I. Introduction

Serious side-effects caused by drug interactions have attracted a great deal of attention and have become a social problem since the coadministration of ketoconazole and terfenadine was reported to cause potentially life-threatening ventricular arrhythmias (Monahan et al., 1990), and an interaction between sorivudine and fluorouracil resulted in fatal toxicity in Japan (Watabe, 1996; Okuda et al., 1997). The possible sites of drug-drug interaction which can change pharmacokinetic profiles include: (1) gastrointestinal absorption, (2) plasma and/or tissue protein binding, (3) carrier-mediated transport across plasma membranes (including hepatic or renal uptake and biliary or urinary secretion), and (4) metabolism. Pharmacodynamic interactions such as antagonism at the receptor may also increase or decrease the effects of a drug.

In this review, after brief comments on (2) and (3), we intend to focus on (4) and to discuss the possibility of the quantitative prediction of drug-drug interactions in vivo based on the analyses of data from literature obtained by in vitro experiments using human liver samples. Furthermore, strategic proposals for avoiding toxic interactions will be given from a pharmacokinetic point of view.

II. Drug-Drug Interactions Other Than Involving Metabolism

A. Drug-drug interactions involving plasma protein binding

Although interactions involving plasma protein binding are well known, they rarely cause clinically serious problems (Rowland and Tozer, 1995; Rolan, 1994). The reasons are summarized below.

The unbound fraction (f_u)^b of a drug in plasma is increased when it is displaced by other drugs at the plasma protein binding sites. Subsequent alterations in plasma concentration profiles can be caused by changes in both clearance (CL) and volume of distribution (V_d) of the drug. The effect on the steady-state concentration (C_ss) and the area under concentration-time curve (AUC) can be predicted from the change in CL. It should be noted that the effect of protein binding replacement depends on the magnitude of CL and the route of administration. As shown in table 1, an analysis based on the well-stirred model has revealed that the protein binding replacement has little effect on the C_ss and AUC for unbound drugs (C_u,ss and AUC_u) after oral administration, which are parameters directly related to the pharmacological and adverse effects, irrespective of the magnitude of CL. In the case of low clearance drugs, C_u,ssand AUC_u after intravenous administration also are affected little by protein binding replacement. The only situation for a possible interaction is after the intravenous administration of a high clearance drug and there are few examples of this in clinical practice (Rolan, 1994).

The alteration of V_d caused by protein binding replacement also has an effect on the blood drug concentration (Rowland and Tozer, 1995). In the case of drugs with a relatively large V_d, V_d increases in parallel with f_u. Although this leads to a transient reduction in total blood concentration caused by the redistribution of the drug into tissues, the unbound concentration is not affected. However, in the case of drugs with a small V_d, which depend on f_u to a lesser extent, the total blood concentration is not affected so much by the change in f_u, but the unbound concentration is greatly altered.

Figure 1 shows the simulation of the effects of protein binding replacement on the blood concentration profile during a constant intravenous infusion, where the protein binding and the tissue distribution of the drug are assumed to reach equilibrium rapidly, i.e., the concentration changes rapidly in response to a change in f_u. In this simulation, changes in both CL and V_d associated with the change in f_uwere considered. As just described above, the steady-state unbound concentration is altered with the change in f_u only for a high clearance drug. It is also clear from figure 1 that, in the case of drugs with a small V_d, a transient increase in the unbound concentration is observed even for a low clearance drug, and caution for the possible occurrence of side effects is needed.

B. Drug-drug interactions at the transport carrier

Very few studies have focused on drug-drug interactions involving carrier-mediated transport across membranes, including the interactions involving renal secretion and reabsorption and those where p-glycoprotein (p-gp) plays a role (Tsuruo et al., 1981;Slater et al., 1986; Kusuhara et al., in press).

Along with metabolism, renal excretion is one of the most important processes affecting the total body clearance of a drug. Alterations in this process caused by drug-drug interactions should, therefore, be carefully considered. Secretion of drugs at the renal tubule is an active transport process, where organic anion transporters, organic cation transporters, and p-gp are known transport carriers (Horiet al., 1982; Takano et al., 1984; Tanigawaraet al., 1992). The renal clearance of a drug is reduced by inhibition of these transport processes. It is known that both organic anion transporters and organic cation transporters exist on both the basolateral membrane (BLM) and the brush border membrane (BBM) and that they are different from each other, whereas p-gp is only present on the BBM. The inhibitors of these transporters interact with other drugs; for example, inhibition of the renal excretion of penicillin and other related drugs by probenecid (Hunter, 1951), methotrexate excretion by nonsteroidal anti-inflammatory drugs (Statkevich et al.,1993), and digoxin excretion by quinidine (Tanigawara et al., 1992) all involve this kind of interaction.

Most studies of pharmacokinetic drug-drug interactions reported so far have been limited to the analysis of hepatic metabolism. However, the hepatic clearance of many drugs has been found to be determined mainly by hepatic uptake (Yamazaki et al., 1995, 1996). The overall intrinsic clearance (CL_int,all) can be expressed using the intrinsic clearance for metabolism (CL_int) and that for membrane permeation (PS) as follows:CLint,all=PSinf·CLint/(PSeff+CLint) Equation 1where PS_inf is intrinsic clearance for influx, and PS_eff is intrinsic clearance for efflux.

It is clear from equation (1) that CL_int,all equals CL_int in the case of drugs with large (PS ≫ CL_int) and symmetrical (PS_inf = PS_eff) membrane permeability. Otherwise, hepatic clearance is affected by the membrane permeability of the drug. In such cases, it is important to evaluate drug-drug interactions involving not only metabolism but also membrane permeation. In our laboratory, several cases of drug-drug interactions were found in rats at the level of transporters involved in hepatobiliary transport as shown below. In the future, similar interactions at the transporter level possibly may be found in the clinical situation. The interactions found in rats include: inhibition of biliary excretion of glucuronides and sulfates of liquiritigenin, a flavonoid, by organic anions such as dibromosulfophthalein (DBSP) and glycyrrhizin, which has a glucuronide moiety (Shimamura et al., 1994); inhibition of biliary excretion of glycyrrhizin by DBSP (Shimamura et al., 1996); inhibition of biliary excretion of leukotriene C₄, which has a glutathione moiety, by DBSP (Sathirakul et al., 1994); and reduction of plasma clearance, based on hepatic uptake and biliary excretion, of octreotide, a small octapeptide, by DBSP and taurocholate (Yamada et al., 1997). In vivo drug-drug interactions involving membrane transport remain to be predicted based on in vitro studies of the membrane permeability of drugs.

III. Drug-Drug Interactions Involving Metabolism in the Liver

As a pharmacokinetic parameter directly related to the pharmacological and/or adverse effects of drugs, it is very important to predict the hepatic clearance. Because the use of animal scale-up is limited in the case of hepatic metabolic clearance due to large inherent interspecies differences, we have developed an alternative methodology to predict in vivo metabolic clearance in the liver; it is based on in vitro studies using mainly rat liver microsomes and isolated rat hepatocytes (Sugiyama and Ooie, 1993; Iwatsubo et al., 1996). Recently, with the greater availability of human liver samples, the method of in vitro/in vivo scaling can now be applied to human studies. We have already demonstrated that the method can be applied to P450 metabolism in humans based on in vitro and in vivo data obtained from the literature (Iwatsubo et al., 1997). However, the prediction of intrinsic clearance was not successful for some drugs, possibly because of the contribution of active transport into the liver and/or first-pass metabolism in the gut.

In order to prevent toxic drug-drug interactions, it is important to quantitatively predict pharmacokinetic changes caused by coadministration of drugs that are known to inhibit the hepatic metabolism of the drug under study (Sugiyama and Iwatsubo, 1996;Sugiyama et al., 1996). In this review, we have focused on the drug-drug interactions via inhibitory mechanisms and have tried to predict in vivo interactions from in vitro data on drug metabolism obtained from the literature.

A. Examples of In Vivo Drug-Drug Interactions Involving P450 Metabolism

Drug-drug interactions involving metabolism are one of the principal problems in clinical practice to evaluate the pharmacological and adverse effects of drugs. Parkinson (1996) summarized examples of substrates, inhibitors, and inducers of the major human liver microsomal P450 enzymes involved in drug metabolism. In the case of drugs that undergo metabolism by CYP3A4 and 2D6, particular attention should be paid to the interactions resulting in alterations in blood concentrations possibly accompanied by a change in its effects, because a number of drugs are metabolized by these enzymes (Bertz and Granneman, 1997). For example, blood concentrations of imipramine and desipramine, substrates for CYP2D6, are elevated several–fold by coadministration of fluoxetine, another substrate for CYP2D6 (Bergstromet al., 1992). Similarly, concentrations of terfenadine, which is metabolized by CYP3A4, are increased in patients taking erythromycin, which is also a substrate for CYP3A4 (Honig et al., 1992). Quinidine is metabolized mainly by CYP3A4 but inhibits the metabolism of substrates for CYP2D6, such as sparteine, rather than those for CYP3A4 (Schellens et al., 1991). Furthermore, in the case of drugs whose metabolism is mediated by multiple isozymes (e.g., diazepam), drug-drug interaction may be complicated because of possible dose-dependent changes in the contribution of each isozyme to the overall metabolism (Iwatsubo et al., 1997).

