Experimental Procedures

Animals and Materials.

Male Sprague-Dawley rats weighing 250 to 300 g (Nihon-ikagaku, Tokyo, Japan) were used throughout the experiments. All animals were treated humanely. The studies reported in this manuscript have been carried out in accordance with the Guide for the Care and Use of Laboratory Animals as adopted and promulgated by the National Institutes of Health. [3′,5′,7-³H]Methotrexate, sodium salt ([³H]methotrexate, 6.50 Ci/mmol) was purchased from Amersham Pharmacia Biotech (Buckinghamshire, England). Methotrexate (Ametopterin), ATP, AMP, and probenecid were from Sigma Chemical Co. (St. Louis, MO).

Uptake of [³H]Methotrexate by Isolated Rat Hepatocytes.

Hepatocytes were isolated from rats by the procedure described previously (Yamazaki et al., 1992). After isolation, the hepatocytes were suspended at 4°C in albumin-free Krebs-Henseleit buffer [5 mM KCl, 1 mM KH₂PO₄, 1.2 mM MgSO₄·7H₂O, 12 mM HEPES, 5 mM glucose, 2 mM CaCl₂, 118 mM NaCl, 24 mM NaHCO₃, pH 7.3] to give a final concentration of 2 × 10⁶ cells/ml. Cell viability was routinely checked by the trypan blue (0.4% w/v) exclusion test (Yamazaki et al., 1992). Isolated hepatocytes with a viability of more than 90% were routinely used. Cellular protein was determined with Bio-Rad protein assay kit using bovine serum albumin as a standard (Yamazaki et al., 1992). The uptake of [³H]methotrexate was initiated by adding [³H]methotrexate and probenecid to the preincubated (3 min at 37°C) cell suspension. At designated times, the reaction was terminated by separating the cells from the medium by using a centrifugal filtration technique described previously (Yamazaki et al., 1992). The cells were dissolved into the alkaline solution, followed by neutralization, and the radioactivity was determined in scintillation cocktail (Clearsol I; Nacalai Tesque Inc., Kyoto, Japan). The inhibition constant (K_i) was obtained by fitting the following equation to the data:Vo(+inhibitor)/Vo(−inhibitor)=1/(1+I/Ki) Equation 1where V_{o(+inhibitor)} andV_{o(−inhibitor)} represent the initial uptake rate of [³H]methotrexate in the presence and absence of inhibitor at a concentration of I. This equation was derived based on the assumption of competitive or noncompetitive inhibition and the fact that the [³H]methotrexate concentration is much lower than the K_m value of methotrexate uptake (under Results).

Uptake of [³H]Methotrexate by CMVs.

CMVs were prepared as described previously (Masuda et al., 1997) and suspended in 50 mM Tris-HCl buffer (pH 7.4) containing 250 mM sucrose and were frozen in liquid N₂ and stored at −100°C until used. The uptake of [³H]methotrexate was measured by a rapid filtration technique as described previously (Masuda et al., 1997). The transport medium (250 mM sucrose and 10 mM MgCl₂ in 10 mM Tris-HCl buffer, pH 7.4) containing [³H]methotrexate and probenecid was preincubated for 3 min at 37°C in presence of 5 mM ATP or AMP and an ATP-generating system (10 mM creatine phosphate and 100 μg/ml creatine phosphokinase). The reaction was started by adding the vesicle preparation (10 μg) to the preincubated transport medium and further incubating it at 37°C. The uptake reaction was stopped by the addition of 1 ml of ice-cold stop buffer that contained 100 mM NaCl, 250 mM sucrose, and 10 mM Tris-HCl (pH 7.4). ATP-dependent uptake was determined by subtracting the uptake in the absence of ATP from that in the presence of AMP. The K_i was obtained based on eq. 1.

Drug Interaction Studies in Vivo.

