Is it time to use modeling of cellular transporter homeostasis to inform drug-drug interaction studies: Theoretical considerations

Abstract

Mathematical modeling has been an important tool in pharmaceutical research for 50+ years and there is increased emphasis over the last decade on using modeling to improve the efficiency and effectiveness of drug development. In an earlier commentary, 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 demonstratethe effects of nanoparticle particles on systemic disposition. The current commentary used 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 transporter homeostasis can lead to drug-drug interaction (DDI) between victim drug (VD) and perpetrator drug (PD), including changes in the area-under-concentration-time-curve of VD in cells that are considered significant by the US Food and Drug Administration (FDA). The model comprised 3 computational components: (a) intracellular transporter homeostasis, (b) pharmacokinetics of extracellular and intracellular VD/PD concentrations, and (c) pharmacodynamics of PD-induced stimulation or inhibition of an intracellular kinetic process. Model-based simulations showed that (a) among the five major endocytic processes, perturbation of transporter internalization or recycling led to the highest incidence and most extensive DDI, with minor DDI for perturbing transporter synthesis and early-to-late endosome and no DDI for perturbing transporter degradation, and (b) three experimental conditions (spatial transporter distribution in cells, VD/PD co-incubation time, extracellular PD concentrations) were determinants of DDI detection. We propose modeling is a useful tool for hypothesis generation and for designing experiments to identify potential DDI; its application further aligns with the model-informed drug development paradigm advocated by FDA.

Graphical Abstract

INTRODUCTION

Drug-drug interactions (DDI) resulting in unexpected or undesirable adverse effects is 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 (4–10).

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., (11–15). 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 (16–25). 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%) (30–34). 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 DDI_significant.

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 (36–40). 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 (41–54). 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 DDI_significant. 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 there have been several PK models on DDI, with strong focus on drug PK and transporter inhibition (55–59). 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. DDI_significant is defined as having PD-induced changes in C-T curve of VD in cells (AUC_VD,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 (63–66). 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, 67–71). 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, 72–74).

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). P_mem is membrane transporter at time t and P_mem,0 is at the baseline value without PD perturbation. All other parameters are denoted in the table.

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 (75–77) 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 Figure 1B. Subscripts are used to denote the location of transporter protein (e.g., P_MEM is protein located on the membrane) and the location of VD or PD (e.g., C_VD,EC is concentration of VD in extracellular fluid and C_PD,cell is concentration of PD in intracellular space). Eq. 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 k_syn as the rate constant), endocytosis (k_EE), recycling (k_RE), transfer from EE to LE (k_LE), and degradation in LE/LYSO (k_deg). Eq. 4-5 describe the time-dependent changes in C_VD,EC and C_VD,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 V_max is the maximal uptake rate and K_M is the VD concentration at 50% V_max. Eq. 6-7 describe the time-dependent changes in C_PD,EC and C_PD,cell including the transport of PD into cells via passive diffusion. Eq. 8-9 describe the pharmacodynamics of PD-induced perturbations (stimulation or inhibition) of individual intracellular trafficking processes as function of C_PD,cell, where EC₅₀ is C_PD,cell that produces 50% of the maximum effect E_max and n is the Hill coefficient.

Model parameterization.

Table 1 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 (38) 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 1.

Model parameter values and sources.

