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Institute for Physics, University of Freiburg, Freiburg, Germany (K.B., J.T.); and Division of Tumor Biochemistry, German Cancer Research Center, Heidelberg, Germany (M.R., K.L., Da.K., Di.K.)
(Received March 4, 2007; accepted May 30, 2007)
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Abstract |
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Several factors affect vectorial transport of small molecules. First, unidirectional transport does not occur at a sufficient rate in the absence of the respective transport proteins in the basolateral and apical membranes, as evidenced by studies in hereditary mutants lacking certain transport proteins (Jansen et al., 2001
; Keppler et al., 2001; Schinkel and Jonker, 2003) or in cell lines stably transfected with cDNAs encoding transport proteins (Cui et al., 2001; Sasaki et al., 2002; Hagenbuch and Meier, 2004). Second, it is affected in the intact organism by blood flow, intravascular binding to proteins, and intracellular metabolism.
To build a mathematical model of vectorial transport, we used a well defined cellular system developed previously (Cui et al., 2001). Polarized cells grown on filter membrane supports were stably transfected with cDNAs encoding the human uptake transporter for organic anions, OATP1B3 (König et al., 2000), and the human apical conjugate export pump ABCC2, also known as multidrug resistance protein 2 (MRP2) (Büchler et al., 1996). Such double-transfected cells exhibit transporter-mediated substrate flux from the basolateral to the apical compartment and, for most compounds, very little intracellular metabolism (Cui et al., 2001; Keppler, 2005; Letschert et al., 2005). Bromosulfophthalein (BSP) is a substrate for both transport proteins, OATP1B3 (König et al., 2000) and ABCC2 (Cui et al., 2001). Moreover, BSP is an established test compound for studies of hepatobiliary elimination in humans and animals (Wolkoff, 1994). Mathematical modeling was performed in this focused cellular system to mediate the vectorial transport of BSP. The same modeling approach can be applied to other polarized cellular systems and to a variety of different substances, thus opening the perspective of quantitative and predictive modeling and the understanding of vectorial transport systems.
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Materials and Methods |
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; Fig. 1).
Immunofluorescence Microscopy. MDCKII cells were grown on ThinCert membrane inserts (diameter, 6 mm; pore size, 0.4 µm; pore density, 1 x 108/cm2; Greiner Bio-One, Frickenhausen, Germany; Letschert et al., 2005) for 3 days at confluence and induced with 10 mM sodium butyrate for 24 h to enhance the expression of recombinant proteins (Cui et al., 1999). Fixation and permeabilization were performed as described previously (Cui et al., 2001). OATP1B3 was detected by the antiserum SKT (König et al., 2000), ABCC2 was detected by the antiserum EAG (Cui et al., 1999), and canine Abcc4 was detected by the purified antiserum SNG (Rius et al., 2003). Nuclei were stained with propidium iodide. Confocal laser scanning microscopy was performed with an LSM 510 META apparatus (Carl Zeiss, Jena, Germany).
Transport Studies. [3H]BSP (0.5 TBq/mmol) was obtained from Hartmann Analytic (Braunschweig, Germany) (Cui et al., 2001). MDCKII cells were grown on ThinCert membrane inserts (diameter, 24 mm; pore size, 0.4 µm; pore density, 1 x 108/cm2; Greiner Bio-One) for 3 days at confluence and induced with 10 mM sodium butyrate for 24 h (Cui et al., 1999). The cells were washed in prewarmed (37°C) transport buffer (142 mM NaCl, 5 mM KCl, 1 mM KH2PO4, 1.2 mM MgSO4, 1.5 mM CaCl2, 5 mM glucose, and 12.5 mM HEPES, pH 7.3). The 3H-labeled substrate was dissolved in transport buffer and added to the basolateral compartment (1.5 ml) at the concentration indicated. After incubation at 37°C, radioactivity in the apical compartment (1.0 ml) was measured by sampling of aliquots from the apical compartment. Cells were washed twice with ice-cold transport buffer containing 0.5% bovine serum albumin and three times with ice-cold transport buffer. Intracellular radioactivity was determined after lyzing the cells with 0.2% sodium dodecyl sulfate.
