Abstract
The objective was to investigate the interplay between transporter expression levels and substrate affinity in controlling the influence of aqueous boundary layer (ABL) resistance on transporter kinetics in an overexpression system. Taurocholate flux was measured across human apical sodiumdependent bile acid transporter (hASBT)MadinDarby canine kidney monolayers on different occasions and kinetic parameters estimated with and without considering ABL. In errorfree simulation/regression studies, flux values were generated across a range of J_{max}, K_{t}, and substrate concentrations. Similar evaluation was performed for transport inhibition studies. Additionally, simulation/regression studies were performed, incorporating 15% random error to estimate the probability of successfully estimating K_{t}. Across different occasions, experimental J_{max} and K_{t} estimates for taurocholate were strongly associated (p < 0.001; r^{2} = 0.82) when ABL was not considered. Simulation/regression results indicate that not considering ABL caused this association, such that K_{t} estimates were highly positively biased at high hASBT expression. In reanalyzing taurocholate flux data using the ABLpresent model, K_{t} was relatively constant across occasions (∼5 μM) and not associated with J_{max} (p = 0.24; r^{2} = 0.13). Simulations suggest that J_{max} and K_{t} collectively determined ABL influence, which is most prominent under conditions of low monolayer resistance. Additionally, not considering ABL lead to negatively biased K_{i} estimates, especially at high J_{max}. Errorinclusive simulation/regression studies indicated that the probability of successfully estimating K_{t} depended on the contribution of ABL resistance to flux; when flux became increasingly ABLlimited, probability of success decreased. Results indicate that ABL resistance can bias K_{t} and K_{i} estimates from overexpression systems, where the extent of bias is determined by transporter expression level and substrate affinity.
Transfected cell models overexpressing specific transporters are a powerful tool to characterize substrate requirements of the transporter, including its ability to translocate drugs and prodrugs (HerreraRuiz et al., 2003; TolleSander et al., 2004; Balakrishnan et al., 2005; Balakrishnan and Polli, 2006). Relative to native cells and in vivo systems, transfected cell models frequently have the advantage of characterizing a transporter without confounding variables, such as other simultaneously expressing transporters with overlapping substrate requirements. This benefit is achieved in part through high expression of the transporter of interest.
We recently developed a stably transfected cell model for the human apical sodiumdependent bile acid transporter (hASBT), using MDCK cells (Balakrishnan et al., 2005) that possesses several favorable properties, including high hASBT expression. This hASBTMDCK model was further developed to yield kinetic estimates of substrates and/or inhibitors (e.g., J_{max}, K_{t}, and K_{i}) that can be used for subsequent quantitativestructure activity relationship (QSAR) analysis. Thus, overexpression systems can be used suitably for functional characterization of transporters.
In general, transporter expression level is expected to vary between occasions (i.e., vary between passages or cell culture conditions) (Yu et al., 1997; Polli et al., 2001). As an example, Fig. 1 summarizes the kinetic analysis of hASBTmediated taurocholate transport across hASBTMDCK monolayers from 12 different occasions. As anticipated, J_{max} estimates varied severalfold across occasions. K_{t} also varied across occasions and exhibited strong, positive association with J_{max} estimates (p < 0.0001; r^{2} = 0.82) (Fig. 1). Ideally, K_{t} can be expected to be constant across occasions and independent of expression levels. However, J_{max} and K_{t} were estimated using a transport model that does not consider contribution of aqueous boundary layer (ABL) resistance. The present manuscript considers ABL as a lumped parameter composed of the apical unstirred water layer (UWL), support filter, and basolateral UWL. These diffusional barriers are encountered in flux studies across a monolayer grown on support filters. These diffusion barriers are lumped together, since it is difficult to reliably delineate them experimentally. Previous theoretical and experimental reports considered the presence of a single UWL situated apical to the biological membrane (i.e., an apical UWL) and indicated that failure to consider the UWL can result in inaccurate K_{t} estimates (Winne, 1973, 1977, 1978; Thomson and Dietschy, 1977, 1980; Thomson, 1979; Barry and Diamond, 1984; Sinko et al., 1996). These reports have indicated the potential for UWL effects on active transport. Based on our previous data and reports by others, we hypothesized that high transporter expression can lower monolayer resistance, resulting in ABLlimited transport of solutes, leading to biased kinetic estimates if ABL is not considered.
One distinction between the present study and previous reports is the use of an overexpression system, where high expression level of transporter was achieved. Previous reports have clearly demonstrated UWL effect on K_{t} estimates, but it is not clear how variability in high transporter expression level impacts the quality of kinetic estimates, as observed in Fig. 1. Use of a monolayer flux assay also underpins a second difference between the present study and previous reports. Previous models assumed a single UWL, followed by a biological membrane (Winne, 1973, 1977, 1978; Thomson and Dietschy, 1977, 1980; Thomson, 1979). These studies evaluated in vivo perfusion studies, where the UWL represents a diffusion barrier between the bulk and the membrane. Unfortunately, the diffusion barriers in a monolayer flux configuration are less determinant since they are present at the apical interface, the basolateral interface, and via the support filter. The present study puts forth a transport model that reflects the cell culture monolayer flux assay. This transport model was extended to identify an inhibition model, an area unexplored by previous studies.
This study evaluates the interplay of transporter expression levels and substrate affinity in determining the role of ABL resistance on transporter kinetics using hASBT as a model transport system. The objectives were to 1) evaluate the effect of J_{max} on the contribution of ABL resistance to transporter kinetics, 2) identify global kinetic conditions when ABL needs to be explicitly considered to accurately estimate kinetic parameters, and 3) identify scenarios under which kinetic estimates are not reliable in spite of ABL consideration, due to ABLdominated transport kinetics. Objective 1 was carried out through a combination of empirical laboratory studies as well as errorfree simulation/regression studies. Objective 2 was conducted through errorfree simulations of both transport and inhibition studies. Objective 3 was carried out through simulations incorporating 15% random error.
Given the broad use of overexpression systems to characterize transporter kinetics and given transporter expression variability over time, these results have implications in the development of high expression cell culture assays, as well as QSAR models and drug discovery efforts that rely on accurate kinetic parameter estimates.
Materials and Methods
Transport Studies: ABLAbsent Model.Figure 2 illustrates two competing models to describe bile acid transport across an hASBTMDCK monolayer. The models differ in the absence or presence of an ABL. In Fig. 2A, the ABLabsent model is illustrated and only considers monolayer resistance to limit flux. Mechanisms of bile acid permeation across the monolayer are active hASBT transport and passive permeability. hASBT is located in the apical membrane and is the dominant mechanism for bile acid absorption (Dawson et al., 2003; Balakrishnan et al., 2005).
