Bias in Estimation of Transporter Kinetic Parameters from Overexpression Systems: Interplay of...

Bias in Estimation of Transporter Kinetic Parameters fromOverexpression Systems: Interplay of Transporter ExpressionLevel and Substrate Affinity

Anand Balakrishnan,1 Naissan Hussainzada, Pablo Gonzalez, Marival Bermejo,Peter W. Swaan, and James E. PolliDepartment of Pharmaceutical Sciences, School of Pharmacy, University of Maryland, Baltimore, Maryland (A.B., N.H., P.G.,P.W.S., J.E.P.); and Department of Pharmacy and Technology, University of Valencia, Valencia, Spain (M.B.)

Received May 5, 2006; accepted October 11, 2006

ABSTRACTThe objective was to investigate the interplay between trans-porter expression levels and substrate affinity in controlling theinfluence of aqueous boundary layer (ABL) resistance on trans-porter kinetics in an over-expression system. Taurocholate fluxwas measured across human apical sodium-dependent bileacid transporter (hASBT)-Madin-Darby canine kidney monolay-ers on different occasions and kinetic parameters estimatedwith and without considering ABL. In error-free simulation/regression studies, flux values were generated across a rangeof Jmax, Kt, and substrate concentrations. Similar evaluationwas performed for transport inhibition studies. Additionally,simulation/regression studies were performed, incorporating15% random error to estimate the probability of successfullyestimating Kt. Across different occasions, experimental Jmaxand Kt estimates for taurocholate were strongly associated (p �0.001; r2 � 0.82) when ABL was not considered. Simulation/regression results indicate that not considering ABL caused

this association, such that Kt estimates were highly positivelybiased at high hASBT expression. In reanalyzing taurocholateflux data using the ABL-present model, Kt was relatively con-stant across occasions (�5 �M) and not associated with Jmax(p � 0.24; r2 � 0.13). Simulations suggest that Jmax and Ktcollectively determined ABL influence, which is most prominentunder conditions of low monolayer resistance. Additionally, notconsidering ABL lead to negatively biased Ki estimates, espe-cially at high Jmax. Error-inclusive simulation/regression studiesindicated that the probability of successfully estimating Kt de-pended on the contribution of ABL resistance to flux; when fluxbecame increasingly ABL-limited, probability of success de-creased. Results indicate that ABL resistance can bias Kt and Kiestimates from overexpression systems, where the extent ofbias is determined by transporter expression level and sub-strate affinity.

Transfected cell models overexpressing specific transport-ers are a powerful tool to characterize substrate require-ments of the transporter, including its ability to translocatedrugs and prodrugs (Herrera-Ruiz et al., 2003; Tolle-Sanderet al., 2004; Balakrishnan et al., 2005; Balakrishnan andPolli, 2006). Relative to native cells and in vivo systems,transfected cell models frequently have the advantage ofcharacterizing a transporter without confounding variables,such as other simultaneously expressing transporters with

overlapping substrate requirements. This benefit is achievedin part through high expression of the transporter of interest.

We recently developed a stably transfected cell model forthe human apical sodium-dependent bile acid transporter(hASBT), using MDCK cells (Balakrishnan et al., 2005) thatpossesses several favorable properties, including highhASBT expression. This hASBT-MDCK model was furtherdeveloped to yield kinetic estimates of substrates and/or in-hibitors (e.g., Jmax, Kt, and Ki) that can be used for subse-quent quantitative-structure activity relationship (QSAR)analysis. Thus, overexpression systems can be used suitablyfor functional characterization of transporters.

In general, transporter expression level is expected to varybetween occasions (i.e., vary between passages or cell cultureconditions) (Yu et al., 1997; Polli et al., 2001). As an example,Fig. 1 summarizes the kinetic analysis of hASBT-mediated

This work was support in part by National Institutes of Health GrantsDK067530 (to J.E.P.) and DK61425 (to P.W.S.).

1 Current affiliation: Merck and Co., Inc. West Point, Pennsylvania.Article, publication date, and citation information can be found at

http://jpet.aspetjournals.org.doi:10.1124/jpet.106.107433.

ABBREVIATIONS: hASBT, human apical sodium-dependent bile acid transporter; MDCK, Madin-Darby canine kidney; HBSS, Hanks’ balancedsalt solution; QSAR, quantitative-structure activity relationship; ABL, aqueous boundary layer; UWL, unstirred water layer; HRP, horseradishperoxidase; OAT, organic anion transporter.

0022-3565/07/3201-133–144$20.00THE JOURNAL OF PHARMACOLOGY AND EXPERIMENTAL THERAPEUTICS Vol. 320, No. 1Copyright © 2007 by The American Society for Pharmacology and Experimental Therapeutics 107433/3163224JPET 320:133–144, 2007 Printed in U.S.A.

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taurocholate transport across hASBT-MDCK monolayersfrom 12 different occasions. As anticipated, Jmax estimatesvaried severalfold across occasions. Kt also varied acrossoccasions and exhibited strong, positive association withJmax estimates (p � 0.0001; r2 � 0.82) (Fig. 1). Ideally, Kt canbe expected to be constant across occasions and independentof expression levels. However, Jmax and Kt were estimatedusing a transport model that does not consider contributionof aqueous boundary layer (ABL) resistance. The presentmanuscript considers ABL as a lumped parameter composedof the apical unstirred water layer (UWL), support filter, andbasolateral UWL. These diffusional barriers are encounteredin flux studies across a monolayer grown on support filters.These diffusion barriers are lumped together, since it is dif-ficult to reliably delineate them experimentally. Previoustheoretical and experimental reports considered the presenceof a single UWL situated apical to the biological membrane(i.e., an apical UWL) and indicated that failure to considerthe UWL can result in inaccurate Kt estimates (Winne, 1973,1977, 1978; Thomson and Dietschy, 1977, 1980; Thomson,1979; Barry and Diamond, 1984; Sinko et al., 1996). Thesereports have indicated the potential for UWL effects on activetransport. Based on our previous data and reports by others,we hypothesized that high transporter expression can lowermonolayer resistance, resulting in ABL-limited transport ofsolutes, leading to biased kinetic estimates if ABL is notconsidered.

One distinction between the present study and previousreports is the use of an overexpression system, where highexpression level of transporter was achieved. Previous re-ports have clearly demonstrated UWL effect on Kt estimates,but it is not clear how variability in high transporter expres-sion level impacts the quality of kinetic estimates, as ob-served in Fig. 1. Use of a monolayer flux assay also underpinsa second difference between the present study and previousreports. Previous models assumed a single UWL, followed bya biological membrane (Winne, 1973, 1977, 1978; Thomsonand Dietschy, 1977, 1980; Thomson, 1979). These studiesevaluated in vivo perfusion studies, where the UWL repre-sents a diffusion barrier between the bulk and the mem-brane. Unfortunately, the diffusion barriers in a monolayerflux configuration are less determinant since they arepresent at the apical interface, the basolateral interface, and

via the support filter. The present study puts forth a trans-port model that reflects the cell culture monolayer flux assay.This transport model was extended to identify an inhibitionmodel, an area unexplored by previous studies.

This study evaluates the interplay of transporter expres-sion levels and substrate affinity in determining the role ofABL resistance on transporter kinetics using hASBT as amodel transport system. The objectives were to 1) evaluatethe effect of Jmax on the contribution of ABL resistance totransporter kinetics, 2) identify global kinetic conditionswhen ABL needs to be explicitly considered to accuratelyestimate kinetic parameters, and 3) identify scenarios underwhich kinetic estimates are not reliable in spite of ABLconsideration, due to ABL-dominated transport kinetics. Ob-jective 1 was carried out through a combination of empiricallaboratory studies as well as error-free simulation/regressionstudies. Objective 2 was conducted through error-free simu-lations of both transport and inhibition studies. Objective 3was carried out through simulations incorporating 15% ran-dom error.