For preloading studies, cells were washed after incubation at 37°C with the labeled substrate as described above. Subsequently, cells were further incubated at 37°C with transport buffer (1.0 ml in the basolateral and 1.0 ml in the apical compartment) in the absence of labeled substrate, and radioactivity was determined as described above.
The paracellular leakage was determined by the addition of 1 µM[3H]inulin (BIOTREND, Köln, Germany) to the basolateral compartment and measurement of the radioactivity appearing in the apical compartment. The paracellular leakage was less than 2% of the radioactivity added for all MDCKII cell clones examined in this study.
Numerical Analysis. Ordinary differential equations were derived from the model depicted in Fig. 2 by assuming Michaelis-Menten kinetics in the linear regime. The kinetic behavior of the transporters OATP1B3 (König et al., 2000) and ABCC2 (Cui et al., 1999) has been characterized, and Michaelis-Menten constants were determined. The equations were integrated by ODESSA (Leis and Kramer, 1988a,b). To ensure that we could identify all parameters while performing the multiexperiment fit, we used a penalized likelihood as cost-function for parameter estimation. This likelihood includes prior knowledge of the parameter distribution (see Supplemental Data). The resulting cost-function was minimized using an optimization routine of the Gauss-Newton type (Hanson and Haskell, 1982; Peifer and Timmer, 2007). Because measurement errors show a linear dependence on the estimated mean value, we re-estimated the standard deviations by applying a linear error model to minimize the fluctuations in the estimated standard deviations (see Supplemental Data).
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Results |
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).
MDCKII cells were also analyzed for the expression and localization of endogenous transport proteins, as suggested by the mathematical modeling. Endogenous canine Abcc4 was localized to the baso-lateral membrane of the MDCKII cells (Fig. 1E). Thus, this endogenous basolateral efflux pump functions in addition to the recombinant human transport proteins. ABCC4 has a broad substrate specificity (Kruh et al., 2007) that includes BSP (data not shown). The influxes, effluxes, and concentration pools are summarized in Fig. 2.
Uptake and Efflux Transport in Polarized Cells. To acquire data, several sets of transport experiments were performed. Vectorial transport of labeled BSP was measured over 60 min at high (10 µM; Fig. 3) and low (10 nM; Fig. 4) concentrations. The intracellular content of labeled BSP was significantly higher in MDCKII cells expressing recombinant OATP1B3 than in the control MDCKII cells (Figs. 3 and 4, bottom), indicating that OATP1B3 is responsible for the uptake and intracellular accumulation of BSP. The release of BSP into the apical chamber was mainly detected in cells expressing recombinant OATP1B3 together with ABCC2 (Figs. 3 and 4, top), indicating that ABCC2 in the apical membrane efficiently mediates the efflux of BSP.
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To assess the contributions of endogenous transport processes, the cells were preloaded (Fig. 5) by adding 3H-labeled BSP to the basolateral chamber for 30 min. After this preloading time, the amounts of radioactivity effluxed into the apical chamber and into the basolateral chamber (basolateral amount), as well as radioactivity accumulated inside the cells, were determined. BSP was strongly accumulated in cells expressing OATP1B3 and, to a lesser extent, in cells expressing OATP1B3 together with ABCC2 (Fig. 5, middle). The MDCKII cells expressing recombinant OATP1B3 and ABCC2 showed the highest efflux of BSP into the apical chamber (Fig. 5, top). However, the major BSP efflux into the basolateral chamber was observed in the cells that had reached the highest intracellular content (Fig. 5, bottom). This efflux is most probably mediated by the endogenous (canine) Abcc4 of the MDCKII cells (Fig. 1E).