From Fig. 2A, the ABLabsent model is as follows: where J is bile acid flux when ABL is absent, J_{max} and K_{t} are the MichaelisMenten constants for hASBTmediated transport, S is bile acid substrate concentration, and P_{p} is the passive permeability coefficient. J_{max} and K_{t} are sometimes denoted V_{max} and K_{m}, respectively, in the transporter literature.
Transport Studies: ABLPresent Model. The ABLpresent model is illustrated in Fig. 2B. The term ABL includes the apical UWL, the support filter, and the basolateral UWL. ABL is considered a lumped parameter made up of these three components, since it is difficult to reliably delineate these individual barriers experimentally. The permeability across the ABL is P_{ABL}, such that this term represents the permeability across barriers other than the monolayer. As discussed below, P_{ABL} was estimated by measuring the permeability of taurocholate across blank filter in the absence of cells.
From Fig. 2B, the apparent resistance to flux is as follows: where R_{app} is the apparent resistance, R_{ABL} is the resistance due to the ABL, and R_{mono} is the resistance due to the monolayer itself (i.e., monolayer resistance). Since permeability is the inverse of resistance, where P_{app} is the apparent permeability, P_{ABL} is the ABL permeability, and P_{mono} is the monolayer permeability. From the contributions of hASBTmediated transport and parallel passive bile acid permeability to monolayer permeability, Substituting eq. 4 into eq. 3,
Since J_{ABL} = P_{app} × S, where J_{ABL} is bile acid flux when ABL is present. Equation 7 is denoted the ABLpresent model.
Comparison of the ABLPresent Model to the Uptake Model of Winne. Equation 7 differs from the uptake model of Winne (1977), which can be written as follows: where J_{UWL} is the flux when a single UWL is present before the membrane, P_{UWL} is the permeability of the UWL, and q = P_{UWL}/(P_{p} + P_{UWL}). J_{max}, K_{t}, P_{p}, and S represent the same parameters in both eqs. 7 and 8. Equation 8 simplifies the original Winne equation by equating the area of the UWL to the area of the membrane as well as by substituting P_{UWL} for the ratio of the diffusivity coefficient to the UWL thickness.
Underpinning the difference between the ABLpresent model and the Winne uptake model is the number and arrangement of diffusion barriers, relative to the biological membrane. In the uptake model of Winne, only an apical UWL is present. Winne et al. applied eq. 8 to assess the role of the UWL in the absorption of phenylalanine (Winne et al., 1979) using the perfused rat jejunal loop. Justification of Winne's model would seem to be the presence of an UWL within the loop lumen, with no other significant diffusion barriers, except the jejunal loop membrane. Strength of the Winne uptake model is its differentiation between the bulk donor solution concentration (S) and the concentration at the UWLmembrane interface, particularly compared against the ABLpresent model.
Winne's model cannot be applied to transport studies across a cell monolayer since it fails to consider diffusional resistances other than the apical UWL. Complicating this scenario is the arrangement of a diffusion barrier on the luminal side of the monolayer (i.e., apical UWL) and two diffusion barriers on the other side (i.e., support filter and basolateral UWL). A further limitation is an insufficient understanding of these diffusion barriers since the permeability of each barrier is difficult to measure in a reliable manner. The approach in the present manuscript was to characterize these three barriers as a single resistivity R_{ABL}, per eq. 2 (i.e., a single permeability P_{ABL}; per eq. 3). This single barrier is denoted the ABL. P_{ABL} was estimated by measuring the permeability of taurocholate across blank filter in the absence of cells (Yu and Sinko, 1997). Briefly, in Fig. 2B, when monolayer present, the support filter, the apical unstirred water layer, and the basolateral unstirred water layer are present and collectively denoted as the ABL. When monolayer absent, these elements are still present. Hence, ABL was estimated by measuring taurocholate flux across blank support filter.
Measure of Monolayer Resistance. Equations 1 and 7 (i.e., the ABLabsent and ABLpresent models) each allow for a nonlinear, MichaelisMententype component as well as linear, passive transport component. The two models differ with respect to the contribution of the ABL on flux. In Fig. 2A, ABL is absent, such that the only ratelimiting barrier in eq. 1 is the monolayer. In Fig. 2B, ABL is present, reflecting that ABL contributes as a barrier to flux in eq. 7. Qualitatively, a high ABL resistance relative to monolayer resistance results in flux limited by ABL. In addition, high monolayer resistance relative to ABL results in flux limited by monolayer, as in Fig. 2A.
The ratio of flux from the ABLpresent model to the flux from the ABLabsent model (J_{ABL}/J) is used to assess the impact of ABL on flux. Of note, J_{ABL}/J is also numerically equivalent to the fraction of total flux resistance that is attributed to the monolayer: where F_{mono} is the fraction of total flux resistance that is due to the monolayer. Appendix 1 derives eq. 9. Monolayer resistance excludes components of the ABL such as the support filter and apical and basolateral UWLs. From eq. 9, J_{ABL}/J = 1 indicates that flux is limited by monolayer resistance only (i.e., F_{mono} = 1). Meanwhile, J_{ABL}/J = 0.1 indicates that the monolayer contributes to only 10% of the total resistance (i.e., F_{mono} = 0.1), with the ABL contributing the remaining 90%.
Transport Inhibition Studies. For competitive inhibition studies of taurocholate transport by bile acids, the following transport inhibition model describes taurocholate transport when ABL is absent: where I is the concentration of inhibitor (i.e., inhibitory bile acid) and K_{i} is inhibition constant. S is substrate concentration (i.e., taurocholate concentration); J_{max}, K_{t}, and P_{p} characterize substrate transport parameters. Equation 10 is denoted the ABLabsent inhibition model.
When the ABL is included, the competitive inhibition model becomes: where P_{ABL} is ABL permeability. Equation 11 is denoted the ABLpresent inhibition model. This model is derived in Appendix 2.
