Linking the population pharmacokinetics of tenofovir and its metabolites with its cellular uptake and metabolism.

Empirical pharmacokinetic models are used to explain the pharmacokinetics of the antiviral drug tenofovir (TFV) and its metabolite TFV diphosphate (TFV-DP) in peripheral blood mononuclear cells. These empirical models lack the ability to explain differences between the disposition of TFV-DP in HIV-infected patients vs. healthy individuals. Such differences may lie in the mechanisms of TFV transport and phosphorylation. Therefore, we developed an exploratory model based on mechanistic mass transport principles and enzyme kinetics to examine the uptake and phosphorylation kinetics of TFV. TFV-DP median Cmax from the model was 38.5 fmol/10(6) cells, which is bracketed by two reported healthy volunteer studies (38 and 51 fmol/10(6) cells). The model presented provides a foundation for exploration of TFV uptake and phosphorylation kinetics for various routes of TFV administration and can be updated as more is known on actual mechanisms of cellular transport of TFV.

Tenofovir disoproxil fumarate (TDF) is an ester prodrug of tenofovir (TFV) and has US Food and Drug Administration approval for the indications of human immunodeficiency virus (HIV) treatment and prevention. After oral administration, TDF is rapidly converted by esterases[1] in plasma to TFV, which is an analog of the endogenous deoxyadenosine monophosphate. TFV is the predominant circulating form[2,3] which can then be taken up by cells normally targeted by HIV for infection (CD4+ lymphocytes). Subsequently, TFV undergoes two phosphorylation steps forming tenofovir diphosphate (TFV-DP), which is an analog of endogenous deoxyadenosine triphosphate. TFV-DP competes with deoxyadenosine triphosphate for incorporation into viral DNA by HIV-1 reverse transcriptase, which then prevents further DNA polymerization once TFV-DP gets incorporated.[4] TFV-DP thus can slow down or inhibit the production of proviral DNA, which is essential for host cell infection and viral replication.

Understanding the clinical pharmacology of the active moiety, TFV-DP, is essential to optimize clinical outcomes. Several empirical pharmacokinetic models are currently used to explain the pharmacokinetics of TFV and TFV-DP after oral administration of TDF.[2,5,6] Most studies have only characterized the pharmacokinetics of TFV[2,7,8,9,10] but some recent studies have also focused on intracellular kinetics of the active anabolite TFV-DP.[6,11,12,13,14] In these studies, the parameters concerning the process of TFV uptake to TFV-DP formation are lumped. The role of the underlying mechanistic aspects of TFV uptake by immunological cells, including intracellular TFV phosphorylation and possible TFV efflux mechanisms, which may determine the pharmacokinetics of TFV-DP in the intracellular space were unexplored according to publicly available data. Thus, there is scope for a mathematical model that can explore mechanisms of TFV uptake and phosphorylation and act as a hypothesis generator for future experiments and models.

Such a mathematical model will require translating findings of basic research toward the goal of simulating clinical outcomes. These findings are generally obtained during preclinical experimentation on enzyme kinetics of drug metabolic reactions and drug transporters prior to the design of clinical trials. However, it was not an established practice until very recently to use such experimental data in predicting phase I clinical studies other than allometric scaling.[15,16,17] Biological drug development has only recently evolved to using such in vitro data to support first-in-human dose calculations by minimally anticipated biological effect levels concepts.[18] Other recent developments include model-based drug development where mathematical models with varied complexity are developed depending on the stage of development,[19,20] physiologically based pharmacokinetic modeling[21,22] and systems based modeling where models account for complex biology and pharmacology. These new approaches to drug development are very useful for predicting pharmacokinetic outcomes in early phase clinical studies where models can provide rational clinical trial designs.

The objective of this analysis was to develop an integrated pharmacokinetic model to account for passive diffusion, a saturable channel-based uptake, MRP4 channel-based efflux, and TFV phosphorylation through kinases using published parameters values. TFV-MP and TFV-DP kinetic profiles in the peripheral blood mononuclear cell (PBMC) compartment were simulated. Finally, the model was taken to the population level in order to compare the predictions to the available clinical data.

Results

Mathematical model of TFV transport to PBMCs

The model used for simulating TFV uptake and conversion to TFV-DP is shown in . A two-compartment pharmacokinetic model with a dosing compartment[6] was used to describe the plasma concentration profile of TFV after oral administration of TDF. Simulations were done for TFV uptake to the PBMCs through diffusion and a saturable transport channel and TFV efflux through MRP4-based activity. Assumptions used in the model and defining equations have been described in the Supplementary Material.

