INTRODUCTION

Drug-drug interactions (DDI) resulting in unexpected or undesirable adverse effects are a recognized clinical problem (1). DDI can be caused by interactions leading to changes in pharmacokinetics (PK) or pharmacodynamics; clinical PK-DDI can be due to interactions causing inhibition or stimulation of (a) absorption from the extravascular sites (e.g., gastrointestinal tract), (b) protein-binding and distribution, (c) metabolism, and (d) transporter-mediated uptake or excretion (2).

US Food and Drug Administration (FDA) expresses low confidence on DDI prediction based on in vitro membrane transporter inhibition due to a lack of in vitro-in vivo extrapolation (3). Two hepatic organic anion transporting polypeptides on the basolateral membranes of hepatocytes (OATP1B1, OATP1B3) mediate the blood-to-liver uptake of multiple clinically important drugs (e.g., statins, antibiotics, antidiabetics, anticancer drugs, cardiac glycosides). Their dysfunction, due to genetic polymorphism or inhibition by other drugs (perpetrator drugs or PD), reduces substrate uptake and metabolism in liver cells and leads to severe adverse events including deaths. Many drugs that are potent OATP inhibitors in vitro cause severe side effects in vivo when co-administered with statins (4,5,6,7,8,9,10).

The field of DDI evaluation has been experiment-centric. Previous in vitro DDI investigations have largely focused on competitive inhibition of the transporter function, where a candidate PD is co-incubated with a victim drug (VD), typically with transporter-overexpressing cells, to determine if PD alters VD uptake into cells. For example, the 2012 FDA guidance highlights studying the VD uptake in the linear range; the typical experimental set-up in the DDI research community is 5-min co-incubation of VD and PD (e.g., (11,12,13,14,15)). This set-up is based on the assumption that PD induces DDI via competitive inhibition of transporter-mediated uptake of VD. Multiple studies have since shown that this paradigm led to under-predictions (e.g., between antivirals and rosuvastatin), high false-negatives (e.g., mibefradil, sirolimus, everolimus, tacrolimus), and severe/fatal adverse events in patients (e.g., statin-related rhabdomyolysis); the discovery of DDI between mibefradil with multiple drugs resulted in its withdrawal from market (16,17,18,19,20,21,22,23,24,25). Some studies have demonstrated schedule-dependent DDI or long-lasting inhibitions by some agents such as cyclosporine A and MRL-A (5, 24). In October 2017, FDA added pre-incubation studies to its recommendation (i.e., incubating the candidate PD with cells for a minimum of 30 min prior to incubation with the VD).

Mathematical modeling has been an important tool in pharmaceutical sciences for 50 + years (26). In 2011, the US National Institutes of Health identified quantitative systems pharmacology (QSP) as a potential new approach to drug development and translational medicine (27). FDA, under the 2017 FDA Reauthorization Act, has committed to adopting model-informed drug development (MIDD) to facilitate the decision-making process and address drug development and regulatory questions (28, 29).

Our group has advocated the use of computation to guide therapy development. An example of successful use is the development of an optimized treatment of nonmuscle-invading bladder cancer; this project involved a 14-center phase III trial comparing the then standard-of-care intravesical mitomycin C for bladder cancer with a model-predicted/optimized treatment. These studies showed that the treatment outcome closely align with model-predictions (18.3% increase in 5-year recurrence-free survival vs. the predicted 18–20%) (30,31,32,33,34). To our knowledge, this is the first demonstration of using QSP-based modeling to guide the phase III clinical trial design. In an earlier commentary in this journal, we applied a multiscale model linking 6 scales (whole body, tumor, vasculature, cell, spatial location, time), together with literature data on nanoparticle and tumor properties, to demonstrate systemic bioequivalence of cancer nanotechnology products does not equal target site bioequivalence (35). In the current commentary, we used modeling to test if and how perturbation of cellular homeostasis of membrane transporters would lead to DDIsignificant.

There are many examples of cellular homeostasis serving as a regulatory mechanism of membrane transporters/receptors, e.g., transferrin receptor, ATP-binding cassette transporters, organic anion transporters, or OATP (36,37,38,39,40). In some cases, internalization of membrane proteins is triggered by phosphorylation, e.g., activation of protein kinase C causes phosphorylation and endocytosis, blocks the cytosol-to-membrane recycling, and/or alters the function of multiple transporters such as OATPs (1A2, 2B1, 1B1), dopamine transporter, serotonin transporter, multidrug resistance-associated protein 2, and cationic amino acid transporter-1 (41,42,43,44,45,46,47,48,49,50,51,52,53,54). Other perturbations of intracellular trafficking, e.g., enhanced lysosomal degradation and Golgi complex disruption reduce the level and transport function of OATP1A2 and OATP1B1 (52). The homeostasis of OATP1B1 and OATP1B3 and responses to perturbation of intracellular processing are largely unknown.