Taurocholate Transport across hASBT Monolayers. Taurocholate was used as a model substrate for hASBT. On 12 occasions, apicaltobasal taurocholate flux was measured across an hASBTMDCK monolayer model, as described previously (Balakrishnan et al., 2005). Briefly, hASBTMDCK cells were seeded at a density of 0.75 million cells/cm^{2} on support filter (polyester Transwell, 0.4μm pore size, 1 cm^{2}; Corning Life Sciences, Corning, NY). Kinetics of hASBTmediated taurocholate flux was assessed from transport studies (n = 3) at differing donor concentrations (1–200 μM spiked with [^{3}H]taurocholate). Transport was performed using HBSS with 10 mM HEPES, pH 6.8, at 37°C and 50 rpm. Sample was obtained from basolateral compartment at 30 min, well after steady state was attained (by 5 min). Sink conditions prevailed in all studies. Sink conditions refer to the low accumulation of substrate into basolateral compartment, as to essentially not bias results. This situation was attained by ensuring that substrate concentration in the receiver compartment never exceeded 10% of donor substrate concentration. In all studies, [^{14}C]mannitol was used to monitor monolayer integrity. In all cases, mannitol permeability was less than 4.0 × 10^{–6} cm/sec. Mass balance ranged from 90 to 120%.
Flux data from each occasion was fitted to the ABLabsent model (i.e., eq. 1) as well as the ABLpresent model (i.e., eq. 7), providing estimates for J_{max}, K_{t}, and P_{p} for each of the two model scenarios. In eq. 7, P_{ABL} was assigned, based upon taurocholate flux data across support filters without monolayers, as discussed below.
Nonlinear regression to eqs. 1 and 7 was performed using SigmaPlot 2000 (SPSS Inc., Chicago, IL). Correlation among parameter estimates was evaluated using Pearson correlation coefficient using SPSS 12.0 (SPSS Inc.).
Taurocholate Uptake into hASBT Monolayers. In contrast to transport studies, uptake studies only concern the translocation of taurocholate across the apical membrane and into the cytosol. On five occasions, taurocholate uptake into hASBTMDCK monolayers were assessed as described previously (Balakrishnan et al., 2005).
In brief, hASBTMDCK cells were seeded at a density of 1.5 million cells/well on 12well plates (Corning Life Sciences). Kinetics of hASBTmediated taurocholate uptake was assessed from uptake studies (n = 3) at differing donor concentrations (1–200 μM spiked with [^{3}H]taurocholate). Studies were performed using HBSS with 10 mM HEPES, pH 6.8, at 37°C and 50 rpm for 10 min. The 10min time point was selected since taurocholate uptake was linear over 10 min (Balakrishnan et al., 2005). The donor solution was removed and the cells were washed three times with chilled sodium free buffer. Cells were lysed using 0.25 ml of 1 N NaOH and neutralized with 0.25 ml of 1 N HCl. Cell lysate was then counted for associated radioactivity using a liquid scintillation counter (Beckman Instruments, Inc., Fullerton, CA).
Flux data from each occasion were fitted to the ABLabsent model (i.e., eq. 1) as well as the ABLpresent model (i.e., eq. 7), providing estimates for J_{max}, K_{t}, and P_{p} for each of the two model scenarios. In eq. 7, P_{ABL} was assigned, based upon diazepam uptake data, as discussed below. Nonlinear regression to eqs. 1 and 7 was performed using SigmaPlot 2000 (SPSS Inc.). Correlation among parameter estimates was evaluated using Pearson correlation coefficient using SPSS 12.0 (SPSS Inc.).
Taurocholate Transport across Support Filter without hASBTMDCK Monolayer to EstimateP_{ABL} for TransportStudies. It is difficult to directly measure the net effect of the aqueous boundary layer at the apical interface, the aqueous boundary layer at the basolateral interface, and the plastic filter (i.e., P_{ABL}) when cell monolayer is present. When an estimate of P_{ABL} is sought, a common approach to measure P_{ABL} is to use blank filter (Imanidis et al., 1996; Yu and Sinko, 1997). Hence, taurocholate transport across blank support filters (i.e., polyester Transwell without cell monolayer) was performed as described above. The underlying assumption in this approach is that the ABL in the ABLpresent model in Fig. 2B is the same whether a monolayer is present or not present. Flux studies were performed using HBSS with 10 mM HEPES, pH 6.8, at 37°C and 50 rpm. At 5 min, sample was collected from the receiver compartment and allowed for sink conditions to be maintained. Taurocholate permeability across blank support filters was 66.1± 6.0 × 10^{–6} cm/s, which was taken to be equal to P_{ABL}. This value was in agreement with that of (Buur and Mork, 1992).
P_{ABL} served as a lumped parameter in eqs. 7 and 11 to characterize ABL, since it is difficult to reliably measure the permeability of the apical unstirred water layer, the support filter, and the basolateral unstirred water layer individually. It should be noted that Yu and Sinko (1997) and Adson et al. (1994) have attempted to uncouple some of these barrier components, although active transport was not considered. Adson et al. (1994) calculated a value for the permeability of the support filter, based upon a porous membrane model and parameters provided by the manufacturer, an approach that may be unreliable (Yu and Sinko, 1997). Yu and Sinko (1997) used an empiric model to simultaneously estimate support filter permeability and the UWLs; the approach required “laborintensive” flux studies across blank filters, where hydrodynamics was varied (Yu and Sinko, 1997).
Diazepam Uptake into hASBTMDCK Monolayer to EstimateP_{ABL} for Uptake Studies. Uptake of radiolabeled diazepam into hASBTMDCK cells was assessed to estimate P_{ABL} for uptake studies. By virtue of its high permeability across bilayers, diazepam is a commonly used marker for measurement of UWL resistance. After 30 s, uptake was stopped by freezing the cells instantaneously over dry ice in alcohol. This process rigidized cell membrane and aimed to minimize back diffusion. Cells were washed twice with icecold buffer and lysed using 1% Triton in 1 N NaOH. Diazepam in cell lysate was quantified using a scintillation counter. Diazepam permeability was 150 ± 3 × 10^{–6} cm/s, which was taken to be equal to P_{ABL} for uptake studies. This P_{ABL} value from the uptake configuration is greater than P_{ABL} from the transport configuration, presumably reflecting that only the apical UWL is present in case of uptake configuration, whereas basolateral UWL and filter support are additional diffusion barriers in the transport configuration.
Simulations for Objective 1: Impact of VaryingJ_{max} on ABLContribution. The ABLpresent model for transport (i.e., eq. 7) was used to simulate flux data. No error was incorporated into these simulations. Values for K_{t}, P_{p}, and P_{ABL} were 5 μM, 0.5 × 10^{–6} cm/s, and 70 × 10^{–6} cm/s, respectively. These values were selected based upon experimental measurements of K_{t}, P_{p}, and P_{ABL}. Values for substrate concentration and J_{max} ranged from 0.5 to 1000 μM and 0.00001 to 0.01 nmol/cm^{2}/s, respectively. J_{max} values were selected based upon observed J_{max} values. Errorfree simulations were systematically performed for all combinations of parameter values. Errorfree flux data were similarly simulated using the ABLabsent model (eq. 1).