Model testing and validation

The mechanistic model developed was used for simulating pharmacokinetic profiles after oral administration of TDF. Initial testing of the model was done through single and multidose simulations for TDF doses of 75, 150, 300, and 600 mg. Single-dose simulations were performed with a time span of 240 h and multidose simulations were performed with a time span of 480 h. Concentration–time courses for plasma TFV, PBMC TFV-MP, and PBMC TFV-DP were plotted. The model that achieved saturation was validated with data from the oral substudy of the MTN-001 trial[23] by a simulation of a population of 100 subjects assumed to be fully adherent. Between subject variability was added from literature[11] on the pharmacokinetic model of TFV with saturable uptake and no variability was assumed on the TFV uptake and metabolism components of the model.

Impact of diffusion on TFV uptake at PBMC level

and Supplementary Figure S1 a–c indicate single- and multidose simulations of Plasma TFV, PBMC TFV, and PBMC TFV-DP levels at TDF doses of 75–600 mg with the model containing diffusion and channel mediated uptake. and Supplementary Figure S2 a–c (refer supplement) show the same for a model containing only channel mediated uptake. No difference was observed between the two scenarios. Hence, diffusion based uptake of TFV will be neglected in the final model to come to a mathematically simpler model.

Model with saturable TFV uptake

and Supplementary Figure S3 a–c indicate single- and multidose simulations of plasma TFV, PBMC TFV-MP, and PBMC TFV-DP levels at TDF doses of 75–600 mg with the model containing a lower Km and a higher kleak across the PBMC. A saturating behavior appears immediately at a TDF dose of above 75 mg and gets more prominent at higher TDF doses. The simulations for the single dose give a plasma TFV tmax of 2 h as predicted before.[6] The single-dose simulations of TDF dose at 300 mg reveal a TFV-DP peak of 11.35 fmol/106 cells and the multidose simulations reveal an end TFV-DP amount of 35 fmol/106 cells.

Model validation

– shows the outcome of adding interindividual variability to the model. , indicates the 5, 50, and 95 percentile values of day 1 of the multiple dosing regimen; , indicates the same for day 14. Steady-state TFV and TFV-DP readings from the MTN-001 study are added in , respectively.

Sensitivity analysis

Supplementary Figure S4 shows the 50 different model responses obtained from the different combinations of parameters tested. depicts the sensitivity indices obtained from the sensitivity analysis. The efflux of TFV from MRP4 (kleak), enzyme concentration (E1) of human adenylate kinase 2 (hAK2), hAK2 turnover number (kcat1), the Michaelis–Menten constant for TFV monophosphorylation (Km1) showed statistically significant indices for all of the outputs. Positive indices were obtained for kcat1 and E1, while negative indices were obtained for kleak and Km1. The negative coefficients suggest that as the respective parameters increase, the outputs decrease, while positive coefficients suggest the opposite.

Discussion

TFV and other nucleoside reverse transcriptase inhibitors are known to exert their effects through their intracellular metabolite thus examining the process of nucleoside reverse transcriptase inhibitor phosphorylation in detail is important to their pharmacological effect. In the model described, a two-compartment model was used to explain the pharmacokinetics of TFV, while the uptake of TFV by PBMCs and subsequent phosphorylation was analyzed in greater detail. Saturable uptake/metabolism was previously modeled by other authors.[6,11] Duwal et al.[6] had estimated a Km of 29 ng/ml for TFV-DP formation by coupling PK model with mechanistic viral dynamics model and reproduced the efficacy curves of TFV monotherapy. The steady-state trough concentrations reported after 300 mg QD and 600 mg QD dosing were 64 and 111 ng/ml respectively.[24] Since the estimated Km value is much lower than the trough concentrations, the uptake for TFV should be nearly saturated at 300 and 600 mg QD dosing. So, we focused our simulations toward capturing the saturation phenomenon. Three possible models for TFV uptake were analyzed: (i) a model where diffusion and a saturable transporter are responsible, (ii) another where only the saturable transporter is responsible, and (iii) a third model which we propose as a way to explain saturable TFV uptake. It was found that under the current parameters selected, diffusion should not play a major role in TFV uptake. This is in agreement with the poor permeability of TFV through physiological membranes due to its negative charge. This led to the development of the prodrug TDF to improve TFV bioavailability, yet the reported absolute bioavailability of TFV is in the range of 0.25–0.32. Moreover, the minimal role of diffusion should be an expected feature if TFV uptake is considered saturable. A prominent role of diffusion would have made TFV uptake proportional to the dose and saturation would not have been observed. TFV diffusion might also be precluded due to much of TFV being in the ionized form at the pH level of blood (pKa1 = 3.8 and pKa2 = 6.7 for TFV[25]; pH of blood = 7.4)