For the simultaneous analysis of 1) the uptake and efflux at sinusoidal membrane, 2) excretion at the canalicular membrane, and 3) net biliary excretion from plasma into the bile, steady-state intravenous co-infusion of methotrexate and probenecid, and the subsequent bolus injection of [³H]methotrexate were performed in rats. Under the ether anesthesia, left and right femoral vein and left femoral artery were cannulated with polyethylene tube (PE-50; Clay Adams, Parsippany, NJ). Bile duct was also cannulated with PE-10. After an intravenous bolus injection (22 μmol/kg methotrexate; 0, 23, 45, 68, or 90 μmol/kg probenecid; and 10 mg/kg inulin), methotrexate (0.164 μmol/min/kg), probenecid (0, 1.1, 2.2, 3.3, or 4.4 μmol/min/kg), and inulin (0.33 mg/min/kg) were simultaneously infused via the femoral vein. Blood was sampled via femoral artery at 60, 120, and 180 min and centrifuged (Microfuge E; Beckman Instruments, Fullerton, CA) to obtain plasma. Bile was sampled at 0 to 30, 30 to 90, 90 to 150, and 150 to 210 min. Both methotrexate and probenecid concentration was determined by HPLC. At 210 min after the start of infusion, [³H]methotrexate (22 μmol/kg) was administered as a bolus via the opposite side of femoral vein, and plasma was obtained at 15, 40, 60, and 80 s after the bolus injection. Approximately a 100-mg piece of the liver was obtained at 30 and 60 s by biopsy technique. At 90 s rats were sacrificed and the liver was resected for the determination of hepatic concentration of methotrexate, probenecid, and [³H]methotrexate. Bile was obtained at 0 to 30, 30 to 60, and 60 to 90 s. The radioactivity in plasma, bile, and the liver were determined by the liquid scintillation counter (LS 6000SE; Beckman Instruments).

Determination of Protein Binding in Plasma and Liver.

Plasma (100 μl) obtained at 180 min during intravenous infusion was directly applied to MPS ultrafiltration tube (Millipore Corporation, Bedford, MA). The filter binding of methotrexate and probenecid was 2.59 and 6.24%, respectively. All binding was normalized with respect to the filter blank. The 25% (w/v) homogenate was prepared from the liver sample obtained at the end of in vivo study using a Teflon homogenizer (Iuchi, Tokyo, Japan) in 50 mM Tris-HCl (pH 7.4). This homogenate was then serially diluted by the same buffer to make 16.6 and 8.3% homogenates, and 1.0 ml of each was applied to Centrisart I 10,000D (Sartorius AG, Goettingen, Germany). The ultrafiltration tube was then centrifuged at 800g for 5 min, and the methotrexate and probenecid concentration in the filtrate was determined by HPLC as unbound concentration. The filter binding of methotrexate and probenecid was 3.07 and 8.08%, respectively. All binding was normalized with respect to the filter blank. The free fraction in plasma (f_p) was determined as the ratio of unbound concentration in the filtrate to the total concentration. For the calculation of free fraction in liver (f_h), the bound concentration in each homogenate was first calculated by subtracting the free concentration from the total concentration, and the ratio of bound to free concentration at 100% homogenate concentration was then extrapolated by the linear regression of the plot of such ratio against the homogenate concentration. The f_h was calculated as the reciprocal of the sum of one plus the ratio of bound to free concentration.

HPLC Determination.

The 25 μl of plasma or the bile diluted 10 times with H₂O was deproteinized with 100 μl of 1 M HClO₄ containing the internal standard (2.5 μg/ml aminopterin for methotrexate and 5.0 μg/ml sulfamethazine for probenecid), followed by centrifugation at 4°C and 10,000g for 10 min. One milliliter of 25% (w/v) liver homogenate was added to 1 ml of 1 M HClO₄containing the internal standard, followed by centrifugation at 4°C and 10,000g for 10 min. The supernatant (100 μl) was neutralized with 25 μl of 3 M K₂HPO₄, and 20 μl of the obtained sample was subjected to HPLC. The HPLC analysis for methotrexate and probenecid was performed according to previous reports (Nurenberg, 1989; Tellingen et al., 1989; Nurenberg et al., 1990;Nakamura et al., 1996) using Inertsil ODS-3 (250 × 4.6 mm, particle size 5 μm) column (Tosoh, Tokyo, Japan). The mobile phase consisted of acetonitrile:0.05 M phosphate buffer (pH 6.2) =1:9 (v/v) for methotrexate and acetonitrile:0.01 M phosphate buffer (pH 7.4) = 1:5 (v/v) for probenecid with a flow rate of 1.0 ml/min. The UV detector was operated at a wavelength of 303 and 254 nm for methotrexate and probenecid, respectively. The detection limit for methotrexate and probenecid was 35 and 50 ng/ml plasma, 35 and 50 ng/ml bile, and 14 and 20 ng/g liver, respectively.