Based on the above information, we developed a 4-scale model (cell membrane, intracellular organelles, spatial location, time) together with literature data on the intracellular processing of membrane receptors and transporters to demonstrate disruption of cellular transporter homeostasis can lead to DDIsignificant. In this report, spatial location refers to where the object-of-interest (e.g., a drug or transporter) is located within a cell (e.g., cell membrane, endocytic organelles, intracellular components). Model simulations were performed to evaluate the effects of perturbation of five major endocytic processes (i.e., transporter internalization, recycling, synthesis, early-to-late endosome transfer, degradation) and to identify the experimental conditions that would affect DDI detection. Note that there have been several PK models on DDI, with strong focus on drug PK and transporter inhibition (55,56,57,58,59). None of these earlier models deal with the intracellular processing of transporters and hence could not be used to evaluate the effects of their perturbations. The current study provides a theoretical analysis of the effects of perturbations of cellular transporter homeostasis.

METHODS

Overview

The computational model for OATP1B1 and OATP1B3 cellular homeostasis and perturbations comprises three components: (a) transporter homeostasis including the endocytic kinetic processes, (b) PK of extracellular and intracellular drug concentrations, and (c) pharmacodynamics of PD-induced stimulation or inhibition of individual endocytic transfer and intracellular processes. The time-dependent processes were described by ordinary differential equations. DDIsignificant is defined as having PD-induced changes in C-T curve of VD in cells (AUCVD,cell) to < 80% or > 125% of the baseline value without PD. These values were selected in part based on the 2017 FDA Draft Guidance (60) that uses a “default no-effect boundary of 80% to 125%” (61) and in part based on the examples that the hepatic clearance of OATP substrates, including pitavastatin, rosuvastatin, atorvastatin, and fluvastatin, is determined by their uptake into metabolizing cells (62).

Model Structure and Assumptions

Figure 1a shows the model that summarizes the current knowledge of intracellular processing of membrane transporters, including biogenesis, endocytic transport, and processing of membrane proteins in general and OATP proteins in particular (63,64,65,66). Briefly, proteins are internalized, e.g., via clathrin- or caveolae-mediated endocytosis, and located in early endosomes (EE), a tubule-vacuolar vesicle whose tubular region undergoes recycling via recycling endosomes (RE) back to the cell membrane while the vacuolar domain matures into multivesicular bodies (MVB), forming intraluminal vesicles (ILV). MVB are exocytosed via exosomes, or mature into late endosomes (LE) and eventually into lysosomes (LYSO) where the endosomal contents are degraded (36, 67,68,69,70,71). For biogenesis, OATP1B1 and OATP1B3 promoters are transactivated by hepatic nuclear factor (HNF) 1α, farnesoid X receptor, or transcription factor Stat5 and repressed by HNF3β; the newly synthesized proteins undergo N-glycosylation in endoplasmic reticulum (ER) and Golgi apparatus, followed by transport to plasma membrane; disruption of OATP1B1 glycosylation leads to retention in ER (65, 66, 72,73,74).

Fig. 1
figure 1

Model structure, governing equations, and model parameters. a Model depicting processes involved in membrane transporter homeostasis (see text). EE, early endosomes; LE, late endosomes; RE, recycling endosomes. Transporter synthesis was zero order whereas all inter-compartmental transfer kinetic processes were first order. b Governing ordinary differential equations (ODE, see text). PMEM is membrane transporter at time t and PMEM,0 is at the baseline value without PD perturbation. All other parameters are denoted in the table

