Model based development of tacrolimus dosing algorithm considering CYP3A5 genotypes and mycophenolate mofetil drug interaction in stable kidney transplant recipients

This study quantifies the interaction between tacrolimus (TAC) and mycophenolate mofetil (MMF) in kidney transplant recipients. Concentrations of TAC, mycophenolic acid (MPA), and metabolites were analyzed and relevant genotypes were determined from 32 patients. A population model was developed to estimate the effect of interaction. Concentrations of TAC were simulated in clinical scenarios and dose-adjusted trough concentrations per dose (C/D) were compared. Effect of interaction was described as the inverse exponential relationship. Major determinants of trough levels of TAC were CYP3A5 genotype and interaction with MPA. The absolute difference in C/D of TAC according to co-administered MMF was higher in CYP3A5 non-expressers (0.55 ng/mL) than in CYP3A5 expressers (0.35 ng/mL). The effect of MMF in determining the TAC exposure is more pronounced in CYP3A5 non-expressers. Based on population pharmacokinetic model, we suggest the TAC dosing algorithm considering the effects of CYP3A5 and MMF drug interaction in stable kidney transplant recipients.

standard error (RSE), IIV in parameter estimates of a developed model are presented in Table 2. CL/F and volume of distribution of TAC were estimated as 21.9 L/h (RSE 16%) and 103 L (RSE 15%), respectively. A combined additive and proportional model was used to account for the residual error of the developed model. The only significant covariate identified for the pharmacokinetic parameters of TAC was CYP3A5 genotype. In CYP3A5 expressers, CL/F of TAC was increased to 1.49-fold (RSE 9%) compared to CYP3A5 non-expressers (Eq. 1). The elimination rate constant (k 90 ) and volume of distribution of MPA acyl glucuronide (AcMPAG) were once estimated in kidney transplant recipients and then fixed to estimated values thereafter. Genotypes of SLCO1B3 and UGT2B7 were identified as significant covariates that influence the pharmacokinetics of MMF. In T carriers of SLCO1B3 334T > G (rs4149117), the volume of distribution of MPA 7-O-glucuronide (MPAG) was increased to 1.2-fold (RSE 10%) compared to GG genotype. In T carriers of UGT2B7 802T > C (rs7439366), formation rate of AcMPAG was decreased to 0.8-fold (RSE 10%) compared to CC genotype.
The interaction effect was modeled as an inverse exponential relationship between the CL/F of TAC and the concentration of MPA (C MPA ) (Eq. 1). The slope parameter which mediates the effect of interaction was estimated as 0.06 (RSE 35%). Inclusion of DDI effect on the CL/F of TAC led to stabilization of model parameter estimates. When the effect of DDI in the full model is removed through the backward elimination procedure, the objective  www.nature.com/scientificreports www.nature.com/scientificreports/ function value (OFV) increases from 1090.6 to 1102.1 (ΔOFV = 11.5). IIV in CL/F of TAC also increases by 9% from 24.3% to 33.3% without the effect of DDI.  TAC was increased from 0.89 ± 0.44 ng/mL to 1.24 ± 0.59 ng/mL in CYP3A5 expressers and from 1.59 ± 0.67 ng/ mL to 2.14 ± 0.88 ng/mL in CYP3A5 non-expressers, respectively. Effect of SLCO1B3 and UGT2B7 genotypes on C/D of TAC was insignificant.
According to the final model and the simulation results, detailed dosing algorithm of TAC was developed. Under the possible combinations of CYP3A5 genotype and the dose of MMF, required dose of TAC is presented in Table 3. Daily dose of 1-6 mg of TAC was required to achieve the target trough concentration, which is in consistent of administered dose range of TAC in patient population. When the patient's genotype is CYP3A5 expresser or the dose of MMF is 250 mg twice daily, larger amount of TAC was needed to achieve target level.