Pharmacokinetic Analysis.

Total body clearance (CL_total), biliary clearance with respect to circulating plasma (CL_bile,p), and biliary clearance with respect to the liver concentration (CL_bile,h) were calculated by the following equations:CLtotal=I/Cpss Equation 2CLbile,p=Vbile/Cpss Equation 3CLbile,h=Vbile/Chss Equation 4where I, C_pss,V_bile, andC_hss represent infusion rate (nmol/min/kg), plasma concentrations at steady state (μM), biliary excretion rate at steady state (nmol/min/kg), and hepatic concentration at steady state (μM), respectively.C_pss was determined as the mean values of the plasma methotrexate concentrations at 60, 120, and 180 min.V_bile was determined as the mean value of biliary excretion rate of methotrexate from 90 to 150 min and that from 150 to 210 min. C_hss was determined as the hepatic methotrexate concentration at the end of in vivo experiment. To calculate C_hss, the specific gravity of the liver was assumed to be unity. Thus, the amount in the liver (nmol/g liver) can be regarded as the hepatic concentration (μM), and the units of CL_bile,hshould be milliliters per minute per kilogram. For calculation of the hepatic uptake clearance (CL_uptake), the biexponential equation was fitted to the plasma concentration-time profile for [³H]methotrexate (C_p) by means of a nonlinear iterative least-squares method using a MULTI program (Yamaoka et al., 1981) and the area under the plasma concentration-time curve (AUC) was calculated from the integration of the exponential equation. The integration plot was obtained by plottingX_liver/C_pagainst AUC/C_p, the initial slope of this plot representing the CL_uptake, whereX_liver represents the amount of [³H]methotrexate once taken up by hepatocytes and calculated as the amount of [³H]methotrexate in the liver plus that recovered in bile. The input data for all the fitting were weighted as the reciprocal of the square of the observed values, and the algorithm used for the fitting was the Damping Gauss Newton method.

The intrinsic clearances for the net biliary excretion (CL_int,bile), hepatic uptake across sinusoidal membrane (P₁), and excretion across canalicular membrane (P₃) was calculated based on the following equations using well stirred model:CLbile,p=QpfpCLint,bile/(Qp+fpCLint,bile(1−hematocrit)/Rb) Equation 5CLuptake=QpfpP1/(Qp+fpP1(1−hematocrit)/Rb) Equation 6P3=CLbile,h/fh Equation 7where Q_p is the hepatic plasma flow rate and was set to be 34.8 ml/min/kg according to our previous data (Kato et al., 1999). The hematocrit is the hematocrit and was set to be 0.45. The R_b is the blood-to-plasma concentration ratio and was measured to be 0.83. The CL_int,bile can be expressed as (Miyauchi et al., 1993):CLint,bile=P1P3/(P2+P3) Equation 8where P₂ represents the intrinsic clearance of the efflux across the sinusoidal membrane from the liver.

In Vitro/in Vivo Extrapolation.

The decrease inP₁ by probenecid was predicted based on the following equation:Ruptake=P1(+inhibitor)/P1(−inhibitor)=1/(1+Iu,plasma/Ki) Equation 9where I_u,plasma was the unbound concentration in the extracellular space andK_i was obtained using isolated hepatocytes. Since probenecid is a low-clearance drug, the probenecid concentration in the extracellular space was assumed to be equal to its concentration in circulating plasma. The decrease inP₃ by probenecid was predicted by the following equation:Rexcretion=P3(+inhibitor)/P3(−inhibitor)=1/(1+Iu,liver/Ki) Equation 10In this case I_u,liver was the unbound probenecid concentration in the liver (f_hC_hss) andK_i was obtained using CMVs.