Given the broad use of overexpression systems to charac-terize transporter kinetics and given transporter expressionvariability over time, these results have implications in thedevelopment of high expression cell culture assays, as well asQSAR models and drug discovery efforts that rely on accu-rate kinetic parameter estimates.

Materials and MethodsTransport Studies: ABL-Absent Model. Figure 2 illustrates

two competing models to describe bile acid transport across anhASBT-MDCK monolayer. The models differ in the absence or pres-ence of an ABL. In Fig. 2A, the ABL-absent model is illustrated and

Fig. 1. Plot of taurocholate Kt estimates versus taurocholate Jmax esti-mates across different days, using ABL-absent model. There was a strongpositive relation between Jmax and Kt for hASBT-mediated taurocholateflux across hASBT-MDCK monolayers. Jmax variation can be ascribed today-to-day variation in hASBT expression. Day-to-day variation in Kt,especially Kt variation that correlates with Jmax, cannot be explained bythe ABL-absent model.

Fig. 2. ABL-absent model and ABL-present model. A and B, two compet-ing models describing bile acid transport across an hASBT-MDCK mono-layer are considered and are denoted the ABL-absent model and theABL-present model. C, ABL-present model for uptake studies. In A, theABL-absent model is illustrated and only considers monolayer resistanceto limit flux, resulting in eq. 1; the resistance due to the support filter andunstirred water layers(s) are considered negligible. Mechanisms of bileacid permeation across the monolayer are active hASBT transport andpassive permeability. In B, the ABL-present model is illustrated. In eq. 7,the support filter, the apical unstirred water layer, and the basolateralunstirred water layer are collectively denoted as the ABL. In uptakestudies (C), the term ABL includes only the apical unstirred water layer.The permeability across the ABL is PABL such that this term representsthe permeability across barriers other than the cell monolayer.

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only considers monolayer resistance to limit flux. Mechanisms of bileacid permeation across the monolayer are active hASBT transportand passive permeability. hASBT is located in the apical membraneand is the dominant mechanism for bile acid absorption (Dawson etal., 2003; Balakrishnan et al., 2005).

From Fig. 2A, the ABL-absent model is as follows:

J �Jmax � SKt � S

� Pp � S (1)

where J is bile acid flux when ABL is absent, Jmax and Kt are theMichaelis-Menten constants for hASBT-mediated transport, S is bileacid substrate concentration, and Pp is the passive permeabilitycoefficient. Jmax and Kt are sometimes denoted Vmax and Km, respec-tively, in the transporter literature.

Transport Studies: ABL-Present Model. The ABL-presentmodel is illustrated in Fig. 2B. The term ABL includes the apicalUWL, the support filter, and the basolateral UWL. ABL is consid-ered a lumped parameter made up of these three components, sinceit is difficult to reliably delineate these individual barriers experi-mentally. The permeability across the ABL is PABL, such that thisterm represents the permeability across barriers other than themonolayer. As discussed below, PABL was estimated by measuringthe permeability of taurocholate across blank filter in the absence ofcells.

From Fig. 2B, the apparent resistance to flux is as follows:

Rapp � RABL � Rmono (2)

where Rapp is the apparent resistance, RABL is the resistance due tothe ABL, and Rmono is the resistance due to the monolayer itself (i.e.,monolayer resistance). Since permeability is the inverse of resis-tance,

1Papp

�1

PABL�

1Pmono

(3)

where Papp is the apparent permeability, PABL is the ABL perme-ability, and Pmono is the monolayer permeability. From the contribu-tions of hASBT-mediated transport and parallel passive bile acidpermeability to monolayer permeability,

Pmono �Jmax

Kt � S� Pp (4)

Substituting eq. 4 into eq. 3,

1Papp

�1

PABL�

1Jmax

Kt � S� Pp

(5)

Papp �

PABL � � Jmax

Kt � S� Pp�

PABL �Jmax

Kt � S� Pp

(6)

Since JABL � Papp � S,

JABL �

PABL � � Jmax

Kt � S� Pp�� S

PABL �Jmax

Kt � S� Pp

(7)

where JABL is bile acid flux when ABL is present. Equation 7 isdenoted the ABL-present model.

Comparison of the ABL-Present Model to the Uptake Modelof Winne. Equation 7 differs from the uptake model of Winne (1977),which can be written as follows:

JUWL � PUWL�S �q2�Kt

q�

Jmax

PUWL� S�

� �q2

4�Kt

q�

Jmax

PUWL� S�2

� qKtS� (8)

where JUWL is the flux when a single UWL is present before themembrane, PUWL is the permeability of the UWL, and q � PUWL/(Pp

� PUWL). Jmax, Kt, Pp, and S represent the same parameters in botheqs. 7 and 8. Equation 8 simplifies the original Winne equation byequating the area of the UWL to the area of the membrane as well asby substituting PUWL for the ratio of the diffusivity coefficient to theUWL thickness.

Underpinning the difference between the ABL-present model andthe Winne uptake model is the number and arrangement of diffusionbarriers, relative to the biological membrane. In the uptake model ofWinne, only an apical UWL is present. Winne et al. applied eq. 8 toassess the role of the UWL in the absorption of phenylalanine (Winneet al., 1979) using the perfused rat jejunal loop. Justification ofWinne’s model would seem to be the presence of an UWL within theloop lumen, with no other significant diffusion barriers, except thejejunal loop membrane. Strength of the Winne uptake model is itsdifferentiation between the bulk donor solution concentration (S)and the concentration at the UWL-membrane interface, particularlycompared against the ABL-present model.

Winne’s model cannot be applied to transport studies across a cellmonolayer since it fails to consider diffusional resistances other thanthe apical UWL. Complicating this scenario is the arrangement of adiffusion barrier on the luminal side of the monolayer (i.e., apicalUWL) and two diffusion barriers on the other side (i.e., support filterand basolateral UWL). A further limitation is an insufficient under-standing of these diffusion barriers since the permeability of eachbarrier is difficult to measure in a reliable manner. The approach inthe present manuscript was to characterize these three barriers as asingle resistivity RABL, per eq. 2 (i.e., a single permeability PABL; pereq. 3). This single barrier is denoted the ABL. PABL was estimated bymeasuring the permeability of taurocholate across blank filter in theabsence of cells (Yu and Sinko, 1997). Briefly, in Fig. 2B, whenmonolayer present, the support filter, the apical unstirred waterlayer, and the basolateral unstirred water layer are present andcollectively denoted as the ABL. When monolayer absent, theseelements are still present. Hence, ABL was estimated by measuringtaurocholate flux across blank support filter.

Measure of Monolayer Resistance. Equations 1 and 7 (i.e., theABL-absent and ABL-present models) each allow for a nonlinear,Michaelis-Menten-type component as well as linear, passive trans-port component. The two models differ with respect to the contribu-tion of the ABL on flux. In Fig. 2A, ABL is absent, such that the onlyrate-limiting barrier in eq. 1 is the monolayer. In Fig. 2B, ABL ispresent, reflecting that ABL contributes as a barrier to flux in eq. 7.Qualitatively, a high ABL resistance relative to monolayer resis-tance results in flux limited by ABL. In addition, high monolayerresistance relative to ABL results in flux limited by monolayer, as inFig. 2A.

The ratio of flux from the ABL-present model to the flux from theABL-absent model (JABL/J) is used to assess the impact of ABL onflux. Of note, JABL/J is also numerically equivalent to the fraction oftotal flux resistance that is attributed to the monolayer:

Fmono �JABL

J(9)

where Fmono is the fraction of total flux resistance that is due to themonolayer. Appendix 1 derives eq. 9. Monolayer resistance excludescomponents of the ABL such as the support filter and apical andbasolateral UWLs. From eq. 9, JABL/J � 1 indicates that flux islimited by monolayer resistance only (i.e., Fmono � 1). Meanwhile,JABL/J � 0.1 indicates that the monolayer contributes to only 10% of

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the total resistance (i.e., Fmono � 0.1), with the ABL contributing theremaining 90%.