Discussion
The present study was the first study to evaluate the effect of DDI between TAC and MMF in stable kidney transplant recipients with the integrated population pharmacokinetic model and further suggest the dosing algorithm of TAC. Although TAC is frequently co-administered with MMF, the magnitude of the interaction effect was unclear and the dosing recommendation with regards to the effect of interaction was scarce. The effect of co-administered MMF and other clinical factors including the dose of TAC and genotypes (CYP3A5, SLCO1B3, and UGT2B7) on the concentration of TAC was evaluated with modelling and simulation. The absolute difference in C/D of TAC according to dose increment of co-administered MMF was higher in CYP3A5 non-expressers than in CYP3A5 expressers (0.35 ng/mL in CYP3A5 expressers vs. 0.55 ng/mL in CYP3A5 non-expressers).
In this research, population pharmacokinetic model-based evaluation was used to simultaneously quantify the effect of DDI, genetic polymorphism, and other known clinical factors on the pharmacokinetics of TAC. The pharmacokinetic model development approach has additional strengths in that researchers can simulate various clinical scenarios based on combinations of identified clinical covariates. A number of studies have proven pharmacokinetic model development as an appropriate approach to elucidate the effect of DDI and/or genotypes [26][27][28] .
In the final population pharmacokinetic model, CYP3A5 genotype was a significant covariate with respect to the CL/F of TAC. Historically, CYP3A5 genotypes were repetitively identified as significant factors in previous population pharmacokinetic studies 5 . As CYP3A5 is involved in the major metabolic pathway of TAC, and MPA showed possible competition for CYP3A in the previous in vitro study 14 , there is a potential for pharmacokinetic interaction. In our research, simulation of the final model revealed that effect of CYP3A5 genotype was more influential in determining the trough levels of TAC than co-administration with MMF. In a previous study which evaluated the interaction between TAC and azole antifungals, the interaction effect differed according to CYP3A5 genotype and was also blunted in CYP3A5 expressers 29 . Because the trough concentration of TAC itself is lower in CYP3A5 expressers, the effect of interaction is observed to be greater in CYP3A5 non-expressers. Therefore, more caution is required when the dose of TAC is adjusted in CYP3A5 non-expressers.
For the population pharmacokinetic model of mycophenolic acid and its metabolites, the population estimate of CL/F of MPA was 3.27 L/h. Low estimate of CL/F of MPA, ranging between 10.2-18.3 L/h has been observed in population pharmacokinetic models with Asian population 30,31 . Researchers suggest the need for lower dose of MMF in Asian population based on observed lower CL/F 32 . Another population pharmacokinetic model showed reduced CL/F of MPA (2.87 L/h) in renal transplant recipients with corticosteroid-free regimen 33 . Although all patients in our model were on steroids, fourteen of them received less than 5 mg/day of prednisolone or its equivalent. Ethnic difference, the dose of co-administered corticosteroids, and limited sampling points might be collectively related to relatively low CL/F compared to other previous studies 30,31,33 .
Genotypes SLCO1B3 and UGT2B7 were included as significant covariates for the volume of distribution of MPAG and formation rate of AcMPAG, respectively. The effect of identified genotype covariates was consistent with previous functional studies. In a study by Picard, et al., hepatic uptake of MPAG was increased and the dose-normalized concentration of MPAG was decreased in SLCO1B3 334T > G (rs4149117) T carriers 19 . Regarding UGT2B7, the AcMPAG metabolic rate was lower in T carriers of UGT2B7 802C > T (rs7439366) genotype in an in vitro human liver microsome study than in C homozygote genotype 34 . Although the pharmacokinetic model of MPA was statistically improved by considering the effect of SLCO1B3 and UGT2B7 genotypes, simulated trough concentrations of TAC were not affected.
In the final model, the concentrations of MPA were linked to the CL/F of TAC with an inverse exponential equation, thereby enabling the dose adjustment of TAC based on the dose of MMF. The estimated value of interaction parameter was 0.06 in inverse exponential equation. The CL/F of TAC is affected by the interaction parameter as well as the IIV of CL/F and CYP3A5 genotypes. To evaluate the clinical significance of the interaction in a collective manner, we simulated the model under the various clinical scenarios. As presented in Table 3, the required dose of TAC changed by 0.5 mg when the dose of MMF changes by 250-500 mg. Moreover, the effect of interaction between TAC and MMF was in line with previous in vitro and clinical studies. A previous in vitro  www.nature.com/scientificreports www.nature.com/scientificreports/ study also observed the inhibition of TAC metabolism when incubated with MPA 14 . In liver transplant recipients, AUC of TAC was increased by approximately 20% when MMF was co-administered 35 .