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As VD uptake into cells requires the presence of transporter on the membrane, the model is focused on the spatial distribution of the transporter protein in a cell. The model assumptions were based in part on the above endocytic mechanisms and in part on the knowledge regarding transferrin homeostasis. OATP refers to either OATP1B1 or OATP1B3. The assumptions included (a) rapid OATP recycling to membrane, (b) degradation of OATP in LE/LYSO, (c) zero-order OATP biosynthesis (75,76,77) at a slower rate relative to other processes; this is based on the finding that ~ 25% of total liver protein is synthesized over 24 h (78) and the finding of no detectable changes in the OATP levels in cell membrane in the absence or presence of a protein synthesis inhibitor cycloheximide after 120 min (43), (d) all other inter-compartmental transfer kinetic processes are first order, (e) the transporter is distributed mainly in membrane, EE, and LE with negligible amounts in other cellular locations (e.g., cytoplasm), (f) OATP substrates enter a cell primarily by OATP-mediated transport and to a minor extent by passive diffusion, e.g., studies in hepatocytes have shown that ~ 80% transporter-mediated uptake for pitavastatin (79, 80), (g) VD exits cells via passive diffusion, (h) non-OATP substrate PD enters or exits cells via passive diffusion and affects only the intracellular processes without competing for transporter-mediated uptake, (i) PD reversibly stimulates or inhibits selected intracellular processes as function of the intracellular PD concentrations, (j) negligible exocytosis of OATP (i.e., OATP is not sorted into MVB, ILV, or exosomes), (k) no significant metabolism or elimination of VD or PD in the cell over the 1-h in vitro incubation, (l) the total amount of cellular OATP at baseline (in the absence of PD) is constant and its lysosomal degradation is offset by de novo protein synthesis (81), and (m) only the free (i.e., not macromolecule-bound) PD is pharmacologically active.

Governing Equations

Equations for the above spatiotemporal processes are shown in Fig. 1b. Subscripts are used to denote the location of transporter protein (e.g., PMEM is protein located on the membrane) and the location of VD or PD (e.g., CVD,EC is concentration of VD in extracellular fluid and CPD,cell is concentration of PD in intracellular space). Equations 1–3 describe the cellular homeostasis of a transporter, including the time-dependent changes in its levels in cell membrane and endocytic organelles, due to synthesis (with ksyn as the rate constant), endocytosis (kEE), recycling (kRE), transfer from EE to LE (kLE), and degradation in LE/LYSO (kdeg). Equations 4–5 describe the time-dependent changes in CVD,EC and CVD,cell due to the saturable transporter-mediated uptake and passive diffusion across the cell membrane of VD and the PD-induced perturbations in transporter homeostasis. The saturable transport of VD is described by Michaelis–Menten kinetics where Vmax is the maximal uptake rate and KM is the VD concentration at 50% Vmax. Equations 6–7 describe the time-dependent changes in CPD,EC and CPD,cell including the transport of PD into cells via passive diffusion. Equations 8–9 describe the pharmacodynamics of PD-induced perturbations (stimulation or inhibition) of individual intracellular trafficking processes as function of CPD,cell, where EC50 is CPD,cell that produces 50% of the maximum effect Emax and n is the Hill coefficient.

Model Parameterization

Table I summarizes the model parameters and their values. The total amount of OATP in a cell was arbitrarily assigned as 100 units, with an initial distribution ratio on cell membrane, EE, and LE (MEM:EE:LE ratio) of 80:18:2. This ratio was selected based on the previous finding of a 85:15 membrane:intracellular ratio for OATP2B1 in MDCKII cells (37) and the semi-quantitative microscopic results showing the substantially higher membrane levels of several OATP transporters vs. intracellular levels (e.g., OATP2B1 in Caco-2 cells and OATP1B1 and OATP1B3 in HEK293 cells (82, 83).

Table I Model Parameter Values and Sources
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For the rate constants, kEE was set at 0.1 min−1 based on the time (10 min) required for transfer from cell membrane to EE (84). Selection of a suitable kLE value was more difficult due to the less definitive literature data. One report indicated a 15–40-min lag time for the endocytosed cargo to appear in LE (84). Another showed that > 99% of the internalized transferrin is recycled to the membrane with < 1% entering and degraded in LE in 2 h (43). A third report showed no detectable OAT1 in LYSO after 45 min (43). We chose a value of 0.0067 min−1, which is the logarithmic mean of 0.001 min−1 (corresponding to < 5% entering LE as observed for transferrin) and 0.025 min−1 (corresponding to a 40-min lag time). The selection of kdiff,VD value was guided by the kinetic data of intracellular accumulation of drugs in HEK293 cells; these drugs showed a wide range of intracellular-to-extracellular ratios (from ~ 1 to > 300) (85). We selected a kdiff,VD value of 0.08 min−1 which satisfied the following two boundaries: (a) yielded a maximal intracellular-to-extracellular ratio of ~ 123 that is in-between the ratio of ~ 50 for simvastatin and ~ 210 for lovastatin and (b) yielded a half-time of 8.7 min to reach 50% of this maximal ratio, which is in-between the half-times for drugs that are or are not substrates of membrane transporters (e.g., 1–2 min for the two statins and > 15 min for a lipophilic agent not known to be a transporter substrate) (85). Transport of small molecule drugs across the cell membrane is usually rapid and occurs in min (86); the kdiff,PD was assigned a value of 0.4 min−1 (13). The value of ksyn was estimated from the turn-over rate of 4000–6000 intracellular proteins, with half-lives ranging from 10 to > 1000 h (87). Using the 10-h half-life, the steady state condition at homeostasis (i.e., rate of synthesis equals rate of degradation), and a zero-order synthesis, we calculated ksyn to be 0.12 units*min−1; this value was identical to the value calculated as kLE * PEE/PLE at homeostasis (see below). The rate constants for the remaining three processes (kRE, kdeg, ksyn), because the intracellular processes are linked to each other, were calculated for homeostatic conditions (see equations in Fig. 1b); e.g., their respective values were 0.438 min−1, 0.060 min−1, and 0.12 unit-min−1 at the baseline MEM:EE:LE ratio of 80:18:2.

