A Physiologically-Based Pharmacokinetic Model of Trimethoprim for MATE1, OCT1, OCT2, and CYP2C8 Drug–Drug–Gene Interaction Predictions

Trimethoprim is a frequently-prescribed antibiotic and therefore likely to be co-administered with other medications, but it is also a potent inhibitor of multidrug and toxin extrusion protein (MATE) and a weak inhibitor of cytochrome P450 (CYP) 2C8. The aim of this work was to develop a physiologically-based pharmacokinetic (PBPK) model of trimethoprim to investigate and predict its drug–drug interactions (DDIs). The model was developed in PK-Sim®, using a large number of clinical studies (66 plasma concentration–time profiles with 36 corresponding fractions excreted in urine) to describe the trimethoprim pharmacokinetics over the entire published dosing range (40 to 960 mg). The key features of the model include intestinal efflux via P-glycoprotein (P-gp), metabolism by CYP3A4, an unspecific hepatic clearance process, and a renal clearance consisting of glomerular filtration and tubular secretion. The DDI performance of this new model was demonstrated by prediction of DDIs and drug–drug–gene interactions (DDGIs) of trimethoprim with metformin, repaglinide, pioglitazone, and rifampicin, with all predicted DDI and DDGI AUClast and Cmax ratios within 1.5-fold of the clinically-observed values. The model will be freely available in the Open Systems Pharmacology model repository, to support DDI studies during drug development.


Introduction
Trimethoprim is an inhibitor of bacterial folic acid metabolism used to treat bacterial infections. It is either applied as monotherapy or in combination with sulfonamides, e.g., sulfamethoxazole ("cotrimoxazole"). Trimethoprim is one of the most frequently-used antibiotics worldwide, ranking fifth after penicillins, cephalosporins, macrolides, and fluoroquinolones, with a global consumption of 5 × 10 9 standard units in 2010 [1].
Due to the frequent prescription of trimethoprim, investigation of its drug-drug interaction (DDI) potential is clinically relevant. The antibiotic is a potent inhibitor of multidrug and toxin-extrusion protein (MATE) 1 and MATE2-K [2], and therefore recommended by the FDA as a clinical MATE inhibitor. Furthermore, trimethoprim less potently inhibits organic cation transporter (OCT) 1 and OCT2 [3,4]. This combined inhibition potential can be observed during clinical studies of trimethoprim with metformin, where co-administration of trimethoprim increases the area under the concentration-time curve (AUC) of metformin by 30% [4]. Metformin is listed by the FDA as the only recommended MATE1, MATE2-K, and OCT2 substrate for clinical DDI studies [2].
The obtained profiles were divided into a training dataset and a test dataset, which were used for model building and model evaluation, respectively.

Trimethoprim PBPK Model Building
Model building was started with an extensive literature search to gain information about physicochemical parameters as well as absorption, distribution, metabolism, and excretion (ADME) processes of trimethoprim.
To simulate trimethoprim in the different organs of the body, virtual individuals were created according to the demographics of the respective clinical studies (ethnicity, sex, age, body weight, and height). If no information was provided, a European, male, 30-year-old individual was assumed, with body weight and height characteristics taken from the PK-Sim ® population database.
Transporters and enzymes involved in trimethoprim ADME were implemented according to current literature, using the PK-Sim ® expression database [19]. Details on their expression and localization in the different organs of the body are provided in the system-dependent parameter table in the Supplementary Materials (Table S19).
Model parameters that could not be informed from literature were optimized by fitting the model simultaneously to all plasma or whole blood concentration-time profiles and f e in urine data of the training dataset.

