Usefulness of Two-Compartment Model-Assisted and Static Overall Inhibitory-Activity Method for Prediction of Drug–Drug Interaction

Abstract

Our study of drug–drug interaction (DDI) started with the clarification of unusually large DDI observed between ramelteon (RAM) and fluvoxamine (FLV). The main cause of this DDI was shown to be the extremely small hepatic availability of RAM (vF_h). Traditional DDI prediction assuming the well-stirred hepatic extraction kinetic ignores the relative increase of vF_h by DDI, while we could solve this problem by use of the tube model. Ultimately, we completed a simple and useful method for prediction of DDI. Currently, DDI prediction becomes more complex and difficult when examining issues such as dynamic changes in perpetrator level, inhibitory metabolites, etc. The regulatory agents recommend DDI prediction by use of some sophisticated methods. However, they seem problematic in requiring plural in vitro data that reduce the flexibility and accuracy of the simulation. In contrast, our method is based on the static and two-compartment models. The two-compartment model has advantages in that it uses common pharmacokinetics (PK) parameters determined from the actual clinical data, guaranteeing the simulation of the reference standard in DDI. Our studies confirmed that dynamic changes in perpetrator level do not make a difference between static and dynamic methods. DDIs perpetrated by FLV and itraconazole were successfully predicted by use of the present method where two DDI predictors [perpetrator-specific inhibitory activities toward CYP isoforms (pA_i, CYPs) and victim-specific fractional CYP-isoform contributions to the clearance (vf_m, CYPs)] are determined successively as shown in the graphical abstract. Accordingly, this approach will accelerate DDI prediction over the traditional methods.

1. INTRODUCTION

Co-administration of sorivudine and 5-fluorouracil (5-FU) caused a tragic death–accident in the past.¹⁾ Thereafter, under the guidance of the regulatory agencies,^2,3) drug manufacturers have been making efforts to anticipate possible drug–drug interactions (DDI) of new chemical entities (NCE) by performing both in vitro and in vivo DDI studies at an early stage. In reality, however, it is not possible to perform clinical studies of all DDIs. Thus, in the common cases, the regulatory agencies recommend their prediction from the in vitro and limited in vivo data.^4–6) Nevertheless, in light of the Food and Drug Administration (FDA) guidance and current findings in this field of research,^7–11) many issues in regard to DDI prediction remain to be solved (Table 1).

Our recent studies on DDI prediction by use of a newly developed two-compartment (comp)-assisted, tube-based, and static overall inhibitory activity method, gave a clue to the solution of some of these issues.^12–15) Thus, the present review focuses on our achievements in DDI prediction by use of this method.

Table 1. Issues Raised in DDI Prediction

(i) Decrease in first-pass effect by DDI

(ii) Dynamic changes in hepatic inhibitor level [Iu(t)]

(iii) DDI mediated by multiple CYP-isoform inhibition

(iv) Gut-wall extraction

(v) Inhibitory activities of metabolites

(vi) Time-dependent CYP inhibition [mechanism-based CYP inhibition (MBI)]

(vii) A gap between in vitro and in vivo Ki,u

(viii) Interplays of enzymes and transporters

2. BACKGROUND

2.1. Unusualness of Ramelteon (RAM)-Victimized DDI

The corresponding author encountered an unusually large DDI caused by co-administration of RAM [Rozerem (melatonin receptor agonist) marketed by Takeda Chemical, Ind.; CYP1A2 and CYP2C19 are RAM’s major and sub eliminating enzymes, respectively] and fluvoxamine (FLV, strong CYP1A2 and CYP2C19 inhibitor), when he was in charge of clinical study and pharmacokinetic (PK) analysis at that company in the early 2000 s. The fold increase in the area under the plasma RAM levels curve (AUCR) was noted to be almost 130¹⁶⁾ (Fig. 1).

Fig. 1. Unusualness of RAM-Victimized DDI

Time-dependent logarithmic plasma RAM-level (vC_p) increase after co-administration of RAM (16 mg) with FLV (100 mg BID) in humans (solid circle) is shown in comparison with the control (open circle) (details in ref. 13).

This magnitude of DDI had been deemed to be difficult to predict by any methods until we devised the mechanism.¹³⁾ The AUCR predicted by either a static method [constant unbound inhibitor (I_u)-based method] as shown below, or a dynamic method (time-dependent I_u-based method) employing physiologically-based pharmacokinetic (PBPK) model, wherein the well-stirred model was applied for the hepatic extraction kinetics, was no more than 5.⁴⁾ Typically, the value of AUCR estimated by a well-stirred model-based static method was:   

(1)

where the parameters for victim and perpetrator (=inhibitor) are prefixed with “v” and “p,” respectively, and (+) indicates the presence of a perpetrator (inhibitor) or co-administration with a perpetrator, and CL_oral, CL_h, int, A_i, overall and K_{i, u, overall} represent oral clearance, intrinsic metabolic-clearance in the liver, overall inhibitory activity and overall unbound inhibition constant for the DDI, respectively.

Although the mechanism of the DDI had been unknown at least until we elucidated it, this medicine was approved in 2008 in the U.S. and allowed for the clinical use, under the condition that concomitant use with FLV must be avoided.

