Williams Medium E (WME) without phenol-red and without L-glutamine and stabilized L-glutamine were obtained from Pan-Biotech-GmbH (Aidenbach, Germany). Penicillin/Streptomycin and ITS-X were obtained from Invitrogen (Karlsruhe, Germany). Bovine serum albumin (BSA) and dimethyl sulfoxide (DMSO) were purchased from Sigma-Aldrich Chemicals (Taufkirchen, Germany). Dexa Inject was obtained from Jenapharm (Jena, Germany). AS, its metabolites and deuterated standards were purchased from Toronto Research Chemicals Inc. (North York, Canada). PBS was obtained from Invitrogen (Karlsruhe, Germany) and Complete Mini, EDTA-free from Roche Diagnostics (Mannheim, Germany). NaPP, sucrose and LiChrosolv were purchased from Merck (Darmstadt, Germany); acetonitrile from Roth (Karlsruhe, Germany), formic acid from Fluka, (Germany), UGT1A3 monoclonal mouse antibody from Abcam (Cambridge, England). Trypsin was purchased from Promega (Mannheim, Germany). Synthetic peptides were purchased from Sigma-Genosys (Haverhill, UK).
Isolation and cultivation of primary human hepatocytes
Tissue samples from human liver resections were obtained from patients undergoing partial hepatectomy. Experimental procedures were performed according to the guidelines of the charitable state-controlled foundation HTCR (Human Tissue and Cell Research) Regensburg, Germany, and the institutional guidelines for liver resections of tumor patients with primary or secondary liver tumors, Technical University Munich, MRI, Munich, Germany. The use of human hepatocytes for research purposes was approved by the local ethics committees of the Ludwig-Maximilians-University of Munich  and the Charité, Humboldt University Berlin , Germany, and written informed consent was obtained from all patients. Hepatocytes were cultured on collagen gel precoated 6-well plates at a density of 1.5·106 cells/well. Cells were allowed to attach to the collagen layer. After transport, culture media was disposed and attached cells were cultured 24 h at 37°C in a humidified chamber with 95%/5% air/CO2 in serum-free medium WME, supplemented with albumin (0.1% (v/v)), penicillin/streptomycin (100 U/ml), stabilized L-glutamine (2 mM), dexamethasone dihydrogenphosphate (0.025% (v/v)) and ITS-X (5 mg insulin, 3.35 μg natrium-selenit, 2.75 mg transferrin and 1 mg ethanolamine), further named SFM.
Incubation with AS was started by disposing the culture media and cultivation of the attached cells at 37°C in a humidified chamber with 95%/5% air/CO2 in 2 ml SFM, supplemented with 10 μM AS, 0.1% (v/v) BSA and 0.1% DMSO. At specified time-points, three wells were further treated for the preparation of samples for the measurement of extracellular and intracellular metabolites, respectively. SFM media was collected and 50 μL formic acid and deuterated internal standard was added for the further measurement of extracellular metabolites. Cells were harvested in pre-cooled albumin-free SFM, disrupted by freeze/thaw and ultra-sonification and centrifuged. The supernatant was used for the determination of intracellular metabolites.
For the preparation of samples for the protein measurements, culture medium was disposed and cells were harvested in pre-cooled PBS, supplemented with Complete Mini EDTA-free (1 Tablet/10 ml Buffer). Cell suspensions were centrifuged 5 min (500 g) at 4°C and cell pellets were resuspended in 150 μL NaPP-buffer (0.1 M, pH 7.4), containing 250 mM sucrose and Complete Mini EDTA-free (1 Tablet/10 ml Buffer). Cells were disrupted by ultra-sonification and lyophilized for the analysis of total protein concentration, CYP3A4 and UGT1A3 content.
For cell number determination, cells from two wells were fixed with methanol-acetic acid fixative solution (10 min at 37°C and 4°C) and afterwards nuclei were stained for 15 min with Meyers Hämalaun (Sigma-Aldrich Chemie GmbH, Germany), rinsed with water and air-dried. Stained nuclei were counted in digital images (10 per well) at 40-fold Magnification (ImageJ Image Processing and Analysis Program).
