Fitting the elementary rate constants of the P-gp transporter network in the hMDR1-MDCK confluent cell monolayer using a particle swarm algorithm

Case Study 8: Status of the Structural Mass Action Kinetic Model of P-gp-Mediated Transport Through Confluent Cell Monolayers

In the first edition of this book, we presented the basics of explicitly incorporating the lipid biochemistry into a confluent cell monolayer transport model and the novel findings of this model up to 2013, including the use of global optimization to fit the elementary rate constants and the efflux active P-glycoprotein (P-gp) membrane concentrations for the transport of four P-gp substrates across MDCKII-hMDR1-NKI confluent cell monolayers. This chapter is an update on that model, which has been focused primarily on discovering how microvilli morphology regulates the efflux active P-gp and the existence of, as yet, unidentified uptake transporters of P-gp substrates in all of the commonly used P-gp expressing cell lines used in the pharmaceutical industry, thereby adding new players to DDI predictions and IVIVE. The structural mass action kinetic model uses the general mass action reactions for P-gp binding and efflux, with the membrane structural parameters for the confluent cell monolayer to predict drug transport over time. Binding of drug to P-gp occurs within the cytosolic monolayer of the apical membrane, according to (a) the molar partition coefficient of the drug to the cytosolic monolayer and (b) the association rate constant, k₁ (M^-1 s^-1), of the drug from the basolateral or apical outer monolayers into the P-gp binding site. Release of substrate from P-gp back into the cytosolic monolayer occurs with a dissociation rate constant k_r (s^-1) or, much less frequently, into the apical aqueous chamber with an efflux rate constant k₂ (s^-1). The model fits the efflux active P-gp concentration, T(0), i.e., the P-gp whose effluxed drug actually reaches the apical aqueous chamber, as opposed to the majority of P-gp whose effluxed drug is reabsorbed back into the same or neighboring microvilli prior to reaching the apical aqueous chamber. Efflux active P-gp largely resides near the tips of the microvilli. We have shown using kinetics and structured illumination microscopy that: (a) efflux active P-gp is controlled by microvilli morphology; (b) there are apical (AT) and basolateral (BT) uptake transporters for P-gp substrates in most, if not all, P-gp expressing cell lines used in the pharmaceutical industry, which exist, but which remain unidentified; (c) the lab-to-lab variability in P-gp IC₅₀ values observed in the P-gp IC₅₀ initiative was due to the conflated inhibition of P-gp and the basolateral digoxin uptake transporters by all 15 P-gp substrates tested in that study; (d) even the IC₅₀ values for P-gp inhibition alone do not obey the Cheng-Prusoff relationship; (e) the fitted elementary rate constants and the molecular dissociation constant Ki for this kinetic model are system independent; and (f) the time dependence of product formation for these confluent cell monolayers is correlated with the P-gp V_max/K_m, when defined by its fitted elementary rate constants and uptake transporter clearances, without any steady-state assumptions.

ABC Family Transporters

The transport of specific molecules across lipid membranes is an essential function of all living organisms. The processes are usually mediated by specific transporters. One of the largest transporter families is the ATP-binding cassette (ABC) family. More than 40 ABC transporters have been identified in human, which are divided into 7 subfamilies (ABCA to ABCG) based on their gene structure, amino acid sequence, domain organization, and phylogenetic analysis. Of them, at least 11 ABC transporters including P-glycoprotein (P-GP/ABCB1), multidrug resistance-associated proteins (MRPs/ABCCs), and breast cancer resistance protein (BCRP/ABCG2) are involved in multidrug resistance (MDR) development. These ABC transporters are expressed in various tissues such as the liver, intestine, kidney, and brain, playing important roles in absorption, distribution, and excretion of drugs. Some ABC transporters are also involved in diverse cellular processes such as maintenance of osmotic homeostasis, antigen processing, cell division, immunity, cholesterol, and lipid trafficking. Several human diseases such as cystic fibrosis, sitosterolemia, Tangier disease, intrahepatic cholestasis, and retinal degeneration are associated with mutations in corresponding transporters. This chapter will describe function and expression of several ABC transporters (such as P-GP, BCRP, and MRPs), their substrates and inhibitors, as well as their clinical significance.