B. Inhibition Mechanism of Drug Metabolism by P450

Drug metabolism by P450 can be inhibited by any of the following three mechanisms.

The first is mutual competitive inhibition caused by coadministration of drugs metabolized by the same P450 isozyme, such as the above-mentioned (see Sec. A.) combinations of imipramine or desipramine and fluoxetine (CYP2D6). In this case, as reported for metoprolol and propafenone (CYP2D6) (Wagner et al., 1987), blood concentrations of both drugs may be increased.

The second is the inactivation of P450 by the drug metabolite forming a complex with P450. This type of inhibition is designated as “mechanism-based inhibition” (Silverman, 1988). Inhibition by macrolide antibiotics, such as erythromycin, is a typical example of this type of interaction. As shown in figure2, P450 demethylates and oxidizes the macrolide antibiotic into a nitrosoalkane that forms a stable, inactive complex with P450 (Periti et al., 1992).

The third is inhibition by the binding of imidazole or a hydrazine group to the haem portion of P450. In the case of cimetidine, the nitrogen in the imidazole ring binds to the haem portion of P450 causing nonselective inhibition of many P450 isozymes (Somogyi and Muirhead, 1987).

C. Inhibition Patterns of Drug Metabolism

The effects of inhibition of drug metabolism on in vivo pharmacokinetics are highly variable and depend on the properties of the drug, the route of administration, etc. (Rowland and Martin, 1973;Tucker, 1992). Except for the case of mechanism-based inhibition, inhibition of drug metabolism can be classified into the following three categories, and the equations corresponding to each inhibition type have been derived (Todhunter, 1979).

1. Competitive Inhibition.

Competitive inhibition is a pattern of the inhibition where the inhibitor competes with the drug for the same binding site within an enzyme protein: E+S⇄ES→E+P Km (Michaelis constant for S) E+I⇄EI Ki (Inhibition constant for I) where E is the enzyme, S is the substrate, ES is the enzyme-substrate complex, P is the product, I is the inhibitor, and EI is the enzyme-inhibitor complex. In the case of competitive inhibition, the metabolic rate (v) can be expressed by the following equation (2):v=Vmax·SKm(1+I/Ki)+S Equation 2where V_max is the maximum metabolic rate.

It is clear from equation (2) that the inhibition by a given concentration of I is marked when the substrate concentration is low and becomes less marked with an increase in the substrate concentration.

2. Noncompetitive Inhibition.

Noncompetitive inhibition is a pattern of inhibition where the inhibitor binds to the same enzyme as the drug but the binding site is different, resulting in a conformation change, etc., of the protein:E+S⇄ES→E+PKmE+I⇄EIKiEI+S⇄EISKmES+I⇄EISKi where EIS is the enzyme-inhibitor-substrate complex. It is assumed that the inhibitor binds to the free enzyme and the ES complex with the same affinity. In the case of noncompetitive inhibition, the metabolic rate can be expressed by the following equation (3):v={Vmax/(1+I/Ki)}·SKm+S Equation 3It is clear from equation (3) that the degree of inhibition does not depend on the substrate concentration.

3. Uncompetitive Inhibition.

Uncompetitive inhibition is a pattern of inhibition where the inhibitor binds only to the enzyme forming a complex with the drug:E+S⇄ES→E+PKmES+I⇄EISKi Unlike competitive and noncompetitive inhibition, the inhibitor cannot bind to the free enzyme. In the case of uncompetitive inhibition, the metabolic rate can be expressed by the following equation (4):v={Vmax/(1+I/Ki)}·SKm/(1+I/Ki)+S Equation 4It is clear from equation (4) that the inhibition becomes more marked with increasing substrate concentration.

The degree of inhibition depends on the inhibition pattern when the substrate concentration is high. However, when the substrate concentration is much lower than K_m (K_m ≫ S), the degree of inhibition (R) is expressed by the following equation (5), independent of the inhibition pattern, except in the case of the uncompetitive inhibition (Tucker, 1992):R=v(+inhibitor)v(−inhibitor)=11+I/Ki Equation 5In clinical situations, the substrate concentration is usually much lower than K_m. In this review, we will discuss the most frequently observed case in which equation (5) can be applied.

D. Prediction of In Vivo Drug-Drug Interactions Based on In Vitro Data

1. General Equations.

The following factors determine the degree of change in C_ss and AUC caused by the drug-drug interaction in vivo:

1)

The route of administration (intravenous or oral, i.e., whether the drug first passes through the liver or not).

2)

Fraction (f_h) of hepatic clearance (CL_h) in total clearance (CL_tot).

3)

Fraction (f_m) of the metabolic process subject to inhibition in CL_h.

4)

Unbound concentration of the inhibitor (I_u) around the enzyme.

5)

Inhibition constant (K_i).

6)

Plasma unbound concentration (C_u,ss) of the drug subject to inhibition.

7)

Michaelis constant (K_m) for the drug subject to inhibition.

f_h and f_m are expressed as follows:fh=CLhCLh+CLr Equation 6 fm=CLint,1CLint,1+CLint,2 Equation 7where CL_h is hepatic clearance, CL_r is renal clearance, and CL_int,1 and CL_int,2represent the intrinsic clearance for the metabolic pathway inhibited and not inhibited by the inhibitor, respectively (CL_int = CL_int,1 + CL_int,2). In equation (6), it is assumed that only the liver and kidney are the clearance organs. Equation (6) can be rearranged to give the following equation:CLr=CLh(1/fh−1) Equation 8Equation (7) can be rearranged to give the following equation:CLint,2=CLint,1(1/fm−1) Equation 9The fractional clearance for a particular metabolic pathway (CL_h,m) can be expressed as f_h multiplied by f_m.

R_c, defined as the degree of increase in C_ss and AUC caused by the drug-drug interaction in vivo, can be calculated as shown below, depending on the route of administration.

a. Intravenous Administration.

The change in AUC after intravenous bolus administration (AUC_iv) and C_ss during intravenous infusion can be expressed by the following equation, if the dose or infusion rate is constant:

Rc=AUCiv(+inhibitor)AUCiv(−inhibitor)=Css(+inhibitor)Css(−inhibitor) Equation 10 =CLtotCLtot′=CLh+CLrCLh′+CLr=CLh+CLh(1/fh−1)CLh′+CLh(1/fh−1) =CLh/fhCLh′+CLh/fh−CLh=1fh·CLh′/CLh+1−fh where ′ represents the value after alteration by the drug-drug interaction.

i. High clearance drug.

Because f_b · CL_int is much larger than the hepatic blood flow rate (Q_h) (Q_h ≪ f_b · CL_int), CL_h is rate-limited by the flow rate (CL_h = Q_h). When the altered CL_h is still rate-limited by the flow rate (CL_h′ = Q_h), i.e., Q_h ≪ f_b. CL_int′, then CL_h′ equals CL_h. Thus, R_c can be calculated to be unity by equation (10), indicating no change in AUC_iv or C_ss. This is not the case when the inhibition is so extensive that CL_h is not limited by the flow rate any more.

ii. Low clearance drug.

In the case of a low clearance drug, CL_h = f_b · CL_int and CL_h′ = f_b. CL_int′. If the protein binding is not altered by the inhibitor, the ratio (y) of CL_h and CL_h′ can be calculated as follows: y=CLh′CLh=fb·CLint′fb·CLint=fb·(CLint,1′+CLint,2)fb·(CLint,1+CLint,2) Equation 11 =CLint,1′+CLint,1(1/fm−1)CLint,1+CLint,1(1/fm−1) =CLint,1′+CLint,1/fm−CLint,1CLint,1/fm =fm·CLint,1′/CLint,1+1−fm Combining equations (10) and (11) yields the following equation: Rc=1fh(fm·CLint,1′/CLint,1+1−fm)+1−fh Equation 12 =1fh·fm·CLint,1′/CLint,1+1−fh·fm Because C_u,ss encountered clinically is usually much less than K_m, CL_int,1 and CL_int′,1can be expressed as follows:CLint,1=Vmax/Km and CLint,1′=Vmax/Km(1+Iu/Ki) where I_u is the unbound concentration of the inhibitor. Therefore,CLint,1′/CLint,1=11+Iu/Ki Equation 13can be derived. Combining equations (12) and (13) yields the following equation:Rc=1fh·fm·{1/(1+Iu/Ki)}+1−fh·fm Equation 14It is clear from equation (14) that, in the case of the intravenous administration of a low clearance drug, the degree of increase in AUC_iv is determined not by K_m or C_u,ss but by K_i, I_u, f_h, and f_m, if K_m ≫ C_u,ss.

b. Oral Administration.

The change in AUC_poafter a single oral administration and that in C_ss,av after repeated oral administration can be expressed by the following equation (15), if the dose and administration interval is constant:

 Rc=AUCpo(+inhibitor)AUCpo(−inhibitor)=Css,av(+inhibitor)Css,av(−inhibitor) Equation 15 =CLoralCLoral′=(CLh+CLr)/(Fh·Fa)(CLh′+CLr)/(Fh′·Fa) ={CLh+CLh(1/fh−1)}/Fh{CLh′+CLh(1/fh−1)}/Fh′ =CLh/fh(CLh′+CLh/fh−CLh)·Fh′Fh =1fh·CLh′/CLh+1−fh·Fh′Fh where F_h is hepatic availability and F_a is the fraction absorbed from the gastrointestinal tract into the portal vein.