Transport Inhibition Studies. For competitive inhibition stud-ies of taurocholate transport by bile acids, the following transportinhibition model describes taurocholate transport when ABL is ab-sent:

J �Jmax � S

Kt�1 � I/Kt� � S� Pp � S (10)

where I is the concentration of inhibitor (i.e., inhibitory bile acid) andKi is inhibition constant. S is substrate concentration (i.e., tauro-cholate concentration); Jmax, Kt, and Pp characterize substrate trans-port parameters. Equation 10 is denoted the ABL-absent inhibitionmodel.

When the ABL is included, the competitive inhibition model be-comes:

JABL �

PABL � � Jmax

Kt�1 � I/Kt� � S� Pp�� S

PABL � � Jmax

Kt�1 � I/Kt� � S�� Pp

(11)

where PABL is ABL permeability. Equation 11 is denoted the ABL-present inhibition model. This model is derived in Appendix 2.

Taurocholate Transport across hASBT Monolayers. Tauro-cholate was used as a model substrate for hASBT. On 12 occasions,apical-to-basal taurocholate flux was measured across an hASBT-MDCK monolayer model, as described previously (Balakrishnan etal., 2005). Briefly, hASBT-MDCK cells were seeded at a density of0.75 million cells/cm2 on support filter (polyester Transwell, 0.4-�mpore size, 1 cm2; Corning Life Sciences, Corning, NY). Kinetics ofhASBT-mediated taurocholate flux was assessed from transportstudies (n � 3) at differing donor concentrations (1–200 �M spikedwith [3H]taurocholate). Transport was performed using HBSS with10 mM HEPES, pH 6.8, at 37°C and 50 rpm. Sample was obtainedfrom basolateral compartment at 30 min, well after steady state wasattained (by 5 min). Sink conditions prevailed in all studies. Sinkconditions refer to the low accumulation of substrate into basolateralcompartment, as to essentially not bias results. This situation wasattained by ensuring that substrate concentration in the receivercompartment never exceeded 10% of donor substrate concentration.In all studies, [14C]mannitol was used to monitor monolayer integ-rity. 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 ABL-absent model

(i.e., eq. 1) as well as the ABL-present model (i.e., eq. 7), providingestimates for Jmax, Kt, and Pp for each of the two model scenarios. Ineq. 7, PABL was assigned, based upon taurocholate flux data acrosssupport filters without monolayers, as discussed below.

Nonlinear regression to eqs. 1 and 7 was performed using Sig-maPlot 2000 (SPSS Inc., Chicago, IL). Correlation among parameterestimates was evaluated using Pearson correlation coefficient usingSPSS 12.0 (SPSS Inc.).

Taurocholate Uptake into hASBT Monolayers. In contrast totransport studies, uptake studies only concern the translocation oftaurocholate across the apical membrane and into the cytosol. Onfive occasions, taurocholate uptake into hASBT-MDCK monolayerswere assessed as described previously (Balakrishnan et al., 2005).

In brief, hASBT-MDCK cells were seeded at a density of 1.5million cells/well on 12-well plates (Corning Life Sciences). Kineticsof hASBT-mediated taurocholate uptake was assessed from uptakestudies (n � 3) at differing donor concentrations (1–200 �M spikedwith [3H]taurocholate). Studies were performed using HBSS with 10mM HEPES, pH 6.8, at 37°C and 50 rpm for 10 min. The 10-min timepoint was selected since taurocholate uptake was linear over 10 min(Balakrishnan et al., 2005). The donor solution was removed and thecells 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 mlof 1 N HCl. Cell lysate was then counted for associated radioactivityusing a liquid scintillation counter (Beckman Instruments, Inc., Ful-lerton, CA).

Flux data from each occasion were fitted to the ABL-absent model(i.e., eq. 1) as well as the ABL-present model (i.e., eq. 7), providingestimates for Jmax, Kt, and Pp for each of the two model scenarios. Ineq. 7, PABL was assigned, based upon diazepam uptake data, asdiscussed below. Nonlinear regression to eqs. 1 and 7 was performedusing SigmaPlot 2000 (SPSS Inc.). Correlation among parameterestimates was evaluated using Pearson correlation coefficient usingSPSS 12.0 (SPSS Inc.).

Taurocholate Transport across Support Filter withouthASBT-MDCK Monolayer to Estimate PABL for TransportStudies. It is difficult to directly measure the net effect of theaqueous boundary layer at the apical interface, the aqueous bound-ary layer at the basolateral interface, and the plastic filter (i.e., PABL)when cell monolayer is present. When an estimate of PABL is sought,a common approach to measure PABL is to use blank filter (Imanidiset al., 1996; Yu and Sinko, 1997). Hence, taurocholate transportacross blank support filters (i.e., polyester Transwell without cellmonolayer) was performed as described above. The underlying as-sumption in this approach is that the ABL in the ABL-present modelin Fig. 2B is the same whether a monolayer is present or not present.Flux studies were performed using HBSS with 10 mM HEPES, pH6.8, at 37°C and 50 rpm. At 5 min, sample was collected from thereceiver compartment and allowed for sink conditions to be main-tained. Taurocholate permeability across blank support filters was66.1 6.0 � 10�6 cm/s, which was taken to be equal to PABL. Thisvalue was in agreement with that of (Buur and Mork, 1992).

PABL served as a lumped parameter in eqs. 7 and 11 to character-ize ABL, since it is difficult to reliably measure the permeability ofthe apical unstirred water layer, the support filter, and the basolat-eral unstirred water layer individually. It should be noted that Yuand Sinko (1997) and Adson et al. (1994) have attempted to uncouplesome of these barrier components, although active transport was notconsidered. Adson et al. (1994) calculated a value for the permeabil-ity of the support filter, based upon a porous membrane model andparameters provided by the manufacturer, an approach that may beunreliable (Yu and Sinko, 1997). Yu and Sinko (1997) used an em-piric model to simultaneously estimate support filter permeabilityand the UWLs; the approach required “labor-intensive” flux studiesacross blank filters, where hydrodynamics was varied (Yu and Sinko,1997).

Diazepam Uptake into hASBT-MDCK Monolayer to Esti-mate PABL for Uptake Studies. Uptake of radiolabeled diazepaminto hASBT-MDCK cells was assessed to estimate PABL for uptakestudies. By virtue of its high permeability across bilayers, diazepamis a commonly used marker for measurement of UWL resistance.After 30 s, uptake was stopped by freezing the cells instantaneouslyover dry ice in alcohol. This process rigidized cell membrane andaimed to minimize back diffusion. Cells were washed twice withice-cold buffer and lysed using 1% Triton in 1 N NaOH. Diazepam incell lysate was quantified using a scintillation counter. Diazepampermeability was 150 3 � 10�6 cm/s, which was taken to be equalto PABL for uptake studies. This PABL value from the uptake config-uration is greater than PABL from the transport configuration, pre-sumably reflecting that only the apical UWL is present in case ofuptake configuration, whereas basolateral UWL and filter supportare additional diffusion barriers in the transport configuration.

Simulations for Objective 1: Impact of Varying Jmax on ABLContribution. The ABL-present model for transport (i.e., eq. 7) wasused to simulate flux data. No error was incorporated into thesesimulations. Values for Kt, Pp, and PABL were 5 �M, 0.5 � 10�6 cm/s,and 70 � 10�6 cm/s, respectively. These values were selected basedupon experimental measurements of Kt, Pp, and PABL. Values forsubstrate concentration and Jmax ranged from 0.5 to 1000 �M and0.00001 to 0.01 nmol/cm2/s, respectively. Jmax values were selected


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based upon observed Jmax values. Error-free simulations weresystematically performed for all combinations of parameter values.Error-free flux data were similarly simulated using the ABL-absentmodel (eq. 1).

