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Vol. 297, Issue 1, 423-436, April 2001


Futile Cycling of Estrone Sulfate and Estrone in the Recirculating Perfused Rat Liver Preparation

Eugene Tan, Thanh Lu and K. Sandy Pang

Department of Pharmaceutical Sciences, Faculty of Pharmacy (E.T., K.S.P.) and Department of Pharmacology, Faculty of Medicine (T.L., K.S.P.), University of Toronto, Toronto, Ontario, Canada

    Abstract
Top
Abstract
Introduction
Experimental Procedures
Results
Discussion
Appendix
References

The futile cycling of estrone sulfate (E1S) and estrone (E1) was investigated in the recirculating, perfused, rat liver preparation. Although E1S was not distributed into bovine erythrocytes, the compound was highly bound to albumin [4% bovine serum albumin (BSA), unbound fraction of 0.03 ± 0.01]. By contrast, E1 was bound and metabolized to estradiol (E2) by bovine erythrocytes, with metabolic clearances of 0.061 to 0.069 ml/min when normalized to the hematocrit. Due to strong binding of E1 to albumin, BSA (4%) greatly reduced the red cell clearance to a minimum (0.0024 to 0.0031 ml/min/unit of hematocrit). Despite the low unbound fractions of E1S (0.027 ± 0.004) and E1 (0.036 ± 0.006), clearances of the simultaneously delivered tracers [3H]E1S and [14C]E1 in perfusate (4% BSA and 20% erythrocytes) by the recirculating, perfused rat liver (flow rate of 0.91 ± 0.1 ml/min/g of liver) were high (0.53 ± 0.08 and 0.85 ± 0.2 ml/min/g of liver, respectively). Although low levels of [3H]E1 were observed following the tracer [3H]E1S, both parent and metabolite species displayed similar decay half-lives that were characteristic of compounds undergoing futile cycling. The same decay profile was observed for [14C]E1S but the half-life of administered [14C]E1 was shorter in comparison. A series-compartment liver model that incorporated previously noted heterogeneity in estrone sulfation and glucuronidation activities among periportal and perivenous hepatocytes, and homogeneity in sinusoidal transport and desulfation was used to explain the discrepant half-lives. The model described a high partitioning of E1 in the endoplasmic reticulum and the segregation of estrone sulfation activities in the cytosolic space from the desulfation and glucuronidation activities in the endoplasmic reticulum space.

    Introduction
Top
Abstract
Introduction
Experimental Procedures
Results
Discussion
Appendix
References

Hepatic drug clearance is regulated by hepatic blood flow, vascular and tissue binding, transport, metabolism, and biliary excretion. Futile cycling, the metabolic interconversion of two substrates involving different enzymes, is an additional process that influences drug and metabolite clearances. Futile cycling has been noted between 4-methylumbelliferone (4-MU) and 4-methylumbelliferyl sulfate (4-MUS) (Ratna et al., 1993) and methylprednisone and methylprednisolone (Ebling and Jusko, 1986). The futile cycling of estrone sulfate (E1S) and estrone (E1), which represents a pharmacologically important biocycle that conserves and regulates endogenous estrogens, however, has not been thoroughly investigated.

Since hepatic processing is a distributed-in-space phenomenon with uptake, metabolism, and efflux occurring repeatedly in hepatocytes along the direction of flow, it is expected that the futile cycling of E1S and E1 in liver would be affected by a dual set of transporters and enzymes and their associated zonal heterogeneities. It is expected that E1 would rapidly diffuse through the cell membrane due to high lipophilicity, as found in recent isolated rat hepatocyte studies (Tan and Pang, 2001). The uptake of E1S into the rat liver involves transport by members of the organic anion transporting polypeptide superfamily, Oatp1, Oatp2 and Oatp4 (Jacquemin et al., 1994; Noé et al., 1997; Cattori et al., 2000), the multispecific organic anion transporter 3, Oat3 (Kusuhara et al., 1999), and the sodium-dependent taurocholate cotransporting polypeptide, Ntcp (Hagenbuch et al., 1991). However, a lack of acinar heterogeneity was observed for the transport of E1S (Tan et al., 1999) and E1 (Tan and Pang, 2001) in rat liver.

In rat hepatocytes, E1S and E1 are highly bound to liver tissue (Tan and Pang, 2001). Consequently, the high and nonlinear binding reduces the cellular unbound concentrations of E1S and E1 for both metabolism and excretion. Estrone sulfate is mainly deconjugated by arylsulfatase C, a microsomal enzyme, to E1, which can be further metabolized to estrone glucuronide (E1G), estradiol (E2), estriol, their glucuronide and sulfate conjugates, and other minor metabolites (Roy et al., 1987). Although arylsulfatase C is found to be evenly dispersed in the liver acinus (El Mouelhi and Kauffman, 1986), estrogen sulfotransferase, which is responsible for the sulfation of E1, is predominantly localized in the perivenous region (Tosh et al., 1996; Tan and Pang, 2001). Both UDP-glucuronosyltransferase-1 (UGT1) and 2 (UGT2) are found to glucuronidate estrone (Tukey and Strassburg, 2000), and the UGTs are predominantly localized in the perivenous region (Tosh and Burchill, 1996). The sulfo- and glucuronide conjugates are found in rat bile, with the multidrug resistance-associated protein Mrp2 (or cmoat) mediating the biliary excretion of E1G (Takikawa et al., 1996). But the transporter(s) involved in E1S excretion into bile is unknown. Mrp2 does not appear to be involved (personal communications with Dr. Dietrich Keppler, University of Heidelberg, Germany).

Drugs bound to vascular components, namely plasma proteins and red blood cells (RBCs), are expected to reduce drug clearances (Pang and Rowland, 1977; Pang et al., 1995). Estrone is bound to both plasma protein and erythrocytes. Consequently, only 3% estrone exists in the unbound form in human blood (Koefoed and Brahm, 1994). In addition, E1 is also metabolized by 17beta -hydroxysteroid dehydrogenase, a cytosolic enzyme in erythrocytes of animals (Challis et al., 1973; Tsang, 1976) and human (Mulder et al., 1972) to E2. By contrast, E1S is highly bound to human plasma protein (1.6% unbound in plasma; Rosenthal et al., 1972) but not to erythrocytes. The determination of the vascular binding and metabolism of E1 and of protein binding of E1S is another important aspect toward the understanding of factors impacting the hepatic clearances of E1 and E1S.

In this communication, the metabolic disposition of simultaneously delivered tracers, [3H]E1S and [14C]E1, was investigated with the recirculating, perfused rat liver preparation. Use of dual radiolabeling of the precursor-product pair allowed for full characterization of the differential metabolism of [3H]E1S and [14C]E1. The strategy was suitable for investigating the effects of vascular and tissue binding, RBC metabolism of E1, transport, metabolism, and the various zonal aspects on the futile cycling between E1S and E1 in the liver, especially when the RBC distribution and metabolism of E1 were fully characterized. Finally, a series-compartment liver model that embodied zonal and subcellular distribution of metabolic enzymes was developed to interpret the perfusion results.

    Experimental Procedures
Top
Abstract
Introduction
Experimental Procedures
Results
Discussion
Appendix
References

Materials. [6,7-3H]E1S (ammonium salt, specific activity, 53 Ci/mmol), [6,7-3H]E1 (specific activity, 40.6 Ci/mmol), and [4-14C]E1 (specific activity, 56.6 Ci/mol) were purchased from PerkinElmer Life Sciences (Boston, MA). All radiochemical purities found by high performance liquid chromatography (HPLC) or thin-layer chromatography (TLC) were greater than 95%. E1S, E1, E2, and bovine serum albumin (BSA) were obtained from Sigma Chemical Co. (St. Louis, MO). All other reagents were of the highest grade available.

Protein Assay and Hematocrit Count. In all preparations, protein was determined by the method of Lowry et al. (1951), with bovine serum albumin as the standard. The hematocrit was measured by capillary centrifugation in a microhematocrit centrifuge (IEC MB Centrifuge, Damon, Fisher Scientific, Mississauga, ON, Canada).

BSA Binding of tracer E1, E2, and E1S. BSA binding of E1, E2, and E1S was investigated using a commercially available ultrafiltration kit (Centricon 3; Amicon Inc., Beverly, MA). Tracer [3H]E1 (3.7 ± 0.1 × 106 dpm/ml), [3H]E1S (1.7 ± 0.1 × 106 dpm/ml), or [3H]E2 (1.1 ± 0.1 × 106 dpm/ml) was added to 4% BSA (v/v) in Krebs-Henseleit-bicarbonate buffer (pH 7.4). After incubating the mixture for 10 min at 37°C, an aliquot (2 ml) was removed into a Centricon tube and centrifuged at 2500g for 20 min. The radioactivities in the original mixture (0.2 ml) and the resulting ultrafiltrate (0.2 ml) were quantified by liquid scintillation spectrometry (model LS6800; Beckman Instruments Canada, Mississauga, ON). Leakage of BSA into the ultrafiltrate was less than 1% of the original protein concentration.

Distribution and Metabolism of E1 in Erythrocytes. Bovine erythrocytes (a generous gift from Ryding Regency Meat Packers Ltd., Toronto, ON) were washed three times with saline and twice with lactated Ringer's solution (Baxter Corporation, Toronto, ON). The distribution and metabolism of tracer [3H]E1 (2.5 ± 0.4 × 105 dpm/ml or 27 ± 4.2 nM) were studied with perfusion media of different compositions: 20 and 60% RBC, in the absence and presence of 4% BSA. Erythrocytes (20 or 60% v/v) and plasma (Krebs-Henseleit-bicarbonate buffer at pH 7.4 containing 0 or 4% BSA and [3H]E1) were mixed and incubated under oxygenation (carbogen, 95% oxygen and 5% carbon dioxide; Canox Gas, Mississauga, ON) at 37°C in the reservoir of the commercially available TWO-TEN Perfuser. Blood samples were taken at 1, 30, 60, 120, and 180 min, and the hematocrit was measured. The 20 and 60% RBC yielded hematocrits (HCTs) of 0.15 ± 0.01 and 0.5 ± 0.03, respectively.

Recirculating Rat Liver Perfusion. Male Sprague-Dawley rats (290-330 g; Charles River Canada, St. Constant, QC, Canada), which were fed ad libitum, were used for perfusion at 10 ml/min. The temperature of the liver was maintained at 37°C with a heating lamp. Surgery was performed under pentobarbital anesthesia (50 mg/kg, intraperitoneal injection), and the surgical procedure and the perfusion apparatus were identical to those described by deLannoy et al. (1993). The perfusion medium consisted of 20% washed bovine erythrocytes, 4% BSA, and 300 mg/dl glucose (50% dextrose injection USP; Travenol Canada, Mississauga, ON) in Krebs-Henseleit-bicarbonate solution (pH 7.4). The rat liver was recirculated with blank medium for 20 min during the equilibration period, followed by perfusion with medium containing [3H]E1S (initial concentration of 2.85 ± 0.23 × 105 dpm/ml or 2.4 ± 0.20 nM) and [14C]E1 (initial concentration of 1.04 ± 0.12 × 105 dpm/ml or 848 ± 94 nM) from a second reservoir (200 ml). Reservoir perfusate (1-2 ml) was sampled at 0, 2.5, 10, 30, 60, 90, 110, 130, and 150 min. The total volume removed from the reservoir was 7% (14 ml) of the initial volume (200 ml), and no attempt was made to correct for the loss in volume. Bile was collected at 5- and 10-min intervals so the mid-time of the interval coincided with the sampling time of the reservoir.