Some kind of mathematical model has to be introduced for the calculation of the hepatic intrinsic clearance (CL_int) in vivo. In order to avoid a false negative prediction of drug-drug interactions, we tried to evaluate the maximum inhibitory effect expected. The well-stirred model was selected as one which can detect the maximum effect of the inhibitor. In the case of oral administration where D is dose, D/AUC_po = D/τ/C_ss,av = CL_h/F_h = f_b · CL_intcan be derived based on the well-stirred model, irrespective of the value of CL_h relative to Q_h, where D is dose. In this model, therefore, either AUC_po or C_ss,av is affected directly by the reduction in CL_int without a contribution from the hepatic blood flow rate. For this reason, the well-stirred model can detect the maximum effect of an inhibitor. Thus, the well-stirred model was used in the following discussion of the prediction of drug-drug interactions after oral administration.

i. High clearance drug.

Because f_b · CL_int is much larger than the hepatic blood flow rate (Q_h ≪ f_b · CL_int), CL_h is rate-limited by the flow rate (CL_h = Q_h). When the altered CL_h is still rate-limited by the flow rate (CL_h′ = Q_h), i.e., Q_h ≪ f_b · CL_int′, then CL_h′ equals CL_h. On the other hand, F_h = Q_h/(f_b · CL_int) and F_h′ = Q_h/(f_b · CL_int′). Therefore, the following equation (16) can be derived from equation (15): Rc=Fh′Fh=CLintCLint′=CLint,1+CLint,2CLint,1′+CLint,2 Equation 16 =CLint,1+CLint,1(1/fm−1)CLint,1′+CLint,1(1/fm−1) =CLint,1/fmCLint,1′+CLint,1/fm−CLint,1 =1fm·CLint,1′/CLint,1+1−fm Furthermore, as C_u,ss encountered clinically is usually much less than K_m, CL_int,1 and CL_int′_,1 can be expressed as follows:CLint,1=Vmax/Km and CLint,1′=Vmax/Km(1+Iu/Ki) Therefore,CLint,1′/CLint,1=11+Iu/Ki Equation 17can be derived. Combining equations (16) and (17) yields the following equation:Rc=1fm·{1/(1+Iu/Ki)}+1−fm Equation 18

ii. Low clearance drug.

Since the first-pass hepatic availability is close to unity for low clearance drugs, the final equation (14) should be the same for intravenous and oral administration.

The effect of the inhibitor on the C_max after oral administration also depends on the clearance of the drug. Assuming that the drug absorption from the gastrointestinal tract is sufficiently rapid, C_max is proportional to F_h. Based on the well–stirred model, F_h can be expressed as follows:Fh=Qh/(Qh+fb·CLint) Equation 19It is clear from equation (19) that F_h is minimally affected by the change in CL_int in the case of a low clearance drug (Q_h ≫ f_b · CL_int: F_h = 1), but is inversely proportional to CL_intin the case of a high clearance drug (Q_h ≪ f_b · CL_int: F_h = Q_h/f_b · CL_int), in which case C_max also changes in inverse proportion to CL_int.

In summary, it is important to know the values of K_i, I_u, f_h, and f_m in order to predict in vivo drug-drug interactions. Approximated f_h and f_m values can be estimated from the urinary recovery of the parent compound and each metabolite. K_i values can be evaluated by kinetic analysis of in vitro data using human liver microsomes and recombinant systems and this has already been done for many compounds. The key, therefore, is the evaluation of I_u.

2. The evaluation of the unbound concentration of the inhibitor in vivo.

Although I_u is the unbound concentration of the inhibitor around the metabolic enzyme in the liver, it is impossible to directly measure this in vivo. However, many drugs are transported into the liver by passive diffusion, allowing for the assumption that the unbound concentration in the liver equals that in the liver capillary at steady-state. This means that estimating the unbound concentration of the inhibitor in the liver capillary may be enough for some drugs. This assumption is not valid, however, in the case of drugs which are actively transported into or out of the liver; the unbound concentration in the liver may be higher in the former case or lower in the latter than in the liver capillary (fig.3). In these cases, another experiment using human hepatocytes, human liver slices, etc., is required to estimate the kinetic parameters for the active transport. Furthermore, the unbound concentration in the liver capillary is always changing and a concentration gradient is formed from the entrance (portal vein) to the exit (hepatic vein). Which of these concentrations should be considered as I_u? An underestimation of I_u may lead to a “false negative” prediction of actually occurring in vivo drug interaction from in vitro data. In order to avoid a false negative prediction caused by underestimation of I_u, the plasma unbound concentration at the entrance to the liver, where the blood flow from the hepatic artery and portal vein meet, was considered the maximum value of I_u and was used in the prediction (I_in,u; fig. 4).

Practically, the maximum plasma concentration in the circulation (I_max) has been estimated for many inhibitors. When the value of I_max is not reported, it can be predicted from both the plasma concentration at a single time point after administration and the pharmacokinetic parameters such as the elimination half life (t_1/2,β).

According to the model in figure 4, influx into the liver consists of contributions from the hepatic artery and portal vein (after gastrointestinal absorption). When the drug is absorbed from the gastrointestinal tract with a first-order rate constant (k_a), the maximum influx rate into the liver (v_in,max) can be expressed as follows:vin,max≦QaImax+QpvImax+ka·D·Fa·e−kat′ Equation 20where Q_a and Q_pv represent the blood flow rate in the hepatic artery and the portal vein, respectively, F_a is the fraction absorbed from the gastrointestinal tract into the portal vein, and t′ is the time after oral administration (after subtraction of the lag-time).

When the absorption rate is maximum (i.e., t′ = 0), the final term in equation (20) can be expressed as k_a · D · F_a and thus:vin,max≦(Qa+Qpv)Imax+ka·D·Fa Equation 21As Q_h =  Q_a +  Q_pv, the following equation can be derived: Equation 22 Therefore, I_in,max can be predicted if the parameters such as k_a and F_a are available for the inhibitor. Taking the plasma protein binding into consideration, the unbound I_in,max (I_in,max,u) can be calculated as I_in,max · f_u. Finally, comparing the value of I_in,max,u as I_in,u and that of K_i obtained in vitro allows the prediction of the maximum degree of in vivo drug-drug interaction caused by metabolic inhibition.

In general, the apparent absorption rate of the orally administered drug is maximum when the gastrointestinal absorption of the drug is so rapid that the rate-limiting step is the gastric emptying rate. A first order rate constant (k_a) of about 0.1 min^{− 1} is reported for gastric emptying in rats and humans (Oberle et al., 1990). On the other hand, the absorption rate constant in humans can be calculated from the time to reach the maximum concentration (T_max) and the elimination constant (k_el) as follows:Tmax=ln(ka/kel)/(ka−kel) Equation 23In practice, however, because of the possible estimation error of T_max caused by interindividual differences etc., the calculated value of k_a sometimes exceeds 0.1 min^{− 1}, though it should never exceed that, theoretically, for gastric emptying. Therefore, the theoretically maximum value of 0.1 min^{− 1} was used for k_a when it was calculated to be larger than 0.1 min^{− 1}. Moreover, in order to avoid a false negative prediction, the maximum k_a of 0.1 min^{− 1} was used to obtain the largest inhibitor concentration if k_a was unknown.

E. Examples of the Prediction of Drug-Drug Interactions Based on Literature Data

The methodology described above (see Section III.D.) has been applied to the prediction of in vivo drug-drug interactions from in vitro data gathered from the literature.

1. Successful Cases of In Vitro/In Vivo Prediction.

a.Tolbutamide-sulfaphenazole. Interactions between tolbutamide and sulfa-agents cause serious side effects such as hypoglycemic shock in patients (Christensen et al., 1963) and exhibit the marked interspecies differences in animals. Veroneseet al. (1990) reported about a five-fold increase in both AUC_po and t_1/2 of tolbutamide in humans following coadministration of 500 mg sulfaphenazole (table2, fig. 5).

The t_1/2 of intravenous tolbutamide is prolonged and the CL_tot is reduced markedly in rats, too, by sulfaphenazole (Sugita et al., 1981). On the contrary, the CL_tot of tolbutamide is increased 15 to 30% in rabbits with little change in the t_1/2 (fig.6) (Sugita et al., 1984). Because tolbutamide is a low clearance drug with a small urinary excretion, the CL_tot after intravenous administration is expressed by the following equation (24):CLtot=D/AUC=fb·CLint Equation 24 Sugita et al. (1984) tried to reconstruct the CL_tot in vivo based on the values of unbound fraction in blood (f_b) and CL_int estimated separately by in vitro binding and metabolic studies. Sulfaphenazole inhibits both plasma protein binding and hepatic metabolism of tolbutamide, causing the increase in f_b and the reduction in CL_int, in both species. Although the CL_int falls to about one-fourth and the f_b increases about two-fold in rats, resulting in about a half-fold reduction in the CL_tot, the CL_int falls to about one-half and the f_bincreases about two-fold in rabbits resulting in little change in the CL_tot (fig. 7). The effects on the CL_int and f_b of tolbutamide are not constant among sulfa-agents; sulfadimethoxine also reduces the CL_int by about one-half in rabbits but increases the f_b more than two-fold, resulting in an increase in the CL_tot and a reduction in the AUC (Sugita et al.,1984).