2.2. Change in Victim’s First-Pass Effect by DDI

After moving to the current affiliation (2005), the corresponding author placed first priority on studies to clarify the mechanism of this DDI. Soon after performing comparative studies on DDIs produced by co-administration of various CYP1A2 and CYP2C19 substrates with FLV (Table 2), he noted that AUCR would be underestimated mainly by the assumption of the well-stirred model, and that this issue could be solved by the tube model as expressed by Eq. 2, as the best alternative to the well-stirred model.¹³⁾

Table 2. DDIs Observed in Co-administration of Various CYP1A2 and CYP2C19 Substrates with FLV (Details Shown in Ref. 13)

	Victim	FLV	AUCR	vFha)
Lansoprazole (LAN)	40 mg	25 mg BID	3.8	0.92
Omeprazole (OME)	40 mg	50 mg BID	5.6	0.7
S-mephenytoin (MEP)	100 mg	87.5 mg QDb)	9.9	0.31
Theophylline (THE)	257 mg	100 mg QD	3.3	0.94
Caffeine (CAF)	250 mg	50 mg BID	13.7	0.93
Tasimelteon (TAS)	5 mg	50 mg QD	6.5	0.57
Tacrine (TAC)	40 mg	100 mg QD	8.3	0.13
Tizanidine (TIZ)	4 mg	50 mg BID	32.6	0.14
Melatonin (MEL)	5 mg	50 mg singlec)	22.7	0.06
RAM	16 mg	100 mg BID	128	0.03

QD, BID and TID represent once, twice and three times a day administration, respectively. vA_e, oral=0 except for THE (vA_e, oral=0.07). a) Estimated from vCL_oral assuming vF_a=1. b) MEP was administered 16 h after multiple FLV doses. c) MEL was administered 3 h after a single FLV dose.

  

(2)

where,   

(3)

  

(4)

where, vA_e, oral, F_a, F_g, F_h, fu_b and Q_h represent urinary excretion ratio of unchanged drug after oral administration, the dose fraction of orally absorbed drug, avoidance of gut-wall extraction, hepatic availability, blood unbound fraction and hepatic blood flow, respectively.

The reason was that Eq. 2 derived from the tube model (Eqs. 3 and 4), which describes well the dependency of AUCR on vF_h, is unlike Eq. 1 (the well-stirred model) which models AUCR as equal to A_i, overall, independently from vF_h (more details in later sections).

2.3. Difficulty of Determination of Dynamic Changes in Hepatic Inhibitor Level [I_u(t)]

Another issue in DDI prediction is how to determine in vivo I_u(t), which is difficult to measure directly but essential for the calculation of A_i, overall or AUCR. The only way would be to estimate it from the blood perpetrator level.¹⁷⁾ Some researchers have proposed a compromised method which allows calculation of the upper limit of I_u (I_{u, portal(max)}) by assuming that I_u is equal to the unbound perpetrator level in the portal blood (inlet of the liver),¹⁸⁾ although it assumed the well-stirred model:   

However, it is evident that this method is not able to explain the prolonged inhibitory activity of FLV.¹⁹⁾ This is because the plasma MEP (CYP2C19 substrate) level in oral administration 16 h after multiple FLV dosing has been reported to be greatly increased [AUCR=approximately 10 (Table 2)], regardless of the fact that at this time period, the unbound perpetrator level in the portal vein would have been decreased to almost equal the systemic plasma unbound level. Accordingly, the DDI produced by FLV could not be explained by the transient increase in the portal vein level.

In order to explain such a prolonged A_i, overall(t) as found in the MEP-victimized DDI,¹⁹⁾ we have developed a three-comp PBPK model that allows us to mathematically calculate I_u(t) [=fu_b×C₂(t)=fu_b×C_hb(t) (time-dependent hepatic blood unbound drug level)], where the liver is assumed to be one of drug pools (compartments having a significantly large volume) and the tube model is applied for this comp¹²⁾ (Fig. 2).

Fig. 2. Three-Comp PBPK Model for the Estimation of Hepatic Blood Inhibitor Level [C_hb(t)=I_u(t)/fu_b] (Details Shown in Ref. 12)

Using this model, we were able to show that a perpetrator such as FLV after oral administration should be first distributed into the liver via the portal vein and therein be pooled for a prolonged period of time before being distributed to the systemic blood, and that this prolonged level is the key to explaining the prolonged A_i, overall(t) (Fig. 3).

Fig. 3. Simulation of Blood and Hepatic Blood FLV Levels after Multiple Oral Administration of FLV (50 mg BID) (Details Shown in Ref. 12)

pC_{hb, u}=pfu_b (0.2)×pC_hb=20 nM

2.4. Traditional Methods for Dynamic Prediction of DDI

In actual DDIs, the blood victim level changes with the dynamic change in the blood perpetrator level. Accordingly, it may be a concern that a static method assuming a constant A_i, overall, cannot predict DDI accurately, although this was swept aside by our later analysis using a static model. Thus, many dynamic methods, assuming either full or semi PBPK models, have been proposed previously.⁴⁾ Their basic concept is to simulate the in vivo levels of a perpetrator and a victim by inputting plural in vitro drug specific parameters as well as predetermined physiological parameters (bottom-up approaches). However, it was a concern that in vitro parameters such as K_i, u would have a large bias, and that the plurality of the input parameters would reduce the flexibility of the simulation, making it difficult to achieve an accurate fit of the time-dependent plasma victim levels. In order to address to this issue, we investigated simpler (dynamic and static) methods than the traditional PBPK models as shown in next section.¹³⁾

