Fitting Transporter Activities to Cellular Drug Concentrations and Fluxes: Why the Bumblebee Can Fly
Authors: Pedro Mendes, Stephen G. Oliver, Douglas B. Kell
Journal: Trends in Pharmacological Sciences (2015)

There has been recent debate as to the relative extents to which cellular transmembrane drug transports occur through any phospholipid bilayer region or is transporter-mediated only. Much recent evidence suggests (perhaps surprisingly) that phospholipid bilayer diffusion is negligible. A recent article in this journal suggested that the expression profile and kinetics of known transporters might not be adequate to explain the most active drug fluxes (of verapamil and propranolol) in Caco-2 cells via transporters only. We show with our own simulations that this is not in fact the case, especially when evolutionary selection is taken into account, and that the Haldane relation accounts straightforwardly for directional differences, even for equilibrative transporters. Typical protein transporters alone can easily account for measured drug fluxes in Caco-2 cells. A recent paper in this journal argued that reported expression levels, kcat and Km for drug transporters could be used to estimate the likelihood that drug fluxes through Caco-2 cells could be accounted for solely by protein transporters. It was in fact concluded that if five such transporters contributed 'randomly' they could account for the flux of the most permeable drug tested (verapamil) 35% of the time. However, the values of permeability cited for verapamil were unusually high; this and other drugs have much lower permeabilities. Even for the claimed permeabilities, we found that a single 'random' transporter could account for the flux 42% of the time, and that two transporters can achieve 10 · 10−6 cm·s−1 90% of the time. Parameter optimisation methods show that even a single transporter can account for Caco-2 drug uptake of the most permeable drug. Overall, the proposal that 'phospholipid bilayer diffusion (of drugs) is negligible' is not disproved by the calculations of 'likely' transporter-based fluxes. A recent paper in this journal argued that reported expression levels, kcat and Km for drug transporters could be used to estimate the likelihood that drug fluxes through Caco-2 cells could be accounted for solely by protein transporters. It was in fact concluded that if five such transporters contributed 'randomly' they could account for the flux of the most permeable drug tested (verapamil) 35% of the time. However, the values of permeability cited for verapamil were unusually high; this and other drugs have much lower permeabilities. Even for the claimed permeabilities, we found that a single 'random' transporter could account for the flux 42% of the time, and that two transporters can achieve 10 · 10−6 cm·s−1 90% of the time. Parameter optimisation methods show that even a single transporter can account for Caco-2 drug uptake of the most permeable drug. Overall, the proposal that 'phospholipid bilayer diffusion (of drugs) is negligible' is not disproved by the calculations of 'likely' transporter-based fluxes. For cases in which a drug must interact with one or more intracellular targets, and for all oral drugs, it is necessary for drugs to cross at least one biomembrane. There is an increasing recognition that to cross intact biological membranes drugs must or do hitchhike on transporters that are normally involved with intermediary metabolism (e.g. [1Dobson P.D. Kell D.B. Carrier-mediated cellular uptake of pharmaceutical drugs: an exception or the rule?.Nat. Rev. Drug Discov. 2008; 7: 205-220Crossref PubMed Scopus (365) Google Scholar, 2Dobson P. et al.Implications of the dominant role of cellular transporters in drug uptake.Curr. Top. Med. 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Finding novel pharmaceuticals in the systems biology era using multiple effective drug targets, phenotypic screening, and knowledge of transporters: where drug discovery went wrong and how to fix it.FEBS J. 2013; 280: 5957-5980Crossref PubMed Scopus (83) Google Scholar, 8Kell D.B. Goodacre R. Metabolomics and systems pharmacology: why and how to model the human metabolic network for drug discovery.Drug Discov. Today. 