Simulated J_{ABL} data were subsequently regressed on to the ABLabsent model to yield estimates of K_{t}, J_{max}, and P_{p}. This approach quantified bias in K_{t}, J_{max}, and P_{p} parameter estimates when ABL was ignored.
Simulations for Objective 2: Identification of Global Kinetic Conditions That Require ABL Consideration. Simulations were performed to identify global kinetic conditions when ABL needs to be explicitly considered to accurately estimate kinetic parameters (e.g., K_{t}, J_{max}, or K_{i}). Simulations were performed for transport and transport inhibition studies.
Transport data were simulated under both ABLpresent and ABLabsent scenarios. P_{p} and P_{ABL} were fixed to be 0.5 × 10^{–6} and 70 × 10^{–6} cm/s, respectively. Values for K_{t} and J_{max} ranged from 0.1 to 10,000 μM and 0.00003 to 0.01 nmol/cm^{2}/s, respectively. Substrate concentration was fixed to onetenth the K_{t} value for each simulation. The impact of ABL was assessed by the ratio J_{ABL}/J. J_{ABL}/J greater than 0.9 indicated that ABL contribution is not significant. J_{ABL}/J less than 0.9 indicated that ABL is significant, such that ABL needs to be considered to accurately estimate kinetic parameters.
Inhibition data were simulated using the ABLabsent and ABLpresent models in a similar manner (i.e., eqs. 10 and 11). Substrate concentration, K_{t}, and K_{i}, values were 2.5, 5, and 50 μM, respectively. Inhibitor concentration ranged from 0.1 to 1000 μM. J_{max} ranged from 0.00001 to 0.01 nmol/cm^{2}/s. Simulated J_{ABL} was subsequently regressed on to the ABLabsent inhibition model to yield estimates of K_{i}. K_{t}, J_{max}, and P_{p} were assigned to the values used in generating the simulated data. This approach quantified bias in K_{i} parameter estimates when ABL was ignored.
Simulations for Objective 3: Identification of Global Kinetic Conditions WhenK_{t} Estimates Are Unreliable as a Result of ABL Contribution. Equation 7 was used with P_{p} = 0.5 × 10^{–6} cm/s and P_{ABL} = 70 × 10^{–6} cm/s to generate initial errorfree flux data. Fifteen scenarios were systematically evaluated for five levels of K_{t} (1, 3, 5, 10, and 25 μM) at each of three levels of J_{max} (0.0001, 0.0003, and 0.001 nmol/s/cm^{2}). Substrate concentrations were 1/20, 1/10, 1/5, 1/2, 1, 2, 5, 10, and 20fold of true K_{t} value. For the scenario K_{t} = 1 μM and J_{max} = 0.001 nmol/s/cm^{2}, substrate concentrations 40, 80, and 160 μM were also included. Flux data for every substrate concentration were simulated in triplicate for each occasion, mimicking triplicate design of in vitro laboratory studies. Random error reflecting percent coefficient of variation = 15% was incorporated into simulated flux data. For each of these 15 scenarios, simulations were performed on 100 occasions. Data from each occasion were regressed onto eq. 7 to estimate K_{t}, J_{max}, and P_{p}, with emphasis on K_{t}. For each simulation scenario, K_{t} estimates from each of the 100 occasions was used to calculate the probability of calculating meaningful K_{t} estimates (i.e., statistically differed from zero based upon 95% confidence interval). Nonlinear regression to eq. 7 was performed using WinNonlin Professional version 4.1 (Pharsight, Mountain View, CA), which was kindly donated by Pharsight.
Cell Surface Biotinylation and Immunoblotting.Figure 1 provides motivation for the present study, presuming that variation in J_{max} was ascribed to variation in hASBT expression. The rank order agreement between cell surface hASBT expression level and J_{max} was assessed though parallel studies involving Western blots and taurocholate transport studies.
hASBTMDCK monolayers were grown as described above (Balakrishnan et al., 2005) and treated with varying levels of sodium butyrate to modulate hASBT expression level. hASBTMDCK monolayers were treated with either 10 mM, 5 mM, or no sodium butyrate to yield monolayers corresponding to three levels of hASBT expression (i.e., high, intermediate, and low). Additionally, untransfected MDCK monolayers were also treated with 10 mM sodium butyrate as negative control
Cell surface expression of hASBT was determined by treating cells with the membraneimpermeant biotinylation reagent sulfosuccinimidyl2(biotinamido) ethyl1,3dithiopropionate (Pierce Chemical, Rockford, IL) for 30 min at room temperature (Visiers et al., 2003). After several washes in phosphatebuffered saline with 0.1 mM CaCl_{2} and 1 mM MgCl_{2}, cells were disrupted in lysis buffer [25 mM TrisHCl, pH 7.5, 300 mM NaCl, 1 mM CaCl_{2}, 1% Triton X100, and 0.5% protease inhibitor cocktail (SigmaAldrich, St. Louis, MO)] for 30 min at 4°C. Biotinylated proteins were recovered by overnight incubation with 100 μl of streptavidinagarose beads per sample (Pierce Chemical Co.) at 4°C using endoverend rotation. The following day, the beads were washed once with lysis buffer, once in highsalt lysis buffer (same as lysis buffer except with 500 mM NaCl and 0.1% Triton X100), and finally twice with 50 mM Tris, pH 7.5. Biotinylated proteins were eluted using 100 μl of SDSpolyacrylamide gel electrophoresis Laemmli buffer, pH 6.8 (SigmaAldrich), for 10 min at 85°C. For each sample, 20 μl was applied to a 12.5% SDSpolyacrylamide gel electrophoresis gel (BioRad, Hercules, CA) and transferred to a polyvinylidene difluoride membrane for immunoblotting. Since hASBT was constructed with a V5 epitope (Balakrishnan et al., 2005), hASBT was detected with the antiV5/horseradish peroxidaseconjugated antibody (1:1000 dilution; Invitrogen, Carlsbad, CA) directed to the V5 epitope located at the C terminus. Bands were detected by chemiluminescence using ECL Plus Western Blotting Detection system (GE Healthcare, Little Chalfont, Buckinghamshire, UK). Blots were then stripped via ECL Detection System protocols and reprobed for the presence of the constitutively expressed plasma membrane marker αintegrin, using antiintegrin α2/VLA2α antibody, followed by donkey antimouse HRPconjugated secondary antibody. αintegrin represents a positive control for cell surface biotinylation of plasma membrane proteins. To confirm cell membrane integrity during biotinylation, the same membrane was also probed for the absence of calnexin, a 90kDa housekeeping protein present in wholecell lysate preparations, using anticalnexin antibody and donkey antirabbit HRPconjugated secondary antibody. Calnexin was absent from biotinylated samples (data not shown), ensuring that only cell surface proteins were biotinlabeled and immunoblotted.