3. METHODS FOR 2-COMP MODEL-ASSISTED DDI SIMULATION

3.1. Calculation of vC_b, oral(−)(t)

Based on 2-comp model (Fig. 4), blood–drug level after intravenous (i.v.) administration [C_b, iv(t)] can be expressed by use of a bi-exponential function as,

Fig. 4. Two-Comp Model and the Relation of Model-Specific Parameters with Common Model-Independent Ones

  

(5)

where K_A and K_B are first-order elimination rate constants; V_A and V_B are volume-related constants, and they are determined by common model-independent PK parameters [CL_tot, V₀, V_dss and K_d] as,   

(6)

  

(7)

  

(8)

Likewise, blood–drug level after oral administration [C_b, oral(t)] can be expressed as,   

(9)

where F and K_ab represent bioavailability and first-order absorption rate constant, respectively.

Thus, vC_b, oral(−)(t) as the reference standard of DDI, can be calculated from knowing vK_ab and vF, along with common model-independent PK parameters (vCL_tot, vV₀, vV_dss and vK_d). Although vF is essential for the calculation of vC_b, oral(t) and is commonly determined from the ratio of vCL_tot (obtained from i.v. administration) to vCL_oral (obtained from oral administration), it can be determined solely from vCL_oral and vA_e, oral, if vF_a×vF_g=1 and therefore vF=vF_h. Accordingly, vF_h can be determined as:   

(10)

Solving Eq. 10 with respect to vF_h   

(11)

Finally, vC_b, oral(−)(t) can be simulated by the use of six common parameters (vA_oral, vCL_oral, vV₀, vV_dss, vK_d and vK_ab) as inputs.

3.2. Calculation of vC_b, oral(+)(t)

We have devised three methods for the simulation of vC_b, oral(+)(t): two static methods (SM1 and SM2) and one dynamic one (SMd), though the study was started with SMd. Firstly, for SM1 assuming constant A_i, overall, vC_b, oral(+)(t) can be calculated by knowing vCL_oral(+), vA_e, oral(+) and vF_h(+), along with vV₀, vV_dss, vK_d and vK_ab which are basically the same as the ones for vC_b, oral(−)(t). Meanwhile, vCL_oral(+), vA_e, oral(+) and vF_h(+) can be determined as vCL_oral/AUCR (Eq. 1), vA_e, oral×AUCR and exp[ln(vF_h)/A_i, overall] (Eq. 4), respectively. Besides, A_i, overall can be determined as a function of AUCR, vF_h and vA_e, oral as:   

(12)

Alternatively,   

(13)

Thus, vC_b, oral(+)(t) can be simulated by SM1, by the use of AUCR as an input parameter, along with the input parameters used for vC_b, oral(−)(t).

SM2 also assumes constant A_i, overall which is equal to one estimated from the perpetrator-specific CYP isoform inhibition constants (pA_i, CYPs: DDI predictor 1) and the fractional CYP isoform contributions to victim clearance (vf_m, CYPs: DDI predictor 2) as determined from the plural DDI datasets, as shown in Eq. 14 where a victim is metabolized by CYP1A2, CYP2C19, CYP3A4 and non-CYP, and a perpetrator inhibits these CYPs.¹⁴⁾   

(14)

where,   

Meanwhile, the outline of SMd is shown in Fig. 5 focusing the “A” related terms such as vK_A(t) and vC_bA, oral(t), where A_i, overall(t) [=1+pC_hb, u(t)/K_{i, u, overall}] and accordingly vCL_int(t) [=vCL_int/A_i, overall(t)] (panel A), and vK_A (panel A) and vK_B, are assumed to change stepwise at narrow time intervals, so that vC_b, oral(t) [vC_bA, oral(t), panel B] changes likewise, keeping the condition of the tube model as vF_h(+)(t)=exp[(ln(vF_h)/A_i, overall(t)] (details described in ref. 13).

Fig. 5. Two-Comp Model-Assisted, and Tube-Based Dynamic Simulation Method (SMd)

3.3. Utilities of SM1, SM2 and SMd

Flow charts of the simulation of vC_b, oral(+)(t) versus vC_b, oral(−)(t) by the use of SM1, SM2 and SMd are shown, with discrimination of inputs and outputs for each simulation method, in Fig. 6. In particular, SM1 uses AUCR and common PK parameters (vCL_oral; vV₀; vV_dss; vK_d; vA_e, oral; vK_ab) as inputs with vF_h, A_i, overall and vF_h(+) as outputs; SM2 uses pA_i, CYPs (DDI predictor 1) and vf_m, CYPs (DDI predictor 2) along with the PK parameters as inputs with vF_h, A_i, overall, vF_h(+) and AUCR as outputs; SMd uses pC_hb, u(t) and K_{i, u, overall} along with the PK parameters as inputs with vF_h, A_i, overall(t), vF_h(+)(t) and AUCR as outputs.

Fig. 6. Flow Charts of the Simulation of vC_b,oral(+)(t) versus vC_b, oral(−)(t) by the Use of SM1, SM2 and SMd

SM1 has a basic utility for simulating time-dependent blood drug level increases with concordance with the actual ones, regardless of pC_hb, u(t) and K_{i, u, overall}. When it is applied to the simulation of DDI where a perpetrator is administered concomitantly or within 2 h before a victim which is common in clinical DDI studies, the accuracy of the simulation is expected to be high equivalently to SMd as shown in sections 4.1 and 4.2. It has an application utility for estimating A_i, overall and one of DDI predictors 1 and 2 which can be used for prediction of unknown DDI by collaboration with SM2, as shown in the next subsection (3.4).