Trimethoprim PBPK Model Evaluation
Trimethoprim model performance was evaluated by comparison of (1) the predicted plasma or whole blood concentration-time and f e in urine profiles to the clinically-observed data of the respective clinical studies, (2) predicted plasma or whole blood concentration values of all studies to their corresponding observed values in goodness-of-fit plots, and (3) predicted to observed f e in urine, AUC, and C max values, where AUC was calculated from the time of drug administration to the time of the last concentration measurement (AUC last ) for both predicted and observed plasma or whole blood concentration-time profiles.
As quantitative measures of the model performance, the mean relative deviation (MRD) of all predicted plasma and whole blood concentrations and the geometric mean fold error (GMFE) of all predicted f e in urine, AUC last , and C max values were calculated according to Equations (1) and (2), respectively. MRD and GMFE values ≤ 2 characterize an adequate model performance.
where c predicted,i = predicted plasma (or whole blood) concentration, c observed,i = corresponding observed plasma (or whole blood) concentration, and k = number of observed values.
where predicted PK parameter i = predicted f e in urine, AUC last , or C max value; observed PK parameter i = corresponding observed f e in urine, AUC last , or C max value; m = number of studies.

DDI and DDGI Modeling
In addition to the previously-described methods for PBPK model evaluation, the ability of the trimethoprim model to adequately predict DDIs was tested. Trimethoprim DD(G)I modeling was performed with three different victim drugs (metformin, repaglinide, and pioglitazone) and one perpetrator drug (rifampicin). The parameters of the previously-developed PBPK models of metformin [20], repaglinide, pioglitazone [21], and rifampicin [22] that were applied for DDI modeling are reproduced in Tables S8, S11, S14 and S17 and DDI model processes are illustrated in Figures S14, S18, S21 and S25 of the Supplementary Materials.
To predict the published trimethoprim DDGI studies with metformin (SLC22A2 808G>T, increased metformin transport) and pioglitazone (CYP2C8*3, increased pioglitazone metabolism), the trimethoprim model was applied with previously-built and evaluated DGI models of metformin and pioglitazone [20,21]. For the competitive inhibition of the variant OCT2 or CYP2C8 isoforms by trimethoprim, the same K i values as for the wildtype transporter or enzyme were applied.
The rifampicin-trimethoprim DDI was modeled as induction of P-gp trimethoprim transport and CYP3A4 trimethoprim metabolism by rifampicin, with simultaneous competitive inhibition of P-gp and CYP3A4. The parameter values to model these interactions were taken from literature (values and references are listed in the rifampicin drug-dependent parameter Table S17 in the Supplementary Materials) and have been evaluated in previous DDI analyses [21,22]. Due to the lack of in vitro information regarding the metabolism of trimethoprim, the clinical data of the rifampicin-trimethoprim DDI were included into the training dataset, and the inducible fraction of trimethoprim metabolism was attributed to metabolism by CYP3A4.
The mathematical implementation of competitive inhibition and rifampicin-dependent induction is shown in Section 1.5 of the Supplementary Materials.

DDI and DDGI Model Performance Evaluation
The DDI and DDGI modeling performance was evaluated by comparison of predicted to observed plasma concentration-time profiles of the respective victim drugs metformin, repaglinide, pioglitazone, or trimethoprim, administered alone and during perpetrator drug co-treatment (trimethoprim or rifampicin). Furthermore, predicted DDI or DDGI AUC last ratios (Equation (3)) and DDI or DDGI C max ratios (Equation (4)) were calculated, and compared to the observed ratios.
DDI or DDGI AUC last ratio = AUC last victim drug during co − administration AUC last victim drug control DDI or DDGI C max ratio = C max victim drug during co − administration C max victim drug control (4) As a quantitative measure of the DDI and DDGI model performance, GMFE values of the predicted AUC last ratios and C max ratios were calculated according to Equation (2).

Sensitivity Analysis
Local sensitivity analysis was performed on the trimethoprim model to investigate the impact of single-model parameters on the predicted AUC, C max , and t max at steady state. Parameters were included in the analysis if they have been optimized, if they were associated with optimized parameters or if they might had a strong impact on the model predictions due to their use in the calculation of permeabilities or partition coefficients. A list of the analyzed parameters is provided in Table S6 of the Supplementary Materials. Sensitivity was calculated as the ratio of the relative change of the simulated AUC, C max , or t max to the relative variation of the tested parameter around the parameter value used in the model, according to Equation (5): where S = sensitivity of the AUC, C max , or t max to the tested model parameter; ∆PK = change of the AUC, C max , or t max ; PK = AUC, C max , or t max predicted with the original model parameter value; p = original model parameter value; ∆p = change of the tested model parameter value. Sensitivity analysis was performed using the highest recommended dose and a relative parameter perturbation of 1000%. The threshold value for sensitivity was set to 0.5; this value signifies that a 100% change of the investigated parameter value causes a 50% change of the predicted AUC, C max or t max .