Extraction and TLC Assays of [3H]E1 and [3H]E2 for the RBC Metabolism Studies. The blood and its derived plasma obtained by instantaneous centrifugation (1.5 ml each) were immediately extracted into ethyl acetate (1:2, v/v). One aliquot (1 ml) of the ethyl acetate extract was directly subjected to liquid scintillation counting, and the total count of the sample was determined against a calibration curve constructed of standards containing varying known counts of [3H]E1 in perfusate and processed in the same fashion. Since [3H]E1 and [3H]E2 were completely extracted into ethyl acetate (>99%), the extraction method furnished a mixture of [3H]E1 and [3H]E2 in each sample except for time zero, when only [3H]E1 was present. The ratio of [3H]E1/[3H]E2 was further given by TLC described below. A second aliquot (1 ml) of the ethyl acetate was spotted onto the Silica Gel GF (250 µm) TLC plate (Analtech, Newark, DE), which had been preloaded with E1 and E2 at the origin to separate [3H]E1 and [3H]E2. The plates were developed in a system of toluene:ethanol (9:1, v/v). Regions for E1 (Rf = 0.76) and E2 (Rf = 0.57) were visualized under UV light and scraped into minicounting vials. After the addition of water (0.5 ml) and liquid scintillation fluor (5 ml, Ready Safe, Beckman Instruments, Canada) into minicounting vials, the radioactivity was quantified by liquid scintillation spectrometry (model LS6800; Beckman Instruments, Palo Alto, CA). Hence, the amounts of [3H]E1 and [3H]E2 in plasma and blood perfusate were quantified by the combined extraction-TLC method. The amounts of E1 and E2 in RBC were, however, calculated by difference between the quantities in plasma and blood perfusate of known hematocrit. The radioactivities were expressed as a percentage of the initial concentration of [3H]E1 used.

HPLC Assays for Quantitation of E1G, E1S, and E1 in the Liver Perfusion Studies. Acetonitrile, which contained 4 µM danazol (the internal standard), was used to terminate any metabolic reactions, with 1:4 (v/v) volume ratio. All perfusate samples (1-2 ml) were immediately transferred to tubes containing acetonitrile (4-8 ml). Contents of the deproteinized samples were dried under nitrogen (Canox Gas) and analyzed by HPLC as described by Tan and Pang (2001). Standards of the calibration curve prepared with samples containing varying known counts of [3H]E1S and [14C]E1 were processed in the same fashion. Bile samples were diluted 1:1 (v/v) with water, and 20-µl aliquots were directly counted. A portion of the diluted bile (20 µl) was subjected to HPLC with internal standardization. The radioactivities in bile and from HPLC radioelution were quantified by liquid scintillation spectrometry. Eluted radioactivities of less than three times the background counts were treated as zeroes. All 3H- and 14C-radioactivities quantified in the samples were higher than 3000 and 1000 dpm, respectively.

Kinetic Modeling of [3H]E1 Metabolism in Erythrocytes and Fitting. Various cellular models were tested for their abilities to predict the disposition of [3H]E1 and [3H]E2 in erythrocytes. The cellular kinetic model that included plasma protein binding and red cell binding and metabolism of E1 (Fig. 1) best described the kinetics of E1 and E2. Mass balanced rate equations (eqs. 1-4) were written to describe the RBC distribution and metabolism of E1 and E2 (Fig. 1). Oxidation of E2 to E1 was not included since preliminary study revealed less than 1% metabolism of E2 to E1 over 3 h. The same was observed by Tsang (1976).


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Fig. 1.   The cellular kinetic model for the description of E1 and E2 in blood perfusate. Plasma protein and red cell binding of E1 and E2 and metabolism of E1 were included in the model. The transport of E1 and E2 was denoted by the bidirectional linear transmembrane clearances and the metabolism of E1 was described by the RBC metabolic intrinsic clearance.

Binding to plasma and RBC is expressed as unbound fractions. The unbound fraction in blood (fblood) is related to that in plasma (fp) and the plasma (CP) and blood (Cblood) concentrations (Pang and Rowland, 1977).
f<SUB><UP>blood</UP></SUB>=<FR><NU>f<SUB><UP>p</UP></SUB></NU><DE>C<SUB><UP>blood</UP></SUB>/C<SUB><UP>p</UP></SUB></DE></FR> (1)
For species such as E1 and E2 but not E1S that distribute into RBC, we assumed that protein and red cell binding and debinding of E1 and E2 occurred almost instantaneously. The binding to plasma albumin results in plasma unbound fractions of E1 (f<UP><SUB>p</SUB><SUP>E<SUB>1</SUB></SUP></UP>) and E2 (f<UP><SUB>p</SUB><SUP>E<SUB>2</SUB></SUP></UP>) whereas their distributions in erythrocytes (RBC) yielded unbound fractions of E1 (f<UP><SUB>rbc</SUB><SUP>E<SUB>1</SUB></SUP></UP>) and E2 (f<UP><SUB>rbc</SUB><SUP>E<SUB>2</SUB></SUP></UP>). For these species, the unbound fraction in blood is related to the HCT and the unbound fractions in plasma and red blood cell (frbc).
f<SUB><UP>blood</UP></SUB>=<FR><NU>1</NU><DE>(1−<UP>HCT</UP>)/f<SUB><UP>p</UP></SUB>+<UP>HCT</UP>/f<SUB><UP>rbc</UP></SUB></DE></FR> (2)
For estimation of the bound concentrations of E1 in plasma ([E1,bound]p), we assume that K<UP><SUB>D</SUB><SUP>E<SUB>1</SUB></SUP></UP> (the binding dissociation constant of E1) > [E1,unbound]p, and this exists for the tracer condition (Tan and Pang, 2001). The Langmuir binding isotherm simplifies to
[<UP>E<SUB>1,bound</SUB></UP>]<SUB><UP>p</UP></SUB>=<FR><NU>n<SUP><UP>E</UP><SUB><UP>1</UP></SUB></SUP>[P<SUB><UP>total</UP></SUB>]<SUB><UP>p</UP></SUB>[<UP>E<SUB>1,unbound</SUB></UP>]<SUB><UP>p</UP></SUB></NU><DE>K<SUP><UP>E<SUB>1</SUB></UP></SUP><SUB><UP>D</UP></SUB></DE></FR> (3)
where (nE1[Ptotal]p) is effective binding concentration, with nE1 being the number of the binding sites on BSA and [Ptotal]p, the total protein concentration in plasma.

The unbound fraction of E1 in plasma (f<UP><SUB>p</SUB><SUP>E<SUB>1</SUB></SUP></UP>) is derived from substitution of eq. 3 into eq. 4
[<UP>E<SUB>1,total</SUB></UP>]<SUB><UP>p</UP></SUB>=[<UP>E<SUB>1,unbound</SUB></UP>]<SUB><UP>p</UP></SUB>+[<UP>E<SUB>1,bound</SUB></UP>]<SUB><UP>p</UP></SUB> (4)

f<SUP><UP>E<SUB>1</SUB></UP></SUP><SUB><UP>p</UP></SUB>=<FR><NU>[<UP>E<SUB>1,unbound</SUB></UP>]<SUB><UP>p</UP></SUB></NU><DE>[<UP>E<SUB>1,total</SUB></UP>]<SUB><UP>p</UP></SUB></DE></FR>=<FR><NU>1</NU><DE><FENCE>1+<FR><NU>n<SUP><UP>E<SUB>1</SUB></UP></SUP>[P<SUB><UP>total</UP></SUB>]<SUB><UP>p</UP></SUB></NU><DE>K<SUP><UP>E<SUB>1</SUB></UP></SUP><SUB><UP>D</UP></SUB></DE></FR></FENCE></DE></FR> (5)
The fixed protein concentration (e.g., 4% BSA) in blood perfusate in the incubation study will change when the BSA concentration is expressed in relation to the plasma when the hematocrit (0, 20, and 60% RBC) is modified. To relate to the in vitro binding data of 4% BSA in plasma to those for the red cell-albumin binding study, the following correction was made. The plasma protein concentration ([Ptotal]p) is related to the protein concentration in blood perfusate, [Ptotal]perfusate, as given below.
[P<SUB><UP>total</UP></SUB>]<SUB><UP>p</UP></SUB>=<FR><NU>[<UP>P<SUB>total</SUB></UP>]<SUB><UP>perfusate</UP></SUB></NU><DE>(1−<UP>HCT</UP>)</DE></FR> (6)
Analogously, the corrected unbound fraction of E1 in perfusate plasma is related to the plasma unbound fraction assessed in vitro (obtained from substitution of eq. 6 into eq. 5)
f<SUP><UP>E<SUB>1</SUB></UP></SUP><SUB><UP>p,cor</UP></SUB>=<FR><NU>f<SUP><UP>E<SUB>1</SUB></UP></SUP><SUB><UP>p</UP></SUB>(1−<UP>HCT</UP>)</NU><DE><UP>1</UP>−<UP>HCT </UP>f<SUP><UP>E<SUB>1</SUB></UP></SUP><SUB><UP>p</UP></SUB></DE></FR> (7)
and the corrected, unbound fraction of E2 in perfusate plasma was described by Eq. 8.
f<SUP><UP>E<SUB>2</SUB></UP></SUP><SUB><UP>p,cor</UP></SUB>=<FR><NU>f<SUP><UP>E<SUB>2</SUB></UP></SUP><SUB><UP>p</UP></SUB>(1−<UP>HCT</UP>)</NU><DE><UP>1</UP>−<UP>HCT </UP>f<SUP><UP>E<SUB>2</SUB></UP></SUP><SUB><UP>p</UP></SUB></DE></FR> (8)
For the 20% RBC and 60% RBC, albumin-free perfusate, the unbound plasma fractions of E1 and E2 equal unity. In the presence of 4% BSA, the plasma unbound fractions of E1 and E2 are expressed in relation to the corrected, unbound plasma fractions of E1 and E2 (f<UP><SUB>p,cor</SUB><SUP>E<SUB>1</SUB></SUP></UP> and f<UP><SUB>p,cor</SUB><SUP>E<SUB>2</SUB></SUP></UP>) as described by eqs. 7 and 8, respectively.