kEE, rate constant of transporter internalization into EE	0.1 min−1, calculated using literature data (see Methods)
kLE, rate constant of transporter transfer from EE to LE	0.0067 min−1, calculated using literature data (see Methods)
kRE, rate constant of transporter recycling to membrane	Calculated as (kEE*PMEM – kLE*PEE)/PEE at homeostasis (e.g., 0.438 min−1 for MEM:EE:LE of 80:18:2)
ksyn, rate constant of transporter biosynthesis	Calculated as kdeg*PLE (e.g., 0.12 unit*min−1 for 80:18:2 MEM:EE:LE, also equals to the value calculated based on a half-life of 10 h (68))
kdeg, rate constant of transporter degradation	Calculated as kLE*PEE/PLE at homeostasis (e.g., 0.06 min−1 for 80:18:2 MEM:EE:LE)
kdiff,PD, rate of passive diffusion of PD across cell membrane	0.4 and 10 min−1
kdiff,VD, rate of passive diffusion of VD across cell membrane	0.08 min−1, calculated using literature data (see Methods)
KM, VD concentration for half-maximal transporter-mediated uptake	4 concentration units (assigned)
Vmax, maximal uptake rate for transporter-mediated VD transport	1000 concentration units-min−1 (assigned)
CVD,EC, extracellular concentration of VD	100 concentration units at time zero (assigned), calculated with Eq. 4 at later times
CPD,EC, extracellular concentration of PD	0.1 to 10 EC50-equivalent at time zero (assigned), calculated with Eq. 6 at later times
CVD,cell and CPD,cell, concentration of VD and PD in cells	Calculated with Eq. 4-7
kx,perturb, PD-induced perturbation of a kinetic process	Calculated with CPD,cell and Eq. 8-9
Px, amount of transporter protein at location x	100 units distributed in membrane, EE and LE (assigned)
Medium:cell volume for a spherical cell with a 6.5 μm radius (average value for HEK-293) (70,73), for 150,000 cells in 1 mL of culture medium: 5798
MEM:EE:LE Ratio (spatial distribution of transporter protein at baseline with no PD) was assigned 9 values from 90:8:2 to 20:78:2

For the rate constants, k_EE 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 k_LE 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 >99% of the internalized transferrin is recycled to the membrane with <1% entering and degraded in LE in 2 h (44). 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 k_diff,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 k_diff,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 k_diff,PD was assigned a value of 0.4 min⁻¹ (13). The value of k_syn 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 k_syn to be 0.12 units*min⁻¹; this value was identical to the value calculated as (k_LE*P_EE/P_LE) at homeostasis (see below). The rate constants for the remaining three processes (k_RE, k_deg, k_syn), because the intracellular processes are linked to each other, were calculated for homeostatic conditions (see equations in Figure 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 AUC_VD,cell, and the ratio of AUC_VD,cell in the absence or presence of PD (i.e., relative AUC or AUCR_VD,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, k_EE, k_RE, k_LE and k_syn). 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 (k_EE, k_RE, k_LE, k_syn) plus transporter degradation (k_deg), (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 C_PD,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 (k_diff,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 E_max at 100% for inhibition (i.e., complete inhibition of a process) and 500% for stimulation (i.e., 5-fold increase). Note that because the cell volume under in vitro conditions was calculated to be ~ 5,800 times less that the extracellular culture medium volume, there were no significant changes in C_PD,EC or C_VD,EC over time. The model-simulated AUCR_VD,cell outputs were analyzed by a separate algorithm that identified the incidence of DDI_significant, i.e., when AUCR_VD,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 C_VD,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 (SI_x) was calculated as the (difference between the AUCR_VD,cell values without and with change in k_x) divided by (δ*k_x), where k_x is k_EE, k_RE, k_LE, k_syn, or k_deg . Multiplication of SI_{x with} (baseline k_x divided by the baseline AUC_VD,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 (Figure 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 C_VD,cell (~100-fold lower) compared to transporter-mediated uptake (Figure 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 C_VD,cell after 15 min.

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 (P_MEM), EE (P_EE), and LE (P_LE), and accumulation of C_VD,cell over time. (B) Contribution of transporter-mediated uptake and passive diffusion of VD to total C_VD,cell.

Model simulations.

