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 kr (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 Vmax/Km, when defined by its fitted elementary rate constants and uptake transporter clearances, without any steady-state assumptions.

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.

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 (krQ), digoxin basolateral uptake clearance (kB), and inhibitor binding affinity to the digoxin basolateral uptake transporter (KQB). 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 krQ 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.

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.

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.

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.

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.

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.

Application of receiver operating characteristic analysis to refine the prediction of potential digoxin drug interactions.

In the 2012 Food and Drug Administration (FDA) draft guidance on drug-drug interactions (DDIs), a new molecular entity that inhibits P-glycoprotein (P-gp) may need a clinical DDI study with a P-gp substrate such as digoxin when the maximum concentration of inhibitor at steady state divided by IC50 ([I1]/IC50) is ≥0.1 or concentration of inhibitor based on highest approved dose dissolved in 250 ml divide by IC50 ([I2]/IC50) is ≥10. In this article, refined criteria are presented, determined by receiver operating characteristic analysis, using IC50 values generated by 23 laboratories. P-gp probe substrates were digoxin for polarized cell-lines and N-methyl quinidine or vinblastine for P-gp overexpressed vesicles. Inhibition of probe substrate transport was evaluated using 15 known P-gp inhibitors. Importantly, the criteria derived in this article take into account variability in IC50 values. Moreover, they are statistically derived based on the highest degree of accuracy in predicting true positive and true negative digoxin DDI results. The refined criteria of [I1]/IC50 ≥ 0.03 and [I2]/IC50 ≥ 45 and FDA criteria were applied to a test set of 101 in vitro-in vivo digoxin DDI pairs collated from the literature. The number of false negatives (none predicted but DDI observed) were similar, 10 and 12%, whereas the number of false positives (DDI predicted but not observed) substantially decreased from 51 to 40%, relative to the FDA criteria. On the basis of estimated overall variability in IC50 values, a theoretical 95% confidence interval calculation was developed for single laboratory IC50 values, translating into a range of [I1]/IC50 and [I2]/IC50 values. The extent by which this range falls above the criteria is a measure of risk associated with the decision, attributable to variability in IC50 values.

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

P-glycoprotein, a human multidrug resistance transporter, has been extensively studied due to its importance to human health and disease. In order to understand transport kinetics via P-gp, confluent cell monolayers overexpressing P-gp are widely used. The purpose of this study is to obtain the mass action elementary rate constants for P-gp's transport and to functionally characterize members of P-gp's network, i.e., other transporters that transport P-gp substrates in hMDR1-MDCKII confluent cell monolayers and are essential to the net substrate flux. Transport of a range of concentrations of amprenavir, loperamide, quinidine and digoxin across the confluent monolayer of cells was measured in both directions, apical to basolateral and basolateral to apical. We developed a global optimization algorithm using the Particle Swarm method that can simultaneously fit all datasets to yield accurate and exhaustive fits of these elementary rate constants. The statistical sensitivity of the fitted values was determined by using 24 identical replicate fits, yielding simple averages and standard deviations for all of the kinetic parameters, including the efflux active P-gp surface density. Digoxin required additional basolateral and apical transporters, while loperamide required just a basolateral tranporter. The data were better fit by assuming bidirectional transporters, rather than active importers, suggesting that they are not MRP or active OATP transporters. The P-gp efflux rate constants for quinidine and digoxin were about 3-fold smaller than reported ATP hydrolysis rate constants from P-gp proteoliposomes. This suggests a roughly 3∶1 stoichiometry between ATP hydrolysis and P-gp transport for these two drugs. The fitted values of the elementary rate constants for these P-gp substrates support the hypotheses that the selective pressures on P-gp are to maintain a broad substrate range and to keep xenobiotics out of the cytosol, but not out of the apical membrane.

If the KI is defined by the free energy of binding to P-glycoprotein, which kinetic parameters define the IC50 for the Madin-Darby canine kidney II cell line overexpressing human multidrug resistance 1 confluent cell monolayer?

From previous fits of drug transport kinetics across confluent Madin-Darby canine kidney II cell line overexpressing human multidrug resistance 1 cell monolayers, we found that a drug's binding constant to P-glycoprotein (P-gp) was significantly smaller than its IC(50) when that drug was used as an inhibitor against another P-gp substrate. We tested several IC(50) candidate functions, including the standard function, the Kalvass-Pollack function, and the efflux ratio, to determine whether any of them yielded an IC(50) = K(I), as would be expected for water-soluble enzymes. For the confluent cell monolayer, the IC(50)/K(I) ratio is greater than 1 for all candidate functions tested. From the mass action kinetic model, we have derived a simple approximate equation that shows how the IC(50)/K(I) ratio depends on the elementary rate constants from our mass action model. Thus, the IC(50) will differ between cell lines and tissues, for the same probe substrate and inhibitor, if there are different membrane concentrations of P-gp, or the probe substrate's elementary rate constants, partition coefficient, binding constant to P-gp, passive permeability, and ability to access the other transporters (if any) in the two cell lines. The mass action model and the approximate equation for the IC(50)/K(I) ratio derived here can be used to estimate the elementary rate constants needed to extrapolate in vitro drug-drug interactions for compounds to the in vivo environment.