Quantification of atorvastatin and its metabolites
AS and ASL, and their para- (ASpOH, ASLpOH) and ortho-hydroxy-metabolites (ASoOH, ASLoOH), were determined by LC-MS-MS analysis using the respective deuterium labeled analogues as internal standards, essentially as described . HPLC separation was performed at 30°C on a XBridge Shield RP18 column (2.1 × 50 mm, 3.5 μm, Waters) using (A) 1 mM formic acid and (B) acetonitrile as mobile phases at a flow rate of 0.4 ml/min. Gradients were programmed as follows: 63% A for 4 min; linear decrease of A to 60% within 9 min; linear decrease of A to 55% within 2.5 min; 55% A for 1 min; increase of A to 63% in 0.2 min. Equilibration time of the column was 20 min. MS-MS analysis was performed on an Esquire HCT ultra ion trap mass spectrometer (Bruker Daltonics, Bremen, Germany) coupled to an HPLC 1100-System (Agilent, Waldbronn, Germany) consisting of binary pump G1312A, degasser G1379A, well-plate sampler G1367A and column thermostat G1330B. The ionization mode was electrospray (ESI), polarity positive, mass range mode ultrascan, and nitrogen was used as a drying and nebulizer gas. The following parameters were applied: nebulizer 45 psi, dry gas 10 l/min, dry temperature 300°C, capillary 4100 V, scan range 200 - 600 m/z.
Precursor and product ions (m/z) of analytes and internal standards, respectively, were ATV (559 and 440.2; 466.2), [2H5]ATV (564 and 445.2; 471.2), ATV-L (541.2 and 448.2), [2H5]ATV-L (546.2 and 453.2), p-OH-ATV (575 and 440.2; 466.2), [2H5]p-OH-ATV (580 and 445.2; 471.2), p-OH-ATV-L (557 and 448.4), [2H5]p-OH-ATV-L (562 and 448.4), o-OH-ATV (575 and 466.4), [2H5]o-OH-ATV (580 and 471.2), o-OH-ATV-L (557 and 448.4), [2H5]o-OH-ATV-L (562 and 448.4). Sample quantification was possible in a range from 0.5 to 500 pmol.
CYP3A4 and UGT1A3 protein quantification
Protein quantification of CYP3A4 and UGT1A3 in human liver microsomes and relative protein quantification of UGT1A3 in lyophilized samples of primary hepatocytes was performed by immunoblotting as described previously [38, 39].
Cell lysates for absolute quantification analysis of CYP3A4 were prepared from lyophilized human primary hepatocytes by sonification in the presence of glass beads in buffer containing Complete Mini-Protease Inhibitor Cocktail, and following homogenization. In the CYP3A4 quantification assay, three synthetic isotopically labeled peptides (13C/15N amino acid) were used as internal standard for calibration. These isotope labeled standard peptides represented sequence analogues to proteotypic peptides of CYP3A4, which arise from tryptic digestion. After acetone precipitation and resolving of the proteins in 8 M Urea, a definite amount of internal standard peptides was added. The sample mixture was reduced with 5 mM DTT and alkylated with 15 mM iodacetamide in 50 mM ammonium bicarbonate. Subsequently samples were digested with trypsin at 42°C for 4 h (enzyme/substrate ratio of 1:10). Efficiency of tryptic digestion was checked by SDS-PAGE followed by silver staining. The resulting peptides were purified using C18 OMIX® Tips (Varian, Darmstadt, Germany) according to manufacturer's suggested protocol and separated on a nanoliter-flow Ultimate HPLC system (Dionex, Idstein, Germany). After injection (15 μl), peptides were trapped and desalted on a precolumn (0.3 mm I.D. × 5 mm PepMapTM, Dionex) at a flow rate of 30 μl/min in 0.1% TFA for 6 min. Peptides were transferred to the separation column (75 μm I.D. × 250 mm PepMapTM column, Dionex) and separated in a linear gradient of mobile phase (A: 0.1% formic acid, B: 84% acetonitrile/0.1% formic acid) from 5% B to 35% B over a period of 35 min with a flow of 290 nl/min. The column effluent was continuously directed into the NanoSpray II source of a 4000QTrap mass spectrometer (Applied Biosystems, Foster City, CA, USA). The MS was set up to run a multiple reaction monitoring experiment essentially, as described previously , including two to three parent-to-product ion transitions for each internal standard peptide as well as the corresponding transitions of native peptide of CYP3A4. The instrument settings were as follows: ion spray voltage, 3-4 kV; interface heater, 150°C; declustering potential, 50 V; collision energy, peptide specific; entrance potential, 10 V; collision cell exit potential, 10 V. MS data were processed by integrating the appropriate peak areas from extracted ion chromatograms by MultiQuantTM Software (Applied Biosystems). The absolute amount of CYP3A4 protein was calculated from the peak area ratio "internal standard peptide/native peptide". Total protein content of the samples were determined by amino acid analysis (AAA) on a Waters 2695 HPLC system using the AccQ•Tag derivatization method (Waters, Eschborn, Germany), according to manufacturer's instructions.