The model with saturable TFV uptake was simulated for a population of 100 subjects with interindividual variability on pharmacokinetic parameters derived from an earlier work.[11] A visual predictive check of the simulations revealed a good match with data from the MTN-001 study.[23] TFV-DP accumulates slowly owing to its long half-life of (48 h in this model).[26] We predict that the model will reach steady state in 14 once daily dosing events. Our model predicted individual TFV-DP amount in the range of 4.715 to 139.5 fmol/106 cells and a median of 38.5 fmol/106 cells which covers the range of most data points from the MTN-001 study. The comparable median Cmax from the MTN-001 study is 51 fmol/106 cells,[23] which our model came close to. Some accuracy is lost for the lower side of population variability, however that is expected since in our simulations, the 100 subjects have 100% adherence but in the MTN-001 trial, only 64% subjects were expected to be perfectly adherent.[27]

To understand what factors the model is the most sensitive to, we conducted sensitivity analysis. The highest relative sensitivity indices were obtained in parameters related to TFV efflux through MRP4 and the monophosphorylation step, thus suggesting that the model is sensitive to these parameters. Ascertaining the details of TFV function in PBMCs would thus require experimentation on these parameters. Differences in these parameters may also reveal how TFV-DP levels in infected and healthy individuals may be different. The median TFV-DP Cmax for infected individuals has been reported to range from 89.9 to 120 fmol/106 cells,[13,28] much higher than for reports in healthy individuals which range from 38 fmol/106 cells in a directly observed daily dosing study[29] and 51 fmol/106 cells in MTN-001.[23]

There are competing hypotheses for TFV transport in PBMCs such as a transporter-mediated process and/or endocytosis.[6,30,31] There is also a dearth of experimental data on types and concentrations of kinases involved in the phosphorylation process. Thus, the model should be further updated to account for future findings. In the future, we will also attempt to extend the model by incorporating viral dynamics and using drug adherence pattern simulation strategies to understand probable efficacy of treatment in patients. It has been suggested that the drug adherence can become a major obstacle for the success of a drug.[32] If poor drug adherence can be predicted through simulations after a trial run, then sufficient intervention may be attempted using appropriate technological means to improve adherence. The mechanistic model may be of use at this point to calculate threshold adherence, below which the drug will fail. Calculation of such a threshold adherence will provide a useful benchmark to make necessary interventions to improve adherence.

In conclusion, we created a template for the modeling of current and future anti-retroviral drugs in various target sites. Experimentation requirements as suggested for TFV through simulations and subsequent sensitivity analysis might also be performed for them. Using such models, it might also be possible to study and provide an explanation for low penetration of antiretroviral drugs in certain organs like testes and the brain.[33,34]

Methods

All the differential equations for the single-dose and multidose simulations were implemented using the ODE15s solver in MATLAB R2013a (MathWorks, Natick, MA). For population simulations, a population of 100 subjects was simulated for multiple TDF doses of 300 mg taken at every 24 h for a period of 14 days with 100% adherence. Simulations were conducted in NONMEM 7.2 (Icon, Ellicott City, MD) using ADVAN8 subroutine. 5, 50 and 95 percentile values of plasma TFV and PBMC TFV-DP at steady state were calculated from the simulations and were compared against data from MTN-001 trial which included an arm with daily oral TDF dosing for 6 weeks, with PK sampling done in plasma and PBMC for 8 h.

Uncertainty and sensitivity analyses

Perturbation of model parameters was performed to identify the input parameters that have the most impact on the outputs. A Latin Hypercube Sampling method was chosen for sampling parameter space based on a comparison of sampling techniques,[35] and sensitivity analysis reported earlier.[36,37]

The model scenario selected for the sensitivity analysis was the one which simulated a saturable TFV uptake. Output parameters chosen were maximum TFV-DP amount in the PBMC compartment (Cmax), TFV-DP amount at 24 h (Ctr) and AUC for TFV-DP concentrations. Each parameter was divided into 50 equal probability density regions based on their uncertainty. Fifty simulation runs were performed with the parameters chosen randomly and without repetition from the possible values. To examine the sensitivity between the output concentrations and the input parameters, the sensitivity indices were determined from linear least squares multiple regression applied to the following relationship:

where i is the number of the output parameter and j is the number of the input parameter. Y is the change in % of the ith output at the kth run from the ith output derived by the initial estimates of the parameters and X is a change in % of the central value of the jth parameter. Confidence intervals for the sensitivity indices were calculated using the “regress” function in Matlab. If the confidence interval did not include zero, then the respective sensitivity index β can be said to significantly impact the output. Input parameters were assigned uncertainty ranges () based on the confidence in the reported central values, quality of the fits and the ability to determine importance of parameters.

Conflict of Interest

The authors declared no conflict of interest.

Author Contributions

K.M. wrote the manuscript. A.C. designed the research. K.M. performed the research. R.N.B., C.W.H., M.F., and A.C. analyzed the data.

Study Highlights

Table 1

Least squares estimates of sensitivity coefficients β

Table 2

Uncertainty for input parameters in the model