Trimethoprim PBPK Model Building and Evaluation
The trimethoprim whole-body PBPK model was built and evaluated using a total number of 66 trimethoprim plasma or whole blood concentration-time profiles and 36 f e in urine profiles (intravenous and oral, single-, and multiple-dose administration), covering a broad dosing range from of 40 to 960 mg. In 47 of the 66 clinical studies, trimethoprim was administered as "cotrimoxazole", i.e., in combination with sulfamethoxazole. According to literature [29,30] and our own analyses, trimethoprim pharmacokinetic profiles are not altered by simultaneous administration of sulfamethoxazole (see Figure S2 in the Supplementary Materials). Consequently, studies with co-administration of trimethoprim and sulfamethoxazole were included for model development.
A table listing all utilized clinical studies is provided in the Supplementary Materials (Table S1).
The final trimethoprim PBPK model applies active efflux via P-gp (most strongly expressed in the intestine and kidney), metabolism by CYP3A4 (mainly in the liver with lower expression in the intestine), an unspecific hepatic clearance, and passive glomerular filtration. Trimethoprim is primarily excreted unchanged in the urine (46-67% of an oral dose [30][31][32]). The implemented ADME processes are visualized in Figure 1 and in Figure S3 of the Supplementary Materials. The drug-dependent parameters of the final model are given in Table 1 and in Table S2 of the Supplementary Materials. The model-specific, system-dependent parameters, with the expression profiles of the incorporated transporter and metabolizing enzymes, are summarized in the system-dependent parameter table in the Supplementary Materials (Table S19).
The good descriptive (training dataset, 13 studies) and predictive (test dataset, 53 studies) performance of the trimethoprim model is demonstrated in Figure (Tables S3 and S4).   Correlations of predicted with observed AUC last (97% within 2-fold) and C max values (98% within 2-fold) are presented in Figure 4 and in Figure S12      Sensitivity analysis of a simulation of 160 mg trimethoprim twice daily, using a parameter perturbation of 1000% and a sensitivity threshold of 0.5, showed that the only parameter value the model predictions are sensitive to is the trimethoprim fraction unbound in plasma, for which a literature value is used in the model (56% [44]). The full quantitative results of the sensitivity analysis are shown in Section 2.5 ( Figure S13) of the Supplementary Materials.

Trimethoprim DDI and DDGI Modeling
Trimethoprim DD(G)I modeling was performed with three different victim drugs (metformin, repaglinide, and pioglitazone) and one perpetrator drug (rifampicin). Tables listing all utilized clinical DDI studies are provided in the Supplementary Materials (Tables S7, S10, S13 and S16). The resulting trimethoprim DDI network with the affected transporters and enzymes is illustrated in Figure 5 and in Figure S1 of the Supplementary Materials. The good DDI model performance is demonstrated in Figure 6, showing representative population predictions of victim drug plasma concentration-time profiles before and during the four different DDIs, compared to observed data. For the rifampicin-trimethoprim DDI study, no plasma concentrations of trimethoprim without rifampicin co-administration were reported. Instead, day 1 and day 8 of the rifampicin-trimethoprim co-administration were shown, and therefore modeled and evaluated. Semilogarithmic as well as linear plots of population predicted compared to observed victim drug plasma concentration-time profiles of all DDI and DDGI studies are shown in Figures S15, S16, S19, S22, S23, S26, and S27 of the Supplementary Materials. For a quantitative evaluation of the DDI performance, predicted and observed DDI and DDGI AUC last , and C max ratios are compared in Figure 7 and listed in the Supplementary Materials, showing overall GMFEs of 1.08, 1.27, 1.32, and 1.08 (AUC last ratios) and of 1.14, 1.11, 1.04, and 1.30 (C max ratios) for the four modeled DDIs (trimethoprim-metformin, trimethoprim-repaglinide, trimethoprim-pioglitazone, and rifampicin-trimethoprim), respectively. All predicted DDI and DDGI AUC last and C max ratios are within 1.5-fold of the observed values. The full quantitative evaluation showing all ratios and GMFE values with ranges is presented in the Supplementary Materials (Tables S9, S12, S15 and S18 and Figures S17, S20, S24 and S28).