Clearance terms were normalized to the hematocrit for purposes of comparison since different hematocrits were used for study. Analogously, the transmembrane clearances of E1 and E2 described by Koefoed and Brahm (1994) were also normalized to the hematocrit to provide <OVL>CL</OVL><UP><SUB>diff,rbc</SUB><SUP>E<SUB>1</SUB></SUP></UP> and <OVL>CL</OVL><UP><SUB>diff,rbc</SUB><SUP>E<SUB>2</SUB></SUP></UP>, respectively. The hematocrit normalized intrinsic clearance of E1 (<OVL>CL</OVL><UP><SUB>int,rbc</SUB><SUP>E<SUB>1</SUB>→E<SUB>2</SUB></SUP></UP>) is expressed as follows.
<OVL><UP>CL</UP></OVL><SUP><UP>E<SUB>1</SUB>→E<SUB>2</SUB></UP></SUP><SUB><UP>int,rbc</UP></SUB>=<FR><NU><UP>CL</UP><SUP><UP>E<SUB>1</SUB>→E<SUB>2</SUB></UP></SUP><SUB><UP>int,rbc</UP></SUB></NU><DE><UP>HCT</UP></DE></FR> (9)
The hematocrit normalized permeation clearances of E1 and E2 across the red cell membrane are
<OVL><UP>CL</UP></OVL><SUP><UP>E<SUB>1</SUB></UP></SUP><SUB><UP>diff,rbc</UP></SUB>=<FR><NU><UP>CL</UP><SUP><UP>E<SUB>1</SUB></UP></SUP><SUB><UP>diff,rbc</UP></SUB></NU><DE><UP>HCT</UP></DE></FR> (10)

<OVL><UP>CL</UP></OVL><SUP><UP>E<SUB>2</SUB></UP></SUP><SUB><UP>diff,rbc</UP></SUB>=<FR><NU><UP>CL</UP><SUP><UP>E<SUB>2</SUB></UP></SUP><SUB><UP>diff,rbc</UP></SUB></NU><DE><UP>HCT</UP></DE></FR> (11)
The hematocrit normalized clearances were multiplied back to the hematocrit to yield the corresponding diffusion and intrinsic clearance for perfusates of varying composition, namely 20 and 60% RBC (see eq. 12 through eq. 15). The equations that describe the rates of change of E1 and E2 in the plasma (P) are
<FR><NU><UP>d</UP>[<UP>E<SUB>1,total</SUB></UP>]<SUB><UP>p</UP></SUB></NU><DE><UP>d</UP>t</DE></FR>=<OVL><UP>CL</UP></OVL><SUP><UP>E<SUB>1</SUB></UP></SUP><SUB><UP>diff,rbc</UP></SUB><UP> HCT</UP><FENCE><UP>f</UP><SUP><UP>E<SUB>1</SUB></UP></SUP><SUB><UP>rbc</UP></SUB>[<UP>E<SUB>1,total</SUB></UP>]<SUB><UP>rbc</UP></SUB></FENCE> (12)

<FENCE>−<FENCE><FR><NU>f<SUP><UP>E<SUB>1</SUB></UP></SUP><SUB><UP>p</UP></SUB>−<UP>HCT </UP>f<SUP><UP>E</UP><SUB><UP>1</UP></SUB></SUP><SUB><UP>p</UP></SUB></NU><DE>1−<UP>HCT </UP>f<SUP><UP>E</UP><SUB><UP>1</UP></SUB></SUP><SUB><UP>p</UP></SUB></DE></FR></FENCE>[<UP>E<SUB>1,total</SUB></UP>]<SUB><UP>p</UP></SUB></FENCE><FENCE>V<SUB><UP>p</UP></SUB></FENCE>

<FR><NU><UP>d</UP>[<UP>E<SUB>2,total</SUB></UP>]<SUB><UP>p</UP></SUB></NU><DE><UP>d</UP>t</DE></FR>=<OVL><UP>CL</UP></OVL><SUP><UP>E<SUB>2</SUB></UP></SUP><SUB><UP>diff,rbc</UP></SUB><UP> HCT</UP><FENCE>f<SUP><UP>E<SUB>2</SUB></UP></SUP><SUB><UP>rbc</UP></SUB>[<UP>E<SUB>2,total</SUB></UP>]<SUB><UP>rbc</UP></SUB></FENCE> (13)

<FENCE>−<FENCE><FR><NU>f<SUP><UP>E<SUB>2</SUB></UP></SUP><SUB><UP>p</UP></SUB>−<UP>HCT </UP>f<SUP><UP>E</UP><SUB><UP>2</UP></SUB></SUP><SUB><UP>p</UP></SUB></NU><DE>1−<UP>HCT </UP>f<SUP><UP>E</UP><SUB><UP>2</UP></SUB></SUP><SUB><UP>p</UP></SUB></DE></FR></FENCE>[<UP>E<SUB>2,total</SUB></UP>]<SUB><UP>p</UP></SUB></FENCE><FENCE>V<SUB><UP>p</UP></SUB></FENCE>
The equations that describe the changes of E1 and E2 in the RBC space (rbc) are
<FR><NU><UP>d</UP>[<UP>E<SUB>1,total</SUB></UP>]<SUB><UP>rbc</UP></SUB></NU><DE><UP>d</UP>t</DE></FR>=<FENCE><OVL><UP>CL</UP></OVL><SUP><UP>E<SUB>1</SUB></UP></SUP><SUB><UP>diff,rbc</UP></SUB><UP> HCT</UP><FENCE><FR><NU>f<SUP><UP>E<SUB>1</SUB></UP></SUP><SUB><UP>p</UP></SUB>−<UP>HCT </UP>f<SUP><UP>E</UP><SUB><UP>1</UP></SUB></SUP><SUB><UP>p</UP></SUB></NU><DE>1−<UP>HCT </UP>f<SUP><UP>E<SUB>1</SUB></UP></SUP><SUB><UP>p</UP></SUB></DE></FR></FENCE>[<UP>E<SUB>1,total</SUB></UP>]<SUB><UP>p</UP></SUB></FENCE> (14)

−(<OVL><UP>CL</UP></OVL><SUP><UP>E<SUB>1</SUB></UP></SUP><SUB><UP>diff,rbc</UP></SUB>+<OVL><UP>CL</UP></OVL><SUP><UP>E<SUB>1</SUB>→E<SUB>2</SUB></UP></SUP><SUB><UP>int,rbc</UP></SUB>)<UP>HCT </UP>f<SUP><UP>E<SUB>1</SUB></UP></SUP><SUB><UP>rbc</UP></SUB>[<UP>E<SUB>1,total</SUB></UP>]<SUB><UP>rbc</UP></SUB><FENCE><FENCE>V<SUB><UP>rbc</UP></SUB></FENCE></FENCE>

<FR><NU><UP>d</UP>[<UP>E<SUB>2,total</SUB></UP>]<SUB><UP>rbc</UP></SUB></NU><DE><UP>d</UP>t</DE></FR>=<FENCE><UP>CL</UP><SUP><UP>E<SUB>2</SUB></UP></SUP><SUB><UP>diff,rbc</UP></SUB><UP> HCT</UP><FENCE><FR><NU>f<SUP><UP>E<SUB>2</SUB></UP></SUP><SUB><UP>p</UP></SUB>−<UP>HCT </UP>f<SUP><UP>E</UP><SUB><UP>2</UP></SUB></SUP><SUB><UP>p</UP></SUB></NU><DE>1−<UP>HCT </UP>f<SUP><UP>E<SUB>2</SUB></UP></SUP><SUB><UP>p</UP></SUB></DE></FR></FENCE>[<UP>E<SUB>2,total</SUB></UP>]<SUB><UP>p</UP></SUB>+<OVL><UP>CL</UP></OVL><SUP><UP>E<SUB>1</SUB>→E<SUB>2</SUB></UP></SUP><SUB><UP>int,rbc</UP></SUB><UP> HCT </UP>f<SUP><UP>E<SUB>1</SUB></UP></SUP><SUB><UP>rbc</UP></SUB>[<UP>E<SUB>1,total</SUB></UP>]<SUB><UP>rbc</UP></SUB>−<OVL><UP>CL</UP></OVL><SUP><UP>E<SUB>2</SUB></UP></SUP><SUB><UP>diff,rbc</UP></SUB><UP> HCT </UP>f<SUP><UP>E<SUB>2</SUB></UP></SUP><SUB><UP>rbc</UP></SUB>[<UP>E<SUB>2,total</SUB></UP>]<SUB><UP>rbc</UP></SUB><FENCE>/V<SUB><UP>rbc</UP></SUB></FENCE></FENCE> (15)
The RBC unbound fractions of E1 (f<UP><SUB>rbc</SUB><SUP>E<SUB>1</SUB></SUP></UP>) and E2 (f<UP><SUB>rbc</SUB><SUP>E<SUB>2</SUB></SUP></UP>) and the metabolic intrinsic clearances were estimated by the least-squares fitting procedure (SCIENTIST version 2; MicroMath Scientific Software, Salt Lake City, UT) with the weighting schemes of unity. The goodness of fit was viewed with respect to the coefficient of variation (standard deviation of parameter estimate/parameter value), the residual plot and the model selection criterion (MSC).

Kinetic Modeling of E1S and E1 Disposition in the Recirculating Rat Liver Preparation. A series-compartment, liver model containing two units representing the periportal (PP) and perivenous (PV) regions of the liver, is the minimalized model for purposes of fitting that best predicted the disposition of E1S and E1 in the recirculating liver preparation (Fig. 2). In this model, a reservoir compartment was included for recirculation of the perfusate. The flow of substrates occurs unidirectionally from the periportal to the perivenous region, and exchange occurs in the tranverse and not the longitudinal direction. Linear (nonsaturable) transport and metabolic intrinsic clearances prevail in view of the tracer condition studied, and the assumption is justified based on the observed Km values (in µM) (Tan and Pang, 2001) being in excess of the tracer concentrations (in nM) studied. Species such as E1S, E1, and E1G that were quantified were modeled. Other metabolites formed from E1 and E1S (E2 and estriol [E3] and their glucuronide and sulfate conjugates such as E2S, E2-3S-17G, E3S, and E3-3S-16G) were collectively represented by M'.


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Fig. 2.   Schematic representation of the liver by a series-compartment, liver model that embodied acinar and subcompartmentalization and subcellular distribution of metabolic enzymes. The bottom chart conveyed the ascinar distributions of enzymatic activities of estrone sulfotransferase, estrone UDP-glucuronosyltransferase, and estrone sulfatase for metabolism of E1S and E1, expressed as percentages of the total metabolic intrinsic clearances.

A new feature of the extended model was the addition of an endoplasmic reticulum compartment, as proposed by Tirona and Pang (1996). This was necessary since the elimination profiles of E1 differed subsequent to the administration of tracer [3H]E1S and [14C]E1. The added compartment segregates the cytosol from the endoplasmic reticulum where microsomal enzymes are found. Estrone sulfotransferase is placed in the cytosolic compartment, whereas estrone sulfatase and UDP-glucuronosyltransferase are placed in the endoplasmic reticulum compartment. In light of the known, zonal distributions of estrone sulfotransferase and estrone sulfatase (Tan and Pang, 2001) and of UDP-glucuronosyltransferase (Tosh and Burchill, 1996) activities in the liver, their enriched zonal metabolic activities were calculated from the previously obtained in vitro data (Fig. 2, bottom panel; see description to follow), as described in previous studies (Abu-Zahra and Pang, 2000).

The assigned volume of sinusoid (Vs), cytosol (Vc), endoplasmic reticulum (Ver), and biliary compartment (Vbile) were 1.4 ml (Schwab et al., 1990), 7.3 ml (Pang et al., 1988), 0.2 ml (Tirona et al., 1996), and 0.07 ml, respectively. The volume of the biliary compartment was the summation of the biliary volume (0.044 ml; Reichen and Paumgartner, 1980) and the void volume (about 0.026 ml) in the bile-duct cannula (PE50, Becton Dickinson, Sparks, MD). The apparent biliary excretion clearance of E1S or E1G was calculated as the biliary excretion rate divided by the midpoint reservoir concentration of each respective species.

Fitting of Data to the Series-Compartment Liver Model. Mass balanced rate equations (see Appendix) were written to describe events of the series-compartment liver model (Fig. 2). The amounts of drug and metabolite in both perfusate and bile were normalized by the dose. Binding to red cell and albumin was assumed to be rapidly equilibrative such that use of on- and off-rate constants was not necessary. Under this instance, the unbound concentrations of E1S and E1 in whole blood perfusate equal those in plasma and in RBC. The unbound fraction in blood may then be calculated from either eq. 1 or eq. 2. The unbound fractions of E1S (f<UP><SUB>cyt</SUB><SUP>E<SUB>1</SUB>S</SUP></UP>) and E1 (f<UP><SUB>cyt</SUB><SUP>E<SUB>1</SUB></SUP></UP>) in the liver cytosol were taken from Tan and Pang (2001).