For the analysis of the interaction involving net biliary excretion, the decrease in CL_int,bile was estimated based on the following equation (see details under Discussion):CLint,bile (+inhibitor)/CLint,bile (−inhibitor)=Ruptake×Rexcretion Equation 11As an alternative method, the decrease in CL_int,bile was estimated from eq. 11 whereR_excretion was obtained usingI_u,plasma instead ofI_u,liver:Rexcretion=P3(+inhibitor)/P3(−inhibitor)=1/(1+Iu,plasma/Ki) Equation 12

Results

Drug Interaction Study in Vivo.

To demonstrate the in vitro/in vivo extrapolation, we first attempted to establish a model of the interaction in rats since in experimental animals we can directly determine the intrinsic clearance for the hepatic uptake and biliary excretion of methotrexate in both in vivo and in vitro systems, and compare the degree of the inhibition between the two systems. During co-infusion of methotrexate and probenecid, the plasma concentration profile and biliary excretion rate of methotrexate attained a steady state within 180 min (Fig. 1). Co-infusion of probenecid increased the plasma methotrexate concentration while reducing its biliary excretion rate (Fig. 1).

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Figure 1

Time profiles for the plasma concentration and biliary excretion of methotrexate during intravenous infusion with various doses of probenecid. Both methotrexate (0.164 μmol/min/kg) and probenecid at 0 (○), 1.1 (●), 2.2 (■), 3.3 (▪), or 4.4 (▵) μmol/min/kg was infused intravenously for 180 min, and the plasma methotrexate concentration (A) and biliary excretion rate of methotrexate (B) were determined by HPLC. The values are expressed as means ± S.E. of four or five rats.

The pharmacokinetic parameters for methotrexate were calculated and shown in Table 1. The CL_bile,p was 64% of CL_total in the absence of probenecid (Table 1). Both CL_total and CL_bile,pwere reduced by probenecid (Table 1). To directly estimate the effect of probenecid on the excretion of methotrexate across the bile canalicular membrane, the CL_bile,h was calculated and was also found to be reduced by probenecid in a dose-dependent manner (Table 1). Neither the f_p norf_h of methotrexate was much affected by probenecid (Table 1). In the present study we also determined the urinary excretion rate of methotrexate. The sum of its biliary and urinary excretion rates accounted for approximately 102 ± 3% of the infusion rate in the absence of probenecid. Thus, the metabolism of methotrexate under these conditions should be minor and any potential effect of an interaction involving metabolism should be minimal as far as the biliary excretion of methotrexate is concerned.

To directly analyze the hepatic uptake of methotrexate, a tracer amount of [³H]methotrexate was administered when the plasma methotrexate concentration has reached steady state, followed by integration plot analysis for the hepatic uptake of [³H]methotrexate (Fig.2). The initial slope of this plot was reduced by probenecid (Fig. 2). The obtained CL_uptake was reduced in a probenecid dose-dependent manner. The CL_uptake was almost comparable with CL_bile,p in the absence of probenecid (Table 1).

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Figure 2

Integration plot for the analysis of hepatic methotrexate uptake. At steady state during the intravenous infusion of methotrexate with various doses of probenecid at 0 (○), 1.1 (●), 2.2 (■), 3.3 (▪), or 4.4 (▵) μmol/min/kg, a tracer amount of [³H]methotrexate was injected intravenously as a bolus, and its plasma and liver concentration profiles were followed. The initial slope in this plot represents the CL_uptake of [³H]methotrexate. The values are expressed as means ± S.E. of four rats.

Inhibition of [³H]Methotrexate Transport by Probenecid Both in Isolated Hepatocytes and CMVs.

It has been reported that methotrexate is actively taken up by isolated rat hepatocytes (Horne et al., 1976; Gewirtz et al., 1984). In the present study, the uptake of [³H]methotrexate by isolated rat hepatocytes was found to be linear up to 3 min during the incubation (data not shown) and, therefore, the initial velocity of its uptake was assessed as the uptake at 2 min. Probenecid inhibits [³H]methotrexate uptake in a concentration-dependent manner. Considering that the [³H]methotrexate concentration in the medium (0.5 μM) was chosen so that it was much lower than its reportedK_m value (5.9 μM, Gewirtz et al., 1980; 23 μM, Honscha and Petzinger, 1999), theK_i was estimated based on eq. 1 and found to be 180 μM (Fig. 3A). Such inhibition by probenecid was compatible with previous findings (K_i = 100–200 μM; Gewirtz et al., 1984).