2014; 19: 171-182Crossref PubMed Scopus (118) Google Scholar, 9Kell D.B. Oliver S.G. How drugs get into cells: tested and testable predictions to help discriminate between transporter-mediated uptake and lipoidal bilayer diffusion.Front. Pharmacol. 2014; 5: 231Crossref PubMed Google Scholar, 10Kell D.B. What would be the observable consequences if phospholipid bilayer diffusion of drugs into cells is negligible?.Trends Pharmacol. Sci. 2015; 36: 15-21Abstract Full Text Full Text PDF PubMed Scopus (37) Google Scholar, 11Lanthaler K. et al.Genome-wide assessment of the carriers involved in the cellular uptake of drugs: a model system in yeast.BMC Biol. 2011; 9: 70Crossref PubMed Scopus (51) Google Scholar, 12Nigam S.K. What do drug transporters really do?.Nat. Rev. Drug Discov. 2015; 14: 29-44Crossref PubMed Scopus (347) Google Scholar]). It is therefore of interest to understand how the use of specific influx and efflux transporters translates into particular transmembrane fluxes and intracellular concentrations (and hence the biological effects of drugs and other solutes). A recent example [13Winter G.E. et al.The solute carrier SLC35F2 enables YM155-mediated DNA damage toxicity.Nat. Chem. Biol. 2014; 10: 768-773Crossref PubMed Scopus (122) Google Scholar] brings the issue into sharp focus, where removing (genetically) just a single transporter decreased the toxicity (and presumably accumulation) of the drug YM155 (sepantronium bromide) by several hundred-fold. The implication of such data is that any 'background' rate involving phospholipid bilayer diffusion must be rather less than 1%, or (as we have put it elsewhere [9Kell D.B. Oliver S.G. How drugs get into cells: tested and testable predictions to help discriminate between transporter-mediated uptake and lipoidal bilayer diffusion.Front. Pharmacol. 2014; 5: 231Crossref PubMed Google Scholar, 10Kell D.B. What would be the observable consequences if phospholipid bilayer diffusion of drugs into cells is negligible?.Trends Pharmacol. Sci. 2015; 36: 15-21Abstract Full Text Full Text PDF PubMed Scopus (37) Google Scholar]) 'phospholipid bilayer diffusion is negligible'. Another recent example (see Figure 2 in ref [14Han T.K. et al.Four cation-selective transporters contribute to apical uptake and accumulation of metformin in Caco-2 cell monolayers.J. Pharmacol. Exp. Ther. 2015; 352: 519-528Crossref PubMed Scopus (79) Google Scholar]) shows that metformin uptake can be accounted for entirely by four transporters. Indeed, this essential lack of permeability in the absence of suitable transporters readily accounts for the failure of drugs to penetrate to the sites where they are required. Anti-tuberculosis drugs provide another important and (for patients) damaging example [15Kjellsson M.C. et al.Pharmacokinetic evaluation of the penetration of antituberculosis agents in rabbit pulmonary lesions.Antimicrob. Agents Chemother. 2012; 56: 446-457Crossref PubMed Scopus (138) Google Scholar, 16Dartois V. The path of anti-tuberculosis drugs: from blood to lesions to mycobacterial cells.Nat. Rev. Microbiol. 2014; 12: 159-167Crossref PubMed Scopus (265) Google Scholar]. The nonlinear nature of many biochemical kinetics, and the complex behaviour of even simple biochemical pathways, means that it is hard to 'guess' what might happen without seeking to model it first (e.g. [17Mendes P. Kell D.B. Non-linear optimization of biochemical pathways: applications to metabolic engineering and parameter estimation.Bioinformatics. 1998; 14: 869-883Crossref PubMed Scopus (546) Google Scholar, 18Kell D.B. Metabolomics, modelling and machine learning in systems biology: towards an understanding of the languages of cells. The 2005 Theodor Bücher lecture.FEBS J. 2006; 273: 873-894Crossref PubMed Scopus (137) Google Scholar, 19Kell D.B. Systems biology, metabolic modelling and metabolomics in drug discovery and development.Drug Discov. Today. 