The interaction between tolbutamide and sulfaphenazole involves both plasma protein binding and hepatic metabolism in humans, too. The main metabolic pathway of tolbutamide in vitro is CYP2C9-mediated hydroxylation, and the metabolite undergoes sequential metabolism forming a carboxylate in vivo (Thomas and Ikeda, 1966; Nelson and O’Reilly, 1961). The K_i of sulfaphenazole, a specific inhibitor of CYP2C9, for tolbutamide methyl hydroxylation in human liver microsomes in vitro is 0.1–0.2 μM (Miners et al.,1988; Back et al., 1988). The I_max of sulfaphenazole after a 500 mg dose was 70 μM in humans, and the absorption term [the second term in equation (22)] was calculated to be 8.0 μM using k_a = 0.0095 min^{− 1}, D = 500 mg, Q_h = 1610 ml/min, and F_a = 0.85. I_in,max was, therefore, calculated to be 78 μM, indicating that the contribution of systemic circulation is greater than that of absorption. Taking the f_u value (0.32) of sulfaphenazole into consideration, I_in,u/K_iwas calculated to be 125–250 (table 2). The plasma protein binding of tolbutamide is also inhibited by sulfaphenazole in humans, resulting in about a three-fold increase in f_b (Christensen et al., 1963). However, the inhibition is considered almost complete in terms of the product of f_b and CL_int because the extent of inhibition of metabolism is much greater than that of its plasma protein binding. The contribution of the CYP2C9-related metabolic pathway of tolbutamide is about 80% of the total (f_h · f_m = CL_h,m/CL_tot = 0.8) (table 2). Therefore, complete inhibition of this metabolic pathway leads to an 80% reduction in CL_int, and the AUC_po is predicted to be five times larger than the control value, which is consistent with the observed increase (table 2).

b. Triazolam-ketoconazole.

Von Moltke et al. (1996) reported that plasma triazolam concentration after oral administration of 0.125 mg was greatly elevated by oral ketoconazole (200 mg), producing a nearly nine-fold reduction in the apparent oral clearance. They predicted this interaction based on in vitro studies using human liver microsomes (table 3). Triazolam is eliminated in humans mainly by CYP3A-mediated metabolism to α-hydroxy (OH)- and 4-OH-triazolam. Ketoconazole is a powerful inhibitor of both these metabolic pathways, with a mean K_ivalue of 0.006 and 0.023 μM, respectively (Von Moltke et al., 1996). In order to estimate ketoconazole concentrations in the liver, they conducted an in vitro study using mouse liver homogenates in human plasma spiked with ketoconazole; a liver/plasma partition ratio of 1.12 was obtained. On the other hand, the partition ratio was calculated to be 2.03 in the in vivo mouse study where the ketoconazole concentrations in plasma and liver were measured. The concentration of ketoconazole in the liver was estimated by multiplying this partition ratio by the total ketoconazole concentration in plasma in the clinical study (0.04–9.32 μM). Using the in vitro K_i values, ketoconazole concentration in the liver, and the contribution of both metabolic pathways (52.5% and 47.5% for α- and 4-OH-pathway, respectively), the predicted degree of reduction (>95%) in triazolam clearance in vivo was consistent with the 88% reduction actually observed in vivo (table 3). However, it should be noted that in this report, the total concentration of the inhibitor was used instead of unbound concentration in the liver. The unbound concentration needs to be estimated because the K_i values obtained in the in vitro studies are based on the concentration in the medium.

Using our method proposed above (see Section III.D.), the ketoconazole-triazolam interaction would be predicted as follows: The I_max,ss of ketoconazole during administration of 200 mg × 2/day was 6.6 μM (Daneshmend et al., 1981), and the absorption term [the second term in equation (22)] was calculated to be 1.4–2.5 μM using k_a = 0.0099–0.018 min^{− 1}, D = 200 mg, Q_h= 1610 ml/min, and F_a =  0.59. The k_a was calculated from equation (23) using the values of T_max and t_1/2( = 0.693/k_el) (Daneshmend et al.,1984). The I_in,max is, therefore, calculated to be 8.0–9.1 μM. Since the f_u of ketoconazole is 0.01, the I_in,max,u is calculated to be 0.080–0.091 μM and the obtained I_in,max,u/K_i value is 13–15 and 3.5–4.0 for the α-OH and 4-OH pathways, respectively, using a K_i value of 0.006 and 0.023 μM, respectively. Therefore, the reduction in the clearance can be estimated as follows, considering the contribution of each pathway to the total metabolism:R=11+(13–15)×0.525+11+(3.5–4.0)×0.475 =0.128–0.143 Thus, an 85.7–87.2% reduction is predicted by this method, which is very close to the observed reduction (88%) (table 3). The degree of the inhibition should be larger if ketoconazole is actively transported into the liver.

Two cases have been shown here in which the interaction that had actually occurred in vivo was successfully predicted based on in vitro metabolism data. On the other hand, we believe that the ability to predict by the above-mentioned methods based on in vitro data should be very high in the case of drug combinations that do not interact with each other in vivo. In other words, the absence of in vivo drug-drug interactions should be successfully predicted, which has been partly confirmed in our study, though the data are not shown here.

2. Interactions Predictable for the Objective Metabolic Pathway but not Predictable for the Overall Data.

a.Sparteine-quinidine. Schellens et al.(1991) reported that the CL_oral of sparteine (dose: 50 mg) fell from 979 to 341 ml/min (35% of the control value) after coadministration of 200 mg quinidine (table4). The main metabolic pathway of sparteine is CYP2D6-mediated dehydration. Because quinidine is a specific inhibitor of CYP2D6, it is reasonable that metabolic inhibition is involved in this quinidine-induced reduction in the CL_oral of sparteine. The K_i of quinidine for the CYP2D6-mediated metabolism in human liver microsomes in vitro is reported to be 0.06 μM. The I_max of quinidine after a dose of 200 mg was 4.1 μM, and the absorption term [the second term in equation (22)] was calculated to be 0.86–22 μM using k_a =  0.0027–0.069 min^{− 1}, D  =  200 mg, Q_h =  1610 ml/min, and F_a =  0.83. I_in,max is, therefore, calculated to be 5–26 μM. Because the f_u of quinidine is 0.15, the I_in,u and I_in,u/K_i are calculated to be 0.75–3.9 μM and 13–65, respectively (table 4). Thus, it was predicted that the dehydration pathway of sparteine would be almost completely inhibited by quinidine. The contribution of the dehydration pathway of sparteine to the total elimination is about 25% (f_h · f_m =  CL_h,m/CL_tot= 0.25) (table 4). Therefore, the complete inhibition of this dehydration pathway will reduce the CL_oral to 75% of the control value, which is about two-fold larger than the observed reduction to 35%. The reasons for this discrepancy may include the possibility that metabolic pathways other than dehydration may also be inhibited by quinidine.

b. Terfenadine-ketoconazole.

Honig et al. (1993) reported that blood concentrations of terfenadine (dose: 60 mg), detectable only in one of six subjects when administered alone (I_max = 7 ng/ml), became detectable in all subjects following coadministration of 200 mg ketoconazole, with the highest I_max in the same subject elevated to 81 ng/ml (table 5). The main elimination pathway of terfenadine is CYP3A4-mediated N-dealkylation and hydroxylation yielding a carboxylate, which may undergo sequential N-dealkylation (Garteiz et al., 1982). K_i values of ketoconazole for terfenadine metabolism in vitro have been reported by two groups. Jurima-Romet et al. (1994) reported the K_i values of 3 and 10 μM in human liver microsomes and <1 and 3 μM in human hepatocytes (Jurima-Romet et al.,1996; Li et al., 1997) for the N-dealkylation and hydroxylation pathways, respectively. Based on the K_ivalues in human liver microsomes reported by Von Moltke et al. (1994), I_in,u/K_i value was calculated to be 3.3–3.8 and 0.33–0.38 for the N-dealkylation and hydroxylation pathways, respectively (table 5) [see our previous review (Itoet al., 1998) for the details]. As the estimated contribution (f_h · f_m = CL_h,m/CL_tot) of these two pathways to the total metabolism was about 0.13 and 0.45, respectively, the increase in the availability and C_max caused by the metabolic inhibition was predicted to be about 1.3-fold according to equation (14). However, the C_max was actually increased more than 10-fold. The possible reasons to explain this great discrepancy include: inaccurate measurements of clinical concentrations of terfenadine being around the detection limit of the assay, and the contribution of the other 50% of the metabolism of terfenadine neglected in the analysis. As shown later (see Section III.H.2.), interactions involving metabolism and/or efflux process in the gut may have some contributions in the in vitro/in vivo discrepancy. If the value of I_in,u/K_i comparable to that for N-dealkylation (3.8) can be applied to other metabolic pathways, the AUC is predicted to increase more than five-fold, which is close to the results in vivo.

