administration (day 8). After warfarin administration, serial blood samples (12 ml each) were collected at 2, 6, 24, 48, 72, 96, 120, 144, 168, 192, 216, 240 h after ingestion. Each blood sample was mixed with the citrate solution, centrifuged, and the plasma divided into two portions as described for the control. The internal standard for the measurement of fluconazole, -(2,4-dichlorophenyl)-1H-imidazole-1-ethanol (100 µl of a 700 µg/ml solution), was added to 1 ml of plasma from one of the plasma portions. The internal standard for the measurement of (R)- and (S)-warfarin levels, pentadeuteriowarfarin, was added to the remaining plasma (2 ml) from that plasma portion (final concentration of 1 µg/ml). The three plasma portions from each serial plasma sample were stored at -20°C until workup for analysis.

Urine was collected throughout the control and fluconazole studies every 24 h and the daily volume noted. For each subject, aliquots (1/100 by volume) were taken from each 24-h urine sample and pooled. Nine milliliters of this pool were spiked with a 1 ml aqueous solution containing deuterated internal standards at final concentrations of 0.1 µg/ml pentadeuteriowarfarin, 1.0 µg/ml each of a mixture of pentadeuteriowarfarin alcohols 1 and 2, and the pentadeuterio-6-, 7-, and 8-hydroxywarfarins. All urine samples were stored at -20°C until workup for analysis.

Prothrombin Time Measurements. The one-stage prothrombin time of plasma was measured by a modification of the method of Quick, as described previously (O'Reilly and Aggeler, 1968). The total anticoagulant effect was determined by measuring the area under the curve for the response of the prothrombin time (AUC_PT) from a semilogarithmic plot by the trapezoidal method for the one-stage prothrombin time expressed in arbitrary units.

Assay for Fluconazole, Warfarin Enantiomers, and Metabolites. Fluconazole plasma concentrations were measured by high performance liquid chromatography as previously described (Black et al., 1996). The extraction and gas chromatography/mass spectrometry assay methods for the measurement of warfarin enantiomers and their metabolites in plasma and urine were as previously described (Toon et al., 1986).

Pharmacokinetic Treatment of Data. A single-compartment model sufficiently described the plasma concentration-time data for (R)- and (S)-warfarin in all subjects. The elimination rate constants, k, were obtained by linear regression analysis and AUC_inf by the trapezoid rule. CL for the individual enantiomers of dose, D, was calculated from CL/F = D/AUC, where F is bioavailability and is assumed to be unity as reported previously (O'Reilly et al., 1966). The apparent volume of distribution, V_ss, and elimination half-life, t, were calculated according to V_ss/F = D/k · AUC and t; = ln2/k, respectively. The formation clearance, CL_f, for each of the metabolites was calculated according to CL_f = f_m · CL, where f_m is the fraction of dose recovered in the urine as a specific metabolite.

Data Analysis. Comparative data are expressed as mean ± (S.D. or S.E.). Statistical analyses were done using Stata 7.0 (Stata Corporation, College Station, TX). A difference in the mean of prothrombin time or the mean of clearance across the control phase and three different fluconazole dose phases was tested for using repeated measures of analysis of variance and determining the p value for the F-statistic. A difference in the mean of the calculated K_iiv value across three different fluconazole dose phases was also similarly tested for.

	Results

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Prothrombin Time. All subjects had a detectable prolongation of the one-stage prothrombin time at 24 h after the dose of pseudoracemic warfarin alone and with all added doses of fluconazole. The peak response occurred 48 to 72 h after warfarin alone and 72 to 120 h after warfarin plus fluconazole. There was little variation between subjects during the first 24 h, followed by increasing variation through the remainder of the period of observation, as the large coefficient of variation after 48 h indicates. The duration of the anticoagulant effect increased with fluconazole dose. It was 4 to 7 days for warfarin alone, 5 to 9 days for warfarin plus 100 mg of fluconazole daily, 6 to 11 days for warfarin plus 200 mg of fluconazole daily, and 8 to 15 days for warfarin plus 300 mg of fluconazole daily (Table 1). The means of the prothrombin times across the control phase and three fluconazole dose phases, Table 1, were significantly different (p < 0.001).