Mechanistic kinetic modeling generates system-independent P-glycoprotein mediated transport elementary rate constants for inhibition and, in combination with 3D SIM microscopy, elucidates the importance of microvilli morphology on P-glycoprotein mediated efflux activity

INTRODUCTION

In vitro transporter kinetics are typically analyzed by steady-state Michaelis-Menten approximations. However, no clear evidence exists that these approximations, applied to multiple transporters in biological membranes, yield system-independent mechanistic parameters needed for reliable in vivo hypothesis generation and testing. Areas covered: The classical mass action model has been developed for P-glycoprotein (P-gp) mediated transport across confluent polarized cell monolayers. Numerical integration of the mass action equations for transport using a stable global optimization program yields fitted elementary rate constants that are system-independent. The efflux active P-gp was defined by the rate at which P-gp delivers drugs to the apical chamber, since as much as 90% of drugs effluxed by P-gp partition back into nearby microvilli prior to reaching the apical chamber. The efflux active P-gp concentration was 10-fold smaller than the total expressed P-gp for Caco-2 cells, due to their microvilli membrane morphology. The mechanistic insights from this analysis are readily extrapolated to P-gp mediated transport in vivo. Expert opinion: In vitro system-independent elementary rate constants for transporters are essential for the generation and validation of robust mechanistic PBPK models. Our modeling approach and programs have broad application potential. They can be used for any drug transporter with minor adaptations.

A new method measuring the interaction of radiotracers with the human P-glycoprotein (P-gp) transporter

In drug development, biomarkers for cerebral applications have a lower success rate compared to cardiovascular drugs or tumor therapeutics. One reason is the missing blood brain barrier penetration, caused by the tracer's interaction with efflux transporters such as the P-gp (MDR1 or ABCB1). Aim of this study was the development of a reliable model to measure the interaction of radiotracers with the human efflux transporter P-gp in parallel to the radiolabeling process. LigandTracer® Technology was used with the wildtype cell line MDCKII and the equivalent cell line overexpressing human P-gp (MDCKII-hMDR1). The method was evaluated based on established PET tracers with known interaction with the human P-gp transporter and in nanomolar concentration (15 nM). [¹¹C]SNAP-7941 and [¹⁸F]FE@SNAP were used as P-gp substrates by comparing the real-time model with an uptake assay and μPET images. [¹¹C]DASB [¹¹C]Harmine, [¹⁸F]FMeNER,[¹⁸F]FE@SUPPY and [¹¹C]Me@HAPTHI were used as tracers without interactions with P-gp in vitro. However, [¹¹C]Me@HAPTHI shows a significant increase in SUV levels after blocking with Tariquidar. The developed real-time kinetic model uses directly PET tracers in a compound concentration, which is reflecting the in vivo situation. This method may be used at an early stage of radiopharmaceutical development to measure interactions to P-gp before conducting animal experiments.

Derivation of a System-Independent Ki for P-glycoprotein Mediated Digoxin Transport from System-Dependent IC50 Data