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Figure 3

Inhibition of [³H]methotrexate transport by probenecid in isolated hepatocytes (A) and CMVs (B). In each experimental system, the initial uptake of [³H]methotrexate was determined for a 2-min incubation in the presence or absence of probenecid. In B, the ATP-dependent uptake of [³H]methotrexate was plotted. The straight lines indicate the fitted lines based on eq. 1. The values are expressed as means ± S.E. of triplicate determination.

It has also been reported (Masuda et al., 1997) that methotrexate excretion across the bile canalicular membrane is mainly mediated by a primary active transport system called the canalicular multispecific organic anion transporter (cMOAT/MRP2). The ATP-dependent uptake of [³H]methotrexate by rat CMVs was linear up to 3 min during incubation (data not shown) and, therefore, the initial velocity of uptake was assessed as the uptake at 2 min at a substrate concentration of 1.0 μM, which was much lower than the reportedK_m value (300 μM; Masuda et al., 1997). Probenecid inhibits the ATP-dependent [³H]methotrexate uptake in a concentration-dependent manner with aK_i of 51.6 μM (Fig. 3B).

Determination of Unbound Probenecid Concentration Both in Plasma and Liver.

For the extrapolation from in vitro to in vivo, we directly determined the unbound inhibitor (probenecid) concentration both in plasma and liver. The plasma probenecid concentration at 180 min after the start of the infusion increased in parallel with its infusion rate (Table 2). Neither thef_p nor thef_h of probenecid exhibited any clear dose-dependent change (Table 2), suggesting that its protein binding both in plasma and liver is almost linear. The unbound concentration of probenecid in the liver (f_hC_hss) was lower than that in plasma (f_pC_pss) (Table2).

Extrapolation for Inhibition of Methotrexate Transport by Probenecid in Vivo from in Vitro Data.

To assess methotrexate transport activity across sinusoidal and canalicular membranes, avoiding the effect of protein binding and plasma flow rate, the intrinsic clearances, P₁ andP₃, respectively, were calculated from the CL_uptake and CL_bile,h(Fig. 4). Based on eqs. 9 and 10, the reduction in P₁ andP₃, respectively, was predicted from the K_i values assessed in vitro and the unbound probenecid concentration measured in vivo (Fig. 4). In each case, the predicted line was comparable with the actual data forP₁ andP₃ (Fig. 4).

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Figure 4

Extrapolation of the interaction between methotrexate and probenecid across sinusoidal and canalicular membranes in vivo from in vitro data. A, reduction in the intrinsic clearance for the hepatic uptake of methotrexate across the sinusoidal membrane (P₁) by probenecid was extrapolated based on eq. 6 and shown as a straight line. The actualP₁ value (■) obtained from the integration plot analysis was normalized by that in the control and also plotted. The P₁ of the control was 23.9 ± 1.1 ml/min/kg. B, reduction in the intrinsic clearance for the excretion of methotrexate across the bile canalicular membrane (P₃) by probenecid was extrapolated based on eq. 7 and shown as a straight line. The actualP₃ value (■) obtained from the steady-state biliary excretion and hepatic unbound concentration of methotrexate was normalized by that in the control and also plotted. The P₃ of the control was 60.6 ± 2.4 ml/min/kg.

Next, to assess the net biliary excretion activity of methotrexate from the extracellular space to the bile, the intrinsic clearance (CL_int,bile) was calculated from CL_bile,p (Fig. 5A). The reduction in CL_int,bile by probenecid was predicted based on eq. 11, the predicted points being slightly lower than the actual data for CL_int,bile (Fig. 5A). When the unbound probenecid concentration in plasma rather than in liver was used for the prediction, the predicted line was also slightly lower than the actual CL_int,bile data (Fig. 5A). Similar results were obtained for the prediction of the organ clearance (CL_bile,p) as shown in Fig. 5B.