Plasma Data. Plasma levels of (R)- and (S)-warfarin were measured for each of the seven subjects and the mean pharmacokinetic parameters calculated (Table 2). For controls the mean half-life of (S)-warfarin was 33 ± 9 h, whereas that for (R)-warfarin was 49 ± 11 h. As expected, fluconazole inhibited the metabolism of both (R)and (S)-warfarin, the effect was dose-dependent, and the volume of distribution was unchanged (Black et al., 1996). On average the clearance of (S)-warfarin was inhibited by 26, 47, and 49% at the 100, 200, and 300 dose levels of fluconazole, respectively, whereas the clearance of (R)-warfarin was reduced by 25, 38, and 42% at the corresponding levels of fluconazole (Table 2).

Urinary Data. Total urinary levels of parent drug and metabolites were determined for all patients (0–216 h collection period). The mean recovery of pseudoracemic warfarin and metabolites in urine for controls was 32% for the (S)-enantiomers and 29% for the (R)enantiomers for a total dose recovery 61% (data not shown). The mean recovery of pseudoracemic warfarin and metabolites in urine in the fluconazole experiments was 31, 32, and 29% for the (S)-enantiomers and 27, 27, and 26% for the (R)-enantiomers. This represented total dose recoveries of 58, 59, and 56% for the 100, 200, and 300 mg of fluconazole doses, respectively (data not shown). These urinary recoveries fall within the normal limits defined in previous studies (Toon et al., 1986; Heimark et al., 1992; O'Reilly et al., 1992; Black et al., 1996). The mean renal clearances of (S)-warfarin and (R)warfarin are presented in Table 2. The means of the clearances for each of the enantiomers across the control phase and the three fluconazole dose phases were significantly different (p < 0.001). The formation clearances for each of the coumarin ring hydroxylated metabolites of both (S)- and (R)-warfarin are given in Table 3.

(S)-Warfarin. As previously reported the formation clearances to the minor and the two major (S)-warfarin metabolites (S)-8-, (S)-6-, and (S)-7-hydroxywarfarin, respectively, were found to be significantly inhibited by fluconazole (Black et al., 1996). On average, the P450 2C9-dependent 7-hydroxylation of (S)-warfarin was inhibited by 31, 55, and 77% by daily doses of fluconazole of 100, 200, and 300 mg, respectively (Table 3). Similarly, the 6-hydroxylation of (S)-warfarin was inhibited, on average, by 45, 49, and 69%, by the same daily doses of fluconazole, respectively (Table 3). Fluconazole inhibition of the 8-hydroxylation of (S)-warfarin, while profound, could not be accurately assessed because of the low level of turnover to this specific metabolite (Table 3).

(R)-Warfarin. As previously reported (Black et al., 1996) fluconazole was effective in inhibiting the formation of the 6-, 7-, and 8-hydroxylated metabolites of (R)-warfarin at all three doses. (R)-6-Hydroxywarfarin formation was inhibited by 43, 48, and 65%, (R)-7-hydroxywarfarin formation was inhibited by 29, 54, and 89%, and (R)-8-hydroxywarfarin formation was inhibited by 83, 72, and 97%, at daily doses of 100, 200, and 300 mg of fluconazole, respectively (Table 3).

Fluconazole Plasma Levels. To insure steady-state fluconazole levels [t_1/2 = 30–40 h (Lazar and Hiligoss, 1990)], fluconazole (100, 200, or 300 mg) was administered once a day for 6 days prior to the administration of a single dose of pseudoracemic warfarin. Mean plasma levels at the 24-time interval ranged from 8.7 to 22 to 29.5 µM for the 100, 200, and 300 mg dose levels, respectively (Table 4).

	Discussion

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The notion of equal enzyme activity in vitro and in vivo assumes that enzyme activity is independent of environment and that equal concentrations of substrate/inhibitor reach the active site of the enzyme when unbound substrate/inhibitor concentrations in microsomes or plasma are equal. With respect to inhibition, a consequence of the assumption is that the ratio of K_i, to its in vivo counterpart K_iiv for a given enzyme (Kunze and Trager, 1996), must be equal to 1. Departure from the ideal value of 1 represents a violation of the assumption and provides a starting point for elucidating the reasons for the violation. Such studies clearly need to be done to help identify the major variables responsible for differences in comparable in vitro and in vivo kinetic parameters. However, even when K_i and K_iiv are not equal, K_iiv rather than K_i is the parameter of choice in terms of predicting the magnitude of drug interactions for drugs cleared by a given enzyme. As indicated above, K_iiv is a true reporter of effect on enzyme activity in vivo, and the purpose of this study was to test the assumption that K_iiv is indeed independent of inhibitor concentration. To that end, inhibition of the P450 2C9-dependent formation of (S)-7-hydroxywarfarin from (S)-warfarin was measured in seven healthy subjects at three different steady-state concentrations of fluconazole, the K_iiv determined and compared at each concentration. Fluconazole was chosen as the inhibitor for CYP2C9 because it is excreted largely unchanged, is only minimally protein-bound, and its K_i value (7–8 µM; Kunze et al., 1996) is not too different from its previously determined K_iiv value (22 µM; Kunze and Trager, 1996)