Discussion
A whole-body PBPK model of trimethoprim for the investigation and prediction of DDIs has been successfully built and evaluated. The model reliably captures the trimethoprim plasma and urine concentration-time profiles over a broad dosing range, for intravenous and oral administration as well as for single-and multiple-dose regimens. Good model performance has been demonstrated by (1) comparison of population predicted plasma or whole blood concentration and f e in urine profiles to observed data, (2) a goodness-of-fit plot and MRD values of the predicted plasma concentrations, (3) goodness-of-fit plots and GMFE values of the predicted f e in urine, AUC last , and C max values, and (4) the good DDI and DDGI performance.
The processes involved in the absorption, distribution, metabolism, and excretion of trimethoprim are not completely characterized or understood. It is known that trimethoprim is mainly excreted unchanged in urine (46-67% of an oral dose [30][31][32]), via glomerular filtration and tubular secretion. In vitro, trimethoprim is a substrate of P-gp [75], MATE1, and MATE2-K [76], but MATE2-K expression in the human kidney is extremely low [77]. The active tubular secretion of trimethoprim via MATE1 also seems unlikely, because the renal clearance of trimethoprim increased after eight days of rifampicin co-administration [16], and induction of MATE1 by rifampicin has not been demonstrated, yet. Furthermore, about 20% of a trimethoprim dose is reported to be metabolized [33], but there is no information available, as to which enzymes are involved in vivo. Implementation of P-gp and CYP3A4 into the trimethoprim model resulted in a good description of the trimethoprim concentration-time profiles observed in plasma and urine. In addition, the trimethoprim plasma concentrations measured during the first and eighth day of rifampicin co-administration and the observed increase in trimethoprim renal clearance on the eighth day of this DDI [16] are well captured by the model after implementation of P-gp and CYP3A4. Another candidate enzyme for trimethoprim metabolism in vivo is CYP2C9 [78], but co-administration of high doses of the CYP2C9 inhibitor, sulfamethoxazole (Ki = 271 µM [79]) showed no effect on trimethoprim plasma concentrations (see [29,30] and Figure S2 in the Supplementary Materials). In addition, the induction of CYP2C9 by rifampicin is not as strong as that of CYP3A4 and using CYP2C9 as the main enzyme for trimethoprim metabolism in the model resulted in an underprediction of the rifampicin DDI effect.
One shortcoming of the presented model might be that according to literature, about 20% of a trimethoprim dose is metabolized [33], but fitting the model to this low value (CYP3A4 metabolism assumed) led to an overprediction of the urinary excretion and to an underprediction of the rifampicin-trimethoprim DDI. By implementation of CYP3A4 metabolism and addition of an unspecific hepatic clearance process, both urinary excretion and rifampicin-trimethoprim DDI could be well described, accepting a higher total fraction metabolized of 30-40%. Summed up, these 30-40% match well with the observed 46-67% of trimethoprim excreted unchanged in urine [30][31][32] and the reported fraction excreted in feces of 4% [80]. Unfortunately, the in vivo trimethoprim metabolism is not completely understood, which led us to include an unspecific clearance into the model. It might be speculated that trimethoprim undergoes tubular reabsorption, which was not implemented in our model but could reduce the slight overprediction of trimethoprim urinary excretion that we see without the unspecific hepatic clearance. However, no transporters involved in tubular reabsorption of trimethoprim are described in the literature, so far. Therefore, the extent of trimethoprim metabolism and the involved enzymes, as well as possible