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Figure 5

Extrapolation of the drug interaction involving net biliary excretion from in vitro data. A, reduction in the intrinsic clearance for the net biliary excretion (CL_int,bile) by probenecid was extrapolated based on eq. 11 whereR_excretion was estimated using eq. 10 (●) or 12 ( ̅ ̅ ̅). The CL_int,bile value (○) observed from the steady-state biliary excretion and plasma unbound concentration of methotrexate was normalized by that in the control and also plotted. The CL_int,bile of the control was 19.8 ± 1.4 ml/min/kg. B, results for the intrinsic clearance obtained in A were converted to the organ clearance. The CL_bile,p (■) observed in vivo and that derived from CL_int,bile following extrapolation from eq. 11 and 10 (▪) or eq. 12 ( ̅ ̅ ̅) are shown.

Discussion

Compared with the prediction of drug interactions involving hepatic metabolism, the prediction of biliary excretion is a more complicated procedure because at least three membrane transport processes have to be considered to successfully predict the excretion. Therefore, we first attempted to demonstrate the prediction of a drug interaction involving each type of membrane transport based on the Michaelis-Menten equation (eqs. 9 and 10). These equations need both the K_i for the inhibition of the transport system and unbound concentration of the inhibitor directly exposed to the transport system. To demonstrate the validity of the prediction method based on these equations, we obtained the former set of information in vitro (Fig. 3), whereas the latter information was obtained from in vivo experiments (Table 2). The predicted lines based on eqs. 9 and 10 were almost identical to the data obtained in vivo (Fig. 4), suggesting that drug interactions associated with membrane transport via sinusoidal and canalicular membranes can be quantitatively predicted based on theK_i values obtained in isolated hepatocytes and CMVs, respectively, when the unbound concentration of the inhibitor is directly estimated both in plasma and liver in vivo.

It should be noted that there is still limited information about the in vitro system that can assess efflux transport on the sinusoidal membrane. Considering such difficulty, we have proposed the method to avoid false negative prediction, by using eq. 11, of the interaction involving net biliary excretion. This is because the most critical factor that should be avoided in such an approach is a false negative prediction. A false negative prediction is one that does not predict a positive interaction that actually exists in a clinical situation. The intrinsic clearance for the net biliary excretion (CL_int,bile) is a hybrid of the intrinsic clearances for each membrane penetration (P₁,P₂, andP₃) as shown in eq. 8. Therefore, the CL_int,bile can be divided into two extreme cases: the case when P₂ ≪P₃, the CL_int,bile should be equal toP₁, whereas in the case whenP₂ ≫P₃, the CL_int,bile should beP₁ ×P₃/P₂. To avoid any false negative predictions, we should only consider the latter case because, in the former case, the inhibition of onlyP₁ has to be considered, whereas in the latter case such inhibition has to be considered for bothP₁ andP₃. If the inhibitor drug also reducesP₂, the CL_int,bile should be increased and, therefore,P₂ does not need to be considered if we want to avoid any false negative predictions. Thus, in all cases, the reduction in CL_int,bile should be, at most, the reduction in P₁ (sinusoidal uptake) multiplied by that in P₃(canalicular efflux) as expressed in eq. 11. In actual fact, by performing such a multiplication, the predicted values in CL_int,bile were only slightly less than the actual values (Fig. 5A), suggesting that this method is suitable for avoiding any false negative predictions. Note that the predicted value based on this method was always lower than the actual CL_int,bile value (Fig. 5A). This is reasonable when we consider that the CL_uptake was almost comparable with the CL_bile,p in the control (Table 1), which means that the rate-limiting step in the net biliary excretion of methotrexate is its uptake (P₂ ≪P₃), and therefore, the CL_int,bile can be approximated asP₁.