Densitometry measurements of hASBT expression level were not performed, since densitometry unfortunately requires high protein expression and αintegrin was not sufficiently high for densitometric measurement. Rather, post hoc analysis of band density using pixel intensity was assessed using NIH Image software (version 1.6.3; (http://rsb.info.nih.gov/nihimage/index.html) for each sodium butyrate treatment level (as well as control untransfected MDCK monolayers). Using a standard rectangular box in NIH Image, pixel intensity of hASBT was measured and normalized against pixel intensity of αintegrin; pixel intensity ratio of hASBT versus αintegrin from each treatment was corrected for background control via subtraction of pixel intensity ratio from untransfected MDCK monolayers and interpreted as hASBT expression level (relative to integrin).
Taurocholate flux in the presence and absence of sodium was measured as described above. J_{max} was estimated and compared with Western blot analysis. Results are shown in Appendix 3.
Results
Simulations for Objective 1: Impact of VaryingJ_{max}on ABL Contribution. Taurocholate permeability across blank support filters was 66.1± 6.0 × 10^{–6} cm/s. Hence, P_{ABL} was fixed at 70 × 10^{–6} cm/s in all simulations.
Figure 3 is a contour plot of the ratio of J_{ABL} versus J, as a function of J_{max} and substrate concentration. J_{ABL}/J greater than 0.9 indicates that ABL contribution was not significant. J_{ABL}/J less than 0.9 indicates that ABL contribution is significant. At a very low J_{max} of 0.00003 nmol/cm^{2}/s, J_{ABL}/J always exceeded 0.9, regardless of substrate concentration. For higher J_{max} scenarios, J_{ABL}/J dropped below 0.9 at low substrate concentrations, but generally returned to about unity at high substrate concentration. At very high J_{max} of 0.01 nmol/cm^{2}/s, flux from the ABLpresent models was 20fold lower than flux from the ABLabsent model at low substrate concentration (i.e., J_{ABL}/J about 0.05). These simulations indicate that ABL limits flux significantly at high J_{max} and low substrate concentration. These simulations follow the results observed in earlier studies (Thomson and Dietschy, 1977, 1980), although the present manuscript attempts to highlight the influence of J_{max} (i.e., expression level), since expression level of transporters can vary across occasions in a cell culture system.
From eq. 3, J_{ABL}/J in Fig. 3 can also be interpreted to be the fraction of total flux resistance that is attributed to the monolayer, F_{mono}. Under conditions of high J_{max} and low substrate concentration, F_{mono} is low, such that ABL is dominant. At low J_{max} and/or high substrate concentration, F_{mono} is large, such that monolayer resistance is dominant and ABL effect is not significant.
Simulated flux data from the ABLpresent model were regressed onto the ABLabsent model to yield estimates of K_{t} and J_{max} as well as P_{p}. This approach quantified bias in K_{t} and J_{max} parameter estimates when ABL is ignored. Parameter value ranges reflect the range of values observed experimentally. Figure 4 plots the true and fitted estimates for K_{t} as a function of J_{max}. The true K_{t} (i.e., the K_{t} value used in simulations) was 5 μM. In Fig. 4, the estimated K_{t} value was about the same as the true K_{t} value when J_{max} was very low. K_{t} estimates below J_{max} of 0.00003 nmol/cm^{2}/s reflected low bias of 0 to 5%. For J_{max} of 0.0003 nmol/cm^{2}/s, K_{t} estimate was about 2fold higher than true K_{t}. For progressively higher J_{max}, K_{t} estimates exhibited very high positive bias (almost 1000fold larger). These results indicate that failure to consider ABL can lead to erroneously large K_{t} estimates at high J_{max}. These results are consistent with experimental taurocholate data in Fig. 1, where high K_{t} was associated with high J_{max}. Simulation results suggest that, in Fig. 1, K_{t} estimates were overestimated due to low monolayer resistance (i.e., low F_{mono}), particularly on occasions when J_{max} was high.
Unlike ABL effect on K_{t} estimates, ABL had no impact on J_{max} estimates (data not shown). This lack of effect is in agreement with earlier studies (Thomson and Dietschy, 1980). There was practical identity between fitted J_{max} and true J_{max} values, indicating that the use of the ABLabsent model did not bias J_{max} estimates. ABL only impacted K_{t} estimates and not J_{max}. Interesting, the ABLabsent and ABLpresent models provided equally good fits to simulated data, based on Akaike information criterion and r^{2} (data not shown).
In the light of abovementioned observations, Fig. 5 reevaluates experimental taurocholate data. The ABLpresent model was used to obtain K_{t} and J_{max} estimates, whose values are plotted in Fig. 5. J_{max} ranged between 0.0001 to 0.001 nmol/s/cm^{2}. K_{t} ranged from about 1 to 12 μM with an average K_{t} estimate of approximately 5 μM. Compared with regression results from the ABLabsent model (i.e., Fig. 1), estimates of K_{t} were about 2 to 3fold lower from the ABLpresent model. J_{max} estimates were the same from each model from both models, as expected from above simulation results. Additionally, P_{p} estimates were the same from both models (data not shown). In contrast to Fig. 1, there was no association between K_{t} estimates and J_{max} estimates in Fig. 5 (p = 0.24; r^{2} = 0.13). This lack of association indicates that correcting for ABL influence lead to a more accurate and less biased estimate of K_{t}.
UWL effects in taurocholate uptake data were also corrected in an analogous fashion (see Appendix 4). It should be noted that the K_{t} estimates for uptake and transport studies were similar (both ∼5 μM), indicating that the configuration of the assay (i.e., uptake versus transport) did not affect K_{t} estimate. This result supports the apical membrane serving as the ratelimiting barrier within the monolayer in transport studies. Hence, a basolateral transporter such as OstαOstβ is not contributing as the ratelimiting barrier. OstαOstβ is a heteromeric transporter that has been recently identified to translocate bile acids in the enterocyte basolateral membrane (Ballatori et al., 2005; Dawson et al., 2005).