The clearance of E1 in erythrocytes (CL<UP><SUB>rbc</SUB><SUP>E<SUB>1</SUB>→E<SUB>2</SUB></SUP></UP>) was determined as dose/area from the in vitro RBC metabolism study. The in vitro Vmax (nmol/min/mg of S9 or cytosolic protein) and the intrinsic clearance (ml/min/mg of S9 or cytosolic protein) for liver metabolism were scaled up with factors, alpha  and beta  (alpha  = 0.8 mg of S9 protein/106 cells; beta  = 0.5 mg of cytosolic protein/106 cells, with 125 × 106 cells/g of liver; Mahler and Cordes, 1966; Lin et al., 1980). The Vmax values for transport (nmol/min/mg of protein) of E1S and E1 obtained from Tan and Pang (2001) were scaled-up with the factor, 200 mg of protein/g of liver (Mahler and Cordes, 1966; Lin et al., 1980). The uptake clearance was expressed as the sum of all of the Vmax/Km for the saturable transport processes and Pdiff, the linear transport clearance; ml/min/g of liver) and the metabolic intrinsic clearance was Vmax/Km (ml/min/g of liver) in view of the tracer conditions employed; the transport clearances were perceived as bidirectional. The various binding, metabolic, and transport parameters obtained experimentally that are necessary for fitting were assigned as constants (Table 6).

Fitting was performed by a software package SCIENTIST (version 2; MicroMath Scientific Software). Transport parameters---the sinusoidal bidirectional transmembrane clearance of E1G (CL<UP><SUB>s</SUB><SUP>E<SUB>1</SUB>G</SUP></UP>), the endoplasmic reticulum influx (CL<UP><SUB>er</SUB><SUP>E<SUB>1</SUB>in</SUP></UP>) and efflux (CL<UP><SUB>er</SUB><SUP>E<SUB>1</SUB>out</SUP></UP>) clearances of E1, the uptake clearances of E1S (CL<UP><SUB>er</SUB><SUP>E<SUB>1</SUB>S</SUP></UP>) and E1G (CL<UP><SUB>er</SUB><SUP>E<SUB>1</SUB>G</SUP></UP>) for the endoplasmic reticulum compartment were obtained by the fitting procedure. Similarly, the biliary intrinsic clearances of E1S (CL<UP><SUB>bile</SUB><SUP>E<SUB>1</SUB>S</SUP></UP>) and E1G (CL<UP><SUB>bile</SUB><SUP>E<SUB>1</SUB>G</SUP></UP>), the sulfation (CL<UP><SUB>int</SUB><SUP>E<SUB>1</SUB>→E<SUB>1</SUB>S</SUP></UP>) and glucuronidation (CL<UP><SUB>int</SUB><SUP>E<SUB>1</SUB>→E<SUB>1</SUB>G</SUP></UP>), and formation intrinsic clearance for the pooled metabolites of E1 (CL<UP><SUB>int</SUB><SUP>E<SUB>1</SUB>→M′</SUP></UP>), and the desulfation (CL<UP><SUB>int</SUB><SUP>E<SUB>1</SUB>S→E<SUB>1</SUB></SUP></UP>) and formation intrinsic clearance of other metabolites of E1S (CL<UP><SUB>int</SUB><SUP>E<SUB>1</SUB>S→M′</SUP></UP>) were optimized by least-square fitting. Data for each experiment for [3H]E1S and its metabolites, [3H]E1 and [3H]E1G, and for [14C]E1 and its metabolites, [14C]E1S and [14C]E1G, given as bolus doses into the reservoir, were fitted simultaneously to the series-compartment, liver model (Fig. 2). The means and standard deviation of the parameter estimates of four experiments (n = 4) are summarized (Table 6). Appropriate weighting schemes of 1/observation (for data of higher values) and 1/observation2 (for data of lower values) were used. The goodness of fit was viewed with respect to the coefficient of variation (standard deviation of parameter estimate/parameter value), the residual plot and the MSC.

Statistical Analysis. All data were presented as the mean ± standard deviation, and the means were compared by use of ANOVA or the paired t test, with the level of significance set at 0.05. The MSC and the Akaike Information Criteria (Akaike, 1974; Ludden et al., 1994) were used to select the appropriate model(s).

    Results
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Abstract
Introduction
Experimental Procedures
Results
Discussion
Appendix
References

Plasma Binding of E1S, E1, and E2. The unbound fraction of E1S in 4% BSA plasma was 0.03 ± 0.01 (n = 3), whereas those for E1 and E2 were 0.05 ± 0.01 and 0.04 ± 0.01, respectively (see Table 1, n = 3). The unbound fractions of E1 and E2 in perfusate of different compositions as determined by eq. 1 are summarized in Table 1.


                              
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TABLE 1
Unbound fractions of E1 and E2 in perfusate of different compositions

Incubation of a Tracer Dose of [3H]E1 in Blood Perfusate. The time courses for [3H]E1 and [3H]E2 in erythrocytes are shown in Fig. 3. Different areas under the concentration-time curves (AUC) for [3H]E1 were noted in the presence and absence of BSA, and similar observations were found for [3H]E2 (Table 2). The RBC clearance of E1 (CL<UP><SUB>rbc</SUB><SUP>E<SUB>1</SUB>→E<SUB>2</SUB></SUP></UP> or 0.035 ± 0.02 ml/min) in 60% RBC blood-perfusate was higher than that of the 20% RBC blood-perfusate (0.0092 ± 0.006 ml/min), and these rates for E2 formation decreased in the presence of 4% BSA (Table 2, Fig. 3). Upon normalization to the hematocrit, normalized values of the RBC clearance of E1 (<OVL>CL</OVL><UP><SUB>rbc</SUB><SUP>E<SUB>1</SUB>→E<SUB>2</SUB></SUP></UP>) in 20 and 60% RBC perfusates became similar (0.061 ± 0.04 and 0.069 ± 0.04 ml/min/HCT, respectively). These were dramatically reduced to 0.0031 ± 0.001 and 0.0024 ± 0.001 ml/min/HCT, respectively, in the presence of 4% BSA. The RBC to plasma partitioning ratios of E1 and E2 in the 20 and 60% RBC albumin-free perfusate were higher than those in the presence of 4% BSA. In the presence of 4% albumin in perfusate, values of approximately unity were obtained for the RBC to plasma partitioning ratio for E1 and E2 (Fig. 4). Moreover, the ratios reached their equilibrium values almost immediately.


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Fig. 3.   Time-dependent profiles for tracer [3H]E1 incubated with perfusates of various composition at 37°C: Amounts of E1 in blood perfusate (A), E1 in plasma (B), E1 in erythrocytes (C), E2 in blood perfusate (D), E2 in plasma (E), and E2 in erythrocytes (F). The experiment was conducted with perfusate of four different compositions: 20% RBC (), 60% RBC (open circle ) at 0% BSA, and 20% RBC (black-triangle) and 60% RBC (diamond ) in 4% BSA. All were means ± S.D. of five experiments, and the lines were the fitted lines based on eqs. 12 to 15 with the optimum weighting scheme of unity.


                              
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TABLE 2
CL and AUC of E1 and E2 in plasma and RBC after incubation with a tracer concentration of [3H]E1 in blood perfusates



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Fig. 4.   RBC to plasma partitioning of E1 (A) and E2 (B) in perfusate of different compositions: 20% RBC () and 60% RBC (open circle ) in the absence of BSA, and 20% RBC (black-triangle) and 60% RBC (diamond ) in 4% BSA. All data were means ± S.D. of five experiments.

Fitted Results for the Kinetic Model of E1 and E2 in Erythrocytes. Upon examination of the composite data for plasma and RBC, the results showed that E1 and E2 rapidly reached equilibrium in less than a minute (Fig. 4). The same observation was found by Koefoed and Brahm (1994). The fitted RBC unbound fractions of E1 (f<UP><SUB>rbc</SUB><SUP>E<SUB>1</SUB></SUP></UP>) and E2, obtained upon the simultaneously fitting of the composite data, were 0.073 ± 0.032 and 0.10 ± 0.07, respectively, showing that both E1 and E2 were highly bound to erythrocytes. The fitted RBC metabolic intrinsic clearance of E1 (<OVL>CL</OVL><UP><SUB>int,rbc</SUB><SUP>E<SUB>1</SUB>→E<SUB>2</SUB></SUP></UP>) was 0.11 ± 0.07 ml/min/HCT. Good fits were obtained although high coefficients of variation were found associated with the fitted parameters. The best fit to the model that considered red blood cell and plasma binding E1 and E2 and metabolism of E1 is presented in Fig. 3, and the optimized parameters of five experiments are summarized in Table 3.


                              
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TABLE 3
Assigned and fitted parameters for the cellular kinetic model that described the distribution and metabolism of E1 and E2 in blood

Metabolism of the Tracer Dose of [3H]E1S in the Perfused Rat Liver Preparation. From the plasma unbound fraction (Table 3), values of the unbound fraction of E1S in the blood perfusate (f<UP><SUB>blood</SUB><SUP>E<SUB>1</SUB>S</SUP></UP>) were 0.027 ± 0.004 according to eq. 1. The apparent hepatic clearance of [3H]E1S was 5.8 ± 0.9 ml/min in the recirculating rat liver perfusion (Table 4). Within 150 min of recirculation, a rapid monoexponential decline of [3H]E1S (t1/2 = 27 ± 1 min) to around 1% of its initial concentration was observed (Fig. 5A). The accumulation of [3H]E1G was higher than that of [3H]E1 in perfusate within the first hour, followed by a gradual descent (Table 4). The decay half-life of [3H]E1 paralleled that of its precursor, [3H]E1S.


                              
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TABLE 4
Hepatic CLs and AUCs of [3H]E1S, [14C]E1, and their metabolites in the recirculating rat liver preparation



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Fig. 5.   Time-dependent profiles of [3H]E1S and [14C]E1 in the recirculating rat liver preparation. All data {[3H]E1S (), [3H]E1 (black-triangle), [3H]E1G (), [14C]E1S (open circle ), [14C]E1 (black-triangle), and [14C]E1G ()} were mean ± S.D. of four experiments. The lines were fitted lines based on average parameters shown in Table 6, with mass balanced rate equations described under Appendix and appropriate weighting schemes.

During recirculation, the excreted amounts of [3H]E1S and [3H]E1G in bile increased with time and reached asymptotic levels at 150 min (Fig. 5B), and the total amounts of [3H]E1S and [3H]E1G found in bile were 2.5 ± 0.4 and 6.5 ± 0.6 percent dose, respectively (Table 5). However, very little [3H]E1 was detected in the bile (below the detection sensitivity). When the biliary excretion clearances for [3H]E1S and [3H]E1G were plotted against time, a time-dependent declining profile was observed for [3H]E1G (Fig. 6B); the bile flow declined slightly with perfusion time, as expected of the rat liver upon depletion of bile salts (Fig. 6A). The excretion clearance of preformed [3H]E1S reached an asymptotic level by 150 min after reaching distribution equilibrium in the system. At the end of the experiment, the radioactivities in reservoir, bile, and liver accounted for 3.5 ± 0.4, 54 ± 3, and 43 ± 6 percent dose, respectively.

                              
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TABLE 5
Biliary excretion of [3H]E1S, [14C]E1, and their metabolites during simultaneous delivery to the recirculating perfused rat liver preparation



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Fig. 6.   A, bile flow rates of the rat liver during the recirculating liver preparation. B, the apparent biliary excretion clearances of [3H]E1S (), [3H]E1G (), [14C]E1S (open circle ), and [14C]E1G (). The apparent biliary excretion clearances of E1S and E1G were calculated as the biliary excretion rate divided by the midpoint reservoir concentration of each respective species. The data were means ± S.D. of four experiments.