Computational Methods

All programming codes, graphical representations, and calculations used the MATLAB language and procedures. Integration of ordinary differential equations was performed using a MATLAB ODE solver (ODE45 or ODE15s). The quantities-of-interest of model simulations are C-T profile of VD in cells, the corresponding AUCVD,cell, and the ratio of AUCVD,cell in the absence or presence of PD (i.e., relative AUC or AUCRVD,cell). All AUC values were calculated using the trapezoidal rule.

Model Simulations

We used the above model and model parameters to simulate the effects of PD-induced perturbations of transporter endocytosis, cytosol-to-membrane recycling, transfer of transporter from EE to LE/LYSO, and de novo synthesis (i.e., by changing the respective individual rate constants, kEE, kRE, kLE, and ksyn). Simulations were performed for (a) 9 initial spatial distribution of transporter proteins (MEM:EE:LE ratios ranging from 90:8:2 to 20:78:2), (b) perturbations of 4 transfer processes (kEE, kRE, kLE, ksyn) plus transporter degradation (kdeg), and (c) 2 types of PD effects (inhibition or stimulation), (d) varying extents of PD perturbations including 3 values for the Hill’s coefficient n (0.5, 1, 2), 5 values of initial CPD,EC (from 0.1 to 10 times the EC50-equivalents), 7 VD-PD co-incubation durations (from 5 to 60 min), and 2 diffusion rates for PD (kdiff,PD values of 10 min−1 and 0.4 min−1). The co-incubation times included the typical 5-min duration used in the 2012 FDA-recommended in vitro investigations of competitive inhibition of OATP-mediated VD uptake and the 30 min pre-incubation duration in the 2017 FDA recommendation. We set Emax at 100% for inhibition (i.e., complete inhibition of a process) and 500% for stimulation (i.e., fivefold increase). Note that because the cell volume under in vitro conditions was calculated to be ~ 5,800 times less than the extracellular culture medium volume, there were no significant changes in CPD,EC or CVD,EC over time. The model-simulated AUCRVD,cell outputs were analyzed by a separate algorithm that identified the incidence of DDIsignificant, i.e., when AUCRVD,cell was < 80% or > 125%.

Sensitivity Analysis to Identify the Critical Endocytic Processes

We performed sensitivity analysis to rank order the individual intracellular processes that, when perturbed, had the greatest effects on CVD,cell at time t and the cumulative AUC from 0 to 60 min. Each rate constant was increased or decreased by 5% (i.e., δ of 0.05) and the sensitivity index (SIx) was calculated as the difference between the AUCRVD,cell values without and with change in kx divided by δ * kx, where kx is kEE, kRE, kLE, ksyn, or kdeg. Multiplication of SIx with baseline kx divided by the baseline AUCVD,cell without PD yielded the dimensionless SI values.

RESULTS

Evaluation of Model Suitability for Transporter Protein Homeostasis

We first evaluated if the model captured the expected homeostasis (i.e., steady state); this condition was confirmed by the constant protein levels in cell membrane, EE, and LE over time (Fig. 2a). We next evaluated if the model captured the differences in drug uptake by passive diffusion and via transporter; this condition was confirmed by the model-simulated results, i.e., much slower uptake for passive diffusion (e.g., 8 vs. 962 concentration unit*min−1) and a much lower contribution of diffusion-mediated uptake to total VD uptake and CVD,cell (~ 100-fold lower) compared to transporter-mediated uptake (Fig. 2b). The model further captured the diffusion-mediated efflux from cells due to the intracellular-to-extracellular concentration gradient at the later times, to yield a plateau CVD,cell after 15 min.