Simulations for Objective 2: Identification of Global Kinetic Conditions That Require ABL Consideration. Since high J_{max} can lead to ABLlimited transport and subsequent positive bias in K_{t} estimate, a second objective was to identify global kinetic conditions when ABL needs to be explicitly considered to accurately estimate kinetic parameters. This assessment was carried out via simulations of the ABLabsent and ABLpresent models, using parameter values that reflect the range of observed parameters. The impact of ABL was assessed by J_{ABL}/J; J_{ABL}/J less than 0.9 indicated that ABL is significant.
Figure 6 plots J_{ABL}/J as a function of K_{t} at varying J_{max} and illustrates the interplay of J_{max} and K_{t} in determining ABL impact. In Fig. 6, at low J_{max} and high K_{t} (i.e., poor substrate for transporter), ABL is not significant, as observed by J_{ABL}/J greater than 0.9 (i.e., F_{mono} > 0.9). Overall flux is controlled by monolayer resistance and not by ABL. Meanwhile, for large J_{max} and/or low K_{t}, J_{ABL}/J is low, which reflects a significant role of ABL. In the case of both high J_{max} and low K_{t}, J_{ABL}/J (i.e., F_{mono}) is less that 0.1, reflecting ABL accounts for over 90% of total resistance to transport. Figure 6 is consistent with observed taurocholate data plotted in Figs. 1 and 5, where ABL was modestly important for low J_{max} and very important at high J_{max}. Similar dependence on J_{max} is evident in Fig. 6.
These results comparing J_{ABL} and J indicate that ABL needs to be explicitly considered for all potent substrates (i.e., K_{t} less than or equal to 10 μM), even in low expression systems (i.e., J_{max} > 0.00003 nmol/cm^{2}/s). Additionally, at J_{max} greater than 0.001 nmol/cm^{2}/s, as observed for hASBTMDCK, ABL needs to be considered even when K_{t} is as large as 100 μM. Given the high hASBT expression from the current hASBTMDCK model, the simulations anticipate the need to employ the ABLpresent model for all native bile acids. Interestingly, these simulations suggest lowered hASBT expression (i.e., lower J_{max}) as an approach to minimize ABL influence on transport. Future laboratory studies will employ hASBTMDCK monolayers with reduced hASBT expression, especially for potent substrates, to minimize ABL influence.
Simulation studies were also performed for transport inhibition studies to identify global kinetic conditions that require ABL consideration for accurate K_{i} estimation. Previous studies have not examined diffusion barrier effects on K_{i} estimation. Figure 7 plots J_{ABL}/J as a function of inhibitor concentration and J_{max}. At low J_{max}, J_{ABL}/J was greater than 0.9, indicating lack of ABL effect. However, J_{ABL}/J decreased with increasing J_{max} and reached 0.4 and lower at J_{max} = 0.01 nmol/cm^{2}/s, indicating significant ABL effect under these conditions. These observations are similar to the results from the corresponding transport simulations (Fig. 3). The consequence of low J_{ABL}/J (observed in Fig. 7) on K_{i} estimates is shown in Fig. 8. Figure 8 plots the true and fitted estimates for K_{i} as a function of J_{max}. The true K_{i} (i.e., the K_{i} value employed in simulations) was 50 μM. For J_{max} of 0.0001 nmol/cm^{2}/s, K_{i} estimate was ∼27 μM (i.e., ∼2fold lower than true K_{i}). For progressively higher J_{max}, K_{i} estimates exhibited very high negative bias (∼10fold lower). These results indicate that failure to consider the contribution of ABL leads to erroneously low K_{i} estimates, particularly at high J_{max}. Figure 9 further details the interplay of J_{max} and K_{t} in determining the impact of ABL on bias in K_{i} estimates, using errorfree data. In all situations, K_{i} estimates were negatively biased, particularly for low K_{t} values, regardless of J_{max}. Bias is greatest at low K_{t} values and high J_{max}, due to low monolayer resistance for the substrate. In essence, when ABL is not considered, K_{i} “takes credit” for the ABL effect, leading to biased K_{i} estimate. This analysis of simulation/regression indicates that bias in K_{i} estimates is greatest when the substrate is very potent (i.e., low K_{t}), and this effect is amplified at high J_{max}.
These simulation results are consistent with experimental taurocholate selfinhibition data (Table 1). For each of the twelve occasions, the ABL absent inhibition model (eq. 10) provided a lower K_{i} than did the ABL present inhibition model (eq. 11).
Simulations for Objective 3: Identification of Global Kinetic Conditions WhenK_{t} Estimates Are Unreliable as a Result of ABL Contribution.Figure 6 indicates that J_{ABL} is less than 10% J for several scenarios. These observations from errorfree simulations motivated a more detailed evaluation, using simulations that incorporate 15% random error. This evaluation aimed to identify conditions under which kinetic parameters cannot be precisely estimated due to the combination of ABLcontrolled transport and modest experimental variability.
Table 2 indicates the probability of successfully estimating K_{t} estimates under different scenarios of K_{t} and J_{max} using errorinclusive simulated flux data. Estimation of K_{t} was deemed successful if the 95% confidence interval for the K_{t} estimate did not include zero. For each of the fifteen scenarios, Table 2 also denotes the percentage of total resistance that is attributed to ABL. As expected from objective 2 results, the probability of successful K_{t} estimation was low when J_{max} was high and true K_{t} was less than 10 μM. For example, the probability was only 10% when true K_{t} = 1 μM and J_{max} = 0.001 nmol/cm^{2}/s. In general, the probability of success increased for progressively lower J_{max} and progressively higher K_{t}. For example, when true K_{t} = 5 μM and J_{max} = 0.0001 nmol/cm^{2}/s, the probability was 91%. This trend is attributed to progressively lower contribution of ABL to overall control of flux. To a first approximation, the probability of failing to estimate K_{t} is equal to the percentage of resistance due to ABL. J_{max} was successfully estimated in almost all occasions, as expected based on previous studies (Thomson and Dietschy, 1980) and results from objective 2 in the present study.
A result not anticipated from errorfree simulation is the modest decrease in successful K_{t} estimation in Table 2 at high K_{t}. At K_{t} of 25 μM, the abovementioned trend was reversed, such that probability of success drops for progressively lower J_{max}. At high K_{t} scenarios, the passive flux component contributes significantly to overall flux, especially when J_{max} is low, leading to modest decrease in successful K_{t} estimation.