Kinetic identification of membrane transporters that assist P-glycoprotein-mediated transport of digoxin and loperamide through a confluent monolayer of MDCKII-hMDR1 cells.

A robust screen for compound interaction with P-glycoprotein (P-gp) has some obvious requirements, such as a cell line expressing P-gp and a probe substrate that is transported solely by P-gp and passive permeability. It is actually difficult to prove that a particular probe substrate interacts only with P-gp in the chosen cell line. Using a confluent monolayer of MDCKII-hMDR1 cells, we have determined the elementary rate constants for the P-gp efflux of amprenavir, digoxin, loperamide, and quinidine. For amprenavir and quinidine, transport was fitted with just P-gp and passive permeability. For digoxin and loperamide, fitting required a basolateral transporter (p < 0.01), which was inhibited by the P-gp inhibitor N-(4-[2-(1,2,3,4-tetrahydro-6,7-dimethoxy-2-isoquinolinyl)ethyl]-phenyl)-9,10-dihydro-5-methoxy-9-oxo-4-acridine carboxamide (GF120918). This means that when digoxin is used as a probe substrate and a compound is shown to inhibit digoxin flux, it could be that the inhibition occurs at the basolateral transporter rather than at P-gp. Digoxin basolateral>apical efflux also required an apical importer (p < 0.05). We propose that amprenavir and quinidine are robust probe substrates for assessing P-gp interactions using the MDCKII-hMDR1 confluent cell monolayer. Usage of another cell line, e.g., LLC-hMDR1 or Caco-2, would require the same kinetic validation to ensure that the probe substrate interacts only with P-gp. Attempts to identify the additional digoxin and loperamide transporters using a wide range of substrates/inhibitors of known epithelial transporters (organic cation transporters, organic anion transporters, organic ion-transporting polypeptide, uric acid transporter, or multidrug resistance-associated protein) failed to inhibit the digoxin or loperamide transport through their basolateral transporter.

P-Glycoprotein (P-gp) expressed in a confluent monolayer of hMDR1-MDCKII cells has more than one efflux pathway with cooperative binding sites.

The multidrug resistance transporter P-glycoprotein (P-gp) effluxes a wide range of substrates and can be affected by a wide range of inhibitors or modulators. Many studies have presented classifications for these binding interactions, within either the context of equilibrium binding or the Michaelis-Menten enzyme analysis of the ATPase activity of P-gp. Our approach is to study P-gp transport and its inhibition using a physiologically relevant confluent monolayer of hMDR1-MDCKII cells. We measure the elementary rate constants for P-gp efflux of substrates and study inhibition using pairwise combinations with a different unlabeled substrate acting as the inhibitor. Our current kinetic model for P-gp has only a single binding site, because a previous study proved that the mass-action kinetics of efflux of a single substrate were not sensitive to whether there are one or more substrate-binding and efflux sites. In this study, using this one-site model, we found that, with "high" concentrations of either a substrate or an inhibitor, the elementary rate constants fitted independently for each of the substrates alone quantitatively predicted the efflux curves, simply applying the assumption that binding at the "one site" was competitive. On the other hand, at "low" concentrations of both the substrate and inhibitor, we found no inhibition of the substrate efflux, despite the fact that both the substrate and inhibitor were being well-effluxed. This was not an effect of excess "empty" P-gp molecules, because the competitive efflux model takes site occupancy into account. Rather, it is quantitative evidence that the substrate and inhibitor are being effluxed by multiple pathways within P-gp. Remarkably, increasing the substrate concentration above the "low" concentration, caused the inhibition to become competitive; i.e., the inhibitor became effective. These data and their analysis show that the binding of these substrates must be cooperative, either positive or negative.

The steady-state Michaelis-Menten analysis of P-glycoprotein mediated transport through a confluent cell monolayer cannot predict the correct Michaelis constant Km.