tubular reabsorption mechanisms need to be further investigated experimentally, to confirm or reject our model assumptions. The presented trimethoprim model is able to adequately predict the MATE1, OCT1, and OCT2 DDI (metformin) as well as the CYP2C8 DDIs (repaglinide and pioglitazone), shown by comparison of predicted to observed plasma concentration-time profiles and predicted compared to observed DDI AUC and C max ratios, with all predicted ratios within 1.5-fold of the observed ratios. Metformin, the only recommended MATE1, MATE2-K, and OCT2 substrate for clinical DDI studies [2], is frequently prescribed (almost 80 million prescriptions in the USA in 2017 [81]) to treat type 2 diabetes mellitus. Also, as trimethoprim is regularly prescribed, co-administration with metformin, leading to increased metformin exposure, can frequently occur. The resulting increased risk of adverse drug events, e.g., in patients treated with high metformin doses or patients with impaired renal function, could be mitigated by applying the model to calculate metformin dose adaptations for the duration of this co-administration.
In addition, the model was successfully applied to predict plasma concentration-time profiles of metformin and pioglitazone in carriers of the SLC22A2 808G>T and CYP2C8*3 alleles, respectively, during co-administration with trimethoprim. The SLC22A2 808G>T allele investigated in this study occurs with a global frequency of 10-14% [8]. Therefore, investigation of its related DDGIs is clinically relevant. Plasma concentration time-profiles are well predicted using an OCT2 K i value from in vitro literature (same value assumed for wildtype and polymorphic transporter), resulting in predicted DDGI AUC and C max ratios within 1.5-fold of the observed values. The second variant allele investigated is the CYP2C8*3 allele, occurring with a frequency of 13% in Caucasians [13]. The model was applied to predict the trimethoprim-pioglitazone DDGI using a CYP2C8 K i value taken from in vitro literature. For the DDGI, no plasma concentration-time profiles were reported and therefore, only predicted and observed DDGI AUC and C max ratios were compared, resulting in predicted DDGI AUC and C max ratios within 1.5-fold and 1.25-fold of observed values, respectively.
Regarding previously-published PBPK models of trimethoprim, there are four earlier models of trimethoprim described in the literature [82][83][84][85]. These models have been built to predict the CYP2C8 DDI and DDGI with rosiglitazone (whole-body PBPK model) [82], to investigate the basolateral and apical kidney transporter DDI with creatinine (two semi-PBPK models) [83,84], or for pediatric scaling (whole-body PBPK model) [85]. The trimethoprim-rosiglitazone DDGI model [82] well describes the rosiglitazone plasma concentration-time profiles in CYP2C8 wildtype and carriers of the CYP2C8*3 allele. Also, the two minimal PBPK models built to describe the creatinine plasma concentration-time profiles during trimethoprim co-administration show a good DDI performance [83,84], without taking SLC22A2 polymorphism into account. Our model was built and evaluated to assess DDIs mediated via CYP2C8, MATE1, OCT1, and OCT2, as well as DDGIs caused by CYP2C8*3 and SLC22A2808G>T polymorphisms, applying one and the same whole-body PBPK model. Our model differs further from the previously-published models, as (1) none of these models was developed using such a large number of clinical studies (66 blood and 36 urine profiles) and (2) this is the first model which attempts to mechanistically describe the tubular secretion of trimethoprim. The good ability of the presented model to describe these different DDIs and DDGIs increases the confidence regarding the modeled trimethoprim concentrations at different sites of action (liver and kidney) and its general applicability for future investigations.