Discussion
Kinetics of hASBTMediated Taurocholate Flux Using ABLAbsent Model. hASBT is under investigation as a target to increase the oral absorption of drug candidates through a prodrug approach (Balakrishnan and Polli, 2006). An hASBTMDCK monolayer model was developed previously (Balakrishnan et al., 2005). Specificity of hASBTmediated transport of taurocholate was based upon a number of observations (e.g., hASBTtransfected versus mocktransfected studies, nosodium versus sodiumcontaining studies, apicaltobasolateral versus basolateraltoapical studies, lack of taurocholate inhibition by DIDS or probenecid, confocal imaging of hASBT in the hASBTMDCK model, and similar K_{t} estimates in monolayer transport and uptake studies). It should be noted that, although the hASBTMDCK is used to elucidate the substrate requirements of hASBT, bile acids are substrates for the recently identified OstαOstβ heteromeric transporter in the enterocyte basolateral membrane (Ballatori et al., 2005; Dawson et al., 2005). However, as noted above, results here do not reflect OstαOstβ kinetic activity, but reflect hASBT kinetic activity, since K_{t} estimates for uptake and transport studies were similar. Additionally, taurocholate transport was unaffected by the OstαOstβ inhibitor bromosulphaelin (Seward et al., 2003; Balakrishnan et al., 2006).
Taurocholate flux across hASBTMDCK monolayers are routinely performed. Motivation for the present study was the observed positive association between taurocholate J_{max} and K_{t} estimates, where the ABLabsent model was used. The ABLabsent model is the model typically used in analyzing flux data from cell culture transporter assay systems. K_{t} and J_{max} estimates exhibited significant variation across occasions. K_{t} ranged from ∼2 to 27 μM. J_{max} ranged between 0.0001 and 0.001 nmol/s/cm^{2}. In Fig. 1, there was a strong linear association between K_{t} and J_{max} estimates (r^{2} = 0.82; p > 0.001). Variability in J_{max} can be ascribed to variability in hASBT expression (see Appendix 3). However, variability in K_{t}, particularly K_{t} variation that is associated with J_{max}, was difficult to explain. This association yielded the following hypothesis: high transporter expression can lower monolayer resistance, resulting in ABLlimited transport of solutes, leading to biased kinetic estimates if ABL is not considered. Three objectives were pursued in challenging this hypothesis.
Simulations for Objective 1: Impact of VaryingJ_{max}on ABL Contribution. The first objective was to evaluate the effect of J_{max} on the contribution of ABL resistance to transporter kinetics. Objective 1 was carried out through a combination of empirical laboratory studies, as well as errorfree simulation/regression studies. Results indicate that failure to consider ABL can lead to erroneously large K_{t} estimates at high J_{max}. Results were consistent with experimental taurocholate data in Fig. 1, where high K_{t} was associated with high J_{max}. Simulation results suggest that, in Fig. 1, K_{t} estimates were overestimated due to low monolayer resistance (i.e., low F_{mono}), particularly on occasions when J_{max} was high.
Figure 5 reevaluates experimental taurocholate data. The ABLpresent model was employed to obtain K_{t} and J_{max} estimates, whose values are plotted in Fig. 5. Compared with regression results from the ABLabsent model (i.e., Fig. 1), estimates of K_{t} were about 2 to 3fold lower from the ABLpresent model. In contrast to Fig. 1, there was no association between K_{t} estimates and J_{max} estimates in Fig. 5 (p = 0.24; r^{2} = 0.13). This lack of association indicates that correcting for ABL influence lead to a more accurate and less biased estimate of K_{t}. It should be noted that variability in K_{t} was not completely eliminated. Contributions to the remaining unexplained variation are variation in flux measurements and parameter estimation error.
Simulations for Objective 2: Identification of Global Kinetic Conditions That Require ABL Consideration. The second objective was to identify global kinetic conditions when ABL needs to be explicitly considered to accurately estimate kinetic parameters. Objective 2 was conducted through errorfree simulations of both transport and inhibition studies. Results indicate that ABL can generally modulate hASBT kinetics, particularly for all potent substrates, even in low expression systems. Additionally, at J_{max} greater than 0.001 nmol/cm^{2}/s, as observed for hASBTMDCK, ABL needs to be considered even when K_{t} is as large as 100 μM. Interestingly, results suggest lower hASBT expression as an approach to minimize ABL influence on transport. Simulation studies were also performed for transport inhibition studies, which revealed that failure to consider the contribution of ABL leads to erroneously low K_{i} estimates, particularly at high J_{max}.
However, it should also be noted that ABL effect depends on substrate K_{t} and J_{max} in the particular assay system, and therefore ABL is not always significant. For example, ABL influence is not significant for a lowaffinity transporter such as hPEPT1. HerreraRuiz et al. (2003) developed a stably transfected hPEPT1MDCK cell line with varying expression levels. K_{t} of glycyl sarcosine was 400 μM. From Fig. 6 here, it can be inferred that ABL influence would not be significant for this substrate until very high J_{max} (i.e., until over 0.001 nmol/s/cm^{2}) is attained. Lack of effect was evident experimentally from HerreraRuiz et al. (2003) since glycyl sarcosine K_{t} estimate did not vary with varying J_{max}. A second example illustrates a modest ABL effect in an organic anion transporter (OAT3) study (Zhang et al., 2004). Uptake of estrone sulfate into rabbit OAT3Chinese hamster ovary exhibited K_{t} and J_{max} of 4 μM and 0.000413 nmol/s/cm^{2}, respectively, indicating high affinity of estrone sulfate for OAT3. From Figs. 4 and 6 here, low K_{t} of estrone sulfate would seem to be overestimated by 2fold.
Simulations for Objective 3: Identification of Global Kinetic Conditions WhenK_{t} Estimates Are Unreliable as a Result of ABL Contribution. The third objective was to identify scenarios under which kinetic estimates are not reliable in spite of ABL consideration, due to ABL dominated transport kinetics. Objective 3 was carried out through simulations incorporating 15% random error, to estimate the probability of successfully estimating K_{t}. In general, the probability of success increased for progressively lower J_{max} and progressively higher K_{t}. To a first approximation, the probability of failing to estimate K_{t} is equal to the percentage of resistance due to ABL.
These results have implication for the functional characterization and development of QSAR models of transporters. QSAR models rely on kinetic parameters (e.g., J_{max}, K_{t}, and K_{i}) to relate structural features of substrate/inhibitor to activity. Data sets for QSAR analysis typically make up kinetic estimates collected across different occasions, including over years, and across laboratories. Since transport expression levels vary across occasions, results here imply the quality of kinetic parameter estimates can vary with occasion, if ABL effects are ignored. Biased kinetic parameters underestimate the affinity of potent substrates and overestimate the inhibition potency of modest and poor inhibitors, leading to error in QSAR models.