Identification of metabolic network structure
Numerous metabolic and physicochemical aspects about AS had to be considered in the initial model building. AS exists in two forms, a very lipophilic lactone (ASL) and a comparably hydrophilic hydroxyl-acid (AS). AS is converted enzymatically via an instable intermediate product into ASL, mediated by different UGT isoenzymes [41, 42]. Recent investigations by ourselves and others have shown that the most important contributor to UGT-driven lactonization is UGT1A3, whereas UGT1A1 plays an insignificant role [38, 42]. AS acids and lactones are inter-converted chemically into each other . However, studies have indicated, that the chemical lactonization of AS to ASL can be neglected at physiological pH of 7.4 . Recent studies highlight, that different PON enzymes might also be possible contributors to the lactone hydrolysis and that PON1 is present in liver [44–48].
Both AS and ASL are hydroxylated in human hepatocytes leading to para- and ortho-hydroxy-metabolites, ASpOH, ASoOH, ASLpOH and ASLoOH [49, 50], mainly catalyzed by CYP3A4 . Recent studies have reported, that CYP2C8 and CYP3A5 also hydroxylate AS to a minor extent [50, 52].
Furthermore, AS is transported into the cell via organic anion transport polypeptides (OATP), and recent studies on recombinant systems showed, that OATP1B1 and OATP2B1 contribute to the AS import [53, 54], which are both expressed in the human liver [55, 56]
OATP1B3 is supposed to be also a main contributor to drug transport , since it shows high gene expression levels in liver , but its importance for AS has not been investigated kinetically so far.
OATP transporters have been reported to be bidirectional facilitated diffusion transporters, independent from ATP and Na+, K+ and H+, but with a possible involvement of reduced glutathione [58, 59]. However, previous investigations on transport mechanisms on rat hepatocytes, showed, that the intracellular concentrations of pitavastatin and other compounds are much higher than outside the cell [33, 34, 60]. Facilitated or passive diffusion do not allow a greater intracellular than extracellular concentration of the parent drug of interest, when the source is the initial extracellular concentration, because it is a concentration-gradient dependent mechanism. Therefore, the import mechanism should be rather considered as active mediated transport, which is not concentration-gradient dependent, rather than as the proposed facilitated diffusion process.
As shown with the recombinantly expressed transporters mentioned above , transport of the acidic metabolites, ASpOH and ASoOH, by OATP1B1 was similar to that of AS, and transport of the corresponding lactones was also mediated by this transporter, although at somewhat lower rates. We therefore assumed that the same OATP transporters are responsible for the import of AS and its hydroxylated and lactone metabolites into hepatocytes.
AS and its hydroxylated metabolites, ASpOH and ASoOH, are actively exported out of the hepatocytes into the bile by the ATP-dependent MDR1 transporter [61, 62]. In addition, acidic and lactone form of AS showed inhibitory effects in transport studies of substrates of MDR1 and MRP2 [63–65], pointing to the competitive transport mechanism of these substrates at this proteins. Further, the transporters MRP1, MRP3 and MRP6 are also reported to be responsible for the transport of organic compounds including AS from inside the hepatocytes into the plasma [56, 66].
Passive diffusion might play also an important role in the transfer of AS, ASL and the corresponding metabolites, ASpOH and ASoOH, ASLpOH and ASLoOH, respectively. Since the acidic forms of AS are rather hydrophilic and the lactone forms of AS are rather lipophilic, it can be assumed that passive diffusion plays a more important role for the lactone forms, and the transporter mediated active transport plays a more important role for the acidic forms, as reported earlier for statins .
Finally, lipophilic drugs have a high affinity to bind non-specifically to proteins, and previous studies concentrated on the modeling of drug binding in the intracellular and the extracellular space as well as on the surface of the cells [60, 68, 69].