3. Interactions Not Predictable by In Vitro/In Vivo Scaling.

a. Imipramine-fluoxetine. Coadministration of tricyclic antidepressants such as imipramine and desipramine with fluoxetine may induce severe side effects including delirium and grand mal seizure (Preskorn et al., 1990). The AUC_poof imipramine (dose: 50 mg) is reported to increase about 1.9-fold after coadministration of 60 mg fluoxetine (table6) (Bergstrom et al., 1992). The main elimination pathways of imipramine are 2-hydroxylation and N-demethylation yielding desipramine, which undergoes further 2-hydroxylation. The 2-hydroxylation pathway is mainly catalyzed by CYP2D6. On the other hand, fluoxetine is a specific inhibitor of CYP2D6 with a K_i of 0.92 μM for the 2-hydroxylation of imipramine in human liver microsomes (Skjelbo and Brosen, 1992). The I_max of fluoxetine after administration of 60 mg is 0.2 μM (Aronoff et al., 1984), and the absorption term [the second term in equation (22)] was calculated to be 0.83 μM using k_a =  0.012 min^{− 1}, D = 60 mg, Q_h = 1610 ml/min, and F_a = 0.80. The k_a was calculated from equation (23) using the values of T_max and t_1/2( = 0.693/kel). Therefore, the I_in,max is 1.02 μM, indicating that absorption makes a major contribution. Because the f_u of fluoxetine is 0.06, the I_in,u and I_in,u/K_i are calculated to be 0.061 μM and 0.066, respectively (table 6). Furthermore, the contribution (f_h · f_m =  CL_h,m/CL_tot) of this metabolic pathway (2-hydroxylation) is about 18% of the total. According to equation (14), therefore, the metabolic inhibition in vivo was not predicted to have a significant effect on the AUC in spite of the approximately 2-fold increase actually observed (table 6). Possible reasons for this discrepancy include the estimation error of K_i and the possibility that other metabolic pathways and pharmacokinetic processes also may be altered by fluoxetine.

b. Caffeine-ciprofloxacin.

Stille et al. (1987) reported that the AUC_po of caffeine (dose: 220 to 230 mg) increased about 1.6-fold after coadministration of 250 mg ciprofloxacin (table 7). The main metabolic pathways of caffeine are 1-demethylation, 3-demethylation, 7demethylation, and 8-hydroxylation, mediated by CYP1A2. Because antimicrobial agents such as ciprofloxacin are specific inhibitors of CYP1A2, metabolic inhibition should be involved in the ciprofloxacininduced increase in the AUC_po of caffeine. The K_i of ciprofloxacin for caffeine 3-demethylation in human liver microsomes in vitro is around 150 μM (Kalow and Tang, 1991). The I_max of ciprofloxacin after administration of 250 mg is 4.3–6.0 μM (Guay et al., 1987), and the absorption term [the second term in equation (22)] was calculated to be 9.3–22 μM using k_a = 0.02–0.04 min^{− 1}, D  =  250 mg, Q_h = 1610 ml/min, and F_a = 0.92. Therefore, the I_in,max was calculated to be 14–28 μM, indicating that the contribution of absorption is greater than that of the systemic circulation. Because the f_u of ciprofloxacin is 0.8, the I_in,u and I_in,u/K_i are calculated to be 11–22 μM and 0.07–0.15, respectively (table 7). The contribution (f_h · f_m = CL_h,m/CL_tot) of this pathway to the total elimination is about 79% (table 7). Therefore, if the maximum value of I_in,u/K_i (0.15) is used in the evaluation of the inhibition of this pathway, the ciprofloxacin-induced increase in the AUC_po of caffeine can be predicted as follows:AUCpo(+inhibitor)/AUCpo(control) =1/{fh·fm/(1+Iu/Ki)+(1−fh·fm)}=1.1 A 1.6-fold increase was actually observed, which indicates a greater degree of inhibition than predicted. Possible reasons for this discrepancy include the estimation error of K_i, the possibility that other metabolic pathways may also be inhibited by ciprofloxacin, and the accumulation of ciprofloxacin in the liver because of active transport. Indeed, we have recently demonstrated that a new quinolone antibiotic, grepafloxacin, is actively taken up by the rat liver (Sasabe et al., 1997).

c. Cyclosporin-erythromycin.

Vereerstraetenet al. (1987) reported that the AUC_po of cyclosporin (dose: 6 mg) increased about 1.6-fold after coadministration of 1.1 g erythromycin (table8). Cyclosporin has many metabolic pathways, among which the metabolism to M1, M17, and M21 are mediated by CYP3A4 (Lensmeyer et al., 1988). These metabolites are sequentially metabolized to form carboxylates in vivo (Pichard et al., 1990). Because erythromycin is a specific inhibitor of CYP3A4, metabolic inhibition should be involved in this increase in the AUC_po of cyclosporin. The K_i of erythromycin for cyclosporin hydroxylation in human liver microsomes in vitro is about 75 μM (Miller et al., 1990). The I_max of erythromycin after a 1.1 g dose is 10–12 μM (Vereerstraetenet al., 1987), and the absorption term [the second term in equation (22)] was calculated to be 15–93 μM using k_a = 0.02–0.10 min^{− 1}, D = 1.1 g, Q_h = 1610 ml/min, and F_a = 0.58. In the calculation of k_ausing k_el( = 0.693/t_1/2) and T_max (Lensmeyer et al., 1988) based on equation (23), the maximum and minimum values were obtained taking the interindividual variation in T_max into consideration. As mentioned above (see Section III.D.2.), however, it would be preferable to use the maximum value of k_a in order to avoid a false negative prediction of the possibility of a drug-drug interaction. Equation (22) gives an I_in,max of 25–105 μM. Because the f_u of erythromycin is 0.16, I_in,u and I_in,u/K_i are calculated to be 4–17 μM and 0.05–0.23, respectively (table 8). The contribution of these metabolic pathways of cyclosporin to the total elimination (CL_oral= f_b · CL_int) is about 76% (f_h · f_m = CL_h,m/CL_tot = 0.76) (table 8). Therefore, if the maximum value of I_in,u/K_i(0.23) is used in the evaluation of the inhibition of these pathways, the erythromycin-induced increase in the AUC_po of cyclosporin can be predicted from equation (14) as follows:AUCpo(+inhibitor)/AUCpo(control) =1/{fh·fm/(1+Iu/Ki)+(1−fh·fm)}=1.2 This value is smaller than the observed 1.6-fold increase in AUC_po.

As mentioned above (see Section III.B.), however, the inhibition by erythromycin may not be due only to a competitive inhibition mechanism. Its demethylated metabolite is known to inactivate P450 by forming a complex with this enzyme (Periti et al., 1992). Therefore, it may be inappropriate to estimate the pharmacokinetic alteration based only on the same methodology used for competitive inhibitors. Another methodology has to be developed for the prediction of in vivo drug-drug interactions based on the so-called “mechanism-based inhibition” of P450 from in vitro data; it should include the possible effects of inhibitor exposure time and the turn-over of the enzyme, as will be discussed later in details (see Section III.G.).

Table 9 summarizes the results of the prediction of drug-drug interactions based on in vitro data. In some cases, in vivo pharmacokinetic parameters (C_max, AUC) were changed to some extent by drug-drug interactions although the values of I_u/K_i calculated from in vitro data were too small to expect any metabolic inhibition in vivo. This finding suggests that alterations in in vivo pharmacokinetic parameters may be caused by other factors such as interactions involving absorption or excretion. Furthermore, in the case of macrolide antibiotics such as erythromycin, the model describing “the mechanism-based inhibition” should be introduced to predict the drug-drug interaction.

In order to avoid false negative predictions, one should not limit an interaction to a particular metabolic pathway, especially when the ratio of the pathway in question to the total clearance (f_h · f_m = CL_h,m/CL_tot) is small, as in the cases with the terfenadine-ketoconazole interactions. The most important factor in the prediction is the accurate estimation of I_u/K_i. In other words, if the calculated value of I_u/K_i for a particular metabolic pathway is high, the possible occurrence of drug interaction in vivo should be suspected, because it is likely that this inhibitor also inhibits another metabolic pathway(s) which has not been identified yet.

F. Procedure for Predicting Inhibitory Effects of Coadministered Drugs on the Hepatic Metabolism of Other Drugs

The following is a proposed procedure for predicting the metabolic inhibition by one drug that is expected to be coadministered with the study drug being developed.

1)

Confirmation of the involvement of P450 by in vitro inhibition studies, e.g., using SKF-525A and CO.

2)

Identification of the P450 isozyme by metabolic studies using human P450 expression systems and the inhibition studies using P450 antibodies or inhibitors specific for each isozyme.

3)

Searching the in vivo pharmacokinetic data for the coadministered drug that possibly inhibits the P450 isozyme catalyzing the metabolism of the drug under investigation. The maximum plasma unbound concentration of the coadministered inhibitor (I_in,max,u) can be estimated by I_max (or I_max,ss), k_a (or T_max and t_1/2), F_a, and f_u as described by equation (22).