2006; 11: 1085-1092Crossref PubMed Scopus (232) Google Scholar]). Thus, a recent article in this journal [20Matsson P. et al.Quantifying the impact of transporters on cellular drug permeability.Trends Pharmacol. Sci. 2015; 36: 255-262Abstract Full Text Full Text PDF PubMed Scopus (0) Google Scholar] (and its subsequent supplementary iformation [21Matsson P. et al.Supplementary Information: addendum to 'Quantifying the impact of transporters on cellular drug permeability'.Trends Pharmacol. Sci. 2015; 36https://doi.org/10.1016/j.tips.2015.02.009Abstract Full Text Full Text PDF Scopus (28) Google Scholar]) sought to carry out just such a modelling study, based on a series of stated assumptions. The authors [20Matsson P. et al.Quantifying the impact of transporters on cellular drug permeability.Trends Pharmacol. Sci. 2015; 36: 255-262Abstract Full Text Full Text PDF PubMed Scopus (0) Google Scholar] also drew a major conclusion that (we consider) was at some variance with the data presented. The two main purposes of the present paper are (i) to go through their data and main argument, and, (ii) because natural evolution has at least one selection step, to study what happens when instead of making assumptions solely about forward modelling, one simply fits the observables to appropriate models and their parameters (Figure 1). Despite our clear previous explanation of this term [9Kell D.B. Oliver S.G. How drugs get into cells: tested and testable predictions to help discriminate between transporter-mediated uptake and lipoidal bilayer diffusion.Front. Pharmacol. 2014; 5: 231Crossref PubMed Google Scholar], Matsson and colleagues [20Matsson P. et al.Quantifying the impact of transporters on cellular drug permeability.Trends Pharmacol. Sci. 2015; 36: 255-262Abstract Full Text Full Text PDF PubMed Scopus (0) Google Scholar] (and many other workers) continue to use the word 'passive' to mean two entirely different things (Figure 2). The first usage involves a thermodynamic statement only, and is best referred to as 'equilibrative' ('passive' transport is thermodynamically equilibrative; the 'active' version requires an input of free energy and is then concentrative). We would stress that, as such, the word 'passive' has nothing of itself to say about a mechanism of how a drug crosses a membrane. However, 'passive' transport is also far too often taken to mean 'transport via bilayer lipoidal' diffusion, a perfectly acceptable intent provided this is made explicit, but one that is then best served by calling it 'bilayer lipoidal diffusion' directly. Carrier-mediated diffusion may be active or passive in the thermodynamic sense (and, for those purposes, is best referred to as either concentrative or equilibrative). A very well-established term for the latter (carrier-mediated equilibrative transport) is 'facilitated diffusion', while the term 'active transport' is perfectly adequate for concentrative transporter-mediated solute influx (or efflux). All of this therefore entirely avoids the ambiguity common with the use of the term 'passive'. We reiterate strongly that much trouble would be avoided if the word 'passive' were dropped completely from all debates about transmembrane drug uptake mechanisms. Conflating the two by showing its truth for one meaning (thermodynamic) but then claiming that this thereby shows the other meaning of bilayer lipoidal is at best unscientific. (Zheng and colleagues [22Zheng Y. et al.pH dependent but not P-gp dependent bidirectional transport study of S-propranolol: the importance of passive diffusion.Pharm. Res. 2015; 32: 2516-2526Crossref PubMed Scopus (12) Google Scholar] illustrate this with an example in which bilayer transport was not even measured directly as a dependent variable, and for a drug whose uptake is stereoselective and hence necessarily transporter-mediated.) Matsson and colleagues [20Matsson P. et al.Quantifying the impact of