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Assuming Michaelis-Menten kinetics in the linear regime, we derived the ordinary differential equations (Table 1) from the model shown in Fig. 2. This procedure is in accordance with similar modeling approaches (Liu and Pang, 2006; Turncliff et al., 2006). The rates of BSP uptake into cells may vary somewhat between different sets of experiments depending on the expression level of OATP1B3. Accordingly, we fitted our model to the data from all of the experiments of the present study by maximizing a penalized likelihood (Good and Gaskins, 1971) as explained in Supplemental Data. The penalized likelihood was introduced to ensure that we could identify all parameters for the multiexperiment fit (see Supplemental Data). Results of the fits are shown in Figs. 3 through 5.
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We found it necessary to include the endogenous transporters in the model. We compared the complete model (Fig. 2) to models lacking selected endogenous transport processes. Each of the smaller models yielded a significantly worse fit of the data than the complete model (see Supplemental Data).
Rate-Determining Steps in Vectorial Transport. Based on our model (Fig. 2), we calculated the contribution of each transport process to the total amount of BSP transported into the apical chamber. The largest amount of BSP was transported by the recombinant uptake transporter OATP1B3, followed by the recombinant apical efflux pump ABCC2, the endogenous efflux pump Endoex-bl (probably Abcc4), and the endogenous uptake transporter Endoin-bl (Fig. 6A). The endogenous apical efflux Endoex-ap and paracellular transport contributed the smallest fractions to the total transported amount. OATP1B3 accounted for approximately 44% of the overall transport, followed by ABCC2 with 28% and the endogenous efflux pump Endoex-bl with approximately 19% (Fig. 6B). The endogenous transporters Endoin-bl and Endoex-ap and paracellular BSP transport together account for less than 10% of the total transport. Since the endogenous efflux pump Endoex-bl (probably Abcc4) transports BSP back into the basolateral chamber, its contribution to the total amount of BSP transported into the apical chamber is actually negative.
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; Conradie et al., 2006). In this analysis, the fractional change of the steady-state flux of a metabolite J is related to the fractional change of an enzyme activity v, defined as 
. For our system, we calculated the relationship of the fractional change of the total flux into the apical chamber, J = dx5/dt, to the fractional change of each transport process in our model (Fig. 7). Since the rate for each transport process in our model is linear and has the form vj = pjxk, the normalized control coefficients read:
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For the double-transfected cells, the control coefficients of OATP1B3 and ABCC2 were the dominant transport processes and were rate-determining in our system. This agrees with the fact that each of the single-transfected cells (i.e., OATB1B3 cells or ABCC2 cells; Cui et al., 2001) exhibit significantly less total vectorial transport than the double-transfected cells. For control cells, on the other hand, the control coefficient of the endogenous transporters Endoin-bl and Endoex-ap, as well as the paracellular flow, are the main processes. The comparison of the control coefficients of the parental cells with the control coefficients of the double-transfected cells shows that the rate-determining step in vectorial transport clearly depends upon the expression level of the respective transport proteins.
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Discussion |
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) as explained in detail in Supplemental Data. This approach provides new qualitative and quantitative insights into the components and dynamic behavior of vectorial transport. In particular, the role of endogenous transport processes was recognized and quantified in addition to the role of the transfected recombinant transporters OATP1B3 and ABCC2.
In this study, our data-based mathematical modeling was supported by application of an in vitro cell culture system that allowed quantitative analyses of a labeled model substance in different compartments at various time points. In several aspects, this biological system with double-transfected polarized cells (Fig. 1) resembles human hepatocytes and the vectorial transport of many substances, including BSP, from the blood circulation into bile (Keppler, 2005).