On the other hand, research by Kagaya, et al. insisted that there is no DDI between TAC and MPA in renal transplant recipients 36 . In that study, patients were divided into five groups according to AUC of MPA and pharmacokinetic parameters of TAC were compared between groups. Statistical comparison according to genotypes (CYP3A5 and UGT2B7) were also done. However, the analyses results according to the AUC of MPA or genotypes were done separately, therefore the results were not directly comparable to those in our study. Another recent research by Rong, et al. showed the lack of interaction between TAC and MMF based on their multiple analysis results including the population covariate modeling, multiple regression, and categorical analysis 37 . However, the most notable difference of our approach is the use of the integrated model-based approach in our study. The integrated modeling approach enables the simultaneous consideration of clinical covariates including genotypes and concentrations of co-administered drugs. The combined effect of co-administered MMF and CYP3A5 genotype was captured in our study.
In clinical practice, the administration of MMF frequently changes due to an adverse event or infection episodes affecting the dose requirement of TAC. Because of TAC's narrow therapeutic index and high IIV in dose-response especially in patients taking MMF concurrently, the current dosing approach may not be an adequate strategy as it neglects the impacts of genetic variability on the system's ability and drug interaction of MMF. For this reason, the pharmacokinetic model for dosing algorithm are useful to aid the flexible adjustment of TAC exposure in response to the change in the administration of MMF according to CYP3A5 genotype. Although some studies developed dosing algorithms of TAC, those algorithms are limited because of fact that they have focused on determining the starting dose or ignored the effect of interaction with co-administered MMF 20,38 . Our study results suggest prescribers to consider monitoring the level of TAC when they initiate or increase the dose of MMF especially in CYP3A5 non-expressers. As a higher level of TAC is a risk for nephrotoxicity, neurotoxicity, or infection and a lower level of TAC is directly linked to acute rejection, this model can aid meticulous maintenance of TAC exposure in both CYP3A5 expressers and non-expressers 39,40 .
The current research has few limitations. Because the model was developed using patients with a median of 5.7 years post-transplant, their HCT or GFR levels were near normal. Due to their low variability, the model did not capture the known effects of HCT and GFR on the pharmacokinetics of TAC and MPA. Therefore, the predictive performance of the developed model might be limited to patients who maintain a stable HCT and graft function. Secondly, though the exposure-response relationship of MMF is known to be nonlinear 41 , we failed to characterize a nonlinear aspect into the model equation. Small dose range width of administered MMF in the study population might explain the reason. Future work is required to generalize the results to more variable situations including the unstable early period after transplantation or the higher dose of TAC or MMF.
In summary, the interaction effect between TAC and MMF was evaluated in kidney transplant recipients. In the final population pharmacokinetic model, CYP3A5 genotype and co-administration with MMF were identified as significant factors in determining the CL/F of TAC. The effect of co-administered MMF in determining the level of TAC exposure is more pronounced in CYP3A5 non-expressers. The structure model explaining the interaction between TAC and MMF can also be served as the reference structure in other clinical situations including an early period after transplantation. By considering the CYP3A5-mediated DDI between TAC and MMF, personalized dose adjustment in accordance with dosing algorithm can be applied in a maintenance period after transplantation. Improvement in post-transplant management including rejection prevention is expected through better maintenance of the TAC concentration in the target range especially in patients taking interacting drugs.

Methods
Study design. The study was designed to assess the pharmacokinetic interaction by serial sampling. Eligible patients took their medications as usual. Inclusion criteria of the study were as follows: (1) at least six months after kidney transplant; (2) oral administration of study drugs, TAC (Prograf ® ) and MMF (Cellcept ® ); and (3) maintained the same dosage and administration methods for at least two weeks prior to the study (for both TAC and MMF). Exclusion criteria were as follows: (1) multi-organ transplantations; (2) gastrointestinal disorders that may affect the absorption of the study drugs; (3) had taken other drugs that may strongly affect the pharmacokinetics of the study drugs; and (4) abnormal liver function with AST or ALT > 3x the upper limit of normal range.