If the plasma concentration of a drug is well below its K_m for the major P450 responsible for its clearance, and this is generally true for most drugs, the classic equation for competitive inhibition in Michaelis-Menten enzyme kinetics can be simplified and rearranged to eq. 1. This equation allows the direct determination of K_iiv. In the equation, [I] = the plasma concentration of inhibitor

at steady state, CL_f(i) = formation clearance to the metabolite of the drug whose formation is inhibited by the inhibitor, and CL_f(c) = formation clearance to that metabolite in the absence of inhibitor (Kunze and Trager, 1996).

A single dose of pseudoracemic warfarin was administered to each subject after fluconazole steady state had been reached (6 days) and serial blood and urine collected over 10 days. Over this time period, anticoagulant activity was monitored by daily prothrombin times determinations. Prothrombin times showed an excellent dose-response relationship with mean AUC_PT increasing with increasing fluconazole dose (Table 1).

The pharmacokinetic parameters calculated from the (S)- and (R)warfarin plasma data were as expected (Table 2) and consistent with previous studies (Toon et al., 1986; Heimark et al., 1992; O'Reilly et al., 1992; Black et al., 1996). Fluconazole inhibited the metabolism of (S)warfarin to a greater extent than that of (R)-warfarin. The extent of inhibition of both warfarin enantiomers was fluconazole dose-dependent whereas the volume of distribution was unchanged (Table 2). Recovery of the warfarin enantiomers and their metabolites from urine after approximately 10 days was about 60% of the administered dose, a value that was consistent with previous studies (Toon et al., 1986; Heimark et al., 1992; O'Reilly et al., 1992; Black et al., 1996). The formation clearances to each of the coumarin ring hydroxylated metabolites of both (S)- and (R)-warfarin in the presence and absence of fluconazole are presented in Table 3. As previously reported, fluconazole is effective in inhibiting the formation of each of the coumarin ring hydroxylated warfarin metabolites but to varying degrees (Black et al., 1996).

Of the various warfarin metabolites that are formed, (R)-10-hydroxywarfarin, (R)-8-hydroxywarfarin, and (S)-6- and 7-hydroxywarfarin are known reporters of P450 3A4 (Kunze et al., 1996), P450 2C19 (Weinkers et al., 1996), and P450 2C9 (Rettie et al., 1992), respectively. Unfortunately, unanticipated analytical problems precluded accurate measurement of (R)-10-hydroxywarfarin levels and its inclusion in the present studies. Levels of (R)-8-hydroxywarfarin and (S)-6- and 7-hydroxywarfarin were measurable and are reported in the form of formation clearances in Table 3. Inspection of the formation clearance values for (R)-8-hydroxywarfarin in the presence of various concentrations of fluconazole (Table 3) reveals that the maximum level of inhibition is attained at even the lowest dose of inhibitor. It is known that both P450 2C19 (low K_m form) and P450 1A2 (high K_m form) catalyze the formation of (R)-8-hydroxywarfarin but that only P450 2C19 is susceptible to inhibition by fluconazole (K_i 2 µM) (Kunze et al., 1996; Weinkers et al., 1996). This suggests that the steady-state fluconazole plasma level of 8.7 µM (Table 4) obtained from the 100 mg daily dose is sufficient to eliminate most of the contribution of P450 2C19 to the formation of (R)-8-hydroxywarfarin. The (R)-8-hydroxywarfarin that is formed is formed by P450 1A2. The magnitude of the degree of inhibition at the fluconazole dose levels studied coupled to the involvement of at least two P450s precludes (R)-8-hydroxywarfarin formation being a useful parameter for testing the assumption that K_iiv is independent of inhibitor concentration. Moreover, these facts do not allow for any useful estimate of K_iiv for P450 2C19.

Similar to (R)-8-hydroxywarfarin, the formation of (S)-6-hydroxywarfarin would not be a good test of the assumption. Its formation is also dependent upon a minimum of two P450s, P450 2C9 (a low K_m form) and P450 3A4 (a high K_m form) (Rettie et al., 1992; Kunze et al., 1996). Conversely, the formation of (S)-7-hydroxywarfarin is dependent upon the activity of a single enzyme, P450 2C9 (Rettie et al., 1992; Kunze et al., 1996). Inhibition of the formation of (S)-7-hydroxywarfarin by different steady state levels of fluconazole presents a clear test of the assumption that K_iiv is independent of inhibitor concentration. At the 100, 200, and 300 mg daily doses of fluconazole, the formation of (S)-7-hydroxywarfarin was inhibited by 31, 55, and 77%, respectively (Table 3).