We performed a total of 9,303 simulations (63 for control, 840 for comparing PDs with 2 k_diff,PD values, and 8,400 for PD-induced perturbations of 5 endocytic transfer rate constants), to examine if and when such perturbations resulted in DDI_significant. The results indicate PD-induced perturbations of endocytosis and intracellular processing of membrane transporters led to substantially lower or higher AUCR_VD,cell and DDI_significant. Table 2 shows the overall incidences of DDI_significant due to PD-induced perturbations and Table 3 shows the break-down of the incidences due to changes in individual endocytic transfer processes and biosynthesis of transporters. These simulation results indicate (a) the rate of PD diffusion into a cell had a relatively minor effect on AUCR_VD,cell, (b) the overall incidence of DDI_significant was 18.7% and all were caused by PD-induced perturbations in 4 intracellular transfer processes with the rank order of k_EE>k_RE>k_syn>k_LE and none by k_deg, (c) the time to reach the maximum change in AUCR_VD,cell depended on the process affected by the PD and was longer for inhibitory PD than for stimulatory PD, and (d) the magnitude of AUCR_VD,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 C_PD,EC. These findings are discussed below.

Table 2. Incidence of DDI_significant as functions of spatial transporter distribution and VD-PD co-incubation time.

Percentages reflect the total incidence of DDI_significant observed in simulations using 9 MEM:EE:LE Ratios, 3 n values (0.5, 1, 2), 5 C_PD,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. E_max for PD-induced inhibition was 100% (i.e., complete inhibition of the process). E_max for PD-induced stimulation was 500% (i.e., 5-fold increase compared to the baseline value).

MEM:EE:LE Ratio	AUCRVD,cell	Incidence of DDIsignificant at Following Co-incubation Time (min)
		5	10	15	20	30	45	60
90:8:2	>125%	0%	0%	0%	0%	0%	0%	0%
	<80%	0%	2.50%	5.00%	6.67%	7.50%	7.50%	9.17%
	Total	0%	2.50%	5.00%	6.67%	7.50%	7.50%	9.17%
80:18:2	>125%	0%	0%	0%	0%	0%	0%	0%
	<80%	2.50%	6.67%	9.17%	12.5%	12.5%	13.3%	13.3%
	Total	2.50%	6.67%	9.17%	12.5%	12.5%	13.3%	13.3%
80:10:10	>125%	0%	0%	0%	0%	0%	0%	0%
	<80%	1.67%	5.83%	7.50%	7.50%	10.0%	11.7%	11.7%
	Total	1.67%	5.83%	7.50%	7.50%	10.0%	11.7%	11.7%
70:28:2	>125%	0%	1.67%	3.33%	5.83%	7.50%	11.7%	11.7%
	<80%	5.00%	9.17%	11.7%	12.5%	15.0%	15.0%	16.7%
	Total	5.00%	10.8%	15.0%	18.3%	22.5%	26.7%	28.4%
70:20:10	>125%	0%	0%	0%	0%	0.83%	1.67%	4.17%
	<80%	5.00%	7.50%	11.7%	12.5%	13.3%	14.2%	15.0%
	Total	5.00%	7.50%	11.7%	12.5%	14.1%	15.9%	19.2%
60:38:2	>125%	1.67%	5.00%	8.3%	11.7%	13.3%	14.2%	18.3%
	<80%	5.00%	10.0%	13.3%	15.0%	15.0%	17.5%	17.5%
	Total	6.67%	15.0%	21.6%	26.7%	28.3%	31.7%	35.8%
50:40:10	>125%	2.50%	5.83%	10.8%	12.5%	15.0%	17.5%	22.5%
	<80%	5.00%	10.0%	13.3%	15.0%	15.8%	17.5%	18.3%
	Total	7.5%	15.8%	24.1%	27.5%	30.8%	35.0%	40.8%
30:60:10	>125%	5.00%	8.33%	13.3%	17.5%	22.5%	25.0%	26.7%
	<80%	5.83%	9.17%	14.2%	15.0%	16.7%	17.5%	22.5%
	Total	10.8%	17.5%	27.5%	32.5%	39.2%	42.5%	49.2%
20:78:2	>125%	3.33%	10.8%	18.3%	21.7%	25.8%	26.7%	28.3%
	<80%	5.83%	8.33%	12.5%	14.2%	15.0%	19.2%	24.2%
	Total	9.16%	19.1%	30.8%	35.9%	40.8%	45.9%	52.5%

Table 3. Contribution of PD-induced perturbations in 4 kinetic processes to DDI_significant.