Simulated JABL data were subsequently regressed on to the ABL-absent model to yield estimates of Kt, Jmax, and Pp. This approachquantified bias in Kt, Jmax, and Pp parameter estimates when ABLwas ignored.

Simulations for Objective 2: Identification of Global Ki-netic Conditions That Require ABL Consideration. Simula-tions were performed to identify global kinetic conditions when ABLneeds to be explicitly considered to accurately estimate kinetic pa-rameters (e.g., Kt, Jmax, or Ki). Simulations were performed fortransport and transport inhibition studies.

Transport data were simulated under both ABL-present and ABL-absent scenarios. Pp and PABL were fixed to be 0.5 � 10�6 and 70 �10�6 cm/s, respectively. Values for Kt and Jmax ranged from 0.1 to10,000 �M and 0.00003 to 0.01 nmol/cm2/s, respectively. Substrateconcentration was fixed to one-tenth the Kt value for each simula-tion. The impact of ABL was assessed by the ratio JABL/J. JABL/Jgreater than 0.9 indicated that ABL contribution is not significant.JABL/J less than 0.9 indicated that ABL is significant, such that ABLneeds to be considered to accurately estimate kinetic parameters.

Inhibition data were simulated using the ABL-absent and ABL-present models in a similar manner (i.e., eqs. 10 and 11). Substrateconcentration, Kt, and Ki , values were 2.5, 5, and 50 �M, respec-tively. Inhibitor concentration ranged from 0.1 to 1000 �M. Jmax

ranged from 0.00001 to 0.01 nmol/cm2/s. Simulated JABL was subse-quently regressed on to the ABL-absent inhibition model to yieldestimates of Ki. Kt, Jmax, and Pp were assigned to the values used ingenerating the simulated data. This approach quantified bias in Ki

parameter estimates when ABL was ignored.Simulations for Objective 3: Identification of Global Ki-

netic Conditions When Kt Estimates Are Unreliable as a Re-sult of ABL Contribution. Equation 7 was used with Pp � 0.5 �10�6 cm/s and PABL � 70 � 10�6 cm/s to generate initial error-freeflux data. Fifteen scenarios were systematically evaluated for fivelevels of Kt (1, 3, 5, 10, and 25 �M) at each of three levels of Jmax

(0.0001, 0.0003, and 0.001 nmol/s/cm2). Substrate concentrationswere 1/20-, 1/10-, 1/5-, 1/2-, 1-, 2-, 5-, 10-, and 20-fold of true Kt value.For the scenario Kt � 1 �M and Jmax � 0.001 nmol/s/cm2, substrateconcentrations 40, 80, and160 �M were also included. Flux data forevery substrate concentration were simulated in triplicate for eachoccasion, mimicking triplicate design of in vitro laboratory studies.Random error reflecting percent coefficient of variation � 15% wasincorporated into simulated flux data. For each of these 15 scenarios,simulations were performed on 100 occasions. Data from each occa-sion were regressed onto eq. 7 to estimate Kt, Jmax, and Pp, withemphasis on Kt. For each simulation scenario, Kt estimates fromeach of the 100 occasions was used to calculate the probability ofcalculating meaningful Kt estimates (i.e., statistically differed fromzero based upon 95% confidence interval). Nonlinear regression toeq. 7 was performed using WinNonlin Professional version 4.1 (Phar-sight, Mountain View, CA), which was kindly donated by Pharsight.

Cell Surface Biotinylation and Immunoblotting. Figure 1provides motivation for the present study, presuming that variationin Jmax was ascribed to variation in hASBT expression. The rankorder agreement between cell surface hASBT expression level andJmax was assessed though parallel studies involving Western blotsand taurocholate transport studies.

hASBT-MDCK monolayers were grown as described above (Bal-akrishnan et al., 2005) and treated with varying levels of sodiumbutyrate to modulate hASBT expression level. hASBT-MDCK mono-layers were treated with either 10 mM, 5 mM, or no sodium butyrateto yield monolayers corresponding to three levels of hASBT expres-sion (i.e., high, intermediate, and low). Additionally, untransfectedMDCK monolayers were also treated with 10 mM sodium butyrateas negative control

Cell surface expression of hASBT was determined by treating cellswith the membrane-impermeant biotinylation reagent sulfosuccin-imidyl-2-(biotinamido) ethyl-1,3-dithiopropionate (Pierce Chemical,Rockford, IL) for 30 min at room temperature (Visiers et al., 2003).After several washes in phosphate-buffered saline with 0.1 mMCaCl2 and 1 mM MgCl2, cells were disrupted in lysis buffer [25 mMTris-HCl, pH 7.5, 300 mM NaCl, 1 mM CaCl2, 1% Triton X-100, and0.5% protease inhibitor cocktail (Sigma-Aldrich, St. Louis, MO)] for30 min at 4°C. Biotinylated proteins were recovered by overnightincubation with 100 �l of streptavidin-agarose beads per sample(Pierce Chemical Co.) at 4°C using end-over-end rotation. The fol-lowing day, the beads were washed once with lysis buffer, once inhigh-salt lysis buffer (same as lysis buffer except with 500 mM NaCland 0.1% Triton X-100), and finally twice with 50 mM Tris, pH 7.5.Biotinylated proteins were eluted using 100 �l of SDS-polyacryl-amide gel electrophoresis Laemmli buffer, pH 6.8 (Sigma-Aldrich),for 10 min at 85°C. For each sample, 20 �l was applied to a 12.5%SDS-polyacrylamide gel electrophoresis gel (Bio-Rad, Hercules, CA)and transferred to a polyvinylidene difluoride membrane for immu-noblotting. Since hASBT was constructed with a V5 epitope (Bal-akrishnan et al., 2005), hASBT was detected with the anti-V5/horse-radish peroxidase-conjugated 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 WesternBlotting Detection system (GE Healthcare, Little Chalfont, Bucking-hamshire, UK). Blots were then stripped via ECL Detection Systemprotocols and reprobed for the presence of the constitutively ex-pressed plasma membrane marker �-integrin, using anti-integrin�2/VLA-2� antibody, followed by donkey anti-mouse HRP-conju-gated secondary antibody. �-integrin represents a positive control forcell surface biotinylation of plasma membrane proteins. To confirmcell membrane integrity during biotinylation, the same membranewas also probed for the absence of calnexin, a 90-kDa housekeepingprotein present in whole-cell lysate preparations, using anti-calnexinantibody and donkey anti-rabbit HRP-conjugated secondary anti-body. Calnexin was absent from biotinylated samples (data notshown), ensuring that only cell surface proteins were biotin-labeledand immunoblotted.

Densitometry measurements of hASBT expression level were notperformed, since densitometry unfortunately requires high proteinexpression and �-integrin was not sufficiently high for densitometricmeasurement. Rather, post hoc analysis of band density using pixelintensity was assessed using NIH Image software (version 1.6.3;(http://rsb.info.nih.gov/nih-image/index.html) for each sodium bu-tyrate treatment level (as well as control untransfected MDCKmonolayers). Using a standard rectangular box in NIH Image, pixelintensity of hASBT was measured and normalized against pixelintensity of �-integrin; pixel intensity ratio of hASBT versus �-inte-grin from each treatment was corrected for background control viasubtraction of pixel intensity ratio from untransfected MDCK mono-layers and interpreted as hASBT expression level (relative to inte-grin).

Taurocholate flux in the presence and absence of sodium wasmeasured as described above. Jmax was estimated and comparedwith Western blot analysis. Results are shown in Appendix 3.