Metabolism of the Tracer Dose of [14C]E1 in the Perfused Rat Liver Preparation. Estrone was highly cleared upon the recirculation of [14C]E1 with an apparent hepatic clearance of 9.4 ± 2.2 ml/min (Table 4), despite that the unbound fraction of E1 in the blood (f<UP><SUB>blood</SUB><SUP>E<SUB>1</SUB></SUP></UP>) was very low. The unbound fraction of E1 in blood (0.036 ± 0.006) based on the plasma unbound fraction and blood/plasma concentration ratio (eq. 1) agreed well with the value (0.053 ± 0.02) estimated according to eq. 2 that utilized the fitted value for f<UP><SUB>rbc</SUB><SUP>E<SUB>1</SUB></SUP></UP> (0.073). The closeness in the values suggest the soundness in the estimation of f<UP><SUB>rbc</SUB><SUP>E<SUB>1</SUB></SUP></UP>. The concentrations of [14C]E1 declined monoexponentially with a slightly shortened half-life of about 20 ± 1.6 min (Fig. 5C). The elimination profile of the metabolite, [14C]E1S, was more prolonged and the half-life was eventually similar to that of [3H]E1S and [3H]E1 but failed to decay in unison with [14C]E1. The accumulation of [14C]E1S and [14C]E1G in the reservoir was comparable and increased within the first hour, followed by a gradual decline thereafter. During the time course of the experiment, the dose-corrected AUC of [3H]E1G, when extrapolated to time infinity, was not different from that of [14C]E1G (P > 0.05). Large variations were, however, observed (Table 4).

The amounts of [14C]E1S and [14C]E1G excreted in bile increased with time and reached asymptotic levels at 150 min (Fig. 5D), yielding 1.7 ± 0.01 and 8.2 ± 0.2 percent dose, respectively (Table 5). These values were not significantly different from those of the [3H]E1S dose (ANOVA, P > 0.05). Again, little [14C]E1 was detected in the bile (below the detection limit). When the biliary excretion clearances of [14C]E1S and [14C]E1G were plotted against time, time-dependent declining excretion clearances were observed for both [14C]E1S and [14C]E1G (Fig. 6B). At the end of the experiment, the radioactivities in reservoir, bile, and liver accounted for 3.3 ± 0.7, 54 ± 6, and 43 ± 8 percent dose.

Fitted Results for the Kinetic Model of E1 and E1S in the Perfused Liver Preparation. Upon simultaneous fitting of perfusate and bile data consisting of [3H]E1, [3H]E1S, [3H]E1G, [14C]E1, [14C]E1S, and [14C]E1G in each study for the same liver preparation, good fits were obtained although high coefficients of variation were found associated with the fitted parameters. Parameter unidentifiability existed among the fitted parameters due to the remoteness of the endoplasmic reticulum with respect to the sampling compartment and the high correlation among parameters. For example, the endoplasmic reticulum efflux clearance (CL<UP><SUB>er</SUB><SUP>E<SUB>1</SUB>out</SUP></UP>), the glucuronidation intrinsic clearance (CL<UP><SUB>int</SUB><SUP>E<SUB>1</SUB>→E<SUB>1</SUB>G</SUP></UP>), and the "pooled" metabolic intrinsic clearance (CL<UP><SUB>int</SUB><SUP>E<SUB>1</SUB>→M′</SUP></UP>) for E1 were all highly correlated, as were the bidirectional transmembrane clearance (CL<UP><SUB>er</SUB><SUP>E<SUB>1</SUB>S</SUP></UP>), the desulfation intrinsic clearance (CL<UP><SUB>int</SUB><SUP>E<SUB>1</SUB>S→E<SUB>1</SUB></SUP></UP>), and the pooled metabolic intrinsic clearance (CL<UP><SUB>int</SUB><SUP>E<SUB>1</SUB>S→M′</SUP></UP>) for E1S. These highly correlated parameters exhibited coefficients of variation larger than one, and their reliability was much reduced. The other parameters exhibited lower coefficients of variation since the parameters were not correlated.

The optimized fit that considered both zonal and subcellular localization of metabolic enzymes is presented in Fig. 5, and the assigned parameters and the mean ± S.D. of the optimized parameters of four experiments are summarized in Table 6. The fitted sinusoidal bidirectional transmembrane clearance for E1G (CL<UP><SUB>s</SUB><SUP>E<SUB>1</SUB>G</SUP></UP>) was 339 ± 22 ml/min. The endoplasmic reticulum influx (CL<UP><SUB>er</SUB><SUP>E<SUB>1</SUB>in</SUP></UP>) and efflux (CL<UP><SUB>er</SUB><SUP>E<SUB>1</SUB>out</SUP></UP>) clearances of E1 were 86 ± 40 and 17 ± 2 ml/min, respectively, suggesting a 5-fold partitioning of E1 into the endoplasmic reticulum compartment. The bidirectional transmembrane clearances of E1S (CL<UP><SUB>er</SUB><SUP>E<SUB>1</SUB>S</SUP></UP>) and E1G (CL<UP><SUB>er</SUB><SUP>E<SUB>1</SUB>G</SUP></UP>) for the endoplasmic reticulum were 742 ± 146 and 0.018 ± 0.001 ml/min, respectively. The biliary intrinsic clearances of E1S (CL<UP><SUB>bile</SUB><SUP>E<SUB>1</SUB>S</SUP></UP>) and E1G (CL<UP><SUB>bile</SUB><SUP>E<SUB>1</SUB>G</SUP></UP>) were 8.0 ± 0.1 and 1.8 ± 0.2 ml/min, respectively. The sulfation (CL<UP><SUB>int</SUB><SUP>E<SUB>1</SUB>→E<SUB>1</SUB>S</SUP></UP>), the glucuronidation (CL<UP><SUB>int</SUB><SUP>E<SUB>1</SUB>→E<SUB>1</SUB>G</SUP></UP>) intrinsic clearances of E1, and the desulfation intrinsic clearance of E1S (CL<UP><SUB>int</SUB><SUP>E<SUB>1</SUB>S→E<SUB>1</SUB></SUP></UP>) were 318 ± 38, 105 ± 30, and 332 ± 44 ml/min, respectively. Last, the pooled metabolic intrinsic clearances for E1 (CL<UP><SUB>int</SUB><SUP>E<SUB>1</SUB>→M′</SUP></UP>) and E1S (CL<UP><SUB>int</SUB><SUP>E<SUB>1</SUB>S→M′</SUP></UP>) in the formation of all other metabolites were 255 ± 60 and 214 ± 57 ml/min, respectively. One should further be aware that these sinusoidal transmembrane, endoplasmic reticulum transmembrane, metabolic intrinsic, and biliary intrinsic clearances are highly interrelated, and the set of values is not unique because other combinations could possibly be consistent with the data.

Inclusion of the endoplasmic reticulum compartment in modeling was justified since a high partitioning of E1 into the endoplasmic reticulum space was observed by Zakim and Vessey (1977). Absence of the endoplasmic reticulum compartment (achieved with high clearances between the endoplasmic reticulum and cytosol) furnished an inferior fit, predicting a much higher formation of [3H]E1 (see simulation in Fig. 7).


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Fig. 7.   Simulated profiles of [3H]E1S, [14C]E1, and their metabolites in the recirculating rat liver preparation based on rapid equilibration of all species between the cytosolic and endoplasmic reticulum compartments. A, time-dependent profiles for [3H]E1S (---), [3H]E1 (- - -), and [3H]E1G (......). B, time-dependent profiles for [14C]E1S (---), [14C]E1 (- - -), and [14C]E1G (......).

Further Simulation for Understanding the Futile Cycling Kinetics of E1 and E1S in the Perfused Liver Preparation. Simulations were further performed based on the fitted and assigned parameters shown in Table 6. If rapid equilibration of the species existed between the cytosolic and endoplasmic reticulum compartments (high transport clearance of 1000 ml/min for E1), similar elimination profile for E1S and E1 would result pursuant to [3H]E1S and [14C]E1 dosing as expected of futile cycling (Fig. 7); values for the transport clearances of E1S and E1G, when increased to 1000 ml/min, failed to further affect the shapes of the curves. With high exchange of E1 between the cytosolic and endoplasmic reticulum compartments (inter-compartmental clearance of 1000 ml/min), the observed, discrepant half-lives of E1 resulting from tracer [14C]E1 dose and not the [3H]E1S dose now disappeared.


                              
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TABLE 6
Assigned and fitted parameters for the distributed-in-space model

Effects of the Reversible Pathway. For understanding the effects of futile cycling on the clearances of estrone and estrone sulfate, the sulfation intrinsic clearance of E1 (CL<UP><SUB>int</SUB><SUP>E<SUB>1</SUB>→E<SUB>1</SUB>S</SUP></UP>) was set to zero to eliminate futile cycling of E1, the formed metabolite. The result was the accumulation of [3H]E1 upon elimination of the resulfation pathway after the [3H]E1S dose (Fig. 8A). The profile of [3H]E1G remained virtually unchanged because sulfation is a minor pathway. When the desulfation intrinsic clearance of E1S (CL<UP><SUB>int</SUB><SUP>E<SUB>1</SUB>S→E<SUB>1</SUB></SUP></UP>) was set as zero to prevent futile cycling of E1S as the formed metabolite of estrone, a greater accumulation of the [14C]E1S resulted, and formation of [14C]E1G was reduced after the [14C]E1 dose (Fig. 8B).


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Fig. 8.   Simulated profiles of E1S, E1, and E1G following the administration of [3H]E1S in the absence of sulfation, with the sulfation intrinsic clearance of E1 (CL<UP><SUB>int</SUB><SUP>E<SUB>1→E</SUB>1S</SUP></UP>) equal to zero (A) and following the administration of [14C]E1 with the desulfation intrinsic clearance of E1S (CL<UP><SUB>int</SUB><SUP>E<SUB>1S→E</SUB>1</SUP></UP>) equal to zero (B), in the recirculating rat liver preparation. The symbols [3H]E1S (), [3H]E1 (black-triangle), and [3H]E1G () in (A) are the mean of four experiments, and the lines---[3H]E1S (---), [3H]E1 (- - -), and [3H]E1G (...) represent the simulated profiles. The symbols---[14C]E1S (open circle ), [14C]E1 (triangle ), and [14C]E1G () in (B) are the mean of four experiments and the lines [14C]E1S (---), [14C]E1 (- - -), and [14C]E1G (...) represent the simulated profiles.

    Discussion
Top
Abstract
Introduction
Experimental Procedures
Results
Discussion
Appendix
References

E1 and E2 are potent estrogens that are bound tightly to albumin and to red blood cells. The erythrocyte distribution of E1 and E2 and metabolism of E1 in the presence and absence of 4% BSA were characterized in our study. Rapid equilibrium was reached for E1 and E2 between plasma and RBC (Fig. 3), justifying use of the unbound fractions instead of the discrete binding association and dissociation rate constants for fitting. The observation was consistent with rapid exchange of E1 and E2 into bovine erythrocytes due to their high lipophilicity (log P values of E1 and E2 are 3.1 and 4.0, respectively) (Howard and Meylan, 1997) and their rapid dissociation from erythrocytes, as suggested by Koefoed and Brahm (1994). Two conclusions may be made regarding the metabolism of E1 in the blood perfusate. First, the presence of a higher hematocrit increased the conversion of E1 to E2 due to the presence of higher quantities of 17beta -hydroxysteroid dehydrogenase in the RBCs (Table 2). Upon normalization to hematocrit, the same RBC clearance of E1 was obtained for both 60% and 20% RBC perfusate. Second, E1 was bound more strongly to BSA than to bovine erythrocytes (Fig. 4), and albumin greatly reduced both the distribution and metabolism of E1 in erythrocytes (Table 2). Due to the stronger binding to BSA, the RBC/plasma partition coefficients of E1 and E2 decreased in the presence of 4% BSA (Fig. 4). The perfusate of 4% BSA and 20% RBC appeared optimal since the perfusate exhibited minimum RBC metabolism of E1 but showed adequate oxygenation of the perfused rat liver preparation (Pang et al., 1988). The unbound fractions of E1S and E1 in this medium were constant (0.027 and 0.036, respectively).