SM2 has a basic utility for predicting time-dependent blood drug level increases by use of predictors 1 and 2. The limiting condition is the same as in SM1. It has an application utility for examining the sensitivity of SM1-based simulation performed by tuning predictors 1 and 2, other than the prediction of unknown DDI by collaboration with SM1.

SMd has a basic utility for simulating time-dependent blood drug level increases by taking pC_hb, u and K_{i, u, overall} into consideration. It has an application utility for examining the sensitivity of time-dependent parameters such as A_i, overall(t) in simulation, as shown in sections 4.1 and 5.3. Although it can simulate DDI with high accuracy, it is not always easy to obtain pC_hb, u(t), as described in section 2.3.

3.4. SM1 and SM2-Collaborated Prediction of Unknown DDI from the Existing DDI Database

Based on the concept of multiple CYP-isoform mediated metabolism as shown above, it is shown that DDI predictors 1 and 2 can be determined stepwise from the existing DDI database, so that unknown DDI can be predicted using these predictors by use of SM2 (Fig. 7).

Fig. 7. Schematic Illustration for SM1 and SM2-Collaborated Prediction of Unknown DDI from the Existing DDI Database

If drug A (vF_h=0.84) is metabolized exclusively [vf_{m, CYP1A2(A)}=vf_{m, CYP3A4(A)}=0] by CYP2C19 [vf_{m, CYP2C19(A)}], and A_i, overall [A_i, overall(A+PM)=4.5] when drug A is administered to CYP2C19 poor-metabolizer (PM), has been predetermined from AUCR [AUCR(A+PM)=5.0] using Eq. 12, then vf_{m, CYP2C19(A)} as DDI predictor 2, can be determined to be 0.78 from Eq. 14, assuming pA_i, CYP2C19=infinite (step 1, SM1). Next, if A_i, overall [A_i, overall(A+X)=3.2] when drug A is co-administered with a CYP-specific inhibitor (inhibitor X), has been predetermined from AUCR [AUCR(A+X)=3.5], then pA_{i, CYP2C19(X)} as DDI predictor 1 can be similarly determined to be 8.8 (step 2, SM1). Additionally, if drug B (vF_h=0.95) is metabolized exclusively by CYP2C19 [vf_{m, CYP2C19(B)}], and A_i, overall [A_i, overall(B+X)=1.95] when drug B is co-administered with inhibitor X, has been predetermined from AUCR [AUCR(B+X)=2.0], then vf_{m, CYP2C19(B)} as DDI predictor 2 can be determined to be 0.55 (step 3, SM1). Thus finally, when drug B is co-administered with another CYP2C19 inhibitor (inhibitor Y) whose pA_i, CYP2C19 (=3.0, DDI predictor 1) has been predetermined after a similar step to step 2, then A_i, overall(B+Y) and therefore AUCR(B+Y) can be predicted to be 1.57 and 1.59 by SM2, respectively, (goal). This was the concept of SM1 and SM2-collaborated prediction of unknown DDI from the existing DDI database.¹⁴⁾

4. SIMULATION OF DDI PERPETRATED BY FLV

4.1. Simulation of DDI Produced by Co-administration of RAM and FLV

Dynamic changes in the blood RAM levels [vC_b(t) versus vC_b(+)(t) changes] after administration of RAM (16 mg) with FLV (100 mg, BID), were simulated by the three methods (SMd, SM1, and SM2; PK parameters shown in ref. 14) (Fig. 8).

Fig. 8. Dynamic and Static Simulation of Plasma RAM Level-Increase in the Presence of FLV

Panel A, simulation of the plasma RAM level (vC_p) increase in the presence of FLV by use of SMd, SM1 and SM2 in comparison with the control; panel B, simulated hepatic blood-unbound FLV (pC_{hb, u}) levels used for SMd and SM1. The PK parameters used for the simulation are shown in ref. 14

A conformed simulation such that both AUCR and fold increase in C_max agreed with the actual values was achieved by the SMd, when K_{i, u, overall} was tuned to 3.3 nM, in contrast to the theoretically generated time-dependent hepatic blood unbound FLV level [pC_hb, u(t) versus static pC_hb, u (=around 50 nM, 2.5 times the level as shown in Fig. 3 in consideration of the non-linear PK of FLV)]. Additionally, simulations were also achieved by the SM1 using A_i, overall=16.1 determined from the actual AUCR, and by the SM2 using A_i, overall=16.3 determined from pA_i, CYPs and vf_m, CYPs (details in ref. 14).