ResultsSimulations for Objective 1: Impact of Varying Jmax

on ABL Contribution. Taurocholate permeability acrossblank support filters was 66.1 6.0 � 10�6 cm/s. Hence, PABL

was fixed at 70 � 10�6 cm/s in all simulations.Figure 3 is a contour plot of the ratio of JABL versus J, as

a function of Jmax and substrate concentration. JABL/Jgreater than 0.9 indicates that ABL contribution was notsignificant. JABL/J less than 0.9 indicates that ABL contri-bution is significant. At a very low Jmax of 0.00003 nmol/


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cm2/s, JABL/J always exceeded 0.9, regardless of substrateconcentration. For higher Jmax scenarios, JABL/J droppedbelow 0.9 at low substrate concentrations, but generally re-turned to about unity at high substrate concentration. Atvery high Jmax of 0.01 nmol/cm2/s, flux from the ABL-presentmodels was 20-fold lower than flux from the ABL-absentmodel at low substrate concentration (i.e., JABL/J about0.05). These simulations indicate that ABL limits flux signif-icantly at high Jmax and low substrate concentration. Thesesimulations follow the results observed in earlier studies(Thomson and Dietschy, 1977, 1980), although the presentmanuscript attempts to highlight the influence of Jmax (i.e.,expression level), since expression level of transporters canvary across occasions in a cell culture system.

From eq. 3, JABL/J in Fig. 3 can also be interpreted to bethe fraction of total flux resistance that is attributed to themonolayer, Fmono. Under conditions of high Jmax and lowsubstrate concentration, Fmono is low, such that ABL is dom-inant. At low Jmax and/or high substrate concentration, Fmono

is large, such that monolayer resistance is dominant andABL effect is not significant.

Simulated flux data from the ABL-present model wereregressed onto the ABL-absent model to yield estimates of Kt

and Jmax as well as Pp. This approach quantified bias in Kt

and Jmax parameter estimates when ABL is ignored. Param-eter value ranges reflect the range of values observed exper-imentally. Figure 4 plots the true and fitted estimates for Kt

as a function of Jmax. The true Kt (i.e., the Kt value used insimulations) was 5 �M. In Fig. 4, the estimated Kt value wasabout the same as the true Kt value when Jmax was very low.Kt estimates below Jmax of 0.00003 nmol/cm2/s reflected lowbias of 0 to 5%. For Jmax of 0.0003 nmol/cm2/s, Kt estimatewas about 2-fold higher than true Kt. For progressivelyhigher Jmax, Kt estimates exhibited very high positive bias(almost 1000-fold larger). These results indicate that failureto consider ABL can lead to erroneously large Kt estimates athigh Jmax. These results are consistent with experimentaltaurocholate data in Fig. 1, where high Kt was associatedwith high Jmax. Simulation results suggest that, in Fig. 1, Kt

estimates were over-estimated due to low monolayer resis-

tance (i.e., low Fmono), particularly on occasions when Jmax

was high.Unlike ABL effect on Kt estimates, ABL had no impact on

Jmax estimates (data not shown). This lack of effect is inagreement with earlier studies (Thomson and Dietschy,1980). There was practical identity between fitted Jmax andtrue Jmax values, indicating that the use of the ABL-absentmodel did not bias Jmax estimates. ABL only impacted Kt

estimates and not Jmax. Interesting, the ABL-absent andABL-present models provided equally good fits to simulateddata, based on Akaike information criterion and r2 (data notshown).

In the light of above-mentioned observations, Fig. 5 reeval-uates experimental taurocholate data. The ABL-presentmodel was used to obtain Kt and Jmax estimates, whosevalues are plotted in Fig. 5. Jmax ranged between 0.0001 to0.001 nmol/s/cm2. Kt ranged from about 1 to 12 �M with anaverage Kt estimate of approximately 5 �M. Compared withregression results from the ABL-absent model (i.e., Fig. 1),estimates of Kt were about 2- to 3-fold lower from the ABL-

Fig. 3. Contour plot showing the effect of ABL on flux for varying Jmax.The plot describes ABL effect by considering the ratio of JABL versus J.JABL is the simulated flux in the ABL-present model (eq. 7), whereas J isthe simulated flux in the ABL-absent model (eq. 1). At the low Jmax valueof 0.00003 nmol/cm2/s, JABL was generally similar to J (i.e., JABL/J ap-proximately unity) over all substrate concentrations. At high transporteractivity (e.g., Jmax � 0.01 nmol/cm2/s), JABL was more than 10-fold lowerthan J, particularly for low substrate concentrations. These simulationsindicate that ABL resistance is dominant under conditions when mono-layer permeability is large (i.e., high Jmax and low substrate concentra-tion).

Fig. 4. Effect of not considering ABL resistance on Kt estimates. Simu-lations were performed using eq. 7 (i.e., ABL-present model) over a rangeof seven Jmax values, using a Kt of 5 �M. This “true Kt” is illustrated witha broken line. Filled circles indicate Kt estimates from fitting simulateddata to eq. 1 (i.e., ABL-absent model). Application of the ABL-absentmodel generally provided Kt estimates larger than 5 �M. Kt estimates atand below Jmax of 0.00003 nmol/cm2/s were biased by 0 to 5%. For Jmax of0.0003 nmol/cm2/s, the Kt estimate was about 10 �M (i.e., 2-fold higherthan true Kt). These results are consistent with experimental tauro-cholate data where larger Kt estimates were calculated at high Jmax usingthe ABL-absent model (i.e., Fig. 1).

Fig. 5. Plot of taurocholate Kt estimates versus taurocholate Jmax esti-mates across different days, using ABL-present model. In contrast to Fig.1 where the ABL-absent model was used, there was no dependence of Kton Jmax when the ABL-present model was used. Kt was practically thesame (about 8 �M) across different days, as expected. Kt estimates fromthe ABL-present model were about 3-fold lower than Kt estimates fromthe ABL-absent model, consistent with the simulations in Fig. 4.


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present model. Jmax estimates were the same from eachmodel from both models, as expected from above simulationresults. Additionally, Pp estimates were the same from bothmodels (data not shown). In contrast to Fig. 1, there was noassociation between Kt estimates and Jmax estimates in Fig.5 (p � 0.24; r2 � 0.13). This lack of association indicates thatcorrecting for ABL influence lead to a more accurate and lessbiased estimate of Kt.

UWL effects in taurocholate uptake data were also cor-rected in an analogous fashion (see Appendix 4). It should benoted that the Kt estimates for uptake and transport studieswere similar (both �5 �M), indicating that the configurationof the assay (i.e., uptake versus transport) did not affect Kt

estimate. This result supports the apical membrane servingas the rate-limiting barrier within the monolayer in trans-port studies. Hence, a basolateral transporter such as Ost�-Ost� is not contributing as the rate-limiting barrier. Ost�-Ost� is a heteromeric transporter that has been recentlyidentified to translocate bile acids in the enterocyte basolat-eral membrane (Ballatori et al., 2005; Dawson et al., 2005).

Simulations for Objective 2: Identification of GlobalKinetic Conditions That Require ABL Consideration.Since high Jmax can lead to ABL-limited transport and sub-sequent positive bias in Kt estimate, a second objective was toidentify global kinetic conditions when ABL needs to be ex-plicitly considered to accurately estimate kinetic parameters.This assessment was carried out via simulations of the ABL-absent and ABL-present models, using parameter valuesthat reflect the range of observed parameters. The impact ofABL was assessed by JABL/J; JABL/J less than 0.9 indicatedthat ABL is significant.

Figure 6 plots JABL/J as a function of Kt at varying Jmax

and illustrates the interplay of Jmax and Kt in determiningABL impact. In Fig. 6, at low Jmax and high Kt (i.e., poorsubstrate for transporter), ABL is not significant, as observedby JABL/J greater than 0.9 (i.e., Fmono 0.9). Overall flux iscontrolled by monolayer resistance and not by ABL. Mean-while, for large Jmax and/or low Kt, JABL/J is low, whichreflects a significant role of ABL. In the case of both highJmax and low Kt, JABL/J (i.e., Fmono) is less that 0.1, reflectingABL accounts for over 90% of total resistance to transport.Figure 6 is consistent with observed taurocholate data plot-

ted in Figs. 1 and 5, where ABL was modestly important forlow Jmax and very important at high Jmax. Similar depen-dence on Jmax is evident in Fig. 6.