Our study with the perfused rat liver preparation had entailed the simultaneous delivery of [3H]E1S and [14C]E1. The scheme allowed for the full characterization of the differential metabolism of the interconverting species. The study design was expected to reveal the underlying influence of vascular binding, transport, tissue binding, metabolism, and excretion on the hepatic clearances of E1S and E1. The hepatic clearances (0.53 ± 0.08 ml/min/g of liver for E1S and 0.85 ± 0.2 ml/min/g of liver for E1 at the blood flow rate of 0.91 ± 0.1 ml/min/g of liver) were lower than values of the sinusoidal transport clearances found previously: 33 ml/min/g of liver for E1S and 184 ml/min/g of liver for E1 (Tan and Pang, 2001). The finding suggests that transport is not rate limiting for E1S and E1 elimination. An unusual observation was that the half-lives of E1, as a preformed species and as the metabolite of E1S, were different. Moreover, parallel decay was observed between E1S and E1 after dosing with E1S as expected of futile cycling but not with E1.

This led us to postulate that the observed difference in half-lives was due to the sequestration of substrates within subcompartments. An extended, distributed-in-space model (the series-compartment liver model; Fig. 2) that incorporated zonal and subcompartmentalization of metabolic enzymes was indeed needed to interpret data of the recirculating liver perfusion of [3H]E1S and [14C]E1. Since this liver model was very complex, the fitting software allowed a maximum capacity of two zonal units only. Thus, more complicated models with higher zonal units were not examined. However, the use of two zonal units in the liver appeared adequate to describe the perfusion data. Inclusion of the endoplasmic reticulum proved absolutely necessary because its absence furnished an inferior fit, predicting a higher formation of [3H]E1 (Fig. 7A).

Segregation of the endoplasmic reticulum from the cytosolic space implies not only distinction in metabolic enzymes but of drug partitioning in the endoplasmic reticulum compartment, membranes that are lipoidal in nature (Tirona and Pang, 1996). Creation of the endoplasmic reticulum compartment can be viewed by the following scenario: E1S is rapidly transported into the endoplasmic reticulum compartment (transport clearance of 740 ± 146 ml/min) and is desulfated rapidly (intrinsic clearance of 332 ± 44 ml/min) to E1 by estrone sulfatase. The metabolite E1 is lipophilic and will likely stay within the endoplasmic reticulum space, presumably due to binding to membranes (Rao, 1998), leading to an imbalance in influx (clearance of 86 ± 40 ml/min) and efflux (clearance of 17 ± 2 ml/min). A similarly high partitioning of E1 into the endoplasmic reticulum was observed by Zakim and Vessey (1977). The close proximity of the membrane bound E1 and UDP-glucuronosyltransferase readily promotes the sequential glucuronidation of E1 (intrinsic clearance of 105 ± 30 ml/min). Since UDP-glucuronosyltransferase is facing the luminal side (Iyanagi et al., 1986), the glucuronide conjugate of E1 is released into the endoplasmic reticulum lumen and transported out to the cytosolic space (0.018 ± 0.001 ml/min) or is excreted into the bile. In addition, E1 and E1S in the endoplasmic reticulum space may also be metabolized by the cytochrome P450s (1A1, 3A4, and 2D) (Martucci and Fishman, 1993) to the "pooled metabolites", M', with metabolic intrinsic clearances of 255 ± 60 and 214 ± 57 ml/min, respectively.

The sulfation intrinsic clearance (318 ± 38 ml/min) was found to differ from previous values (11.2 ml/min) (Tan and Pang, 2001) that was estimated in the absence of the endoplasmic reticulum compartment. Rapid equilibration for the species between the cytosolic and endoplasmic reticulum compartments would effectively merge these subcompartments. As shown by the simulations (achieved with high CLer), the different elimination half-lives of E1 (Fig. 5) now disappeared in the absence of the endoplasmic reticulum compartment, rendering similar decay profiles for E1S and E1 (Fig. 7). Upon further probing of the partitioning species, E1 and not E1S nor E1G was found to be important (simulations not shown). The pattern is characteristic of both drug and metabolite undergoing futile cycling (Ebling and Jusko, 1986; Tan and Pang, 2001). It may thus be concluded that the partitioning of E1 into the endoplasmic reticulum had resulted in different elimination half-lives for E1 in the recirculating liver preparation. To understand the influence of the futile cycling of E1S and E1 on the hepatic clearance of E1S and E1, simulations were further performed by obliterating the reversible pathway in the futile cycle. The simulation showed a greater accumulation of [14C]E1S from [14C]E1 in the absence desulfation (Fig. 8B), and a greater formation of [3H]E1 from [3H]E1S in the absence of sulfation pathway (Fig. 8A).

The fit also revealed that the sinusoidal bidirectional transmembrane clearance of E1G was similar to that of E1S (Table 6). Although Kanai et al. (1996) had suggested that E1G transport was mediated by Oatp1 in a set of inhibition studies, direct data describing E1G uptake in rat liver was lacking. The biliary intrinsic clearances of E1S and E1G were 8.0 ± 0.1 and 1.8 ± 0.2 ml/min, respectively. Upon multiplying the biliary intrinsic clearance with the cytosolic unbound fraction, the "effective" biliary intrinsic clearance of E1S (0.7 ml/min) becomes smaller than that of E1G (1.8 ml/min), whose biliary excretion appeared to be mediated by Mrp2 (Takikawa et al., 1996). In addition, a time-dependent decline in the biliary excretion clearances for the metabolites, [3H]E1G, [14C]E1S, and [14C]E1G, was observed (Fig. 6B). Since these metabolites were formed in liver and were immediately excreted into the bile, this led to a component of biliary clearance that was not accounted for by the metabolite in circulation. A similar phenomenon was observed for the liver perfusion of enalapril and enalaprilat (deLannoy et al., 1993). However, the biliary excretion profiles of metabolites, E1S and E1G, were similar for both [3H]E1S and [14C]E1 doses (Figs. 5 and 6). As for the preformed [3H]E1S, the excretion clearance reached asymptotic levels at 150 min, after reaching distribution equilibrium in the system. The bile flow rate declined with perfusion time due to the depletion of bile salts in the liver.

In conclusion, E1 was highly bound to red blood cells and albumin and was metabolized by bovine erythrocytes to E2. There were at least two factors governing the RBC metabolism of E1, a higher hematocrit in blood increased the metabolism whereas albumin greatly attenuated RBC metabolism. The hepatic clearances of the simultaneously delivered tracer [3H]E1S and [14C]E1 were high in the rat liver preparation. Moreover, E1 was highly partitioned into the endoplasmic reticulum compartment, yielding different elimination profiles for E1S and E1. The notion was substantiated upon degeneration of endoplasmic reticulum and the cytosolic spaces, obliterating the subcellular partitioning of E1 in the cell and rendering parallel decay profiles of E1 and E1S. In general, futile cycling decreases the formation of the metabolite, which undergoes interconversion but increases formation of other noncycling metabolites. Presently, the complex kinetics of futile cycling are described adequately by a series-compartment (distributed-in-space) model that encompasses transport, metabolic heterogeneity, vascular binding and metabolism, and tissue binding. It is speculated that the above conceptual framework would apply to physiologically relevant conditions in humans if a high partitioning of E1 exists and the same rate-limiting factors prevail.

    Footnotes

Accepted for publication January 4, 2001.

Received for publication October 19, 2000.

This work was supported by the Medical Research Council of Canada (MT-15657). Eugene Tan was a recipient of graduate scholarships from the Natural Sciences and Engineering Research Council and Medical Research Council of Canada.

Send reprint requests to: Dr. K. Sandy Pang, Faculty of Pharmacy, University of Toronto, 19 Russell St., Toronto, ON M5S 2S2 Canada. E-mail: ks.pang{at}utoronto.ca

    Abbreviations

4-MU, 4-methylumbelliferone; 4-MUS, 4-MU sulfate; E1, estrone; E1S, E1 sulfate; E1G, E1 glucuronide; E2, estradiol; UGT, UDP-glucuronosyltransferase; RBC, red blood cell; HPLC, high performance liquid chromatography; TLC, thin layer chromatography; BSA, bovine serum albumin; HCT, hematocrit; MSC, model selection criterion; AUC, area under the concentration time profile; ANOVA, analysis of variance; CL, clearance.

    Appendix
Top
Abstract
Introduction
Experimental Procedures
Results
Discussion
Appendix
References

Based on mass balance, the terminologies used to describe differential equations for the series-compartment liver model (Fig. 2) are given as follows; superscript N denotes the zonal unit in the rat liver where (N - 1) = 1 as periportal (compartment I) and (N - 1) = 2 as perivenous (compartment II). [X]r, [X]<UP><SUB>s</SUB><SUP>N</SUP></UP>, [X]<UP><SUB>cyt</SUB><SUP>N</SUP></UP>, [X]<UP><SUB>er</SUB><SUP>N</SUP></UP>, and [X]<UP><SUB>bile</SUB><SUP>N</SUP></UP> denote the total concentrations of species X in the reservoir, sinusoidal, cytosolic, endoplasmic reticulum, and biliary compartments, respectively. A<UP><SUB>bile</SUB><SUP>X</SUP></UP> is the amount of species X excreted in bile. Qblood and Qbile are the total blood flow rate and the bile flow rate, respectively. Vr, Vs, Vcyt, Ver, and Vbile represent the volume of the reservoir, sinusoidal, cytosolic, endoplasmic reticulum, and bile compartments, respectively. CL<UP><SUB>s</SUB><SUP>X</SUP></UP>, CL<UP><SUB>er</SUB><SUP>X</SUP></UP>, and CL<UP><SUB>bile</SUB><SUP>X</SUP></UP> denote the bidirectional transmembrane clearance of species X at the sinusoidal, endoplasmic reticulum, and canalicular membranes, respectively. However, CL<UP><SUB>er</SUB><SUP>X in</SUP></UP> and CL<UP><SUB>er</SUB><SUP>X out</SUP></UP> represent the influx and efflux clearances, respectively, for the species X in the endoplasmic reticulum space. CL<UP><SUB>int</SUB><SUP>X→Y</SUP></UP> is the metabolic intrinsic clearance of species X, which is being metabolized to species Y. RBC metabolism of E1 to E2 is expressed with respect to the RBC clearance of (CL<UP><SUB>rbc</SUB><SUP>E<SUB>1</SUB>→E<SUB>2</SUB></SUP></UP>). M' represents all metabolites of E1 except E1S and E1G. The fractions, f<UP><SUB>blood</SUB><SUP>X</SUP></UP> and f<UP><SUB>cyt</SUB><SUP>X</SUP></UP>, are the unbound fraction of species X in the perfusate and cytosol, respectively.