transporters on cellular drug permeability.Trends Pharmacol. Sci. 2015; 36: 255-262Abstract Full Text Full Text PDF PubMed Scopus (0) Google Scholar] proposed, as a model, the well-known Caco-2 cell system, and sought to estimate how 'likely' it was, given the known expression profiles and kcat values of a subset of transporters, whether or not they could reasonably be expected to account for the fluxes observed in the case of two drugs (propranolol and verapamil) with unusually high permeabilities. At first glance, this is an interesting idea. Note that Caco-2 cells are thought (from transcriptomics or proteomics measurements) to express several hundred (e.g. [23Sun D. et al.Comparison of human duodenum and Caco-2 gene expression profiles for 12,000 gene sequences tags and correlation with permeability of 26 drugs.Pharm. Res. 2002; 19: 1400-1416Crossref PubMed Scopus (346) Google Scholar, 24Anderle P. et al.Intestinal membrane transport of drugs and nutrients: genomics of membrane transporters using expression microarrays.Eur. J. Pharm. 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Thus, some of the authors of [20Matsson P. et al.Quantifying the impact of transporters on cellular drug permeability.Trends Pharmacol. Sci. 2015; 36: 255-262Abstract Full Text Full Text PDF PubMed Scopus (0) Google Scholar] already published that there is an enormous expression level of an 'HPT1' human peptide transporter [26Hayeshi R. et al.Comparison of drug transporter gene expression and functionality in Caco-2 cells from 10 different laboratories.Eur. J. Pharm. Sci. 2008; 35: 383-396Crossref PubMed Scopus (204) Google Scholar, 27Ahlin G. et al.Endogenous gene and protein expression of drug-transporting proteins in cell lines routinely used in drug discovery programs.Drug Metab. Dispos. 2009; 37: 2275-2283Crossref PubMed Scopus (99) Google Scholar] (indeed it is the highest expressed transporter in Caco-2 cells in each of the 10 laboratories participating in [26Hayeshi R. et al.Comparison of drug transporter gene expression and functionality in Caco-2 cells from 10 different laboratories.Eur. J. Pharm. Sci. 2008; 35: 383-396Crossref PubMed Scopus (204) Google Scholar]), but such a transporter seems to make no appearance at all in [20Matsson P. et al.Quantifying the impact of transporters on cellular drug permeability.Trends Pharmacol. Sci. 2015; 36: 255-262Abstract Full Text Full Text PDF PubMed Scopus (0) Google Scholar]. Thus, in the absence of any knowledge, nor of the inclusion of such highly expressed transporters, these estimates are always likely to be underestimates. We entirely appreciate the complexities of biological systems, and hence, the difficulty of reproducing the behaviour of even the well-established Caco-2 system. However, to give an indication of the variance observable within and between laboratories, Box 1 shows some of the data from precisely such a comparison [26Hayeshi R. et al.Comparison of drug transporter gene expression and functionality in Caco-2 cells from 10 different laboratories.Eur. J. Pharm. Sci. 2008; 35: 383-396Crossref PubMed Scopus (204) Google Scholar]. Obviously the variance between laboratories for the three drugs atenolol, metoprolol and talinolol is at least an order of magnitude (sometimes more), with their median values for A → B being ca 0.5, 45 and 1.34 · 10−6 cm·s−1.Box 1Inter-Laboratory Comparison of Caco-2 PermeabilitiesData are replotted from Table 4 of [26Hayeshi R. et al.Comparison of drug transporter gene expression and functionality in Caco-2 cells from 10 different laboratories.Eur. J. Pharm. Sci. 2008; 35: 383-396Crossref PubMed Scopus (204) Google Scholar] and illustrate that even within labs, and certainly between labs, there can be variations of an order of magnitude or more in Caco-2 permeability measurements. The three drugs shown (atenolol, metoprolol, talinolol) are encoded by shape, and the laboratories by the colour of the symbols. There were two separate 'batches' of Caco-2 cells tested (Figure I). Data are