It has been previously demonstrated that IC₅₀ values for inhibition of digoxin transport across confluent polarized cell monolayers are system-dependent. Digoxin IC₅₀ data from five laboratories participating in the P-glycoprotein (P-gp) IC₅₀ Initiative, using Caco-2, MDCKII-hMDR1 or LLC-PK1-hMDR1 cells, were fitted by the structural mass action kinetic model for P-gp-mediated transport across confluent cell monolayers. We determined their efflux-active P-gp concentration [T(0)], inhibitor elementary dissociation rate constant from P-gp (k_rQ), digoxin basolateral uptake clearance (k_B), and inhibitor binding affinity to the digoxin basolateral uptake transporter (K_QB). We also fitted the IC₅₀ data for inhibition of digoxin transport through monolayers of primary human proximal tubule cells (HPTCs). All cell systems kinetically required a basolateral uptake transporter for digoxin, which also bound to all inhibitors. The inhibitor k_rQ was cell system-independent, thereby allowing calculation of a system-independent Ki. The variability in efflux-active P-gp concentrations and basolateral uptake clearances in the five laboratories was about an order of magnitude. These laboratory-to-laboratory variabilities can explain more than 60% of the IC₅₀ variability found in the principal component analysis plot in a previous study, supporting the hypothesis that the observed IC₅₀ variability is primarily due to differences in expression levels of efflux-active P-gp and the basolateral digoxin uptake transporter. HPTCs had 10- to 100-fold lower efflux-active P-gp concentrations than the overexpressing cell lines, whereas their digoxin basolateral uptake clearances were similar. HPTC basolateral uptake of digoxin was inhibited 50% by 10 μM ouabain, suggesting involvement of OATP4C1.

Extrapolation of Elementary Rate Constants of P-glycoprotein-Mediated Transport from MDCKII-hMDR1-NKI to Caco-2 Cells

The best parameters for incorporation into mechanistic physiologically based pharmacokinetic models for transporters are system-independent kinetic parameters and active (not total) transporter levels. Previously, we determined the elementary rate constants for P-glycoprotein (P-gp)-mediated transport (on- and off-rate constants from membrane to P-gp binding pocket and efflux rate constant into the apical chamber) using the structural mass action kinetic model in confluent MDCKII-hMDR1-NKI cell monolayers. In the present work, we extended the kinetic analysis to Caco-2 cells for the first time and showed that the elementary rate constants are very similar compared with MDCKII-hMDR1-NKI cells, suggesting they primarily depend on the interaction of the compound with P-gp and are therefore mostly independent of the in vitro system used. The level of efflux active (not total) P-gp is also fitted by our model. The estimated level of efflux active P-gp was 5.0 ± 1.4-fold lower in Caco-2 cells than in MDCKII-hMDR1-NKI cells. We also kinetically identified the involvement of a basolateral uptake transporter for both digoxin and loperamide in Caco-2 cells, as found previously in MDCKII-hMDR1-NKI cells, due to their low passive permeability. This demonstrates the value of our P-gp structural model as a diagnostic tool in detecting the importance of other transporters, which cannot be unambiguously done by the Michaelis-Menten approach. The system-independent elementary rate constants for P-gp obtained in vitro are more fundamental parameters than those obtained using Michaelis-Menten steady-state equations. This suggests they will be more robust mechanistic parameters for incorporation into physiologically based pharmacokinetic models for transporters.

Microvilli Morphology Can Affect Efflux Active P-Glycoprotein in Confluent MDCKII -hMDR1-NKI and Caco-2 Cell Monolayers

From fits of drug transport kinetics across confluent MDCKII-hMDR1-NKI and Caco-2 cell monolayers we estimated the levels of efflux active P-glycoprotein (P-gp) in these two cell lines (companion paper). In the present work, we compared the efflux active P-gp number to the total P-gp level, using liquid chromatography-tandem mass spectrometry, and showed that in Caco-2 cells total P-gp is about 10-fold greater than efflux active P-gp, whereas in MDCKII-hMDR1-NKI cells these values are within twofold. We further visualized the microvilli in MDCKII-hMDR1-NKI and Caco-2 cells using three-dimensional structured illumination super-resolution microscopy and found that the microvilli in Caco-2 cells are taller and more densely packed than those in MDCK-hMDR1-NKI cells. We hypothesized over 10 years ago that only P-gp at the tips of the microvilli contribute significantly to efflux activity, whereas the remaining P-gp are involved in a futile cycle of efflux of amphipathic drugs from the microvillus membrane, followed by their reabsorption into the same or nearby microvillous membranes. The difference between the levels of total and efflux active P-gp in Caco-2 cells can be explained by the more densely packed microvilli in Caco-2 cells, which would lead to a substantial fraction of P-gp not contributing to final release of drug into the apical chamber. Our results suggest that the effect of microvilli morphology differences between in vitro and in vivo systems must be considered when scaling transporter activity for efflux transporters of amphipathic compounds, for example, P-gp.