Reservoir:
<FR><NU><UP>d</UP>[<UP>E<SUB>1</SUB></UP>]<SUB><UP>r</UP></SUB></NU><DE><UP>d</UP>t</DE></FR>={Q<SUB><UP>blood</UP></SUB>([<UP>E<SUB>1</SUB></UP>]<SUP><UP>II</UP></SUP><SUB><UP>s</UP></SUB>−[<UP>E<SUB>1</SUB></UP>]<SUB><UP>r</UP></SUB>)−<UP>CL</UP><SUP><UP>E<SUB>1</SUB>→E<SUB>2</SUB></UP></SUP><SUB><UP>rbc</UP></SUB>f<SUP><UP>E<SUB>1</SUB></UP></SUP><SUB><UP>blood</UP></SUB>[<UP>E<SUB>1</SUB></UP>]<SUB><UP>r</UP></SUB>}<FENCE>V<SUB><UP>r</UP></SUB></FENCE>

<FR><NU><UP>d</UP>[<UP>E<SUB>1</SUB>S</UP>]<SUB><UP>r</UP></SUB></NU><DE><UP>d</UP>t</DE></FR>={Q<SUB><UP>blood</UP></SUB>([<UP>E<SUB>1</SUB>S</UP>]<SUP><UP>II</UP></SUP><SUB><UP>s</UP></SUB>−[<UP>E<SUB>1</SUB>S</UP>]<SUB><UP>r</UP></SUB>)}<FENCE>V<SUB><UP>r</UP></SUB></FENCE>

<FR><NU><UP>d</UP>[<UP>E<SUB>1</SUB>G</UP>]<SUB><UP>r</UP></SUB></NU><DE><UP>d</UP>t</DE></FR>={Q<SUB><UP>blood</UP></SUB>([<UP>E<SUB>1</SUB>G</UP>]<SUP><UP>II</UP></SUP><SUB><UP>s</UP></SUB>−[<UP>E<SUB>1</SUB>G</UP>]<SUB><UP>r</UP></SUB>)}<FENCE>V<SUB><UP>r</UP></SUB></FENCE>

<FR><NU><UP>d</UP>[<UP>M′</UP>]<SUB><UP>r</UP></SUB></NU><DE><UP>d</UP>t</DE></FR>={Q<SUB><UP>blood</UP></SUB>([<UP>M′</UP>]<SUP><UP>II</UP></SUP><SUB><UP>s</UP></SUB>−[<UP>M′</UP>]<SUB><UP>r</UP></SUB>)+<UP>CL</UP><SUP><UP>E<SUB>1</SUB>→E<SUB>2</SUB></UP></SUP><SUB><UP>rbc</UP></SUB> f<SUP><UP>E<SUB>1</SUB></UP></SUP><SUB><UP>blood</UP></SUB>[<UP>E<SUB>1</SUB></UP>]<SUB><UP>r</UP></SUB>}<FENCE>V<SUB><UP>r</UP></SUB></FENCE>

Nth Sinusoidal Compartment:
<FR><NU><UP>d</UP>[<UP>E<SUB>1</SUB></UP>]<SUP><UP>N</UP></SUP><SUB><UP>s</UP></SUB></NU><DE><UP>d</UP>t</DE></FR>={Q<SUB><UP>blood</UP></SUB>([<UP>E<SUB>1</SUB></UP>]<SUP>(<UP>N</UP>−1)</SUP><SUB><UP>s</UP></SUB>−[<UP>E<SUB>1</SUB></UP>]<SUP><UP>N</UP></SUP><SUB><UP>s</UP></SUB>)+<UP>CL</UP><SUP><UP>E<SUB>1</SUB></UP></SUP><SUB><UP>s</UP></SUB>(f<SUP><UP>E<SUB>1</SUB></UP></SUP><SUB><UP>cyt</UP></SUB>[<UP>E<SUB>1</SUB></UP>]<SUP><UP>N</UP></SUP><SUB><UP>cyt</UP></SUB>−f<SUP><UP>E<SUB>1</SUB></UP></SUP><SUB><UP>blood</UP></SUB>[<UP>E<SUB>1</SUB></UP>]<SUP><UP>N</UP></SUP><SUB><UP>s</UP></SUB>)

<UP>−CL</UP><SUP><UP>E<SUB>1</SUB>→E<SUB>2</SUB></UP></SUP><SUB><UP>rbc</UP></SUB> f<SUP><UP>E<SUB>1</SUB></UP></SUP><SUB><UP>blood</UP></SUB>[<UP>E<SUB>1</SUB></UP>]<SUP><UP>N</UP></SUP><SUB><UP>s</UP></SUB>}<FENCE>V<SUB><UP>s</UP></SUB></FENCE>

<FR><NU><UP>d</UP>[<UP>E<SUB>1</SUB>S</UP>]<SUP><UP>N</UP></SUP><SUB><UP>s</UP></SUB></NU><DE><UP>d</UP>t</DE></FR>={Q<SUB><UP>blood</UP></SUB>([<UP>E<SUB>1</SUB>S</UP>]<SUP>(<UP>N</UP>−1)</SUP><SUB><UP>s</UP></SUB>−[<UP>E<SUB>1</SUB>S</UP>]<SUP><UP>N</UP></SUP><SUB><UP>s</UP></SUB>)

+<UP>CL</UP><SUP><UP>E<SUB>1</SUB>S</UP></SUP><SUB><UP>s</UP></SUB>(f<SUP><UP>E<SUB>1</SUB>S</UP></SUP><SUB><UP>cyt</UP></SUB>[<UP>E<SUB>1</SUB>S</UP>]<SUP><UP>N</UP></SUP><SUB><UP>cyt</UP></SUB>−f<SUP><UP>E<SUB>1</SUB>S</UP></SUP><SUB><UP>blood</UP></SUB>[<UP>E<SUB>1</SUB>S</UP>]<SUP><UP>N</UP></SUP><SUB><UP>s</UP></SUB>)}<FENCE>V<SUB><UP>s</UP></SUB></FENCE>

<FR><NU><UP>d</UP>[<UP>E<SUB>1</SUB>G</UP>]<SUP><UP>N</UP></SUP><SUB><UP>s</UP></SUB></NU><DE><UP>d</UP>t</DE></FR>={Q<SUB><UP>blood</UP></SUB>([<UP>E</UP><SUB>1</SUB><UP>G</UP>]<SUP>(<UP>N</UP>−1)</SUP><SUB><UP>s</UP></SUB>−[<UP>E<SUB>1</SUB>G</UP>]<SUP><UP>N</UP></SUP><SUB><UP>s</UP></SUB>)

+<UP>CL</UP><SUP><UP>E<SUB>1</SUB>G</UP></SUP><SUB><UP>s</UP></SUB>([<UP>E<SUB>1</SUB>G</UP>]<SUP><UP>N</UP></SUP><SUB><UP>cyt</UP></SUB>−[<UP>E</UP><SUB>1</SUB><UP>G</UP>]<SUP><UP>N</UP></SUP><SUB><UP>s</UP></SUB>)}<FENCE>V<SUB><UP>s</UP></SUB></FENCE>

<FR><NU><UP>d</UP>[<UP>M′</UP>]<SUP><UP>N</UP></SUP><SUB><UP>s</UP></SUB></NU><DE>dt</DE></FR>={Q<SUB><UP>blood</UP></SUB>([<UP>M′</UP>]<SUP>(<UP>N</UP>−1)</SUP><SUB>s</SUB>−[<UP>M′</UP>]<SUP><UP>N</UP></SUP><SUB><UP>s</UP></SUB>)+<UP>CL</UP><SUP><UP>E<SUB>1</SUB>→E<SUB>2</SUB></UP></SUP><SUB><UP>rbc</UP></SUB> f<SUP><UP>E<SUB>1</SUB></UP></SUP><SUB><UP>blood</UP></SUB>[<UP>E</UP><SUB>1</SUB>]<SUP><UP>N</UP></SUP><SUB><UP>s</UP></SUB>}<FENCE>V<SUB><UP>s</UP></SUB></FENCE>
For N = 1, [X]<UP><SUB>s</SUB><SUP><IT>(</IT>N<IT>−1)</IT></SUP></UP> = [X]r

Nth Cytosolic Compartment:
<FR><NU><UP>d</UP>[<UP>E<SUB>1</SUB></UP>]<SUP><UP>N</UP></SUP><SUB><UP>cyt</UP></SUB></NU><DE><UP>d</UP>t</DE></FR>={<UP>CL</UP><SUP><UP>E<SUB>1</SUB></UP></SUP><SUB><UP>s</UP></SUB>f<SUP><UP>E</UP><SUB><UP>1</UP></SUB></SUP><SUB><UP>blood</UP></SUB>[<UP>E<SUB>1</SUB></UP>]<SUP><UP>N</UP></SUP><SUB><UP>s</UP></SUB>+<UP>CL</UP><SUP><UP>E<SUB>1</SUB> out</UP></SUP><SUB><UP>er</UP></SUB>[<UP>E<SUB>1</SUB></UP>]<SUP><UP>N</UP></SUP><SUB><UP>er</UP></SUB>

−(<UP>CL</UP><SUP><UP>E<SUB>1</SUB> in</UP></SUP><SUB><UP>er</UP></SUB>+<UP>CL</UP><SUP><UP>E<SUB>1</SUB></UP></SUP><SUB><UP>s</UP></SUB><UP>+CL</UP><SUP><UP>E<SUB>1</SUB>→E<SUB>1</SUB>S</UP></SUP><SUB><UP>int</UP></SUB>)f<SUP><UP>E<SUB>1</SUB></UP></SUP><SUB><UP>cyt</UP></SUB>[<UP>E<SUB>1</SUB></UP>]<SUP><UP>N</UP></SUP><SUB><UP>cyt</UP></SUB>}<FENCE>V<SUB><UP>cyt</UP></SUB></FENCE>

<FR><NU><UP>d</UP>[<UP>E<SUB>1</SUB>S</UP>]<SUP><UP>N</UP></SUP><SUB><UP>cyt</UP></SUB></NU><DE><UP>d</UP>t</DE></FR>={<UP>CL</UP><SUP><UP>E<SUB>1</SUB>S</UP></SUP><SUB><UP>s</UP></SUB>f<SUP><UP>E<SUB>1</SUB>S</UP></SUP><SUB><UP>blood</UP></SUB>[<UP>E<SUB>1</SUB>S</UP>]<SUP><UP>N</UP></SUP><SUB><UP>s</UP></SUB>+<UP>CL</UP><SUP><UP>E<SUB>1</SUB>S</UP></SUP><SUB><UP>er</UP></SUB>[<UP>E<SUB>1</SUB>S</UP>]<SUP><UP>N</UP></SUP><SUB><UP>er</UP></SUB>+<UP>CL</UP><SUP><UP>E<SUB>1</SUB>→E<SUB>1</SUB>S</UP></SUP><SUB><UP>int</UP></SUB>f<SUP><UP>E<SUB>1</SUB></UP></SUP><SUB><UP>cyt</UP></SUB>[<UP>E<SUB>1</SUB></UP>]<SUP><UP>N</UP></SUP><SUB><UP>cyt</UP></SUB>

−(<UP>CL</UP><SUP><UP>E<SUB>1</SUB>S</UP></SUP><SUB><UP>er</UP></SUB>+<UP>CL</UP><SUP><UP>E<SUB>1</SUB>S</UP></SUP><SUB><UP>s</UP></SUB>+<UP>CL</UP><SUP><UP>E<SUB>1</SUB>S</UP></SUP><SUB><UP>bile</UP></SUB>)f<SUP><UP>E<SUB>1</SUB>S</UP></SUP><SUB><UP>cyt</UP></SUB>[<UP>E<SUB>1</SUB>S</UP>]<SUP><UP>N</UP></SUP><SUB><UP>cyt</UP></SUB>}<FENCE>V<SUB><UP>cyt</UP></SUB></FENCE>

<FR><NU><UP>d</UP>[<UP>E<SUB>1</SUB>G</UP>]<SUP><UP>N</UP></SUP><SUB><UP>cyt</UP></SUB></NU><DE><UP>d</UP>t</DE></FR>={<UP>CL</UP><SUP><UP>E<SUB>1</SUB>G</UP></SUP><SUB><UP>s</UP></SUB>[<UP>E<SUB>1</SUB>G</UP>]<SUP><UP>N</UP></SUP><SUB><UP>s</UP></SUB>+<UP>CL</UP><SUP><UP>E<SUB>1</SUB>G</UP></SUP><SUB><UP>er</UP></SUB>[<UP>E<SUB>1</SUB>G</UP>]<SUP><UP>N</UP></SUP><SUB><UP>er</UP></SUB>−(<UP>CL</UP><SUP><UP>E<SUB>1</SUB>G</UP></SUP><SUB><UP>er</UP></SUB>+<UP>CL</UP><SUP><UP>E<SUB>1</SUB>G</UP></SUP><SUB><UP>s</UP></SUB>+<UP>CL</UP><SUP><UP>E<SUB>1</SUB>G</UP></SUP><SUB><UP>bile</UP></SUB>)[<UP>E<SUB>1</SUB>G</UP>]<SUP><UP>N</UP></SUP><SUB><UP>cyt</UP></SUB>}<FENCE>V<SUB><UP>cyt</UP></SUB></FENCE>
For zonal distribution of estrogen sulfotransferase, the intrinsic clearances (CL<UP><SUB>int</SUB><SUP>E<SUB>1</SUB>→E<SUB>1</SUB>S</SUP></UP>) in the periportal (I) and perivenous (II) compartments are 20% and 80%, respectively, of the total, sulfation intrinsic clearance (CL<UP><SUB>int</SUB><SUP>E<SUB>1</SUB>→E<SUB>1</SUB>S</SUP></UP>).