After steady state had been reached, trough levels of fluconazole plasma concentrations were determined for the remainder of the study at 24-h intervals immediately preceding the next fluconazole dose at each of the dose levels (Table 4). Although a 24-h sampling does not provide the mean fluconazole concentration over the dosing interval, it does provide a consistent steady-state concentration of fluconazole that can be conveniently sampled throughout the course of the study without jeopardizing the question of whether or not K_iiv remains constant.³ K_iiv was then calculated for each of the fluconazole doses using eq. 1, the mean steady-state 24-h fluconazole plasma concentrations and the (S)-7-hydroxywarfarin formation clearance values from Table 4. The results are presented in Table 4. The values of K_iiv at the three fluconazole dosage levels of 100, 200, and 300 mg were found to be 30.7 ± 23.7, 19.6 ± 3.8, and 17.9 ± 7.5 µM, respectively. In addition, the K_iiv value for a 400-mg dose of fluconazole calculated from the 24-h fluconazole concentration, and (S)-hydroxywarfarin clearance data determined in the earlier study (Black et al., 1996) was found to be 19.8 ± 3.5. Except for the 100-mg dose experiment, the agreement between the K_iiv values for the various fluconazole-dosing levels was excellent. The reason for the greater diversity in individual K_iiv values for the 100-mg dose experiment is unknown but is presumably due to an unrecognized source of experimental error. Despite the unexplainably erratic estimate of K_iiv from the 100-mg dose experiment, the evidence overall confirms the hypothesis that K_iiv is independent of inhibitor concentration. This conclusion is based on 1) the excellent agreement between K_iiv values at the 200-, 300-, and 400-mg dose levels, 2) the mean K_iiv value for the 100-mg dose experiment is not significantly different from the K_iiv values for the other three doses, 3) the slope of a plot of all individual CL_f(c)/CL_f(i) ratio values versus fluconazole dose for the four dose levels gives a composite K_iiv value of 20.4 µM, Fig. 1, and 4) the confirmatory results of the two earlier studies (Yao et al., 2001, 2003). Thus, the independence of K_iiv from inhibitor concentration as well as substrate identity as previously determined (Kunze and Trager, 1996) provides strong support for the notion that K_iiv can be expected to be a powerful tool for predicting and assessing the magnitude of drug interactions involving competitive enzyme inhibition.

View larger version (11K): [in this window] [in a new window]   FIG. 1. A plot of the CLf(c)/CLf(i) ratio values versus 24-h fluconazole trough concentration values for each subject in the four warfarin/fluconazole interaction studies (100-, 200-, 300-, and 400-mg fluconazole dose levels).

	Footnotes

 
This study was supported in part by Grant 32165 from the National Institutes of Health (Bethesda, MD).

¹ Abbreviations used are: P450, cytochrome P450; K_iiv, in vivo constant for competitive inhibition of an enzyme; K_i, in vitro constant for competitive inhibition of an enzyme; AUC, area under the curve; PT, the response of the prothrombin time; CL, clearance limits; F, bioavailability; V_ss, apparent volume of distribution.

² The classic expression for competitive enzyme inhibition is

(1)

where i = fraction of inhibition, [I] = inhibitor concentration, [S] = substrate concentration, K_m is the Michaelis-Menten constant for the substrate, and K_i is the inhibition constant.

³ The difference between the mean fluconazole concentration over 24 h and the 24-h fluconazole concentration, ranges between 10 and 20% with the mean value being higher (Kunze and Trager, 1996). Thus, use of the 24-h value in eq. 2 would be expected to lead to a slightly lower value for K_iiv than would be obtained using the mean value. This is exactly what is found. Using the data from the earlier paper by Kunze and Trager (1996), the mean fluconazole concentrations over 24 h yielded a K_iiv of 22.5 ± 3.5 µM whereas the fluconazole concentrations from the same study at 24-h postdose yielded a K_iiv of 19.8 ± 3.5 µM.

Address correspondence to: Dr. William F. Trager, Box 357610, Department of Medicinal Chemistry, University of Washington, Seattle, WA 98195. E-mail: trager{at}u.washington.edu

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