Fig. 2
figure 2

Evaluation of suitability of model and model parameter values. a The plots show apparent steady state levels of transporter proteins in cell membrane (PMEM), EE (PEE), and LE (PLE) and accumulation of CVD,cell over time. b Contribution of transporter-mediated uptake and passive diffusion of VD to total CVD,cell

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Model Simulations

We performed a total of 9,303 simulations (63 for control, 840 for comparing PDs with 2 kdiff,PD values, and 8,400 for PD-induced perturbations of 5 endocytic transfer rate constants), to examine if and when such perturbations resulted in DDIsignificant. The results indicate PD-induced perturbations of endocytosis and intracellular processing of membrane transporters led to substantially lower or higher AUCRVD,cell and DDIsignificant. Table II shows the overall incidences of DDIsignificant due to PD-induced perturbations and Table III shows the break-down of the incidences due to changes in individual endocytic transfer processes and biosynthesis of transporters. These simulation results indicate that (a) the rate of PD diffusion into a cell had a relatively minor effect on AUCRVD,cell, (b) the overall incidence of DDIsignificant was 18.7% and all were caused by PD-induced perturbations in 4 intracellular transfer processes with the rank order of kEE > kRE > ksyn > kLE and none by kdeg, (c) the time to reach the maximum change in AUCRVD,cell depended on the process affected by the PD and was longer for inhibitory PD than for stimulatory PD, and (d) the magnitude of AUCRVD,cell changes caused by PD depended on the cell property (i.e., baseline spatial transporter distribution or MEM:EE:LE ratio), VD-PD co-incubation time, and CPD,EC. These findings are discussed below.

Table II Incidence of DDIsignificant as Functions of Spatial Transporter Distribution and VD-PD Co-incubation Time. Percentages Reflect the Total Incidence of DDIsignificant Observed in Simulations Using 9 MEM:EE:LE Ratios, 3 n Values (0.5, 1, 2), 5 CPD,EC (0.1, 0.3, 1, 3, and 10 EC50-Equivalents), and 7 VD-PD Co-incubation Times (from 5 to 60 min), as Described in Text. Emax for PD-Induced Inhibition Was 100% (i.e., Complete Inhibition of the Process). Emax for PD-Induced Stimulation Was 500% (i.e., fivefold Increase Compared to the Baseline Value)
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Table III Contribution of PD-Induced Perturbations in 4 Kinetic Processes to DDIsignificant. Simulations and Calculations of Incidence of DDIsignificant Are as Described in Table I. The Effects of Individual Perturbations on AUCRVD,cell (> 125% or < 80%) Are Noted. Neither Inhibition Nor Stimulation of kdeg Resulted in DDIsignificant (Not Shown)
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Relationship Between Diffusion Rate and Extracellular Concentration of PD on Spatial Transporter Distribution and DDI

We compared two PDs, both inhibited the sorting of EE content to RE (i.e., lowering kRE) but had a 25-fold difference in kdiff,PD (0.4 and 10 min−1); the simulations used Hill coefficient n of 1 and 80:18:2 MEM:EE:LE ratio. Both PDs reduced the PMEM and increased the PEE and PLE (Fig. 3). A higher kdiff,PD led to more rapid CPD,cell increases, e.g., reaching 50% of CPD,EC at 0.07 min for kdiff,PD of 10 min−1 vs. 1.7 min for kdiff,PD of 0.4 min−1; the differences were greatest during the first 15 min and diminished at later times (< 2% at 60 min). However, the higher kdiff,PD only marginally altered the CPD,cell and did not significantly altered the spatial transporter distribution nor AUCRVD,cell. In contrast, increasing the CPD,EC from 1 to 10 EC50-equivalents resulted in much greater changes in spatial transporter distribution (from 15% reduction in PMEM after 15-min co-incubation to 55% reduction) and significant reduction of AUCRVD,cell (from no change to < 80%).