Simulations and calculations of incidence of DDI_significant, are as described in Table 1. The effects of individual perturbations on AUCR_VD,cell (>125% or <80%) are noted. Neither inhibition nor stimulation of k_deg resulted in DDI_significant (not shown).

MEM:LE:LE Ratio	Incidence of DDIsignificant (AUCRVD,cell of <80% or >125%) due to PD-induced perturbations
	kEE		kRE		ksyn		kLE
	Inhibition >125%	Stimulation <80%	Inhibition <80%	Stimulation >125%	Inhibition <80%	Stimulation >125%	Inhibition >125%	Stimulation <80%
90:8:2	0%	3.45%	2.02%	0%	0%	0%	0%	0%
80:18:2	0%	6.90%	3.10%	0%	0%	0%	0%	0%
80:10:10	0%	5.36%	2.62%	0%	0%	0%	0%	0%
70:28:2	1.67%	8.45%	3.69%	4.29%	0%	0%	0%	0%
70:20:10	0.71%	7.98%	3.33%	0.24%	0%	0%	0%	0%
60:38:2	2.86%	8.93%	4.40%	7.02%	0%	0.48%	0%	0%
50:40:10	3.45%	8.93%	4.52%	7.86%	0%	1.07%	0%	0.12%
30:60:10	4.76%	9.29%	4.64%	8.81%	0%	3.33%	0%	0.48%
20:78:2	5.12%	9.52%	3.81%	8.45%	0%	5.71%	0%	0.36%

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 k_RE) but had a 25-fold difference in k_diff,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 P_mem and increased the P_EE and P_LE (Figure 3). A higher k_diff,PD led to more rapid C_PD,cell increases, e.g., reaching 50% of C_PD,EC at 0.07 min for k_diff,PD of 10 min⁻¹ vs. 1.7 min for k_diff,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 k_diff,PD only marginally altered the C_PD,cell and did not significantly altered the spatial transporter distribution nor AUCR_VD,cell. In contrast, increasing the C_PD,EC from 1 to 10 EC₅₀-equivalents resulted in much greater changes in spatial transporter distribution (from 15% reduction in P_MEM after 15 min co-incubation to 55% reduction) and significant reduction of AUCR_VD,cell (from no change to <80%).

Figure 3. Effect of PD diffusion rate.

Model-based simulation results on the changes of AUCR_VD,cell induced by PD with two different diffusion rate constants into cells (k_diff,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 k_RE). 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 C_PD,EC of 1 EC₅₀-equivalent (top panels) and 10 EC₅₀-equivalents (bottom panels).

Perturbation of individual endocytic processes.

Of the five endocytic processes, perturbation of transporter internalization (k_EE) or recycling (k_RE) led to the greatest AUCR_VD,cell changes and the highest incidence of DDI_significant (Figure 4 and Table 2). In comparison, inhibition of transporter synthesis (k_syn) or EE-to-LE transfer (k_LE) did not lead to significant AUCR_VD,cell changes and their stimulation led to relatively minor changes under limited circumstances (e.g., high C_PD,EC and low P_MEM). This is because the changes in P_MEM, which determines the VD uptake, are primarily affected by perturbations of k_EE and k_RE (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 (k_deg), neither inhibition nor stimulation resulted in significant AUCR_VD,cell changes, as the degraded protein did not re-enter the cell membrane. As summarized below, the stimulation of k_RE and k_syn and inhibition of k_EE and k_LE resulted in increased AUCR_VD,cell whereas k_RE/k_syn inhibition and k_EE/k_LE stimulation resulted in decreased AUCR_VD,cell. This is because processes that enhance P_MEM, such as inhibiting k_EE or stimulating k_RE, increase VD uptake and AUCR_VD,cell, whereas processes that reduce P_MEM reduce AUCR_VD,cell.