In summary, our combined data indicate that the ABL resistance layer can have significant impact on carriermediated solute transport in overexpression systems. This effect was always observed for hASBTMDCK, but it was most prominent on occasions when J_{max} was high. Failure to consider ABL lead to positively biased estimates of K_{t} and negatively biased estimates of K_{i}. The extent of bias is determined collectively by expression level and substrate affinity, such that ABL effect is most prominent for conditions that lead to lowered monolayer resistance (i.e., high J_{max} and low K_{t}). Results provide three possibilities: 1) monolayer resistance is sufficiently high (i.e., low J_{max} and high K_{t}) such that ABL can be ignored and kinetic parameters can be estimated with accuracy and precision; 2) monolayer resistance is sufficiently high but ABL cannot be ignored for the accurate and precise estimation of kinetic estimates; and 3) monolayer resistance for substrate is low (high J_{max} and low K_{t}) such that flux is highly ABLcontrolled, and even consideration of ABL does not allow for accurate and precise estimation of kinetic parameters.
APPENDIX 1
The objective of Appendix 1 is to derive eq. 9. For the ABLpresent model:
Hence, in comparing the relative resistances in the ABLabsent model and the ABLpresent model, where F_{mono} is the fraction of total flux resistance that is due to the monolayer.
APPENDIX 2
The objective of Appendix 2 is to derive the ABLpresent inhibition model (i.e., eq. 11).
Substrate flux in the presence of an inhibitor when ABL is absent is described by where I is the concentration of inhibitor (i.e., inhibitory bile acid), and K_{i} is inhibitory constant. S is substrate concentration (i.e., taurocholate concentration); J_{max}, K_{t}, and P_{p} characterize substrate transport parameters.
In the ABLpresent model, since permeability is the inverse of resistance, where P_{app} is the apparent permeability, P_{ABL} is the ABL permeability, and P_{mono} is the monolayer permeability.
From eq. 17, monolayer permeability in the presence of inhibitor is Substituting eq. 19 into eq. 18, since J_{ABL} = P_{app} × S,
APPENDIX 3
The objectives of Appendix 3 are to 1) provide support for the presumption that, in Fig. 1, variation in J_{max} can be ascribed to variation in hASBT expression; and 2) provide further support that ABL influence is modulated by J_{max}. Figure 1 inspired the hypothesis that high transporter expression can lower monolayer resistance, resulting in ABLlimited transport of solutes, leading to biased kinetic estimates if ABL is not considered.
Figure 10 shows Western blot analysis of hASBT expressed at cell surface (Fig. 10A) as well as correlation between measure J_{max} and hASBT expression level (relative to integrin) (Fig. 10B). In Fig. 10A, Western blots were consistent with expected results, where hASBT expression decreased in the following order: lane A (hASBTMDCK treated with 10 mM sodium butyrate) > lane B (hASBTMDCK treated with 5 mM sodium butyrate) > lane C (hASBTMDCK treated with no sodium butyrate) > lane D (untransfected MDCK). In Fig. 10B, hASBT expression level from band density analysis using pixel intensity provided linear association (r^{2} = 0.994) with measured taurocholate J_{max} values, which were 10.0 ± 0.3 × 10^{–4}, 6.59 ± 0.21 × 10^{–4}, and 1.29 ± 0.05 × 10^{–4} nmol/cm^{2}/s for lanes A, B, and C, respectively. Untransfected MDCK (lane D) showed no active taurocholate flux. Hence, variation in J_{max} was attributable to variation in hASBT expression at cell surface. A similar analysis was performed by Irie et al. (2006), where PEPT1 mRNA level was linearly associated with GlySar J_{max} values (r = 0.55) across Caco2 clones (Irie et al., 2006).
As expected, when ABLinfluence was not considered, the K_{t} estimates were positively association with J_{max}; K_{t} values were 19.6 ± 2.4, 15.3 ± 1.72, and 7.47 ± 0.50 μM for lanes A, B, and C, respectively. When the ABLpresent model was applied to this same data, this association was abolished; K_{t} values were 3.24 ± 1.01, 3.73 ± 0.70, 5.77 ± 0.40 μM for lanes A, B, and C, respectively. Result here from hASBTMDCK monolayers subjected to differing levels of induction by sodium butyrate provide further support that ABL influence is modulated by J_{max}.
APPENDIX 4
The objective of Appendix 4 is to evaluate the ability of the ABLpresent model to accurately estimate kinetic parameter estimates from uptake studies (i.e., J_{max} and K_{t}), relative to the Winne uptake model. Taurocholate uptake data from five occasions were regressed onto eqs. 7 and 8 using SigmaPlot 2000 (SPSS Inc.). Kinetic parameters were compared via the paired t test.
This comparison is motivated since Winne's uptake model is tailored for uptake configuration. Winne's uptake model would seem not be applicable to transport studies, by virtue of its high identifiability as an uptake model. Favorable performance of the ABLpresent model in assessing uptake data, compared with the Winne's uptake model, would support the ABLpresent model to serve as a single form to analyze both transport and uptake data that require ABL consideration.
For each occasion, J_{max} and K_{t} values from the ABLpresent model were statistically indistinguishable from J_{max} and K_{t} values from Winne's uptake model (p > 0.05). Additionally, the ABLpresent model effectively eliminated the bias in K_{t} that otherwise results from ABL. As was observed from transport studies in Fig. 1, there was a positive, linear association between K_{t} and J_{max}, when the ABLabsent model was applied to uptake data (r^{2} = 0.79). Application of the ABLpresent model markedly attenuated the association (r^{2} = 0.08), as did the Winne uptake model.
Favorable performance of the ABLpresent model in assessing uptake data supports the ABLpresent model to serve as a single form to analyze both transport and uptake data that require ABL consideration.
Footnotes

This work was support in part by National Institutes of Health Grants DK067530 (to J.E.P.) and DK61425 (to P.W.S.).

Article, publication date, and citation information can be found at http://jpet.aspetjournals.org.

doi:10.1124/jpet.106.107433.

ABBREVIATIONS: hASBT, human apical sodiumdependent bile acid transporter; MDCK, MadinDarby canine kidney; HBSS, Hanks' balanced salt solution; QSAR, quantitativestructure activity relationship; ABL, aqueous boundary layer; UWL, unstirred water layer; HRP, horseradish peroxidase; OAT, organic anion transporter.

↵1 Current affiliation: Merck and Co., Inc. West Point, Pennsylvania.
 Received May 5, 2006.
 Accepted October 11, 2006.
 The American Society for Pharmacology and Experimental Therapeutics