These simulations showed that the unusually large magnitude of RAM-FLV DDI (AUCR=129) can be attributed to both the large A_i, overall (around 16), and the extremely low vF_h of RAM (0.03). This finding was also confirmed by the simulations of other FLV-perpetrated DDIs (next section).¹⁴⁾ The concordance of the dynamic and static simulations showed that the dynamic changes in blood perpetrator level would have little impact on DDI. This result was also confirmed by the simulations of other FLV-perpetrated DDIs.¹⁴⁾

4.2. Simulation of DDIs Produced by Co-administration of Other CYP1A2 and CYP2C19 Substrates and FLV

DDIs produced by co-administration of CYP1A2 and CYP2C19 substrates and FLV were simulated, in order to compare them with each other, including the RAM-victimized DDI, on the A_i, overall(t) and vF_h (Table 2) basis (SMd and SM1), and also to examine the predictability of the DDIs from pA_i, CYPs and vf_m, CYPs (SM2).¹⁴⁾ Typical examples (8 sets of DDI) are shown in Fig. 9.

Fig. 9. Simulation of Plasma CYP1A2 and CYP2C19 Substrate Level Increases after Co-administration with FLV, by Use of SMd, SM1 and SM2

Panel A, MEL (5 mg)+FLV (50 mg single); panel B, TIZ (4 mg)+FLV (50 mg BID); panel C, TAC (40 mg)+FLV (100 mg QD); panel D, TAS (5 mg)+FLV (50 mg BID); panel E, CAF (250 mg)+FLV (50 mg BID); panel F, THE (257 mg)+FLV (100 mg QD); panel G, MEP (100 mg)+FLV (87.5 mg QD); panel H, OME (40 mg)+FLV (50 mg BID). The PK parameters used for the simulations are shown in ref. 14, and the data of AUCR and vF_h are shown in Table 2.

SMd-based simulation confirmed that blood victim level increases can be simulated simply by tuning a single parameter (K_{i, u, overall}). In addition, SM1-based simulations confirmed that blood victim level increases are almost entirely determined on the static basis, regardless of their dynamic changes.

Factorial analysis based on these simulations demonstrated that the K_{i, u, overall} obtained in the SMd are almost equivalent to the static ones [=pC_hb, u/(A_i, overall−1)], and that they are not much different among the DDIs, despite the great difference in AUCR (the same is true for A_i, overall) (Fig. 10A), rendering this difference in AUCR large compared to the difference in vF_h(+)/vF_h [or 1/vF_h in case of vF_h(+) sufficiently large]¹⁴⁾ (Fig. 10B).

Fig. 10. Factorial Analysis of FLV-Perpetrated, CYP1A2 and CYP2C19 Substrate DDIs

Panel A, comparison of K_{i, u, overall} obtained in the SMd and SM1 among victims in FLV-perpetrated DDIs; panel B, comparison of AUCR/A_i,overall and F_h/F_h(+) determined in SM1 among the same victims.

These results confirmed that the tube-based method is an appropriate method for the prediction of DDI, unlike the well-stirred model.

4.3. Predictability of Unknown DDIs Perpetrated by FLV by Use of DDI Predictors 1 and 2

Upon simulation of the above FLV-perpetrated DDIs by SM2, we determined pA_i, CYPs of FLV at different doses.¹⁴⁾ Firstly, pA_{i, CYP1A2 (FLV 100 mg QD)} (=18) was determined from the A_i, overall (CAF-FLV), assuming vf_{m, CYP1A2 (CAF)} (=0.94). pA_{i, CYP2C19 (FLV 100 mg BID)} (=1+pC_hb, u/K_{i, u, overall}=20 nM) was determined from the K_{i, u, overall} (2.6 nM) for DDI (MEP-FLV),¹⁹⁾ and assuming vf_{m, CYP1A2 (MEP)} (=1.0). pA_{i, CYP3A4 (FLV 25 mg BID)} (=1.3) was determined from the A_i, overall (OME-FLV), assuming vf_m, CYP1A2/vf_m, CYP3A4 (=0.92/0.08). Then, since FLV is a competitive CYP inhibitor (Table 3), pA_i, CYPs at different doses could be determined using the following equation:

Table 3. pA_i,.CYPs of FLV

Daily dose n×pD	pAi,CYP1A2	pAi, CYP2C19	pAi, CYP2D6	pAi, CYP3A4
2×25 mg	9.5	6	1	1.3
1×100 mg	18	10	1	1.6
2×100 mg	35	20	1	2.3

  

(15)

Meanwhile, vf_m, CYPs of a single-CYP-isoform substrate were determined straightforwardly from the actual A_i, overall (single dataset), while those of triple-CYP-isoform substrates were determined using plural DDI datasets¹⁴⁾ (Table 4). For instance, vf_m, CYP1A2/vf_m, CYP2C19 /vf_m, CYP3A4 (=0.73/0.20/0.07) of RAM were determined with the aid of the data on DDIs perpetrated by ketoconazole (KTCZ: 200 mg BID; weak CYP2C19 but strong CYP3A4 inhibitor; AUCR/A_i, overall=1.82/1.21), fluconazole (FLCZ: 200 mg QD; weak CYP3A4 but strong CYP2C19 inhibitor; AUCR/A_i, overall=2.36/1.33).

Table 4. vf_m, CYPs of CYP1A2 and CYP2C19 Substrates

	No. of CYP isoformsa)	vfm, CYP1A2	vfm, CYP2C19	vfm, CYP3A4	1-vfm, nonCYP
RAM	3	0.73	0.20	0.07	0.00
MEL	3	0.62	0.24	0.14	0.00
TIZ	3	0.75	0.20	0.05	0.00
TAC	1	0.75	0.00	0.00	0.25
TAS	3	0.70	0.05	0.25	0.00
CAF	1	0.94	0.00	0.00	0.06
THE	1	0.78	0.00	0.00	0.22
OME	2	0.00	0.92	0.08	0.00
OME (PMb))	1	0.00	0.00	1.00	0.00
MEP	1	0.00	1.00	0.00	0.00

a) Based on iv vitro human liver microsome (HLM) experiments. b) Poor metabolizer with CYP2C19.