Conclusions
In this study, a carefully-developed mechanistic whole-body PBPK model of trimethoprim is presented. The model adequately predicts the trimethoprim pharmacokinetics following intravenous and oral administration over a broad range of dosing regimens. In addition, the model was qualified by prediction of DDI studies with the victim drugs metformin, repaglinide, and pioglitazone and by prediction of DDGI studies with metformin and pioglitazone.  Table S1: Clinical studies of trimethoprim; Table S2: Drug-dependent parameters of the final trimethoprim PBPK model; Table S3: MRD values of trimethoprim plasma (or whole blood) concentration predictions; Table S4: Predicted and observed trimethoprim fractions excreted unchanged in urine; Table S5: Predicted and observed trimethoprim AUC last and C max values; Table S6: Parameters evaluated during trimethoprim sensitivity analysis; Table S7: Clinical studies investigating the trimethoprim-metformin DDI and DDGI; Table S8: Drug-dependent parameters of the metformin PBPK model; Table S9: Predicted and observed trimethoprim-metformin DDI and DDGI AUC last and C max ratios; Table S10: Clinical studies investigating the trimethoprim-repaglinide DDI; Table S11: Drug-dependent parameters of the repaglinide PBPK model; Table S12: Predicted and observed trimethoprim-repaglinide DDI AUC last and C max ratios; Table S13: Clinical studies investigating the trimethoprim-pioglitazone DDI and DDGI; Table S14: Drug-dependent parameters of the pioglitazone PBPK model; Table S15: Predicted and observed trimethoprim-pioglitazone DDI and DDGI AUC last and C max ratios; Table S16: Clinical studies investigating the rifampicin-trimethoprim DDI; Table S17: Drug-dependent parameters of the rifampicin PBPK model; Table S18: Predicted and observed rifampicin-trimethoprim DDI AUC last and C max ratios; Table S19: System-dependent parameters; Figure S1: Trimethoprim DDI network; Figure S2: Comparison of trimethoprim administered alone or together with sulfamethoxazole as "cotrimoxazole"; Figure S3: Schematic illustration of the trimethoprim ADME processes in the model; Figure S4: Trimethoprim plasma concentration-time profiles (semilogarithmic); Figure S5: Trimethoprim plasma concentration-time profiles after "cotrimoxazole" administration (semilogarithmic); Figure S6: Trimethoprim plasma concentration-time profiles (linear); Figure S7: Trimethoprim plasma concentration-time profiles after "cotrimoxazole" administration (linear); Figure S8: Trimethoprim fraction excreted unchanged in urine profiles; Figure S9: Trimethoprim fraction excreted unchanged in urine profiles after "cotrimoxazole" administration; Figure S10: Trimethoprim predicted compared to observed plasma concentration values; Figure S11: Trimethoprim predicted compared to observed fractions excreted unchanged in urine; Figure S12: Trimethoprim predicted compared to observed AUC last and C max values; Figure S13: Trimethoprim sensitivity analysis; Figure S14: Trimethoprim-metformin DDI model processes; Figure S15: Metformin plasma concentration-time profiles before and during trimethoprim DDI and DDGI (semilogarithmic); Figure S16: Metformin plasma concentration-time profiles before and during trimethoprim DDI and DDGI (linear); Figure S17: Metformin predicted compared to observed DDI and DDGI AUC last and C max ratios; Figure S18: Trimethoprim-repaglinide DDI model processes; Figure S19: Repaglinide plasma concentration-time profiles before and during trimethoprim DDI; Figure S20: Repaglinide predicted compared to observed DDI AUC last and C max ratios; Figure S21: Trimethoprim-pioglitazone DDI model processes; Figure S22: Pioglitazone plasma concentration-time profiles before and during trimethoprim DDI and DDGI (semilogarithmic); Figure S23: Pioglitazone plasma concentration-time profiles before and during trimethoprim DDI and DDGI (linear); Figure S24: Pioglitazone predicted compared to observed DDI and DDGI AUC last and C max ratios; Figure S25: Rifampicin-trimethoprim DDI model processes; Figure S26: Trimethoprim and rifampicin plasma concentration-time profiles of the rifampicin DDI (semilogarithmic); Figure S27: Trimethoprim and rifampicin plasma concentration-time profiles of the rifampicin DDI (linear); Figure S28: Trimethoprim predicted compared to observed DDI AUC last and C max ratios.