Figure 4. Effects of spatial transporter distribution and VD-PD co-incubation time.

Model-based simulation results on the changes of AUCR_VD,cell as functions of PD-induced perturbations in k_EE, k_RE, k_syn and k_LE, spatial transporter distribution (MEM:EE:LE Ratio) and co-incubation time. The plots show the simulation results obtained using n of 1. E_max for PD-induced inhibition was 100% (i.e., complete inhibition of the process). E_max for PD-induced stimulation was 500% (i.e., 5-fold 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 AUCR_VD,cell of 125% (top) or 80% (bottom). (A) Simulation results obtained at five MEM:EE:LE Ratio values, using C_PD,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 C_PD,EC values of 0.1, 0.3, 1, 3 and 10 EC₅₀-equivalents.

Stimulation of k_EE, which corresponded to enhanced transporter internalization, led to reduced AUCR_VD,cell. Inhibition of k_EE had the opposite effect and increased the AUCR_VD,cell. In both cases, the magnitude in AUCR_VD,cell changes and the incidence of DDI_significant depended on the transporter MEM:EE:LE Ratio, C_PD,EC and VD-PD incubation time (Figure 4 and Table 2). For example, under the conditions of n of 1 and C_PD,EC of 1 EC₅₀-equivalent, a change in MEM:EE:LE Ratio from 80:18:2 to 20:78:2 caused the AUCR_VD,cell to reach the <80% level at an earlier time (6.31 min vs. 11.3 min). Increasing the C_PD,EC to 10 EC₅₀-equivalents further increased the incidence and shortened the time to reach DDI. Note that k_EE inhibition caused a lower incidence of DDI_significant compared to k_EE 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 k_EE inhibition was limited in part by the initial P_MEM (i.e., a complete inhibition of k_EE 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 k_RE led to more rapid recycling and reappearance of the endocytosed transporter on cell membrane and elevated the AUCR_VD,cell, whereas inhibition of k_RE yielded opposite effects (Figure 4 and Table 2). As for k_EE, changes in AUCR_VD,cell and DDI_significant depended on MEM:EE:LE Ratio, C_PD,EC and VD-PD co-incubation time. For example, under the conditions of n of 1 and C_PD,EC of 1 EC₅₀-equivalent, DDI_significant 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 C_PD,EC to 10 EC₅₀-equivalents increased the incidence and shortened the time to reach DDI. Note the higher incidence of DDI due to k_RE inhibition or stimulation when P_mem dropped below 70%.

Inhibition of k_syn did not cause DDI_significant, whereas its stimulation resulted in AUCR_VD,cell of >125%, all of which were observed when P_MEM was ≤60%.

Inhibition of k_LE did not result in AUCR_VD,cell of <80%, whereas its stimulation resulted in a low incidence (up to 0.48%) of AUCR_VD,cell of >125%. Similar to the situation of k_syn, all incidences of DDI were observed at low P_MEM 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 (Figure 4, Tables 1 and 2), as follows. First, the frequency and severity of DDI depended on the baseline spatial transporter distribution, and generally increased at lower P_mem. For example, the incidence of DDI at 60 min increased by 4-fold from ~9% to ~36% when the membrane transporter decreased from 90% to 60%. Note that only a few situations did not show AUCR_VD,cell >125% irrespective of the changes in k_EE, k_RE , k_syn or k_LE (either stimulation or inhibition), i.e., three situations of ≥80% P_mem (MEM:EE:LE Ratios of 90:8:2, 80:18:2 and 80:10:10) for k_EE or k_RE, and five situations of ≥70% P_mem for k_syn or k_LE. In contrast, AUCR_VD,cell of <80% or >125% were observed at all other MEM:EE:LE Ratios. Additional simulations showed the Ratio cut-off for AUCR_VD,cell to increase to >125% was 79:19:2 (0.83% incidence at 60 min) whereas the Ratio cut-off to decrease AUCR_VD,cell to <80% was 99:0.5:0.5 (0.83% incidence at 20 min).