These results comparing JABL and J indicate that ABLneeds to be explicitly considered for all potent substrates (i.e.,Kt less than or equal to 10 �M), even in low expressionsystems (i.e., Jmax 0.00003 nmol/cm2/s). Additionally, atJmax greater than 0.001 nmol/cm2/s, as observed for hASBT-MDCK, ABL needs to be considered even when Kt is as largeas 100 �M. Given the high hASBT expression from the cur-rent hASBT-MDCK model, the simulations anticipate theneed to employ the ABL-present model for all native bileacids. Interestingly, these simulations suggest loweredhASBT expression (i.e., lower Jmax) as an approach to mini-mize ABL influence on transport. Future laboratory studieswill employ hASBT-MDCK monolayers with reduced hASBTexpression, especially for potent substrates, to minimize ABLinfluence.

Simulation studies were also performed for transport inhi-bition studies to identify global kinetic conditions that re-quire ABL consideration for accurate Ki estimation. Previousstudies have not examined diffusion barrier effects on Ki

estimation. Figure 7 plots JABL/J as a function of inhibitorconcentration and Jmax. At low Jmax, JABL/J was greaterthan 0.9, indicating lack of ABL effect. However, JABL/Jdecreased with increasing Jmax and reached 0.4 and lower atJmax � 0.01 nmol/cm2/s, indicating significant ABL effectunder these conditions. These observations are similar to theresults from the corresponding transport simulations (Fig. 3).The consequence of low JABL/J (observed in Fig. 7) on Ki

estimates is shown in Fig. 8. Figure 8 plots the true and fittedestimates for Ki as a function of Jmax. The true Ki (i.e., the Ki

value employed in simulations) was 50 �M. For Jmax of0.0001 nmol/cm2/s, Ki estimate was �27 �M (i.e., �2-foldlower than true Ki). For progressively higher Jmax, Ki esti-mates exhibited very high negative bias (�10-fold lower).These results indicate that failure to consider the contribu-tion of ABL leads to erroneously low Ki estimates, particu-larly at high Jmax. Figure 9 further details the interplay of

Fig. 6. Interplay of Jmax and Kt in determining the impact of ABL on flux.JABL and J were simulated using the ABL-present and ABL-absentmodels, respectively, over a range of Jmax and Kt. The combination of Jand Kt significantly determined the role of ABL on flux. When Jmax wasvery low, ABL is only significant when Kt is very low. For progressivelyhigher Jmax, ABL is significant for a wider range of Kt values. The effectof ABL is most prominent for conditions that allow for high monolayerpermeability (i.e., high Jmax and low Kt), such that JABL is 10-fold lowerthan J.

Fig. 7. Contour plot showing the effect of ABL on flux in the presence ofinhibitor for varying Jmax. The plot describes ABL effect by consideringthe ratio of JABL versus J. Simulations were performed using S � 2.5 �M,Kt � 5 �M, Pp � 0.5 � 10�6 cm/s, and Ki � 5 �M. The contour plotindicates that the interplay of Jmax and inhibitor concentration can col-lectively limit the effective monolayer permeability and hence the contri-bution of ABL in overall resistance to flux. At the low Jmax value of0.00003 nmol/cm2/s, JABL was generally similar to J over all inhibitorconcentrations. At high transporter activity (e.g., Jmax � 0.01 nmol/cm2/s), JABL was significantly lower than J, particularly for low inhibitorconcentrations. These simulations indicate that ABL resistance is domi-nant under conditions when monolayer permeability is high (i.e., highJmax and low inhibitor concentration).


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Jmax and Kt in determining the impact of ABL on bias in Ki

estimates, using error-free data. In all situations, Ki esti-mates were negatively biased, particularly for low Kt values,regardless of Jmax. Bias is greatest at low Kt values and highJmax, due to low monolayer resistance for the substrate. Inessence, when ABL is not considered, Ki “takes credit” for theABL effect, leading to biased Ki estimate. This analysis ofsimulation/regression indicates that bias in Ki estimates isgreatest when the substrate is very potent (i.e., low Kt), andthis effect is amplified at high Jmax.

These simulation results are consistent with experimentaltaurocholate self-inhibition data (Table 1). For each of thetwelve occasions, the ABL absent inhibition model (eq. 10)provided a lower Ki than did the ABL present inhibitionmodel (eq. 11).

Simulations for Objective 3: Identification of GlobalKinetic Conditions When Kt Estimates Are Unreliableas a Result of ABL Contribution. Figure 6 indicates thatJABL is less than 10% J for several scenarios. These obser-vations from error-free simulations motivated a more de-tailed evaluation, using simulations that incorporate 15%

random error. This evaluation aimed to identify conditionsunder which kinetic parameters cannot be precisely esti-mated due to the combination of ABL-controlled transportand modest experimental variability.

Table 2 indicates the probability of successfully estimatingKt estimates under different scenarios of Kt and Jmax usingerror-inclusive simulated flux data. Estimation of Kt wasdeemed successful if the 95% confidence interval for the Kt

estimate did not include zero. For each of the fifteen scenar-ios, Table 2 also denotes the percentage of total resistancethat is attributed to ABL. As expected from objective 2 re-sults, the probability of successful Kt estimation was lowwhen Jmax was high and true Kt was less than 10 �M. Forexample, the probability was only 10% when true Kt � 1 �Mand Jmax � 0.001 nmol/cm2/s. In general, the probability ofsuccess increased for progressively lower Jmax and progres-sively higher Kt. For example, when true Kt � 5 �M and Jmax

� 0.0001 nmol/cm2/s, the probability was 91%. This trend isattributed to progressively lower contribution of ABL to over-all control of flux. To a first approximation, the probability offailing to estimate Kt is equal to the percentage of resistancedue to ABL. Jmax was successfully estimated in almost all

Fig. 8. Effect of not considering ABL resistance on Ki estimates. Simu-lations were performed using eq. 11 (i.e., ABL-present model for inhibi-tion) over a range of six Jmax values, using a Kt of 5 �M and Ki of 50 �M.This “true Ki” is illustrated with a broken line. Filled circles indicate Kiestimates from fitting simulated data to eq. 10 (i.e., ABL-absent model forinhibition). Application of the ABL-absent model generally provided Kiestimates lower than 5 �M. Qualitatively, this negative bias is oppositethe positive bias observed in Fig. 4 for Kt, although both simulationsindicate ABL to limit substrate flux. Ki estimates at and below Jmax of0.00001 nmol/cm2/s were biased by 0 to 10%. For Jmax of 0.0003 nmol/cm2/s, the Ki estimate was about 10 �M (i.e., more than 5-fold lower thantrue Ki).

Fig. 9. Interplay of Jmax and Kt in determining ABL impact on Ki esti-mate. Error-free data were generated via the ABL-present transportinhibition model (i.e., eq. 11) over a range of substrate Kt values and Jmaxvalues, using a true Ki of 50 �M. This true Ki is illustrated as a brokenline. Data were subsequently fit to the ABL-absent inhibition model (i.e.,eq. 10), with the estimated Ki values plotted. In all cases, Ki estimateswere negatively biased, particularly for low Kt values, regardless of Jmax.

TABLE 1ABL influence on taurocholate inhibition kineticsTaurocholate Ki values were calculated using both the ABL-present inhibition modeland the ABL-absent inhibition model. As expected from simulation results (Figs. 8and 9), Ki values from ABL-absent inhibition model was always lower than the Kiestimates from ABL-present inhibition model. Values are the average of threeobservations S.E.M.