PURPOSE: Typically, the kinetics of membrane transport is analyzed using the steady-state Michaelis-Menten (or Eadie-Hofstee or Hanes) equations. This approach has been successful when the substrate is picked up from the aqueous phase, like a water-soluble enzyme, for which the Michaelis-Menten steady-state analysis was developed. For membrane transporters whose substrate resides in the lipid bilayer of the plasma membrane, like P-glycoprotein (P-gp), there has been no validation of the accuracy of the steady-state analysis because the elementary rate constants for transport were not known. METHODS: Recently, we fitted the mass action elementary kinetic rate constants of P-gp transport of three different drugs through a confluent monolayer of MDCKII-hMDR1 cells. With these elementary rate constants in hand, we use computer simulations to assess the accuracy of the steady-state Michaelis-Menten parameters. This limits the simulation to parameter ranges known to be physiologically relevant. RESULTS: Using over 2,300 different vectors of initial elementary parameters spanning the space bounded by the three drugs, which defines 2,300 "virtual substrates", the concentrations of substrate transported were calculated and fitted to Eadie-Hofstee plots. Acceptable plots were obtained for 1,338 cases. CONCLUSION: The fitted steady-state Vmax values from the analysis correlated to within a factor of 2-3 with the values predicted from the elementary parameters. However, the fitted Km value could be generated by a wide range of underlying "molecular" Km values. This is because of the convolution of the drug passive permeability kinetics into the fitted Km. This implies that Km values measured in simpler systems, e.g., microsomes or proteoliposomes, even if accurate, would not predict the Km values for the confluent monolayer system or, by logical extension, in vivo. Reliable in vitro-in vivo extrapolation seems to require using the elementary rate constants rather than the Michaelis-Menten steady-state parameters.

The elementary mass action rate constants of P-gp transport for a confluent monolayer of MDCKII-hMDR1 cells.

The human multi-drug resistance membrane transporter, P-glycoprotein, or P-gp, has been extensively studied due to its importance to human health and disease. Thus far, the kinetic analysis of P-gp transport has been limited to steady-state Michaelis-Menten approaches or to compartmental models, neither of which can prove molecular mechanisms. Determination of the elementary kinetic rate constants of transport will be essential to understanding how P-gp works. The experimental system we use is a confluent monolayer of MDCKII-hMDR1 cells that overexpress P-gp. It is a physiologically relevant model system, and transport is measured without biochemical manipulations of P-gp. The Michaelis-Menten mass action reaction is used to model P-gp transport. Without imposing the steady-state assumptions, this reaction depends upon several parameters that must be simultaneously fitted. An exhaustive fitting of transport data to find all possible parameter vectors that best fit the data was accomplished with a reasonable computation time using a hierarchical algorithm. For three P-gp substrates (amprenavir, loperamide, and quinidine), we have successfully fitted the elementary rate constants, i.e., drug association to P-gp from the apical membrane inner monolayer, drug dissociation back into the apical membrane inner monolayer, and drug efflux from P-gp into the apical chamber, as well as the density of efflux active P-gp. All three drugs had overlapping ranges for the efflux active P-gp, which was a benchmark for the validity of the fitting process. One novel finding was that the association to P-gp appears to be rate-limited solely by drug lateral diffusion within the inner monolayer of the plasma membrane for all three drugs. This would be expected if P-gp structure were open to the lipids of the apical membrane inner monolayer, as has been suggested by recent structural studies. The fitted kinetic parameters show how P-gp efflux of a wide range of xenobiotics has been maximized.

Exact kinetic analysis of passive transport across a polarized confluent MDCK cell monolayer modeled as a single barrier.

Knowledge of the passive permeability coefficient for new drugs is useful for estimating the fraction absorbed across the gastrointestinal tract. The commonly used approximate formula for the passive permeability coefficient is based on the initial rate of permeation across cell monolayers, requires measurement during the linear phase of permeation, and is not applicable when there is significant back flux of compound or mass balance problem. To develop a rigorous equation that can be used at any time point, i.e., that is valid outside of the linear phase, the mass action equations were integrated for a standard single barrier model of passive permeability. The simple analytical solution found also allows correction for both loss of drug (e.g., due to binding and/or hydrolysis) and sampling volume loss for multiple time point experiments. To test this equation, we measured the passive permeation of three well characterized drugs (amprenavir, quinidine, and loperamide) across confluent monolayers of MDCKII-hMDR1 cells. The potent P-glycoprotein inhibitor GF120918 was used to inhibit P-glycoprotein activity, so only passive permeability was determined. Dramatically different time-dependent behavior was observed for the three compounds, with loperamide showing significant loss of compound, and loperamide and quinidine causing plasma membrane modifications over time. The simple and exact equation for the permeability coefficient developed here works from start of transport to equilibrium, being valid when the commonly used approximate equation may not be. Thus, the exact equation is safer to use in any context, even for single time point estimates in high-throughput permeability assays.