Fig. 3
figure 3

Effect of PD diffusion rate. Model-based simulation results on the changes of AUCRVD,cell induced by PD with two different diffusion rate constants into cells (kdiff,PD) of 0.4 min−1 (blue) and 10 min−1 (red); both PD acted to reduce the transporter transfer from EE to RE (i.e., inhibiting kRE). The plots show the simulation results obtained using the parameter values of n of 1, 80:18:2 MEM:EE:LE ratio, and two initial CPD,EC of 1 EC50-equivalent (top panels) and 10 EC50-equivalents (bottom panels). a PD uptake into cell (EC50-equivalents). b Transporter distribution. c AUCRVD,cell

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Perturbation of Individual Endocytic Processes

Of the five endocytic processes, perturbation of transporter internalization (kEE) or recycling (kRE) led to the greatest AUCRVD,cell changes and the highest incidence of DDIsignificant (Fig. 4 and Table II). In comparison, inhibition of transporter synthesis (ksyn) or EE-to-LE transfer (kLE) did not lead to significant AUCRVD,cell changes and their stimulation led to relatively minor changes under limited circumstances (e.g., high CPD,EC and low PMEM). This is because the changes in PMEM, which determines the VD uptake, are primarily affected by perturbations of kEE and kRE (see Eq. 1–2) due to their higher values (i.e., more rapid processes) compared to the other two processes. For the remaining process of transporter degradation (kdeg), neither inhibition nor stimulation resulted in significant AUCRVD,cell changes, as the degraded protein did not re-enter the cell membrane. As summarized below, the stimulation of kRE and ksyn and inhibition of kEE and kLE resulted in increased AUCRVD,cell whereas kRE/ksyn inhibition and kEE/kLE stimulation resulted in decreased AUCRVD,cell. This is because processes that enhance PMEM, such as inhibiting kEE or stimulating kRE, increase VD uptake and AUCRVD,cell, whereas processes that reduce PMEM reduce AUCRVD,cell.

Fig. 4
figure 4

Effects of spatial transporter distribution and VD-PD co-incubation time. Model-based simulation results on the changes of AUCRVD,cell as functions of PD-induced perturbations in kEE, kRE, ksyn, and kLE; spatial transporter distribution (MEM:EE:LE ratio); and co-incubation time. The plots show the simulation results obtained using n of 1. Emax for PD-induced inhibition was 100% (i.e., complete inhibition of the process). Emax for PD-induced stimulation was 500% (i.e., fivefold increase compared to the baseline value). Solid lines: changes induced by stimulation of respective parameters. Dotted lines: changes induced by inhibition of respective parameters. Red horizon lines indicate AUCRVD,cell of 125% (top) or 80% (bottom). a Simulation results obtained at five MEM:EE:LE ratio values, using CPD,EC of 1 EC50-equivalent, to demonstrate the trend and the full range of the changes. b Simulation results obtained at one MEM:EE:LE ratio of 80:18:2 and five CPD,EC values of 0.1, 0.3, 1, 3, and 10 EC50-equivalents

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Stimulation of kEE, which corresponded to enhanced transporter internalization, led to reduced AUCRVD,cell. Inhibition of kEE had the opposite effect and increased the AUCRVD,cell. In both cases, the magnitude in AUCRVD,cell changes and the incidence of DDIsignificant depended on the transporter MEM:EE:LE ratio, CPD,EC, and VD-PD incubation time (Fig. 4 and Table II). For example, under the conditions of n of 1 and CPD,EC of 1 EC50-equivalent, a change in MEM:EE:LE ratio from 80:18:2 to 20:78:2 caused the AUCRVD,cell to reach the < 80% level at an earlier time (6.31 min vs. 11.3 min). Increasing the CPD,EC to 10 EC50-equivalents further increased the incidence and shortened the time to reach DDI. Note that kEE inhibition caused a lower incidence of DDIsignificant compared to kEE stimulation because (a) the value of maximal stimulation was set at a higher level compared to the maximal inhibition (500% vs. 100%) and (b) the effect of kEE inhibition was limited in part by the initial PMEM (i.e., a complete inhibition of kEE would cause all proteins to remain on the membrane, or from the baseline level of 80% to 100%, which equals a relatively small 25% increase).

Stimulation of kRE led to more rapid recycling and reappearance of the endocytosed transporter on cell membrane and elevated the AUCRVD,cell, whereas inhibition of kRE yielded opposite effects (Fig. 4 and Table II). As for kEE, changes in AUCRVD,cell and DDIsignificant depended on MEM:EE:LE ratio, CPD,EC, and VD-PD co-incubation time. For example, under the conditions of n of 1 and CPD,EC of 1 EC50-equivalent, DDIsignificant was reached at an earlier time at the 20:78:2 ratio compared to the 70:28:2 ratio (8.3 min vs. 37.9 min), and increasing the CPD,EC to 10 EC50-equivalents increased the incidence and shortened the time to reach DDI. Note the higher incidence of DDI due to kRE inhibition or stimulation when PMEM dropped below 70%.