OccasionTaurocholate Ki Values

ABL-Absent Inhibition Model ABL-Present Inhibition Model

�M

1 1.45 0.21 2.88 0.252 1.25 0.30 4.10 0.323 2.78 0.53 8.30 0.644 0.65 0.22 1.22 0.105 3.35 0.76 12.11 0.606 0.90 0.18 1.69 0.097 4.09 0.26 5.56 0.248 2.10 0.09 2.63 0.169 4.67 0.32 6.43 0.36

10 0.30 0.22 2.07 0.1111 0.69 0.30 2.91 0.1312 3.96 0.42 6.33 0.25

TABLE 2Probability of obtaining statistically significant Kt estimate underdifferent scenarios of Kt and Jmax

Kt was estimated on 100 occasions for each scenario using simulated data thatincorporated 15% random error. The probability of successful Kt estimation was thepercentage of occasions when the 95% confidence interval for Kt did not include zero.Tabulated in parentheses is the percentage of total resistance due to ABL (percent-age of ABL resistance). When Jmax is high, probability of successful Kt estimationwas low, especially when true Kt was less than 10 �M. At progressively lower Jmax,the chance of successful Kt estimation improved. For most of the scenarios evaluated,the probability of successful Kt estimation depended on the contribution of ABLresistance to flux (i.e. percent ABL resistance); when flux became increasinglyABL-limited, chances of success decreased.

Kt

Probability of Successful Kt Estimation

Jmax 0.001nmol/cm2/s



�M

1 10 (94) 13 (81) 65 (59)3 19 (83) 58 (59) 90 (32)5 43 (74) 79 (46) 91 (15)

10 59 (58) 92 (30) 84 (12)25 87 (36) 86 (15) 64 (5)


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occasions, as expected based on previous studies (Thomsonand Dietschy, 1980) and results from objective 2 in thepresent study.

A result not anticipated from error-free simulation is themodest decrease in successful Kt estimation in Table 2 athigh Kt. At Kt of 25 �M, the above-mentioned trend wasreversed, such that probability of success drops for progres-sively lower Jmax. At high Kt scenarios, the passive fluxcomponent contributes significantly to overall flux, especiallywhen Jmax is low, leading to modest decrease in successful Kt

estimation.

DiscussionKinetics of hASBT-Mediated Taurocholate Flux Us-

ing ABL-Absent Model. hASBT is under investigation as atarget to increase the oral absorption of drug candidatesthrough a prodrug approach (Balakrishnan and Polli, 2006).An hASBT-MDCK monolayer model was developed previ-ously (Balakrishnan et al., 2005). Specificity of hASBT-me-diated transport of taurocholate was based upon a number ofobservations (e.g., hASBT-transfected versus mock-trans-fected studies, no-sodium versus sodium-containing studies,apical-to-basolateral versus basolateral-to-apical studies,lack of taurocholate inhibition by DIDS or probenecid, confo-cal imaging of hASBT in the hASBT-MDCK model, and sim-ilar Kt estimates in monolayer transport and uptake studies).It should be noted that, although the hASBT-MDCK is usedto elucidate the substrate requirements of hASBT, bile acidsare substrates for the recently identified Ost�-Ost� hetero-meric transporter in the enterocyte basolateral membrane(Ballatori et al., 2005; Dawson et al., 2005). However, asnoted above, results here do not reflect Ost�-Ost� kineticactivity, but reflect hASBT kinetic activity, since Kt esti-mates for uptake and transport studies were similar. Addi-tionally, taurocholate transport was unaffected by the Ost�-Ost� inhibitor bromosulphaelin (Seward et al., 2003;Balakrishnan et al., 2006).

Taurocholate flux across hASBT-MDCK monolayers areroutinely performed. Motivation for the present study wasthe observed positive association between taurocholate Jmax

and Kt estimates, where the ABL-absent model was used.The ABL-absent model is the model typically used in analyz-ing flux data from cell culture transporter assay systems. Kt

and Jmax estimates exhibited significant variation acrossoccasions. Kt ranged from �2 to 27 �M. Jmax ranged between0.0001 and 0.001 nmol/s/cm2. In Fig. 1, there was a stronglinear association between Kt and Jmax estimates (r2 � 0.82;p 0.001). Variability in Jmax can be ascribed to variabilityin hASBT expression (see Appendix 3). However, variabilityin Kt, particularly Kt variation that is associated with Jmax,was difficult to explain. This association yielded the followinghypothesis: high transporter expression can lower monolayerresistance, resulting in ABL-limited transport of solutes,leading to biased kinetic estimates if ABL is not considered.Three objectives were pursued in challenging this hy-pothesis.

Simulations for Objective 1: Impact of Varying Jmax

on ABL Contribution. The first objective was to evaluatethe effect of Jmax on the contribution of ABL resistance totransporter kinetics. Objective 1 was carried out through acombination of empirical laboratory studies, as well as error-

free simulation/regression studies. Results indicate thatfailure to consider ABL can lead to erroneously large Kt

estimates at high Jmax. Results were consistent with exper-imental taurocholate data in Fig. 1, where high Kt was asso-ciated with high Jmax. Simulation results suggest that, inFig. 1, Kt estimates were over-estimated due to low mono-layer resistance (i.e., low Fmono), particularly on occasionswhen Jmax was high.

Figure 5 reevaluates experimental taurocholate data. TheABL-present model was employed to obtain Kt and Jmax

estimates, whose values are plotted in Fig. 5. Compared withregression results from the ABL-absent model (i.e., Fig. 1),estimates of Kt were about 2- to 3-fold lower from the ABL-present model. In contrast to Fig. 1, there was no associationbetween Kt estimates and Jmax estimates in Fig. 5 (p � 0.24;r2 � 0.13). This lack of association indicates that correctingfor ABL influence lead to a more accurate and less biasedestimate of Kt. It should be noted that variability in Kt wasnot completely eliminated. Contributions to the remainingunexplained variation are variation in flux measurementsand parameter estimation error.

Simulations for Objective 2: Identification of GlobalKinetic Conditions That Require ABL Consideration.The second objective was to identify global kinetic conditionswhen ABL needs to be explicitly considered to accuratelyestimate kinetic parameters. Objective 2 was conductedthrough error-free simulations of both transport and inhibi-tion studies. Results indicate that ABL can generally modu-late hASBT kinetics, particularly for all potent substrates,even in low expression systems. Additionally, at Jmax greaterthan 0.001 nmol/cm2/s, as observed for hASBT-MDCK, ABLneeds to be considered even when Kt is as large as 100 �M.Interestingly, results suggest lower hASBT expression as anapproach to minimize ABL influence on transport. Simula-tion studies were also performed for transport inhibitionstudies, which revealed that failure to consider the contribu-tion of ABL leads to erroneously low Ki estimates, particu-larly at high Jmax.

However, it should also be noted that ABL effect dependson substrate Kt and Jmax in the particular assay system, andtherefore ABL is not always significant. For example, ABLinfluence is not significant for a low-affinity transporter suchas hPEPT1. Herrera-Ruiz et al. (2003) developed a stablytransfected hPEPT1-MDCK cell line with varying expressionlevels. Kt of glycyl sarcosine was 400 �M. From Fig. 6 here, itcan be inferred that ABL influence would not be significantfor this substrate until very high Jmax (i.e., until over 0.001nmol/s/cm2) is attained. Lack of effect was evident experi-mentally from Herrera-Ruiz et al. (2003) since glycyl sar-cosine Kt estimate did not vary with varying Jmax. A secondexample illustrates a modest ABL effect in an organic aniontransporter (OAT3) study (Zhang et al., 2004). Uptake ofestrone sulfate into rabbit OAT3-Chinese hamster ovary ex-hibited Kt and Jmax of 4 �M and 0.000413 nmol/s/cm2, re-spectively, indicating high affinity of estrone sulfate forOAT3. From Figs. 4 and 6 here, low Kt of estrone sulfatewould seem to be overestimated by 2-fold.