In this method, however, the critical point in humans is the estimation of I_u,liver by sampling the liver and measuring the unbound inhibitor concentration. In addition, it is quite difficult to demonstrate that the f_hestimated using liver homogenate as in the present study is really the same as the unbound fraction in the liver in vivo although no really suitable methods for the determination of the unbound fraction in organs/tissues have been reported to date. Therefore, we usedI_u,plasma instead ofI_u,liver to predict theR_excretion value (eq. 12). Also, in such a case, the predicted line was not very different from the actual values (Fig. 5A), supporting the validity of this method. For inhibitors other than probenecid, however,I_u,liver may be much higher than theI_u,plasma due to its concentrative uptake by hepatocytes. Kanamitsu et al. (2000) proposed a method to determine such differences betweenI_u,plasma andI_u,liver by using isolated hepatocytes treated with ATP depletors or left untreated.

If the inhibitor drug is administered orally, its concentration in the extracellular space may be higher than that in the circulation because of the hepatic first-pass effect. To estimate the extracellular inhibitor concentration, Ito et al. (1998a,b) proposed using the maximum value for the unbound inhibitor concentration in the portal vein by considering the supply from the circulating plasma as well as the drug absorbed from gastrointestinal lumen following oral administration (Ito et al., 1998a,b).Unbound inhibitor concentration in the portal vein≤ (Unbound fraction in blood)× ((Maximum inhibitor concentration in circulating blood) +(Absorption rate constant)×Dose ×(Fraction of the dose absorbed)/(Hepatic blood flow rate)) Equation 13To evaluate the suitability of this equation for predicting transporter-mediated interactions, we applied it to the well known digoxin-quinidine interaction (Hedman et al., 1990) where quinidine reduced the biliary clearance of digoxin to approximately half the control value in humans. Since, in that study, quinidine (400 mg) was administered orally and the maximum inhibitor concentration in circulating plasma was reported to be 4.5 μM (Hedman et al., 1990), the estimated maximum value for the unbound inhibitor concentration in the portal vein was 5 μM where the unbound fraction in plasma, the absorption rate constant, the fraction of the dose absorbed, the hepatic blood flow rate and R_b were assumed to be 0.08, 0.1 min⁻¹, 1, 1600 ml/min, and 1. Since the K_i for the inhibition of digoxin uptake by quinidine in isolated human hepatocytes is over 50 μM (Olinga et al., 1998), whereas theK_m of quinidine for P-glycoprotein is 5 μM (Muller et al., 1994), the predicted biliary clearance based on eq. 11 using the maximum value for the unbound inhibitor concentration in the portal vein was 50% of the control in the presence of quinidine. If the unbound inhibitor concentration in circulating blood was used instead of the maximum value for the unbound inhibitor concentration in the portal vein, the predicted value was 93% of the control. Thus, this calculation supports the validity of the prediction based on eq. 11 using the maximum value for the unbound inhibitor concentration in the portal vein, although further examples demonstrating such validity are needed before being able to draw a final conclusion.

Finally, to confirm the validity of this prediction approach, identification of transporters responsible for methotrexate excretion should also be important. Methotrexate excretion across the canalicular membrane is reported to be mainly mediated by cMOAT/MRP2 (Masuda et al., 1997) since its excretion is greatly reduced in cMOAT/MRP2-deficient rats. On the other hand, its uptake mechanism by isolated hepatocytes is still controversial. Methotrexate is a folate analog and potently inhibits the uptake of folates by isolated rat hepatocytes (Horne et al., 1978), whereas the inhibition of methotrexate uptake by folates was only minimal at folate concentrations greater than the K_m for folate uptake (Gewirtz et al., 1980). A pH dependence was clearly evident in the uptake of folates, whereas this was not as marked for methotrexate uptake (Horne, 1990). Thus, the uptake mechanism of methotrexate would appear to differ to some extent from that of folates. Honscha et al. (2000) recently cloned a transporter, RL-MTX-1, which may be important as a Na⁺-dependent transporter for methotrexate.

In summary, our data in rats suggest that drug interactions associated with membrane transport via the sinusoidal and canalicular membranes can be quantitatively predicted based on theK_i values obtained in vitro and the unbound concentration of the inhibitor drug in the circulating plasma and the liver, respectively. To predict the degree of inhibition of net biliary clearance, the inhibition of each membrane transport process needs to be combined to avoid false negative predictions.