The SM2 simulations shown in Figs. 8 and 9 suggested that any victim-DDI perpetrated by FLV can be successfully predicted by using these predetermined (permanent) pA_i, CYPs for FLV (Table 3), as far as predictor 2 (vf_m, CYPs) and vCL_oral (or vF_h) of the victim (another DDI predictor) are determined.

5. PREDICTION OF CYP3A4-MEDIATED DDI

5.1. Approaches of Gut-Wall Extraction in CYP3A4-Mediated DDI

We also studied whether DDI caused by a CYP3A4 substrate and a CYP3A4 inhibitor can be predicted in a similar way to the above.¹⁵⁾ However, the solution of issues (iv), (v) and (vi) shown in Table 1 was a key to success in the simulation.²⁰⁾

Concerning issue (iv), it is common for an orally-administered CYP3A4 substrate to be subjected to CYP3A4-mediated gut-wall extraction (vF_g<1; the gut wall first-pass effect) as well as hepatic extraction (vF_h, the hepatic first-pass effect), and accordingly subjected to a decrease in the bioavailability (vF=vF_g×vF_h<1, in case of vF_a=1)²¹⁾ (Fig. 11).

Fig. 11. Compartment Model for Gut-Wall and Hepatic Extractions

The model consists of compartments representing the gastro-intestinal (GI) tract, the gut wall, the liver and the systemic circulation. vCL_g, perm, vCL_g, CYP3A4, and Q_gut represent gut-wall permeability clearance, CYP3A4-mediated gut-wall metabolic clearance, and gut-wall blood flow, respectively.

Thus, the decrease in the gut-wall extraction (increase in vF_g) expected by co-administration with a CYP3A4 inhibitor will have an impact on the prediction of CYP3A4-mediated DDI. However, if significant gut-wall extraction occurs with a CYP3A4 substrate, it will not be easy to accurately predict the vF_g and its change (increase) in the presence of an inhibitor with discrimination of vF_h. Although many reports have addressed the prediction of vF_g, the methods seem not necessarily reliable, and we cannot solve this since they will depend largely on vF_a (true for substrates of both CYP3A4 and P-glycoprotein).²²⁾

The situation is different for midazolam (MDZ) and triazolam (TRZ); they exhibit complete oral absorption (vF_a=1), and have been used as the most preferable CYP3A4 probe to examine CYP3A4-inhibitory potential of NCE in clinical DDI studies.²³⁾ Their vF_g values have been determined with high confidence from the PK after iv and oral administrations,²¹⁾ and also from the AUCR in their co-administration with grapefruit juice (GFJ) which shows gut-wall specific CYP3A4 inhibition [vF_g(+)=1] at a single administration of an appropriate strength GFJ (ex. single or double strength)^24,25) (Fig. 12).

Fig. 12. SM1-Based Simulations of Plasma TRZ and MDZ Level Increases Caused by GFJ

Panel A, TRZ (0.25 mg)+GFJ (single administration of double strength GFJ) (ref. 25); panel B, MDZ (2 mg)+GFJ (single administration of single strength GFJ) (ref. 24). Details are shown in the supplementary material in ref. 15.

Thus, we focused on the simulation of DDI produced by co-administration of MDZ (or TRZ) with various CYP3A4 inhibitors. This was because we could determine the pA_i, CYP3A4 of these inhibitors, which are essential for the SM2-based DDI prediction, with high confidence.

5.2. Simulation of DDIs Produced by Co-administration of MDZ with Typical CYP3A4 Inhibitors

Next, we have performed simulations of MDZ and TRZ-victimized DDIs produced by co-administration with perpetrators listed in the FDA guidance,²⁾ by use of SM1 and SM2.¹⁵⁾ In particular, we assumed a complete increase in vF_g in the presence of a moderate or strong perpetrator [vF_g(+)=1], against vF_g=0.5 (MDZ) and vF_g=0.7 (TRZ), and verified this assumption with simultaneous simulations using the data of iv and oral administration of the victims. Consequently, conformed simulations were achieved by SM1, and pA_i, CYP3A4 of each perpetrator was successfully determined. Additionally, conformed simulations were also achieved by SM2 using the pA_i, CYP3A4s determined from the SM1 simulations (details shown in ref. 15). The plasma MDZ level increases by co-administration with four inhibitors [KTCZ; itraconazole (ITCZ); clarithromycin (CLM); erythromycin (ERT)], and their pA_i, CYPs determined by the SM1 are shown in Fig. 13 and Table 5, respectively.

Fig. 13. Simulation of MDZ-Victimized DDIs Produced by Co-administration with CYP3A4 Inhibitors by Use of SM1 and SM2

Panel A, MDZ (7.5 mg)+KTCZ (400 mg QD) (AUCR=11.0); panel B, MDZ (7.5 mg)+ITCZ (200 mg QD) (AUCR=10.1); panel C, MDZ (4 mg)+CLM (500 mg BID)(AUCR=5.0); panel D, MDZ (15 mg)+ERT (500 mg TID) (AUCR=4.7). The PK parameters used for the simulations are shown in ref. 15.