Simulations for Objective 3: Identification of GlobalKinetic Conditions When Kt Estimates Are Unreliableas a Result of ABL Contribution. The third objective wasto identify scenarios under which kinetic estimates are notreliable in spite of ABL consideration, due to ABL dominated


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transport kinetics. Objective 3 was carried out through sim-ulations incorporating 15% random error, to estimate theprobability of successfully estimating Kt. In general, theprobability of success increased for progressively lower Jmax

and progressively higher Kt. To a first approximation, theprobability of failing to estimate Kt is equal to the percentageof resistance due to ABL.

These results have implication for the functional charac-terization and development of QSAR models of transporters.QSAR models rely on kinetic parameters (e.g., Jmax, Kt, andKi) to relate structural features of substrate/inhibitor to ac-tivity. Data sets for QSAR analysis typically make up kineticestimates collected across different occasions, including overyears, and across laboratories. Since transport expressionlevels vary across occasions, results here imply the quality ofkinetic parameter estimates can vary with occasion, if ABLeffects are ignored. Biased kinetic parameters underestimatethe affinity of potent substrates and overestimate the inhi-bition potency of modest and poor inhibitors, leading to errorin QSAR models.

In summary, our combined data indicate that the ABLresistance layer can have significant impact on carrier-medi-ated solute transport in overexpression systems. This effectwas always observed for hASBT-MDCK, but it was mostprominent on occasions when Jmax was high. Failure to con-sider ABL lead to positively biased estimates of Kt and neg-atively biased estimates of Ki. The extent of bias is deter-mined collectively by expression level and substrate affinity,such that ABL effect is most prominent for conditions thatlead to lowered monolayer resistance (i.e., high Jmax and lowKt). Results provide three possibilities: 1) monolayer resis-tance is sufficiently high (i.e., low Jmax and high Kt) such thatABL can be ignored and kinetic parameters can be estimatedwith accuracy and precision; 2) monolayer resistance is suf-ficiently high but ABL cannot be ignored for the accurate andprecise estimation of kinetic estimates; and 3) monolayerresistance for substrate is low (high Jmax and low Kt) suchthat flux is highly ABL-controlled, and even consideration ofABL does not allow for accurate and precise estimation ofkinetic parameters.

APPENDIX 1The objective of Appendix 1 is to derive eq. 9. For the

ABL-present model:

Rapp � RABL � Rmono (12)

Hence, in comparing the relative resistances in the ABL-absent model and the ABL-present model,

Fmono �Rmono

Rmono � RABL(13)

where Fmono is the fraction of total flux resistance that is dueto the monolayer.

Fmono �1/Pmono

1/Papp(14)

Fmono �S/J

S/JABL(15)

Fmono �JABL

J(16)

APPENDIX 2The objective of Appendix 2 is to derive the ABL-present

inhibition model (i.e., eq. 11).Substrate flux in the presence of an inhibitor when ABL is

absent is described by

J �Jmax � S

Kt�1 � I/Kt� � S� Pp � S (17)

where I is the concentration of inhibitor (i.e., inhibitory bileacid), and Ki is inhibitory constant. S is substrate concentra-tion (i.e., taurocholate concentration); Jmax, Kt, and Pp char-acterize substrate transport parameters.

In the ABL-present model, since permeability is the in-verse of resistance,

1Papp

�1

PABL�

1Pmono

(18)

where Papp is the apparent permeability, PABL is the ABLpermeability, and Pmono is the monolayer permeability.

From eq. 17, monolayer permeability in the presence ofinhibitor is

Pmono �Jmax

Kt�1 � I/Kt� � S� Pp (19)

Substituting eq. 19 into eq. 18,

1Papp

�1

PABL�

1Jmax

Kt�1 � I/Kt� � S� Pp

(20)

Papp �

PABL � � Jmax

Kt�1 � I/Kt� � S� Pp�

PABL �Jmax


(21)

since JABL � Papp � S,

JABL �

PABL � � Jmax

Kt�1 � I/Kt� � S� Pp� � S

PABL �Jmax


(22)

APPENDIX 3The objectives of Appendix 3 are to 1) provide support for

the presumption that, in Fig. 1, variation in Jmax can beascribed to variation in hASBT expression; and 2) providefurther support that ABL influence is modulated by Jmax.Figure 1 inspired the hypothesis that high transporter ex-pression can lower monolayer resistance, resulting in ABL-limited transport of solutes, leading to biased kinetic esti-mates if ABL is not considered.

Figure 10 shows Western blot analysis of hASBT expressedat cell surface (Fig. 10A) as well as correlation betweenmeasure Jmax and hASBT expression level (relative to inte-


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grin) (Fig. 10B). In Fig. 10A, Western blots were consistentwith expected results, where hASBT expression decreased inthe following order: lane A (hASBT-MDCK treated with 10mM sodium butyrate) lane B (hASBT-MDCK treated with5 mM sodium butyrate) lane C (hASBT-MDCK treatedwith no sodium butyrate) lane D (untransfected MDCK).In Fig. 10B, hASBT expression level from band density anal-ysis using pixel intensity provided linear association (r2 �0.994) with measured taurocholate Jmax values, which were10.0 0.3 � 10�4, 6.59 0.21 � 10�4, and 1.29 0.05 �10�4 nmol/cm2/s for lanes A, B, and C, respectively. Untrans-fected MDCK (lane D) showed no active taurocholate flux.Hence, variation in Jmax was attributable to variation inhASBT expression at cell surface. A similar analysis wasperformed by Irie et al. (2006), where PEPT1 mRNA levelwas linearly associated with Gly-Sar Jmax values (r � 0.55)across Caco-2 clones (Irie et al., 2006).

As expected, when ABL-influence was not considered, theKt estimates were positively association with Jmax; Kt values

were 19.6 2.4, 15.3 1.72, and 7.47 0.50 �M for lanes A,B, and C, respectively. When the ABL-present model wasapplied to this same data, this association was abolished; Kt

values were 3.24 1.01, 3.73 0.70, 5.77 0.40 �M forlanes A, B, and C, respectively. Result here from hASBT-MDCK monolayers subjected to differing levels of inductionby sodium butyrate provide further support that ABL influ-ence is modulated by Jmax.

APPENDIX 4The objective of Appendix 4 is to evaluate the ability of the

ABL-present model to accurately estimate kinetic parameterestimates from uptake studies (i.e., Jmax and Kt), relative tothe Winne uptake model. Taurocholate uptake data from fiveoccasions were regressed onto eqs. 7 and 8 using SigmaPlot2000 (SPSS Inc.). Kinetic parameters were compared via thepaired t test.

This comparison is motivated since Winne’s uptake modelis tailored for uptake configuration. Winne’s uptake modelwould seem not be applicable to transport studies, by virtueof its high identifiability as an uptake model. Favorableperformance of the ABL-present model in assessing uptakedata, compared with the Winne’s uptake model, would sup-port the ABL-present model to serve as a single form toanalyze both transport and uptake data that require ABLconsideration.

For each occasion, Jmax and Kt values from the ABL-present model were statistically indistinguishable from Jmax

and Kt values from Winne’s uptake model (p 0.05). Addi-tionally, the ABL-present model effectively eliminated thebias in Kt that otherwise results from ABL. As was observedfrom transport studies in Fig. 1, there was a positive, linearassociation between Kt and Jmax, when the ABL-absentmodel was applied to uptake data (r2 � 0.79). Application ofthe ABL-present model markedly attenuated the association(r2 � 0.08), as did the Winne uptake model.

Favorable performance of the ABL-present model in as-sessing uptake data supports the ABL-present model to serveas a single form to analyze both transport and uptake datathat require ABL consideration.

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Address correspondence to: Dr. James E. Polli, Department of Pharmaceu-tical Sciences, School of Pharmacy, University of Maryland, 20 Penn St., HSF2Rm 623, Baltimore, MD 21201. E-mail: [email protected]


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