replotted from Table 4 of [26Hayeshi R. et al.Comparison of drug transporter gene expression and functionality in Caco-2 cells from 10 different laboratories.Eur. J. Pharm. Sci. 2008; 35: 383-396Crossref PubMed Scopus (204) Google Scholar] and illustrate that even within labs, and certainly between labs, there can be variations of an order of magnitude or more in Caco-2 permeability measurements. The three drugs shown (atenolol, metoprolol, talinolol) are encoded by shape, and the laboratories by the colour of the symbols. There were two separate 'batches' of Caco-2 cells tested (Figure I). Regarding the choice of drugs, Mattson and colleagues [20Matsson P. et al.Quantifying the impact of transporters on cellular drug permeability.Trends Pharmacol. Sci. 2015; 36: 255-262Abstract Full Text Full Text PDF PubMed Scopus (0) Google Scholar] state "Classical examples include propranolol and verapamil. These have permeability coefficients across Caco-2 intestinal epithelial cell monolayers (the most commonly used cellular barrier for permeability studies) in the range 200–1000 · 10−6 cm·s−1 [28Engman H. et al.Enantioselective transport and CYP3A4-mediated metabolism of R/S-verapamil in Caco-2 cell monolayers.Eur. J. Pharm. Sci. 2003; 19: 57-65Crossref PubMed Scopus (21) Google Scholar, 29Avdeef A. et al.Caco-2 permeability of weakly basic drugs predicted with the double-sink PAMPA pKa(flux) method.Eur. J. Pharm. Sci. 2005; 24: 333-349Crossref PubMed Scopus (181) Google Scholar]." Actually the rate published for R- or S-verapamil in [28Engman H. et al.Enantioselective transport and CYP3A4-mediated metabolism of R/S-verapamil in Caco-2 cell monolayers.Eur. J. Pharm. Sci. 2003; 19: 57-65Crossref PubMed Scopus (21) Google Scholar] was ∼100 · 10−6 cm·s−1, and even decreased as concentrations exceeded 100 μM, presumably because of substrate inhibition, with a similar value in [29Avdeef A. et al.Caco-2 permeability of weakly basic drugs predicted with the double-sink PAMPA pKa(flux) method.Eur. J. Pharm. Sci. 2005; 24: 333-349Crossref PubMed Scopus (181) Google Scholar]. Some of the authors of Matsson et al. [20Matsson P. et al.Quantifying the impact of transporters on cellular drug permeability.Trends Pharmacol. Sci. 2015; 36: 255-262Abstract Full Text Full Text PDF PubMed Scopus (0) Google Scholar] in their reference 19 [30Bergström C.A.S. et al.Absorption classification of oral drugs based on molecular surface properties.J. Med. 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Toxicol. 2005; 1: 175-185Crossref PubMed Scopus (363) Google Scholar] gave 50 · 10−6 cm·s−1, while that for propranolol in Figure 3 of [29Avdeef A. et al.Caco-2 permeability of weakly basic drugs predicted with the double-sink PAMPA pKa(flux) method.Eur. J. Pharm. Sci. 2005; 24: 333-349Crossref PubMed Scopus (181) Google Scholar] was ∼700 · 10−6 cm·s−1, but no matter. Corti and colleagues [34Corti G. et al.Development and evaluation of an in vitro method for prediction of human drug absorption - II. Demonstration of the method suitability.Eur. J. Pharm. Sci. 2006; 27: 354-362Crossref PubMed Scopus (82) Google Scholar] (their Table 2) give 41.9, 106 cm·s−1 for propranolol and 15.8 · 10−6 cm·s−1 for verapamil. This said, the 'observable' rates stated in Figure 3A(i) of [20Matsson P. et al.Quantifying the impact of transporters on cellular drug permeability.Trends Pharmacol. Sci. 2015; 36: 255-262Abstract Full Text Full Text PDF PubMed Scopus (0) Google Scholar] as 1310 · 10−6 cm−1 for verapamil and 230.10−6 cm−1 for propranolol come from Table 3 of a paper by Avdeef [29Avdeef A. et al.Caco-2 permeability of weakly basic drugs predicted with the double-sink PAMPA pKa(flux) method.Eur. J. Pharm. Sci. 2005; 24: 333-349Crossref PubMed Scopus (181) Google Scholar] (P. Matsson, personal communication), and are obviously at some variance with these other numbers. (They are based on a very rapid stirring – 700 rpm – that does not occur adjacent to natural epithelia.) 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