Table 5. pA_i, CYP3A4s Determined from SM1-Based Simulations of MDZ-Victimized DDIs

Perpetrators	Daily dose n×pD	pAi, CYP3A4	CYP3A4 inhibitiona) (%)	MBI
KTCZ	1×400 mg	9.60	89.6	No
ITCZ	1×200 mg	11.2	91.1	No
CLM	2×500 mg	2.50	60.0	Yes
ERT	3×500 mg	2.48	59.7	Yes

a) Calculated from (1-1/A_i, overall)×100.

Concerning CYP inhibition type, it is known that KTCZ and ITCZ are competitive inhibitors, while CLM and ERT are non-competitive (MBI).^10,26) Because of competitive inhibition, we were able to determine the pA_i, CYPs at different doses of KTCZ and ITCZ similarly to FLV, which we could use for DDI prediction at different doses of perpetrators (see later section). We were not able to determine pA_i, CYPs at different doses of CLM and ERT in the same way. Nevertheless, the doses of these perpetrators are commonly fixed in the clinical studies, to those shown in Table 5, so that there is no problem in the prediction of DDI in the clinical studies.

Concerning gut-wall CYP3A4 inhibition, it was shown that a perpetrator will exhibit pA_{i, CYP3A4 (gut)} equivalent or larger than pA_i, CYP3A4 in the liver, and that a perpetrator exhibiting MBI (ex. CLM and ERT) will exhibit almost complete inhibition toward the gut-wall CYP3A4 [vF_g(+)=unity],^26–28) regardless of incomplete inhibition of the hepatic CYP3A4 [pA_i, CYP3A4, around 2.5, Quinney’s simulations²⁶⁾ (next section)]. The value of A_i, overall determined in DDI produced by MDZ plus CLM (3.3) (Fig. 13C) was confirmed to be the same as found by Quinney’s simulations (next section).

5.3. Insignificance of Inhibitory Activities of Metabolites and MBI upon DDI Prediction

CYP inhibition by a perpetrator’s metabolites is known to be common occurrence. ITCZ is known to have 3 metabolites active in CYP inhibition, and Templeton et al.²⁷⁾ predicted dynamic changes in total fold decrease in CL_h, int [A_i, overall(t)] produced by ITCZ and its metabolites, suggesting that this complex should be taken into consideration in dynamic DDI simulation. However, our study based on the Templeton’s simulation showed that inhibition by multiple inhibitors including metabolites does not make a difference between the SMd and SM1-based simulations (Fig. 14).

Fig. 14. Impacts on Inhibitory Metabolites on DDI Observed in Co-administration of MDZ with ITCZ

Panel A, A_i, overall(t) due to ITCZ and its metabolites (cited from ref 27); panel B, comparison of vC_p simulation between SMd [A_i, overall(t)] and SM1 (A_i, overall=3.8). The more details are shown in ref. 15.

Concerning MBI (issue 6), A_i, overall(t) of a perpetrator (enzyme inactivator) is expected to be less sensitive to the changes in the blood perpetrator level than that of competitive inhibitors. In our study based on Quinney’s simulations,¹⁵⁾ the remaining CYP3A4 activity after exposure by CLM was shown to be determined by the balance of the rates of the inactivation as a function of the perpetrator concentration at the enzyme site and the reproduction of CYP3A4, and the inactivation was shown to last several days even after complete elimination of CLM from the blood circulation (Fig. 15A). Thus, the lasting effect could be explained by the slower reproduction of CYP3A4. This characteristic would work in favor of the approximation of A_i, overall(t) to be the time-independent one (A_i, overall) (Fig. 15B). It was suggested that this characteristic of MBI has little impact on the present DDI prediction. However, the steady state maximum inactivation at the liver site was shown to be achieved one week after multiple perpetrator doses (Fig. 15A). Therefore, it would be safer when the present method is applied to DDI produced by multiple perpetrator doses, as is common in clinical DDI studies.

Fig. 15. CYP3A4 Activity Decrease in the Liver and Intestine Following CLM Exposure (500 mg BID) and A_i, overall(t)

CYP3A4 activity decrease (panel A) was cited from ref. 26. A_i, overall(t) (inverse of CYP3A4 activity, panel B) was calculated in this review.

5.4. Additional Examples of CYP3A4-Mediated DDI Simulation

Additionally, SM2-based DDI simulations were performed using the reported DDIs between various CYP3A4 substrates [ex. lidocaine (LID), zopiclone (ZOP) and alprazolam (ALP)] versus ITCZ as a strong CYP3A4 inhibitor, and versus ERT as a moderate CYP3A4 inhibitor. They were simultaneous in respect to different perpetrators toward the same victim. Consequently, conformed simulations were achieved by both SM1 and SM2 (Fig. 16). The values of vf_m, CYPs as DDI predictor 2 are shown in Table 6.

Fig. 16. Predictive Simulation of DDIs Observed between Various CYP3A4 Substrates versus ITCZ, and versus ERT

Victims: lidocaine (LID), zopiclone (ZOP) and alprazolam (ALP). vF_g=unity for all the victims.