4)

Evaluation of the unbound concentration of inhibitor in the liver, which may be larger than I_in,max,u in the case of an inhibitor that is actively transported into hepatocytes (fig. 3). The unbound concentration ratio (liver/plasma) should be measured by the method given below (see Section III.H.1.) using human hepatocytes (or rat isolated hepatocytes if human samples are not available). A 5- to 10-fold safety margin may also be considered for the concentration ratio if there are no experimental results available.

5)

In vitro measurement of the K_i of the inhibitor for the metabolism of the study drug using human liver microsomes or human P450 expression systems.

6)

Assessing the possibility of metabolic inhibition by comparing the values of I_in,max,u and K_i. If the I_in,max,u/K_i value is larger than 0.3–1, you may want to consider designing the in vivo drug interaction studies. The limit of I_in,max,u/K_i value should depend on the pharmacodynamic and/or toxicodynamic features and the therapeutic window of the drug investigated.

Although a more precise and quantitative prediction requires the collection of more information and/or elaborate experiments, the authors think that the judgment of “absence of a metabolic drug-drug interaction” may be reliable if the interaction is not expected by this prediction method. The above metodology has been proposed based on the idea of avoiding false negative predictions. Therefore, it should be kept in mind that some of the predicted drug-drug interactions may not take place in vivo. We speculate that more than 80 combinations could be judged as “non-interacting” if 100 kinds of drug-drug interactions are investigated, at random, by this methodology. Of the less than 20 combinations involving possible interactions, cautious investigations using human in vivo studies would be necessary for some combinations, taking the therapeutic range, pharmacokinetic/pharmacodynamic characteristics, and severity of the adverse effects into consideration.

G. Mechanism-Based Inhibition

1. Characteristics of Mechanism-Based Inhibition.

In 1993, 15 Japanese patients with cancer and herpes zoster died from 5-fluorouracil (5-FU) toxicity caused by high blood concentrations caused by an interaction between 5-FU and sorivudine, an antiviral drug (Pharmaceutical Affairs Bureau, 1994). The interaction between sorivudine and 5-FU is based on “mechanism-based inhibition”, which differs from the competitive or noncompetitive inhibition described so far (Desgranges et al., 1986; Okuda et al.,1997). A mechanism-based inhibitor is metabolized by an enzyme to form a metabolite which covalently binds to the same enzyme, leading to irreversible inactivation of the enzyme. Several terms such as “mechanism-based inactivation,” “enzyme-activated irreversible inhibition,” “suicide inactivation,” and “k_catinhibition” have all been used as alternatives to “mechanism-based inhibition” (Silverman, 1988). It should be noted, however, that the inhibition is not called “mechanism-based inhibition” when the inhibitor is metabolically activated by an enzyme and inactivates another. Sorivudine is converted by gut flora to 5-bromovinyluracil (BVU), which is metabolically activated by dihydropyrimidine dehydrogenase (DPD), a rate-limiting enzyme in the metabolism of 5-FU (fig. 8) (Okuda et al., 1995). Then, the activated BVU irreversibly binds to DPD itself. This type of interaction needs more attention than the common type of inhibition, because the inhibitory effect remains after elimination of the inhibitor (sorivudine, BVU) from blood and tissue and this can lead to serious side-effects.

Many drugs other than sorivudine also are reported to be mechanism-based inhibitors, including macrolide antibiotics such as erythromycin and troleandomycin (against CYP3A4) (Periti et al., 1992), furafylline (against CYP1A2) (Kunze and Trager, 1993), and orphenadrine (against CYP2B1) (Murray and Reidy, 1990).

2. Kinetic Analysis of Mechanism-Based Inhibition: Analysis of In Vitro Data.

Is it also possible to predict the extent of in vivo interactions from in vitro data in the case of mechanism-based inhibition? The first step in making such predictions is to construct a model describing the inhibition. Waley (1985) proposed the model shown in figure 9 for mechanism-based inhibition. Mass-balance equations for the enzyme-inhibitor complexes (EI and EI′) and the inactive enzyme (E_inact) can be expressed as follows:d(EI)/dt=k+1·[I]·E−(k−1+k2)·EI Equation 25 d(EI′)/dt=k2·EI−(k3+k4)·EI′ Equation 26 dEinact/dt=k4·EI′ Equation 27where E and [I] represent the concentration of the active enzyme and the mechanism-based inhibitor, respectively. Because the total concentration of the enzyme (E_o) is maintained at a constant level,Eo=E+EI+EI′ Equation 28Combining equations (25), (26), and (28) yields the following equation, assuming a steady-state for EI and EI′ (i.e., d(EI)/dt  =  0 and d(EI′)/dt  =  0): EI′=k+1·k2·[I]·Eo/((k+1·k2+k+1(k3+k4)) Equation 29 ·[I]+(k3+k4)(k−1+k2)) Therefore, the initial inactivation rate of the enzyme under steady-state conditions (V_inact =  dE_inact/dt) can be expressed as follows using equations (27) and (29):Vinact=k+1·k2·k4·[I]·Eo/((k+1·k2+k+1(k3+k4)) Equation 30 ·[I]+(k3+k4)(k−1+k2)) =(k2·k4/(k2+k3+k4)·[I]·Eo)/((k3+k4)/(k2 +k3+k4)·(k−1+k2)/k+1+[I]) As the initial inactivation rate of the enzyme at steady-state is equal to the initial decreasing rate of the active enzyme,Vinact=−dE/dt(t=0)=kobs·E(t=0)=kobs·Eo Equation 31where k_obs represents the apparent inactivation rate constant of the enzyme. The following equation can be derived from equations (30) and (31):kobs=Vinact/Eo=kinact·[I]o/(Ki,app+[I]o) Equation 32wherekinact=k2·k4/(k2+k3+k4) Equation 33 Ki,app=(k3+k4)/(k2+k3+k4)·(k−1+k2)/k+1 Equation 34Parameters (k_inact, K_i,app) required for predicting this model can be determined by in vitro studies as follows (fig. 10):

〈1〉  Preincubate the enzyme suspension for an appropriate period in the presence of various concentrations of inhibitor.

〈2〉  Mix the substrate solution with the enzyme suspension to measure the initial metabolic rate of the substrate so that the remaining enzymatic activity can be determined. The incubation time for this measurement should be as short as possible (around 1–3 min) compared with the preincubation time, in order to minimize the reaction of the inhibitor with the enzyme during the incubation.

〈3〉  Plot the logarithm of the enzymatic activity against the preincubation time. The apparent inactivation rate constant (k_obs) can be determined from the slope of the initial linear phase.

〈4〉  Obtain the parameters (k_inact, K_i,app) from the relationship between k_obs and the initial inhibitor concentration ([I]_o) using the nonlinear least squares regression method.

Table 10 summarizes the results of the analysis of various combinations of P450 isozymes and mechanism-based inhibitors (Chiba et al., 1995). The “partition ratio” in table 10 is defined as k₃/k₄ and can be obtained as the ratio of the amount of the inhibitor released as the product and the amount covalently bound to the enzyme. The larger the contribution of this inactivation pathway to the total elimination of the inhibitor in the in vitro system, the smaller the partition ratio. The partition ratio of the most powerful mechanism-based inhibitor is zero (every turnover produces inactivated enzyme).

It is clear from this model analysis that, in the case of mechanism-based inhibition, the inhibitor is metabolically activated by an enzyme and irreversibly inactivates the same enzyme by covalent binding, exhibiting the following characteristics:

a.

Preincubation time-dependent inhibition of the enzyme (time-dependence).

b.

No inhibition if cofactors necessary for producing the activated inhibitor (eg., NADPH for P450 metabolism) are not present in the preincubation medium.

c.

Potentiation of the inhibition depending on the inhibitor concentration (saturation kinetics).

d.

Slower inactivation rate of the enzyme in the presence of substrate compared with its absence (substrate protection).

e.

Enzyme activity not recovered following gel filtration or dialysis (irreversibility).

f.

1:1 Stoichiometry of the inhibitor and the active site of the enzyme (stoichiometry of inactivation).

Mechanism-based inhibitors should satisfy these criteria.

3. Prediction of In Vivo Interactions from In Vitro Data in the Case of Mechanism-Based Inhibition.

How can inhibitory effects in vivo be estimated from the microscopic inhibition parameters obtained from in vitro studies?

A simulation study was carried out using the perfusion model in figure11 and the pharmacokinetic parameters in table 11. The inhibitor is assumed to inactivate a certain CYP isozyme in the liver in a “mechanism-based” manner. The differential equations for the substrate (S) and inhibitor (I) can be expressed as follows:

For S;Vh·(dCh/dt) Equation 35 =Q·Cportal−Q·Ch/Kp−fb·CLint·Ch/Kp CLint=Vmax/(Km+fb·Ch/Kp) Equation 36 Vmax=Vmax(0)·Eact(t)/Eo Equation 37  Vportal·(dCportal/dt)=Q·Csys+Vabs−Q·Cportal Equation 38 Vabs=ka·D·F·e−ka·t Equation 39 Vd·(dCsys/dt)=Q·Ch/Kp−Q·Csys Equation 40For I;Vh·(dIh/dt)=Q·Iportal−Q·Ih/Kp−fb·CLint·Ih/Kp Equation 41 CLint=Vmax/(Km+fb·Ih/Kp) Equation 42 Vportal·(dIportal/dt)=Q·Isys+Vabs−Q·Iportal Equation 43 Vabs=ka·D·F·e−ka·t Equation 44 Vd·(dIsys/dt)=Q·Ih/Kp−Q·Isys Equation 45where Q represents blood flow rate, C_sys and I_sys represent concentration in systemic blood, V_d represents volume of distribution in the central compartment, C_portal and I_portal represent concentration in portal vein, V_portal represents volume of portal vein, C_h and I_h represent concentration in the liver, V_h represents volume of liver, f_brepresents unbound fraction in blood, CL_int represents intrinsic metabolic clearance, F_a represents fraction absorbed from the gastrointestinal tract, K_m represents Michaelis constant for the metabolic elimination, V_maxrepresents maximum metabolic rate, and K_p represents liver-to-blood concentration ratio.