Inhibition of ksyn did not cause DDIsignificant, whereas its stimulation resulted in AUCRVD,cell of > 125%, all of which were observed when PMEM was ≤ 60%.

Inhibition of kLE did not result in AUCRVD,cell of < 80%, whereas its stimulation resulted in a low incidence (up to 0.48%) of AUCRVD,cell of > 125%. Similar to the situation of ksyn, all incidences of DDI were observed at low PMEM levels (≤ 50%).

Effects of Experimental Conditions on DDI Detection

We used model simulations to identify three experimental conditions that played a role in detecting PD-induced DDI (Fig. 4, Tables I and II), as follows. First, the frequency and severity of DDI depended on the baseline spatial transporter distribution and generally increased at lower PMEM. For example, the incidence of DDI at 60 min increased by fourfold from ~ 9 to ~ 36% when the membrane transporter decreased from 90 to 60%. Note that only a few situations did not show AUCRVD,cell > 125% irrespective of the changes in kEE, kRE, ksyn, or kLE (either stimulation or inhibition), i.e., three situations of ≥ 80% PMEM (MEM:EE:LE ratios of 90:8:2, 80:18:2, and 80:10:10) for kEE or kRE and five situations of ≥ 70% PMEM for ksyn or kLE. In contrast, AUCRVD,cell of < 80% or > 125% were observed at all other MEM:EE:LE ratios. Additional simulations showed that the ratio cut-off for AUCRVD,cell to increase to > 125% was 79:19:2 (0.83% incidence at 60 min) whereas the ratio cut-off to decrease AUCRVD,cell to < 80% was 99:0.5:0.5 (0.83% incidence at 20 min).

The second important experimental condition was the initial CPD,EC. Figure 4b shows the results obtained for the 80:18:2 MEM:EE:LE ratio. Increasing CPD,EC enhanced the PD-induced perturbations, shortened the time to reach DDIsignificant, and increased the frequency of DDIsignificant. A PD that stimulated a process, by increasing the k value, produced the maximal perturbation more rapidly than a PD that inhibited a process. For example, the change in AUCRVD,cell at CPD,EC of 10 EC50-equivalents reached 50% of the highest level at 4.3 min after stimulation vs. 8.2 min after inhibition for kEE and at 2.7 min after stimulation vs. 15.2 min after inhibition for kEE..

The third important experimental condition was the VD-PD co-incubation time; increasing the time increased the incidence of DDIsignificant due to perturbations of kEE, kRE, kLE, or ksyn, e.g., the maximum incidence increased from ~ 6% after 5 min to ~ 18% after 15 min, 26% after 30 min, and 28% after 60 min and the average incidence increased from < 3% at 5 min to > 11% at 30 min and > 14% at 60 min (Table I). Figure 4 shows that the effect of co-incubation time further depended on the spatial transporter distribution in the cell. The maximum incidence of DDIsignificant increased with time (2.5% at 5 min to 13.3% at 60 min; Table I) at MEM:EE:LE ratio of 80:18:2 and with decreased PMEM (9% at 90% PMEM to 28% at 20% PMEM; Table I) and depended on the homeostasis process that was perturbed (e.g., perturbations of kEE yielded higher incidence of DDIsignificant compared to perturbations of kLE).

Sensitivity Analysis

Results of sensitivity analysis (Fig. 5) showed that AUCRVD,cell was affected differently by PD-perturbation of kEE, kRE, ksyn, and kLE. The SI values generally increased with increasing VD-PD co-incubation time. The overall SI values, calculated for the cumulative AUCRVD,cell over 60 min, (a) showed a rank order of kEE > kRE > ksyn > kLE and (b) increased with decreasing PMEM. For example, the SI values for kEE and kRE increased from ~ 0.2 and ~ 0.19 at the 80:18:2 MEM:EE:LE ratio, respectively, to ~ 0.7 and ~ 0.5 at the 20:78:2 ratio.