The model shows excellent agreement with the experimental data. The optimal fit of the model was achieved by maximizing a penalized likelihood (Good and Gaskins, 1971) and required the inclusion of endogenous transport processes of the MDCKII cell, in addition to the stably expressed recombinant human transporters OATP1B3 and ABCC2. The role of endogenous transport proteins in the MDCKII cells was addressed by preloading experiments, which enabled quantitative measurements of efflux from the cells into the apical and basolateral chambers. The excellent agreement of the model with the experimental data indicates that transcellular diffusion was not required as an additional parameter, at least in the case of the hydro-philic BSP. A similar modeling approach could be taken with the introduction of other recombinant transport proteins, such as uptake mediated by OATP2B1 and the efflux pump ABCC2 (Kopplow et al., 2005) or the sodium-dependent bile acid uptake transporter NTCP and the efflux pump ABCB11 (Mita et al., 2006).
As expected, the greatest contributions to the transport of BSP came from recombinant OATP1B3 and ABCC2 (44 and 28% of total transport, respectively). Surprisingly, endogenous basolateral efflux, designated Endoex-bl, amounted to 19%, which is in line with the significant amount of the endogenous protein Abcc4 in the basolateral membrane. In hepatocytes, basolateral efflux pumps, including ABCC3 and ABCC4, also play an important role in overall transport of small molecules (Rius et al., 2003). The basolateral efflux in the MDCKII cells was initially indicated by model comparison, leading to the best fit with the experimental data. This efflux was verified and further quantified by preloading experiments. Notably, all other processes integrated into our model together amount to less than 10% of the transport. This small contribution is in accordance with the normalized control coefficients for the fluxes in the double-transfected cells. Thus, variations in the activity of OATP1B3 or ABCC2 have the greatest effect on total flux. Since the control coefficients for OATP1B3 and ABCC2 are similar, a rate-determining step cannot be singled out in this cellular system. This will be different when the activity of one of the six processes described in our model is significantly changed, as can be seen for the control coefficients of the MDCKII control cells where other partial processes dominate total vectorial flux.
In conclusion, the polarized cell system for studies on vectorial transport (Cui et al., 2001; Sasaki et al., 2002) was successfully used for data-based mathematical modeling and resulted in the quantification of individual transport steps in a complex system. This quantitative modeling greatly expands the mostly qualitative previous knowledge on the vectorial transport of endogenous and xenobiotic substances. Accordingly, predictions can be made for the time course of transport and for the relative contribution of single transport steps to the overall transport. The calculation of control coefficients enabled the identification of rate-determining single steps in overall vectorial transport. Moreover, the modeling approach in this study has been useful for the identification of previously unexpected partial processes, such as the quantitatively important basolateral efflux (Endoex-bl). This additional transport process is well explained by the detection of endogenous Abcc4 in the MDCKII cells. The inclusion of this process was necessary to obtain excellent agreement between the experimental data and the mathematical model. Thus, data-based quantitative mathematical modeling led to new qualitative as well as quantitative insight into the biological system. In this study, we focused on BSP as a well known model substance for the analysis of hepatobiliary elimination. However, this modeling approach may be applied to other substances, e.g., cholecystokinin octapeptide CCK-8, the vectorial transport of which has been characterized recently (Letschert et al., 2005), and other polarized cellular systems, such as quadruple-transfected MDCKII cells (Kopplow et al., 2005).
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Acknowledgments |
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Footnotes |
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ABBREVIATIONS: OATP1B3, human organic anion-transporting polypeptide, member 1B3; ABCC2, human ATP-binding cassette transporter, subfamily C, member 2; MRP2, multidrug resistance protein 2; BSP, bromosulfophthalein; MDCKII, Madin-Darby canine kidney cells strain II; Abcc4, canine ATP-binding cassette transporter, subfamily C, member 4; ABCC3, human ATP-binding cassette transporter, subfamily C, member 3; Endoex-ap, apical endogenous efflux transporter; Endoex-bl, basolateral endogenous efflux transporter; Endoin-bl, basolateral endogenous uptake transporter.
The online version of this article (available at http://dmd.aspetjournals.org) contains supplemental material. 
Address correspondence to: Dr. Dietrich Keppler, Division of Tumor Biochemistry, German Cancer Research Center, Im Neuenheimer Feld 280, 69120 Heidelberg, Germany. E-mail: d.keppler{at}dkfz.de
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