The following assumptions were made in the mass-balance equations (35 to 45):

a.

S and I are simultaneously administered orally.

b.

Both S and I are eliminated only in the liver and their elimination can be described by the Michaelis-Menten equation.

c.

Distribution of S and I in the liver rapidly reaches equilibrium, and the unbound concentration in the hepatic vein is equal to that in the liver at equilibrium (well-stirred model).

d.

The unbound molecule in the liver is related to the elimination.

e.

The contribution of the CYP isozyme subject to inactivation is small in total elimination of the inhibitor in the liver (i.e., the elimination of the inhibitor itself is not altered by inactivation of the enzyme).

f.

Gastrointestinal absorption can be described by a first-order rate constant.

Furthermore, it should be noted that V_max of the substrate is assumed to be proportional to the amount of active enzyme (E_act) in equation (37).

The differential equations for active and inactive enzyme in the liver (E_act and E_inact, respectively) can be described as follows: dEactdt=−kinact·Eact·fb·Ih/KpKi,app+fb·Ih/Kp+kdeg(Eo−Eact) Equation 46 dEinactdt=kinact·Eact·fb·Ih/KpKi,app+fb·Ih/Kp−kdeg·Einact Equation 47where k_deg represents the degradation rate constant (turnover rate constant) of the enzyme. The initial conditions (at t = 0) are E_act = E_o and E_inact = 0. In the absence of an inhibitor, the enzyme level in the liver is at steady-state and the degradation rate (k_deg · E_o) is equal to the synthesis rate, which is assumed to be unaffected by an inhibitor.

a. Basic simulation.

Using the physiological model in figure 11 and the parameters in table 11, time courses of inhibitor blood concentrations, active enzyme levels in the liver (E_act), and substrate blood concentrations have been simulated with the dose of the inhibitor ranging from 0 to 50,000 μmol (fig. 12). The above eight differential equations (three for the substrate, three for the inhibitor, and two for the enzyme level in the liver) were numerically solved. The elimination rate of the active enzyme (E_act) increases with an increasing dose of the inhibitor, resulting in the prolonged elimination of the substrate.

b. Effect of the turnover rate of the enzyme.

The effect of the turnover rate constant of the enzyme (k_deg) on the profiles of E_act and the substrate elimination were investigated in the simulation study. Basic parameters in table 11 were used except that k_deg was changed to cover the range of 0.00005–0.005 min^{− 1}. As the inhibitor itself is gradually eliminated from blood and liver, the enzyme level recovers to reach its initial level by replacement of the inactivated enzyme by newly synthesized enzyme (fig. 13). The faster the turnover rate of the enzyme, the faster the enzyme level is restored to its initial level.

c. Timing of inhibitor administration.

One of the characteristics of the mechanism-based inhibition is that the effect remains even after the inhibitor is eliminated from the body. Therefore, the inhibitory effect may depend on the timing of the substrate administration, even if the same dose of the inhibitor is administered. Simulations shown in figure14 indicate that the most potent inhibitory effect can be obtained by having an appropriate interval between administration of the inhibitor and the substrate. Too short an interval will lead to completion of the kinetic event of the substrate before sufficient inactivation of the enzyme occurs, and too long an interval will allow the enzyme to recover. Both situations will result in a reduction of the inhibitory effect.

d. Possibility of in vitro/in vivo scaling.

Figure15 shows the effects of two parameters obtained in the in vitro studies (k_inact and K_i,app) on the simulated in vivo profiles of E_act and substrate blood concentrations. As expected, in vivo inactivation of the enzyme and prolongation of substrate elimination become marked with a larger k_inact and a smaller K_i,app. In the future, it will be necessary to examine whether this method can properly predict in vivo effects from in vitro data. What kind of approach should be taken to verify this methodology? For example, although estimation of the unbound concentration of inhibitor in the liver is important for any prediction, it is impossible to measure this, especially in humans. Instead, kinetic parameters can be determined to fit the inhibitor blood concentration profile, which is measured in most cases. However, undetermined parameters, such as the liver-to-plasma concentration ratio, need to be varied within certain limits in the simulation study so that the range of alteration in the profiles of E_act and substrate can be predicted.

It is also important to confirm the validity of the prediction method in animal studies, where the inhibition studies can be performed both in vitro (using e.g. liver microsomes for P450) and in vivo. Because invasive experiments are possible in this case, including measurements of the distribution kinetics of the inhibitor in the liver, this may allow for more accurate predictions.

H. Problems To Be Solved for the More Precise Prediction of Drug-Drug Interactions

1. Estimation of the Tissue Unbound Concentration of the Inhibitor That Is Actively Transported into Hepatocytes.

As described above (see Section III.D.), in vivo drug-drug interactions based on inhibition of hepatic metabolism can be predicted by the values of K_i and the unbound concentration of the inhibitor in the liver, which cannot be directly measured in vivo. The analyses have been based on the assumption that the steady-state unbound concentration of the inhibitor in the liver is equal to that in the hepatic capillary (sinusoid), because many drugs are transported into hepatocytes by passive diffusion. However, in the case of an inhibitor that is concentrated in hepatocytes by active transport (Yamazakiet al., 1995, 1996), the extent of the interaction may be underestimated if plasma concentrations are used in the prediction.

Zomorodi and Houston (1995) investigated the effect of omeprazole on diazepam metabolism using rat liver microsomes and hepatocytes. Omeprazole inhibited both 3-hydroxylation and N-demethylation of diazepam, and the K_i in hepatocytes was smaller than that in microsomes for both pathways (table12). On the other hand, as shown in figure 16, the in vivo clearance of diazepam was reduced depending on omeprazole concentration, which was maintained under steady-state conditions. In this in vivo study, the K_i was calculated to be 57 μM from equation (48).CL=CLo/(1+Iss/Ki) Equation 48where CL_o represents diazepam clearance in the absence of omeprazole, and I_ss represents the steady-state total plasma concentration of omeprazole. The in vivo K_i showed closer agreement with the K_i values obtained in hepatocytes than with those observed in microsomes (table 12). Their results, however, should be interpreted cautiously, because the K_iwas calculated based on the amount of drug added to the medium instead of the unbound concentration, and the total plasma concentration in vivo was used as the I_ss in equation (48) instead of the unbound concentration, which should be related to the metabolic inhibition. As shown in figure 17, K_m or K_i values obtained in the metabolism studies based on the medium concentration of substrates and inhibitors, respectively, may be smaller in hepatocytes than in microsomes if the molecule is actively transported into hepatocytes. The difference is reflected in the cell-to-medium unbound concentration ratio (C/M ratio) as shown in equation (49): C/M ratio=Km(MS)/Km(Cell)=Ki(MS)/Ki(Cell) Equation 49where MS and Cell in parentheses indicate the values obtained in microsomes and in cells, respectively. Therefore, the difference in the K_i values of omeprazole obtained in liver microsomes and hepatocytes may be explained by the accumulation of omeprazole in hepatocytes by active transport.

The active transport of drugs can be evaluated by measuring the drug uptake into hepatocytes or liver slices in the presence and absence of adenosine triphosphate (ATP)-depletors such as rotenone and FCCP (Yamazaki et al., 1993; Nakamura et al., 1994). Assuming both active transport and passive diffusion for the influx into hepatocytes and only passive diffusion for the efflux from the hepatocytes (figure 18), the initial uptake velocity in the presence of an adequate concentration of ATP-depletor represents the uptake by passive diffusion, because the active transport of the drug is completely inhibited. C/M ratio in the steady-state can be described by equation (50):C/M ratio=(PSactive+PSpassive)/PSpassive=vo/vpassive Equation 50where PS_active and PS_passive represent the membrane permeation clearance by active transport and passive diffusion, respectively; v_o and v_passiverepresent the initial uptake velocity obtained in the absence and presence of ATP-depletors, respectively. This C/M ratio can also be calculated by measuring the steady-state drug concentration (sum of the bound and unbound forms) in the cell and that in the medium in the absence and presence of the ATP-depletor as follows: Ccell/Cmedium(control)Ccell/Cmedium(+ATP­depletor) Equation 51 =Ccell,free/fT/Cmedium(control)Ccell,free/fT/Cmedium(+ATP­depletor) =Ccell,free(control)Cmedium=C/M ratio where C_cell and C_medium represent steady-state total drug concentration in the cell and that in the medium, respectively; C_cell,free represents steady-state unbound drug concentration in the cell; and f_T represents the unbound fraction in the cell. It is assumed that f_T is not affected by the ATP-depletor and that C_cell,free equals C_medium in the presence of the ATP-depletor. Equation (51) can be used even when active transport is involved in the efflux process out of the hepatocytes, whereas equation (50) cannot be applied in such a case.