Fig. 5
figure 5

Sensitivity of AUCRVD,cell to PD-induced perturbations of various kinetic processes. The values of individual rate constants (kEE, kRE, ksyn, and kLE) were altered by 5% (increase or decrease) and the resulting changes in AUCRVD,cell were used to calculate the sensitivity indices (SI) as described in text. The plots show the results obtained for δ of + 5% at five MEM:EE:LE ratios, to demonstrate the trend and the full range of the indices; the table shows the SI values calculated for the cumulative AUCRVD,cell over 60 min. Similar results were obtained for δ of − 5% (not shown)

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DISCUSSION

The goal of this commentary is to demonstrate the utility of modeling in the context of MIDD and transporter-mediated DDI. Using the multiscale model, established by integrating the common mathematical approaches and PK tools, and the general knowledge of the intracellular processing of membrane receptor/transporter, we investigated if and how PD-induced perturbation of transporter homeostasis may cause DDI. The model-based simulation results identified at least four intracellular homeostasis processes (transporter internalization, recycling, synthesis, early-to-late endosome transfer) for which PD-induced stimulation or inhibition would lead to DDIsignificant and at least three experimental conditions that, because they determined the frequency and extent of DDI, require attention. First, the typical 5-min VD-PD co-incubation that has been used to study competitive inhibition of VD uptake would be insufficient to detect the DDIsignificant caused by perturbations of transporter homeostasis, whereas a 30-min co-incubation, similar to the duration of PD pre-incubation recommended by the 2017 FDA Guidance (60), would be more effective in detecting DDIsignificant. Second, using a higher CPD,EC may shorten the duration of pre- or co-incubation. Third, the fraction of PMEM plays an important role in homeostasis-related DDI, which brings up the need to know (a) if transfecting cells with the transporter genes alters the spatial transporter distribution and (b) if the DDI identified in the transfected cells reflects the DDI in the parent cells. In view of the importance of DDI in drug development and drug usage, we advocate additional studies to experimentally verify the model simulation results. We further recommend using experimental designs and conditions that, based on the simulation results, are likely to yield the highest incidence of DDIsignificant. These conditions include using cells that are known to have different baseline spatial transporter distribution, high initial CPD,EC, and at several VD-PD co-incubation times (e.g., 5 to 60 min).

The current study used 13 model assumptions (see “METHODS” section), including three assumptions derived from previous literature data (OATP biosynthesis, transporter-mediated uptake of OATP substrates, rapid recycling of transporter to membrane), seven assumptions based on the general pharmacological principles or the general knowledge on endocytic processes (e.g., first order inter-compartmental transfer, distribution of transporter in endocytic organelles, degradation of transporter in LE/LYSO, transmembrane transport of non-OATP substrates via passive diffusion, VD exits cells via passive diffusion, concentration-dependent reversible PD effects, only the free PD is pharmacologically active), and two assumptions are based on the absence of contradicting data (negligible exocytosis of OATP, homeostasis of OATP at baseline in the absence of PD). However, the remaining assumption of no significant metabolism or elimination of VD or PD in the cell over the 1-h in vitro incubation, which was used mainly to simplify the model, is likely an over-simplification since inhibition of VD uptake into the metabolizing hepatic cells is expected to reduce the VD elimination and hence the DDI. In addition, the current model has not accounted for the potential feedback regulatory processes, e.g., the perturbation of transporter homeostasis may trigger compensatory processes. For refinement, the multiscale model described in Fig. 1 can be adapted to evaluate (a) other treatment schedules such as pre-incubation with PD (e.g., by adding a delayed addition of VD into the extracellular culture medium in the PK computation module), (b) PD-induced perturbations of multiple endocytic processes simultaneously (e.g., weakly basic or lysosomotropic drugs such as chloroquine that, by elevating the pH of multiple endocytic organelles, may affect multiple rate constants including kEE, kLE, or kRE), (c) effects of intracellular drug metabolism (e.g., extend the model to include elimination and effects of inhibitors of lysosomal degradation and intracellular proteasomes), and (d) combinations of drugs that can together perturb multiple intracellular homeostasis simultaneously.

The current study is focused on the effects of perturbations of cellular transporter homeostasis on the cellular PK of VD. On the other hand, the DDI-derived host toxicities are determined by the systemic PK of VD. Additional multiscale modeling studies to link the current, cell-scale model to a whole body-scale model would provide a systems-based approach to depict how the changes in cellular VD concentrations affect the plasma VD concentrations and thereby enable the evaluation of the role of cellular transporter homeostasis in DDI. We propose that modeling is a useful tool for hypothesis generation and for designing experiments to identify potential DDI and that its application aligns with the model-informed drug development paradigm advocated by FDA.