The mathematical model can be described by the system of non-linear ordinary differential equations
where the change in extracellular, intracellular or unspecific bound metabolite concentration c
in the extra - or intracellular compartment with V
is effected by the conversion or production of contributing chemical or enzymatic reactions or by transport steps r
, respectively. The extracellular volume, , equals to the volume of the media used. The intracellular volume, , equals to the total volume of all cells used, and is determined by multiplying the cell number by the volume of a single hepatocyte, estimated to be 14.1 pL by the approximation of a spherical shape with a diameter of 30 μm .
Appropriate reaction kinetics r
are modeled for the CYP3A4 hydroxylation, the UGT1A3 lactonization, the chemical and enzymatic lactone hydrolysis and intracellular unspecific binding to macromolecules.
Previous studies determined substrate inhibition kinetics of the CYP3A4 mediated hydroxylation of AS on human microsomes . However, inhibition effects contribute severely only at a concentration higher than 100 μM. Furthermore, our model approach considers the competitive nature of alternative substrates, by integrating the CYP3A4 hydroxylation of AS and ASL as reaction kinetics describing the competitive conversion of alternative substrates to alternative products, illustrated for the hydroxylation of AS to ASpOH
(see Additional file 1 - Derivation of Atorvastatin kinetics at CYP3A4).
The lactonization of AS to ASL is mediated by UGT1A3 enzymes and the reaction is formulated as substrate inhibition kinetics .
The lactone metabolites are either hydrolyzed chemically to the respective acid metabolites  inside (c) or outside (m) the cell, or enzymatically by the contribution of PON enzymes inside the cell. Both reactions are described as first order kinetics
Unspecific binding of intracellular metabolites to macromolecules is formulated as
with the dissociation coefficient k
and the intracellular fraction unbound 
which describes the ratio between the intracellular free concentration to the sum of intracellular free and bound concentration, and , in equilibrium (index eq) (see Additional file 2 - Derivation of kinetics of unspecific protein binding). However, the intracellular free and bound concentrations in equilibrium are not measurable; therefore, the fraction unbound fu
is set as a parameter to be estimated in the parameter optimization procedure.
Transport steps include active import and export of the metabolites as well as passive diffusion steps. Both active import by OATP1B1 or OATP2B1 and export of AS are described as Michaelis-Menten-kinetics [53, 54]
whereas the active transport kinetics of the other metabolites are assumed to be of first-order .
Besides the active transport, metabolites undergo passive diffusion through the double-layer lipid-membrane. Passive diffusion, described as
is driven by the concentration difference between outside and inside the cell, , over the lipid-membrane with thickness d, through all cells with the total surface area A
, and controlled by the diffusion coefficient D
and is comprised as the permeability coefficient P
Optimization procedure for estimation of model parameters
The optimization procedure is based on evolutionary strategies which are implemented with JavaEva (WSI Computer Science Department, Center for Bioinformatics, University of Tübingen, Germany) and a MVA (main vector adaptation) mutation operator . The optimization procedure estimates the parameters in equations (2) to (9) based on the optimization criterion
where the deviation of calculated and measured concentrations divided by the measurement standard deviation s
, squared and summed over all metabolites J and all time points N, has to reach a minimum. Additional optimization constraints are fu
, because the lactones have a higher lipophilicity than the acids and the metabolites are supposed to be more hydrophilic than the corresponding parent lactone or acid drug.
The integration of the differential equations (1) using the reaction kinetics in equations (2) to (9) was performed by the differential algebraic equation solver LIMEX (Konrad-Zuse-Zentrum für Informationstechnik, Berlin) .
Relative abundance approach for prediction of r
For pharmacokinetic predictions taking inter-individual variability of CYP3A4 and UGT1A3 expression levels into account, maximal rate parameters are predicted via a relative abundance approach, which is based on the assumption that the maximal rate of the reaction is proportional to the enzyme concentration:
The maximal velocities of the respective enzyme e, here CYP3A4 or UGT1A3, in the conversion to the product P
in the liver of interest li is estimated from the respective maximal rate and the enzyme concentration in the reference liver and the enzyme concentration in the liver of interest li.
The mathematical model of AS metabolism was coded in FORTRAN language and linked to the numerical integrator LIMEX, also written in FORTRAN. After compilation to the executable program, optimization was started by the call of JavaEva. The mathematical model is supplemented as SBML-file for review purpose.