Table 6. vF_g, vF_h and vf_m, CYPs of Victims Metabolized by Multiple CYP Isoforms

Victims	vFg	vFh	vfm, CYP1A2	vfm, CYP2C9	vfm, CYP3A4	vfm, non CYP
MDZ	0.5	0.60	0	0	0.85	0.15a)
TRZ	0.7	0.72	0	0	1.0	0
LID	1	0.26	0.5	0.1	0.4	0
ZOP	1	0.75	0	0	0.5	0.5b)
ALP	1	0.96	0	0	1	0

a) N-Glucronide. b) Decarbpxylation.

In these simulations, vF_g of all the victims was assumed to be unity, using a simple judgment that compares vF_g-determining PK parameters (vfu_b, vF_h, and vf_m, CYP3A4) with those for TRZ as a reference standard. More detail was shown in the supplementary material in ref. 15.

6. PERSPECTIVE OF ISSUES (VII) AND (VIII) RAISED IN DDI PREDICTION

6.1. Variability of K_i, u in Vitro

PBPK methods commonly employ in vitro K_i, u for DDI prediction. However, the value may have a bias. Greenblatt et al. reported the considerable variability of KTCZ K_i, u determined from HLM-CYP3A4, through analysis of the values reported from different research groups in the past²⁹⁾ (Fig. 17).

Fig. 17. Distribution of 76 Ketoconazole K_i Values from Published Studies, Reported in Ref. 29

Thus far, sources of the variability are uncertain. Yao et al. reported the inhibitory effect of microsome degradation products (polyunsaturated fatty acids) on human CYP enzyme.³⁰⁾ This report suggested that the contamination of HLM with the degradation products underestimates in vitro CL_h, int and accordingly overestimates K_i, u. Thus, we have examined this possibility in the reported K_i, u of FLV on a theoretical basis. The result suggested overestimation of K_i, u due to the gap of victim clearance between in vitro and in vivo (Fig. 18). Therefore, in vitro K_i, u, as commonly used in the PBPK-based methods, would preferably be avoided in DDI prediction.

Fig. 18. Overestimation of in Vitro K_i, u of FLV Due to the Gap of Victim Clearance between in Vitro and in Vivo

The values for vCL_int gap correspond to the ones shown as λ_HLM in the table in ref. 15.

6.2. Modification of Hepatic Extraction Model to Meet with Enzyme-Transporter Interplays

Varma et al. have reported a new hepatic extraction model, where the “overall” hepatic intrinsic clearance (CL_{h, int, overall}) of a transporter-and-enzyme substrate is expressed by a hybrid equation, including a term (PS_p+CL_h, int) in the denominator and a term (PS_p+PS_a)×CL_h, int in the numerator, and is discriminated from “common” hepatic intrinsic clearance (CL_h, int) which is defined by the traditional hepatic extraction kinetics model¹¹⁾ (Fig. 19).

Fig. 19. Extended Net-Effect Model for Hepatic Extraction Kinetic

Importantly, a term (PS_p+PS_a)/(PS_p+CL_h, int) (=K_p, u, u), “hepatic tissue to hepatic plasma partition coefficient,” reflects a relative increase in the cytosolic unbound-drug level to the unbound plasma level in case of PS_a/PS_p>>1 and consequently the increase in the overall hepatic clearance. Meanwhile, if a drug is not a transporter substrate (PS_a=0), then K_p, u, u becomes smaller than unity, depending on the PS_p-to-CL_h, int ratio (=r). If a victim drug exhibits such a characteristic, DDI perpetrated by a weak or moderate CYP inhibitor will be diminished or weakened.

Nevertheless, this scenario will not be possible in common DDIs, in the light of the present successful DDI predictions (r>>1; PS_a=0). Varma et al. also proposed a categorization of NCEs, arranging K_p, u, u into four classes based on the well-known pharmaceutical classification system: the majority are substrates of hepatic uptake transporters such as OATPs. Therefore, the present victim drugs (K_p, u, u=1 resulting from r>>1 and PS_a=0) would all be outliers of K_p, u, u<1 and K_p, u, u>1, and this modification would not be necessary.

7. CONCLUSION

The present review summarizes our current achievements in DDI prediction. The main cause of the unusually large DDI between RAM and FLV was attributed to the extremely small vF_h of RAM. Traditional DDI prediction assuming the well-stirred hepatic extraction kinetic ignores the relative increase of vF_h by DDI, while we could solve this problem by use of the tube model. Finally, we completed a simple and useful method for prediction of DDI.

Currently, DDI prediction becomes more complex, making it difficult to respond to various issues. The regulatory agents recommend DDI prediction by use of PBPK methods. However, these are problematic in that they require plural in vitro data which reduce the flexibility and accuracy of the simulation. In contrast, our method is based on the static and two-comp models. The two-comp model has advantages in that it uses common PK parameters determined from actual clinical data, guaranteeing the simulation of the reference standard in DDI. Our studies confirmed that dynamic changes in perpetrator level do not make a difference between static and dynamic methods. The reported DDIs perpetrated by FLV and ITCZ were successfully predicted by use of the present method where two DDI predictors (pA_i, CYPs and vf_m, CYPs) are determined successively as shown in the graphical abstract. The results strongly suggested that DDI produced by a given victim and a standard inhibitor, or a given inhibitor and a standard victim, can be predicted in high confidence, with the aid of the existing DDI database.

This approach will accelerate prediction of DDI produced by NCEs, marking an improvement over the traditional methods.

Conflict of Interest

The authors declare no conflict of interest.

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