Nakamura et al. (1994) reported that FCCP, rotenone, or sodium azide causes a marked reduction in the uptake of [³H]cimetidine into isolated rat hepatocytes that parallel the reduction in cellular ATP (fig.19). The unbound concentration ratio of cimetidine in hepatocytes in this case can be calculated to be about 5.6 according to equation (50). If the unbound concentration ratio in a linear condition (C_medium ≪ K_m) is calculated from equations (50) and (52) using the values of V_max, K_m, and PS_passive which were determined by fitting the initial uptake velocity (v_o) to equation (53), a value of 7.1 can be obtained:PSactive=Vmax/(Km+Cmedium) Equation 52  vo=VmaxCmedium/(Km+Cmedium)+PSpassiveCmedium Equation 53Here, in this calculation, it is assumed that carrier-mediated saturable uptake represents active transport. The K_i value of cimetidine for the metabolism of ethoxyresorufin and those values for α-hydroxylation and 4-hydroxylation of triazolam in human liver microsomes are 600 μM, 36 μM, and 160 μM, respectively (Knodellet al., 1991; Von Moltke et al., 1996). The unbound concentration ratios (liver/plasma) when the intracellular unbound concentration is 600 μM, 160 μM, and 36 μM are calculated to be about 1.5, 3.7, and 6.4, respectively, using the parameters for carrier-mediated transport reported by Nakamura et al.(1994). This calculation indicates that the lower the plasma concentration of inhibitor, the higher the liver-to-plasma unbound concentration ratio, when the carrier-mediated active transport (influx) is operating.

We previously reported (Yamazaki et al., 1993) that concentration of pravastatin, an HMG-CoA reductase inhibitor, in isolated rat hepatocytes was about 3- to 7-fold higher than that in medium because of active transport. It was also suggested that simvastatin and lovastatin, which competitively inhibited the hepatic uptake of pravastatin, may be transported by the same carrier as pravastatin (Yamazaki et al., 1993). Since the HMG-CoA reductase inhibitors such as fluvastatin, simvastatin, and pravastatin inhibit CYP2C9-mediated 4′-hydroxylation of diclofenac (Transonet al., 1996), the concentrative uptake into hepatocytes should be taken into consideration in predicting interactions involving these drugs.

In the future, more accurate predictions of in vivo drug-drug interactions may become possible by estimating the unbound concentration of the inhibitor in the liver in in vitro studies.

2. Evaluation of Drug-Drug Interactions Involving Drug Metabolism in the Gut.

CYP3A4, an enzyme that metabolizes many drugs, including cyclosporin, exists not only in the liver but also in the gut; it plays an important role in the first-pass metabolism after oral administration of its substrates (Kolars et al., 1991, 1992;Thummel et al., 1996). De Waziers et al. (1990)have used Western blot analysis and shown that CYP3A4 is highly expressed in the duodenum and jejunum, secondly to the liver, in humans (fig. 20).

As shown in figure 21, the bioavailability (BA) of cyclosporin after oral administration was reduced by coadministration of rifampicin, an inducer of CYP3A4, and increased by coadministration of ketoconazole or erythromycin, which are inhibitors of CYP3A4 (Hebert et al., 1992; Gomezet al., 1995; Gupta et al., 1989). Wu et al. (1995) attempted to differentiate the absorption and first-pass gut and hepatic metabolism of cyclosporin in humans by a kinetic analysis of the change in BA by rifampicin-induced induction and ketoconazole- or erythromycin-induced inhibition of CYP3A4-mediated metabolism. Based on the model shown in figure22, BA after oral administration can be expressed as follows using the fraction of the drug dose absorbed into and through the gastrointestinal membranes (F_abs), the fraction of the absorbed dose that passes through the gut into the hepatic portal blood unmetabolized (F_g), and the hepatic first-pass availability (F_h):BA=FabsFgFh Equation 54 =Fabs(1−Eg)(1−Eh) where E_g and E_h represent gut and hepatic extraction ratio, respectively. Assuming that F_abs is not altered by the enzyme inducer or the inhibitor, BA after coadministration of the interacting drug can be expressed as follows:BA=Fabs(1−XgEg)(1−XhEh) Equation 55where X_g and X_h represent the changes in the gut and hepatic extraction ratio, respectively, during coadministration of the interacting drug. Assuming that the drug is eliminated only by the liver and kidney, as is the case for many drugs, E_h can be calculated by the following equation:Eh=CLh/Qh=(CLtot−CLr)/Qh Equation 56where CL_tot can be estimated from the dose divided by the AUC after intravenous administration and CL_r can be estimated by multiplying CL_tot and the urinary excretion rate of the parent compound. Furthermore, X_h in equation (55) can be obtained as the ratio of E_h in the presence and absence of the interacting drug. Equations (54) and (55) then contain three unknown parameters (F_abs, E_g, and X_g), allowing the calculation of E_g and X_g by fixing the value of F_abs. The maximum value of F_abs was set at 1 (complete absorption), and the minimum value was calculated by dividing BA by F_h(=1  −  E_h) at the time when the metabolism was inhibited by the interacting drug (assuming F_g =  1). As shown in table13, the calculated extraction ratio in the gut was always larger than that in the liver, irrespective of the value of F_abs. Furthermore, X_g was larger than X_h when F_abs<86% in the case of rifampicin coadministration and was smaller than X_h in the case of erythromycin coadministration, indicating that the interaction observed in the gut is about the same or larger than that observed in the liver.

Therefore, the drug-drug interaction based on metabolic inhibition in the gut after oral administration cannot be neglected, especially for the drugs metabolized by CYP3A4. The methodology for the prediction of in vivo first-pass gut metabolism from in vitro studies using human gut samples needs to be established.

On the other hand, it is known that p-gp exists in the luminal membrane of gut epithelial cells and acts as an efflux transporter (Saitoh and Aungst, 1995; Terao et al., 1996). Recent studies have revealed the overlapping substrate specificity of CYP3A4 and p-gp. As shown in table 14, many substrates of CYP3A4 are reported to be substrates or inhibitors of p-gp (Wacheret al., 1995). In another study (Schuetz et al.,1996) using a cell line derived from a human colon adenocarcinoma, it was shown that many of the p-gp inducers also induce CYP3A4, suggesting the possibility of common regulatory factors for these proteins (table15).

Benet (1995, 1996) has pointed out the possibility that the synergistic effects of CYP3A4-mediated metabolism and p-gp-mediated efflux in the gut epithelium may result in an unexpectedly high first-pass effect in the gut after oral administration. Thus, the inhibition or induction of CYP3A4 and/or p-gp caused by drug-drug interactions may affect the first-pass effect in the gut.

The effects of gut metabolism and efflux from epithelial cells to the lumen on the absorption of orally administered drugs were investigated by a simulation study. Based on the compartment model shown in figure23, the fraction of the drug absorbed into the portal vein (F_a) can be expressed as follows:Fa=P3CLint+P31−exp−α1×CLint+P3P2+CLint+P3 Equation 57where P₂, P₃, and CL_intrepresent the clearance for efflux from the cell to the lumen, absorption from the cell to the portal vein, and intracellular metabolism, respectively, and α₁ is the membrane permeation constant from the lumen into the cell. α₁ is a hybrid parameter with no dimensions, consisting of the transit time in the lumen, diffusion in the unstirred water layer, and the permeability through the brush-border membrane of the gut epithelial cells:α1=P1,app×tgi¯Vav Equation 58where P_1,app represents the apparent influx clearance from the lumen into the cell, t̅g̅i̅ ̅ represents small intestinal transit time, and V_av represents the average luminal volume.

The results are shown in figure 24. When CL_int+ P₃ is much larger than P₂, equation (57) can be rearranged to yield equation (59):Fa=P3CLint+P3{1−exp(−α1)} Equation 59In this case, F_a is not affected by a change in P₂ possibly caused by inhibition of p-gp (fig. 24 left panel). If CL_int + P₃ is much smaller than P₂, equation (60) can be derived:Fa=P3CLint+P31−exp−α1×CLint+P3P2 Equation 60Here, the reduction of P₂ is directly reflected in the change in F_a (fig. 24 right panel). This indicates that F_a is increased with the reduction in P₂ when the initial value of P₂ is large, i.e., in the case of the drugs extensively transported out of the cell into the lumen. This effect of reducing P₂ is more marked if the influx clearance of the drug into the cell (α₁) is relatively small (fig. 24 right panel). The results in figure 24 suggest that the effect of p-gp inhibition caused by drug-drug interactions on drug absorption may depend on the relative extent of each process (influx from the lumen into the epithelial cell, efflux from the cell to the lumen, intracellular metabolism, and transport from the cell to the portal vein).

In the future, in addition to metabolic studies using human gut samples, drug-drug interactions involving the efflux process should be quantitatively evaluated by transport studies using intestinal brush border membrane vesicles to allow for more precise predictions of in vivo drug-drug interactions.