The study was conducted in compliance with the Declaration of Helsinki, the International Conference on Harmonization Guidelines for Good Clinical Practice 42 . This study was approved by the institutional review board (IRB No. C-1604-014-753) of Seoul National University Hospital (Seoul, Korea). All subjects were given written informed consent (Clinicaltrials.gov identifier NCT02808065).

Population pharmacokinetic model development. Population pharmacokinetic model was developed
to estimate pharmacokinetic parameters of TAC and MMF in consideration of the effect of interaction and clinical covariates. Population pharmacokinetic parameter estimates were obtained by using user defined subroutine ADVAN6. Model development procedure consisted of sequential steps of structure model building, explanation of the residual error, and identification of significant covariates. The structure model from previous research, which has characterized the interaction effect between TAC and MMF with an inverse exponential equation, was fitted to observed concentrations from kidney transplant recipients 23 . This is presented in Fig. 2. The pharmacokinetics of TAC was explained by two-compartment, first-order absorption with lag time, and first-order elimination. The structure model of MMF included compartments of MPA, MPAG, AcMPAG, and gallbladder. Pharmacokinetics of MPA was described by two-compartment and first-order absorption. Elimination route of MPA was limited to the metabolic clearance to MPAG and AcMPAG. Enterohepatic circulation was modeled with the gallbladder compartment and a mass transfer rate constant between the gallbladder and the gastrointestinal tract. Model event time parameter (MTIME) was introduced to control the transfer of bile acid from the gallbladder into the gastrointestinal tract. Because of the relatively short period of blood sampling window, it was not enough to fully characterize the absorption and enterohepatic circulation process of study drugs. Therefore, pharmacokinetic parameters related to absorption (absorption rate constant and lag time) and enterohepatic circulation (percentage of enterohepatic circulation, transfer rate constant, and model event time) were fixed to values from the population pharmacokinetic models for healthy volunteers 23 . Effect of interaction was modelled as inverse proportional model as was in healthy volunteer 23 .
IIV in pharmacokinetic parameters was assumed for apparent clearance and volume of distribution of TAC and MPA. Residual error was assessed as an additive, proportional, or combined additive and proportional model.
After the development of the structure model, the significance of covariates was tested. Continuous covariates including body weight, age, serum creatinine, MDRD eGFR, and HCT were centered on the median and categorical covariates like genotypes were tested as a binary variable. The effect of covariates was explored with a stepwise covariate modeling procedure. On the other hand, the statistical significance of model with covariates was determined based on the difference between OFVs which were computed by the log-likelihood ratio test. In case of forward inclusion, the effect of included covariate was regarded significant if an objective function value decreased by more than 3.84 (p < 0.05). In backward elimination procedure, if covariates were included and the OFVs increased to more than 6.63 (p < 0.01), the corresponding covariates were excluded. NONMEM version 7.3 (ICON Development Solutions, Hanover, MD) was used to develop a population pharmacokinetic model. Perl-speaks-NONMEM version 4.4.8, Xpose 4, and R version 3.2.2 were used to aid a modeling process and to generate graphical outputs 44,45 . Model evaluation. In the process of population pharmacokinetic model development, various model evaluation methods were applied. Scientific plausibility of final estimates, RSE of estimates, objective function value, and shrinkage were evaluated to test the appropriateness of the model 46,47 . The goodness-of-fit plot was used to assess model fit and distribution of residuals 46 . Predictive performance of the model was evaluated with a prediction-corrected VPC 48 .  (7), compartment for gall bladder (8), compartment for mycophenolic acid acyl glucuronide (9). TAC, tacrolimus; K a , absorption rate constant; k 23 , k 32 , k 56 , and k 65 , intercompartment rate constants; CL, clearance; MPA, mycophenolic acid; MPAG, MPA 7-O-glucuronide; AcMPAG, MPA acyl glucuronide; k 57 and k 59 , metabolized rate constants for mycophenolic acid; EHC, enterohepatic circulation; k 78 , biliary recirculation of MPAG into GI; k 70 and k 90 , eliminated rate constants; k 84 , gallbladder emptying rate constant; Meal times were used to trigger timing of gall bladder emptying.