A novel application of t-statistics to objectively assess the quality of IC50 fits for P-glycoprotein and other transporters

Current USFDA and EMA guidance for drug transporter interactions is dependent on IC₅₀ measurements as these are utilized in determining whether a clinical interaction study is warranted. It is therefore important not only to standardize transport inhibition assay systems but also to develop uniform statistical criteria with associated probability statements for generation of robust IC₅₀ values, which can be easily adopted across the industry. The current work provides a quantitative examination of critical factors affecting the quality of IC₅₀ fits for P-gp inhibition through simulations of perfect data with randomly added error as commonly observed in the large data set collected by the P-gp IC₅₀ initiative. The types of errors simulated were (1) variability in replicate measures of transport activity; (2) transformations of error-contaminated transport activity data prior to IC₅₀ fitting (such as performed when determining an IC₅₀ for inhibition of P-gp based on efflux ratio); and (3) the lack of well defined “no inhibition” and “complete inhibition” plateaus. The effect of the algorithm used in fitting the inhibition curve (e.g., two or three parameter fits) was also investigated. These simulations provide strong quantitative support for the recommendations provided in Bentz et al. (2013) for the determination of IC₅₀ values for P-gp and demonstrate the adverse effect of data transformation prior to fitting. Furthermore, the simulations validate uniform statistical criteria for robust IC₅₀ fits in general, which can be easily implemented across the industry. A calibration of the t-statistic is provided through calculation of confidence intervals associated with the t-statistic.

Compartmental models for apical efflux by P-glycoprotein--part 1: evaluation of model complexity

PURPOSE

With the goal of quantifying P-gp transport kinetics, Part 1 of these manuscripts evaluates different compartmental models and Part 2 applies these models to kinetic data.

METHODS

Models were developed to simulate the effect of apical efflux transporters on intracellular concentrations of six drugs. The effect of experimental variability on model predictions was evaluated. Several models were evaluated, and characteristics including membrane configuration, lipid content, and apical surface area (asa) were varied.

RESULTS

Passive permeabilities from MDCK-MDR1 cells in the presence of cyclosporine gave lower model errors than from MDCK control cells. Consistent with the results in Part 2, model configuration had little impact on calculated model errors. The 5-compartment model was the simplest model that reproduced experimental lag times. Lipid content and asa had minimal effect on model errors, predicted lag times, and intracellular concentrations. Including endogenous basolateral uptake activity can decrease model errors. Models with and without explicit membrane barriers differed markedly in their predicted intracellular concentrations for basolateral drug exposure. Single point data resulted in clearances similar to time course data.

CONCLUSIONS

Compartmental models are useful to evaluate the impact of efflux transporters on intracellular concentrations. Whereas a 3-compartment model may be sufficient to predict the impact of transporters that efflux drugs from the cell, a 5-compartment model with explicit membranes may be required to predict intracellular concentrations when efflux occurs from the membrane. More complex models including additional compartments may be unnecessary.

A structural model for the mass action kinetic analysis of P-gp mediated transport through confluent cell monolayers