The second important experimental condition was the initial C_PD,EC. Figure 4B shows the results obtained for the 80:18:2 MEM:EE:LE Ratio. Increasing C_PD,EC enhanced the PD-induced perturbations, shortened the time to reach DDI_significant, and increased the frequency of DDI_significant. 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 AUCR_VD,cell at C_PD,EC of 10 EC₅₀-equivalents reached 50% of the highest level at 4.3 min after stimulation vs. 8.2 min after inhibition for k_EE, and at 2.7 min after stimulation vs. 15.2 min after inhibition for k_EE..

The third important experimental condition was the VD-PD co-incubation time; increasing the time increased the incidence of DDI_significant due to perturbations of k_EE, k_RE, k_LE or k_syn, 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 1). Figure 4 shows the effect of co-incubation time further depended on the spatial transporter distribution in the cell. The maximum incidence of DDI_significant increased with time (2.5% at 5 min to 13.3% at 60 min; Table 1) at MEM:EE:LE Ratio of 80:18:2 and with decreased P_mem (9% at 90% P_mem to 28% at 20% P_mem; Table 1), and depended on the homeostasis process that was perturbed (e.g., perturbations of k_EE yielded higher incidence of DDI_significant compared to perturbations of k_LE).

Sensitivity analysis.

Results of sensitivity analysis (Figure 5) showed that AUCR_VD,cell was affected differently by PD-perturbation of k_EE, k_RE, k_syn and k_LE. The SI values generally increased with increasing VD-PD co-incubation time. The overall SI values, calculated for the cumulative AUCR_VD,cell over 60 min, (a) showed a rank order of k_EE > k_RE > k_syn > k_LE, and (b) increased with decreasing P_mem. For example, the SI values for k_EE and k_RE 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.

Figure 5. Sensitivity of AUCR_VD,cell to PD-induced perturbations of various kinetic processes.

The values of individual rate constants (k_EE, k_RE, k_syn and k_LE) were altered by 5% (increase or decrease) and the resulting changes in AUCR_VD,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 AUCR_VD,cell over 60 min. Similar results were obtained for δ of −5% (not shown).

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 DDI_significant, 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 DDI_significant 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 DDI_significant. Second, using a higher C_PD,EC may shorten the duration of pre- or co-incubation. Third, the fraction of P_mem 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 DDI_significant. These conditions include using cells that are known to have different baseline spatial transporter distribution, high initial C_PD,EC, and at several VD-PD co-incubation times (e.g., 5 to 60 min).

The current study used 13 model assumptions (see Methods), 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 Figure 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 k_EE, k_LE, or k_RE), (c) effects of intracellular drug metabolism (e.g., extend the model to include elimination and effects of inhibitors of lysosomal degradation and intracellular proteosomes), 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 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.

Abbreviations used in text:

AUC_VD,cell

area under C-T curve of VD in cells

AUCR_VD,cell

AUC_VD,cell in PD-treated cells relative to control without PD treatment

C_PD,EC and C_PD,cell

extracellular and intracellular PD concentrations, respectively

C_VD,EC and C_VD,cell

extracellular and intracellular VD concentrations, respectively

C-T

concentration-time

DDI

drug-drug Interaction

DDI_significant

significant DDI or when AUCR_VD,cell is >125% or <80% of AUC_VD,cell in the absence of PD

EC₅₀

concentration of PD that causes 50% effect

EE

early endosome

ER

endoplasmic reticulum

FDA

US Food and Drug Administration

ILV

intraluminal vesicles

k_x

rate constant for transfer of transporter to compartment x from the immediately previous compartment

LE

late endosome

LYSO

lysosome

MEM:EE:LE Ratio

ratio of amounts of transporter in cell membrane, EE and LE

MIDD

model-informed drug development

MVB

multivesicular bodies

OATP

organic anion transporter polypeptide

ODE

ordinary differential equations

PD

perpetrator drug

QSP

quantitative systems pharmacology

RE

recycling endosome

SI

sensitivity index