Kinetically differentiating influenza hemagglutinin fusion and hemifusion machines.

Membrane fusion mediated by influenza virus hemagglutinin (HA) yields different phenotypes depending on the surface density of activated HAs. A key question is whether different phenotypes arise from different fusion machines or whether different numbers of identical fusion machines yield different probabilistic outcomes. If fusion were simply a less probable event than hemifusion, requiring a larger number of identical fusion machines to occur first, then two predictions can be made. First, fusion should have a shorter average delay time than hemifusion, since there are more machines. Second, fusion should have a longer execution time of lipid mixing after it begins than hemifusion, since the full event cannot be faster than the partial event. Using a new automated video microscopy technique, we simultaneously monitored many HA-expressing cells fusing with erythrocytes and identified individual cell pairs with either full or only partial redistribution of fluorescent lipids. The full lipid mixing phenotype also showed contents mixing, i.e., fusion. Kinetic screening of the digitized fluorescence data showed that the execution of lipid mixing after the onset is faster for fusion than hemifusion. We found no correlation between the delay times before the onset of lipid mixing and the final fusion phenotype. We also found that the execution time for fusion was faster than that for hemifusion. Thus, we provide the first experimental evidence for fusion and hemifusion arising from different machines.

Architecture of the influenza hemagglutinin membrane fusion site.

The mechanism of influenza hemagglutinin (HA) mediated membrane fusion has been intensively studied for over 20 years after the bromelain-released ectodomain of HA at neutral pH was first crystallized. Nearly 10 years ago, the low-pH-induced "spring coiled" conformational change of HA was predicted from peptide chemistry and confirmed by crystallography. Other work has yielded a wealth of knowledge on the observed changes in HA fusion/hemifusion phenotypes as a function of site-specific mutations of HA, or added amphipathic molecules or particular IgGs. It is becoming clear that the conformational changes predicted by the crystallography are necessary to cause fusion and that interfering with these changes can block fusion or reduce it to hemifusion. What is not known is how the conformational changes cause fusion. In particular, while it is generally agreed that fusion requires an aggregate of HAs, how the aggregate may act to transduce the energy of the HA conformational changes to creating the initial fusion defect is not known. We have used a comprehensive mass action kinetic model of HA-mediated fusion to carry out a "meta-analysis" of several key data sets, using HA-expressing cells and using virions. The consensus result of these detailed kinetic studies was that the fusion site of influenza hemagglutinin (HA) is an aggregate with at least eight HAs. The high-energy conformational change of only two of these HAs within the aggregate permits the formation of the first fusion pore. This "8 and 2" result was required to best fit all the data. We review these studies and how this kinetic result can guide and constrain HA fusion models. The kinetic analysis suggests that the sequence of fusion intermediates starts with protein control and ends with lipid control, which makes sense. While curvature intermediates, e.g. the lipid stalk, are almost certainly within the fusion sequence, the "8 and 2" result does not suggest that they are the first step after HA aggregation. The stabilized hydrophobic defect model we have proposed as a precursor to the lipid stalk can form and is consistent with the "8 and 2" result.

Measuring pKa of activation and pKi of inactivation for influenza hemagglutinin from kinetics of membrane fusion of virions and of HA expressing cells.

The data for the pH dependence of lipid mixing between influenza virus (A/PR/8/34 strain) and fluorescently labeled liposomes containing gangliosides has been analyzed using a comprehensive mass action kinetic model for hemaglutinin (HA)-mediated fusion. Quantitative results obtained about the architecture of HA-mediated membrane fusion site from this analysis are in agreement with the previously reported results from analyses of data for HA-expressing cells fusing with various target membranes. Of the eight or more HAs forming a fusogenic aggregate, only two have to undergo the "essential" conformational change needed to initiate fusion. The mass action kinetic model has been extended to allow the analysis of the pKa for HA activation and pKi for HA inactivation. Inactivation and activation of HA following protonation were investigated for various experimental systems involving different strains of HA (A/PR/8/34, X:31, A/Japan). We find that the pKa for the final protonation site on each monomer of the trimer molecule is 5.6 to 5.7, irrespective of the strain. We also find that the pKi for the PR/8 strain is 4.8 to 4.9. The inactivation rate constants for HA, measured from experiments done with PR/8 virions fusing with liposomes and X:31 HA-expressing cells fusing with red blood cells, were both found to be of the order of 10(-4) s(-1). This number appears to be the minimal rate for HA's essential conformational change at low HA surface density. At high HA surface densities, we find evidence for cooperativity in the conformational change, as suggested by other studies.