The structural model for P-gp mediated transport across confluent cell monolayers uses the generally accepted mass action reactions for P-gp binding and efflux, together with the known structural parameters for P-gp (large substrate binding site accessible from the membrane) and the apical plasma membrane in which it resides (lipid bilayer partition coefficient of substrate and volume of apical plasma membrane allow estimation of substrate concentration at binding site). The model considers binding of substrate to P-gp from within the inner leaflet of the apical membrane, with an on rate constant, k 1 (M(-1)s(-1)), and off rate constant k r (s(-1)), as well as an efflux rate constant from P-gp into the apical chamber, k 2 (s(-1)). The model also explicitly estimates the active P-gp protein level, known as P-gp efflux active surface density T(0). For each new drug, fitting these parameters requires use of multiple initial drug concentrations and multiple time points at each concentration, until steady state is reached between P-gp-mediated efflux into the apical chamber and passive permeability from apical chamber back into the cytosol. Although this model optimally requires a larger than usual dataset for analysis, it does provide important mechanistic information through estimates of these on, off and efflux rate constants, as well as efflux active P-gp surface density. This more detailed description of efflux from polarized confluent cell monolayers has (1) provided insight into the unexpected relationship between P-gp IC50 and K i in this system, (2) highlighted the kinetic need for GF120918 inhibitable apical and basolateral uptake transporters for digoxin, and (3) provided possible explanations for the extreme lab-to-lab variability in P-gp IC50 values observed for inhibition of digoxin transport. This model can also be used to distinguish between efflux active P-gp and total apical plasma membrane P-gp, which may be important when P-gp is expressed in a microvillous membrane.

Computational approaches to analyse and predict small molecule transport and distribution at cellular and subcellular levels

Quantitative structure-activity relationship (QSAR) studies and mechanistic mathematical modeling approaches have been independently employed for analysing and predicting the transport and distribution of small molecule chemical agents in living organisms. Both of these computational approaches have been useful for interpreting experiments measuring the transport properties of small molecule chemical agents, in vitro and in vivo. Nevertheless, mechanistic cell-based pharmacokinetic models have been especially useful to guide the design of experiments probing the molecular pathways underlying small molecule transport phenomena. Unlike QSAR models, mechanistic models can be integrated from microscopic to macroscopic levels, to analyse the spatiotemporal dynamics of small molecule chemical agents from intracellular organelles to whole organs, well beyond the experiments and training data sets upon which the models are based. Based on differential equations, mechanistic models can also be integrated with other differential equations-based systems biology models of biochemical networks or signaling pathways. Although the origin and evolution of mathematical modeling approaches aimed at predicting drug transport and distribution has occurred independently from systems biology, we propose that the incorporation of mechanistic cell-based computational models of drug transport and distribution into a systems biology modeling framework is a logical next step for the advancement of systems pharmacology research.

Transport inhibition of digoxin using several common P-gp expressing cell lines is not necessarily reporting only on inhibitor binding to P-gp

We have reported that the P-gp substrate digoxin required basolateral and apical uptake transport in excess of that allowed by digoxin passive permeability (as measured in the presence of GF120918) to achieve the observed efflux kinetics across MDCK-MDR1-NKI (The Netherlands Cancer Institute) confluent cell monolayers. That is, GF120918 inhibitable uptake transport was kinetically required. Therefore, IC₅₀ measurements using digoxin as a probe substrate in this cell line could be due to inhibition of P-gp, of digoxin uptake transport, or both. This kinetic analysis is now extended to include three additional cell lines: MDCK-MDR1-NIH (National Institute of Health), Caco-2 and CPT-B2 (Caco-2 cells with BCRP knockdown). These cells similarly exhibit GF120918 inhibitable uptake transport of digoxin. We demonstrate that inhibition of digoxin transport across these cell lines by GF120918, cyclosporine, ketoconazole and verapamil is greater than can be explained by inhibition of P-gp alone. We examined three hypotheses for this non-P-gp inhibition. The inhibitors can: (1) bind to a basolateral digoxin uptake transporter, thereby inhibiting digoxin's cellular uptake; (2) partition into the basolateral membrane and directly reduce membrane permeability; (3) aggregate with digoxin in the donor chamber, thereby reducing the free concentration of digoxin, with concomitant reduction in digoxin uptake. Data and simulations show that hypothesis 1 was found to be uniformly acceptable. Hypothesis 2 was found to be uniformly unlikely. Hypothesis 3 was unlikely for GF120918 and cyclosporine, but further studies are needed to completely adjudicate whether hetero-dimerization contributes to the non-P-gp inhibition for ketoconazole and verapamil. We also find that P-gp substrates with relatively low passive permeability such as digoxin, loperamide and vinblastine kinetically require basolateral uptake transport over that allowed by +GF120918 passive permeability, while highly permeable P-gp substrates such as amprenavir, quinidine, ketoconazole and verapamil do not, regardless of whether they actually use the basolateral transporter.

Variability in P-glycoprotein inhibitory potency (IC₅₀) using various in vitro experimental systems: implications for universal digoxin drug-drug interaction risk assessment decision criteria

A P-glycoprotein (P-gp) IC₅₀ working group was established with 23 participating pharmaceutical and contract research laboratories and one academic institution to assess interlaboratory variability in P-gp IC₅₀ determinations. Each laboratory followed its in-house protocol to determine in vitro IC₅₀ values for 16 inhibitors using four different test systems: human colon adenocarcinoma cells (Caco-2; eleven laboratories), Madin-Darby canine kidney cells transfected with MDR1 cDNA (MDCKII-MDR1; six laboratories), and Lilly Laboratories Cells--Porcine Kidney Nr. 1 cells transfected with MDR1 cDNA (LLC-PK1-MDR1; four laboratories), and membrane vesicles containing human P-glycoprotein (P-gp; five laboratories). For cell models, various equations to calculate remaining transport activity (e.g., efflux ratio, unidirectional flux, net-secretory-flux) were also evaluated. The difference in IC₅₀ values for each of the inhibitors across all test systems and equations ranged from a minimum of 20- and 24-fold between lowest and highest IC₅₀ values for sertraline and isradipine, to a maximum of 407- and 796-fold for telmisartan and verapamil, respectively. For telmisartan and verapamil, variability was greatly influenced by data from one laboratory in each case. Excluding these two data sets brings the range in IC₅₀ values for telmisartan and verapamil down to 69- and 159-fold. The efflux ratio-based equation generally resulted in severalfold lower IC₅₀ values compared with unidirectional or net-secretory-flux equations. Statistical analysis indicated that variability in IC₅₀ values was mainly due to interlaboratory variability, rather than an implicit systematic difference between test systems. Potential reasons for variability are discussed and the simplest, most robust experimental design for P-gp IC₅₀ determination proposed. The impact of these findings on drug-drug interaction risk assessment is discussed in the companion article (Ellens et al., 2013) and recommendations are provided.

Membrane transporters in drug development

Membrane transporters have wide, but specific tissue distributions. They can impact on multiple endogenous and xenobiotic processes. Knowledge and awareness within the pharmaceutical industry of their impact on drug absorption, distribution, metabolism and elimination (ADME) and drug safety is growing rapidly. Clinically important transporter-mediated drug-drug interactions (DDIs) have been observed. Up to nine diverse transporters are implicated in the DDIs of a number of widely prescribed drugs, posing a significant challenge to the pharmaceutical industry. There is a complex interplay between multiple transporters and/or enzymes in the ADME and pharmacogenomics of drugs. Integrating these different mechanisms to understand their relative contributions to ADME is a key challenge. Many different factors complicate the study of membrane transporters in drug development. These include a lack of specific substrates and inhibitors, non-standard in vitro tools, and competing/complementary mechanisms (e.g. passive permeability and metabolism). Discovering and contextualizing the contribution of membrane transporters to drug toxicity is a significant new challenge. Drug interactions with key membrane transporters are routinely assessed for central nervous system (CNS) drug discovery therapies, but are not generally considered across the wider drug discovery. But, there is interest in utilizing membrane transporters as drug delivery agents. Computational modeling approaches, notably physiology-based/pharmacokinetic (PB/PK) modeling are increasingly applied to transporter interactions, and permit integration of multiple ADME mechanisms. Because of the range of tissues and transporters of interest, robust transporter, in vitro to in vivo, scaling factors are required. Empirical factors have been applied, but absolute protein quantitation will probably be required.