Nth Endoplasmic Reticulum Compartment:
<FR><NU><UP>d</UP>[<UP>E<SUB>1</SUB></UP>]<SUP><UP>N</UP></SUP><SUB><UP>er</UP></SUB></NU><DE><UP>d</UP>t</DE></FR>={<UP>CL</UP><SUP><UP>E<SUB>1</SUB> in</UP></SUP><SUB><UP>er</UP></SUB> f<SUP><UP>E<SUB>1</SUB></UP></SUP><SUB><UP>cyt</UP></SUB>[<UP>E</UP><SUB>1</SUB>]<SUP><UP>N</UP></SUP><SUB><UP>cyt</UP></SUB>+<UP>CL</UP><SUP><UP>E<SUB>1</SUB>S→E<SUB>1</SUB></UP></SUP><SUB><UP>int</UP></SUB>[<UP>E<SUB>1</SUB>S</UP>]<SUP><UP>N</UP></SUP><SUB><UP>er</UP></SUB>−(<UP>CL</UP><SUP><UP>E<SUB>1</SUB> out</UP></SUP><SUB><UP>er</UP></SUB><UP>+CL</UP><SUP><UP>E<SUB>1</SUB>→M′</UP></SUP><SUB><UP>int</UP></SUB><UP>+CL</UP><SUP><UP>E<SUB>1</SUB>→E<SUB>1</SUB>G</UP></SUP><SUB><UP>int</UP></SUB>)[<UP>E<SUB>1</SUB></UP>]<SUP><UP>N</UP></SUP><SUB><UP>er</UP></SUB>}<FENCE>V<SUB><UP>er</UP></SUB></FENCE>

<FR><NU><UP>d</UP>[<UP>E<SUB>1</SUB>S</UP>]<SUP><UP>N</UP></SUP><SUB><UP>er</UP></SUB></NU><DE><UP>d</UP>t</DE></FR>={<UP>CL</UP><SUP><UP>E<SUB>1</SUB>S</UP></SUP><SUB><UP>er</UP></SUB> f<SUP><UP>E<SUB>1</SUB>S</UP></SUP><SUB><UP>cyt</UP></SUB>[<UP>E<SUB>1</SUB>S</UP>]<SUP><UP>N</UP></SUP><SUB><UP>cyt</UP></SUB>−(<UP>CL</UP><SUP><UP>E<SUB>1</SUB>S</UP></SUP><SUB><UP>er</UP></SUB><UP>+CL</UP><SUP><UP>E<SUB>1</SUB>S→E<SUB>1</SUB></UP></SUP><SUB><UP>int</UP></SUB><UP>+CL</UP><SUP><UP>E<SUB>1</SUB>S→M′</UP></SUP><SUB><UP>int</UP></SUB>)[<UP>E<SUB>1</SUB>S</UP>]<SUP><UP>N</UP></SUP><SUB><UP>er</UP></SUB>}<FENCE>V<SUB><UP>er</UP></SUB></FENCE>

<FR><NU><UP>d</UP>[<UP>E<SUB>1</SUB>G</UP>]<SUP><UP>N</UP></SUP><SUB><UP>er</UP></SUB></NU><DE><UP>d</UP>t</DE></FR>={<UP>CL</UP><SUP><UP>E<SUB>1</SUB>G</UP></SUP><SUB><UP>er</UP></SUB>[<UP>E<SUB>1</SUB>G</UP>]<SUP><UP>N</UP></SUP><SUB><UP>cyt</UP></SUB><UP>+CL</UP><SUP><UP>E<SUB>1</SUB>→E<SUB>1</SUB>G</UP></SUP><SUB><UP>int</UP></SUB>[<UP>E<SUB>1</SUB></UP>]<SUP><UP>N</UP></SUP><SUB><UP>er</UP></SUB><UP>−CL</UP><SUP><UP>E<SUB>1</SUB>G</UP></SUP><SUB><UP>er</UP></SUB>[<UP>E<SUB>1</SUB>G</UP>]<SUP><UP>N</UP></SUP><SUB><UP>er</UP></SUB>}<FENCE>V<SUB><UP>er</UP></SUB></FENCE>

<FR><NU><UP>d</UP>[<UP>M′</UP>]<SUP><UP>N</UP></SUP><SUB><UP>er</UP></SUB></NU><DE><UP>d</UP>t</DE></FR>={<UP>CL</UP><SUP><UP>E<SUB>1</SUB>→M′</UP></SUP><SUB><UP>int</UP></SUB>[<UP>E<SUB>1</SUB></UP>]<SUP><UP>N</UP></SUP><SUB><UP>er</UP></SUB>+<UP>CL</UP><SUP><UP>E<SUB>1</SUB>S→M′</UP></SUP><SUB><UP>int</UP></SUB>[<UP>E<SUB>1</SUB>S</UP>]<SUP><UP>N</UP></SUP><SUB><UP>er</UP></SUB>}<FENCE>V<SUB><UP>er</UP></SUB></FENCE>
For zonal distribution of the UDP-glucuronosyltransferases, the intrinsic clearances CL<UP><SUB>int</SUB><SUP>E<SUB>1</SUB>→E<SUB>1</SUB>G</SUP></UP> in the periportal (I) and perivenous (II) compartments are 33% and 67%, respectively, of the total glucuronidation intrinsic clearance (CL<UP><SUB>int</SUB><SUP>E<SUB>1</SUB>→E<SUB>1</SUB>G</SUP></UP>). As for the zonal distribution of estrone sulfatase, the intrinsic clearances CL<UP><SUB>int</SUB><SUP>E<SUB>1</SUB>S→E<SUB>1</SUB></SUP></UP> in the periportal (I) and perivenous (II) compartments are both 50% of the total sulfation intrinsic clearance (CL<UP><SUB>int</SUB><SUP>E<SUB>1</SUB>S→E<SUB>1</SUB></SUP></UP>).

Bile Compartment. Since the bile flow rate decreased with the perfusion time, the bile flow rate used in the fitting procedure was based on the following relation (Qbile = 0.0114 - 0.000029t) obtained upon regression of the bile flow rate versus time.

Countercurrent bile flow was modeled. Bile excreted into compartment II flowed into compartment I.

When N = 1
<FR><NU><UP>d</UP>[<UP>E<SUB>1</SUB>S</UP>]<SUP><UP>I</UP></SUP><SUB><UP>bile</UP></SUB></NU><DE><UP>d</UP>t</DE></FR>={<UP>CL</UP><SUP><UP>E<SUB>1</SUB>S</UP></SUP><SUB><UP>bile</UP></SUB>f<SUP><UP>E<SUB>1</SUB>S</UP></SUP><SUB><UP>cyt</UP></SUB>[<UP>E<SUB>1</SUB>S</UP>]<SUP><UP>I</UP></SUP><SUB><UP>cyt</UP></SUB>+Q<SUB><UP>bile</UP></SUB>([<UP>E<SUB>1</SUB>S</UP>]<SUP><UP>II</UP></SUP><SUB><UP>bile</UP></SUB>−[<UP>E<SUB>1</SUB>S</UP>]<SUP><UP>I</UP></SUP><SUB><UP>bile</UP></SUB>)}<FENCE>V<SUB><UP>bile</UP></SUB></FENCE>

<FR><NU><UP>d</UP>[<UP>E<SUB>1</SUB>G</UP>]<SUP><UP>I</UP></SUP><SUB><UP>bile</UP></SUB></NU><DE><UP>d</UP>t</DE></FR>={<UP>CL</UP><SUP><UP>E<SUB>1</SUB>G</UP></SUP><SUB><UP>bile</UP></SUB>f<SUP><UP>E<SUB>1</SUB>G</UP></SUP><SUB><UP>cyt</UP></SUB>[<UP>E<SUB>1</SUB>G</UP>]<SUP><UP>I</UP></SUP><SUB><UP>cyt</UP></SUB>+Q<SUB><UP>bile</UP></SUB>([<UP>E<SUB>1</SUB>G</UP>]<SUP><UP>II</UP></SUP><SUB><UP>bile</UP></SUB>−[<UP>E<SUB>1</SUB>G</UP>]<SUP><UP>I</UP></SUP><SUB><UP>bile</UP></SUB>)}<FENCE>V<SUB><UP>bile</UP></SUB></FENCE>
When N = 2
<FR><NU><UP>d</UP>[<UP>E<SUB>1</SUB>S</UP>]<SUP><UP>II</UP></SUP><SUB><UP>bile</UP></SUB></NU><DE><UP>d</UP>t</DE></FR>={<UP>CL</UP><SUP><UP>E<SUB>1</SUB>S</UP></SUP><SUB><UP>bile</UP></SUB>f<SUP><UP>E<SUB>1</SUB>S</UP></SUP><SUB><UP>cyt</UP></SUB>[<UP>E<SUB>1</SUB>S</UP>]<SUP><UP>I</UP></SUP><SUB><UP>cyt</UP></SUB>+Q<SUB><UP>bile</UP></SUB>([<UP>E<SUB>1</SUB>S</UP>]<SUP><UP>II</UP></SUP><SUB><UP>bile</UP></SUB>}<FENCE>V<SUB><UP>bile</UP></SUB></FENCE>

<FR><NU><UP>d</UP>[<UP>E<SUB>1</SUB>S</UP>]<SUP><UP>II</UP></SUP><SUB><UP>bile</UP></SUB></NU><DE><UP>d</UP>t</DE></FR>={<UP>CL</UP><SUP><UP>E<SUB>1</SUB>S</UP></SUP><SUB><UP>bile</UP></SUB>f<SUP><UP>E<SUB>1</SUB>S</UP></SUP><SUB><UP>cyt</UP></SUB>[<UP>E<SUB>1</SUB>S</UP>]<SUP><UP>I</UP></SUP><SUB><UP>cyt</UP></SUB>+Q<SUB><UP>bile</UP></SUB>([<UP>E<SUB>1</SUB>S</UP>]<SUP><UP>II</UP></SUP><SUB><UP>bile</UP></SUB>}<FENCE>V<SUB><UP>bile</UP></SUB></FENCE>
The excretion rates of E1S and E1G in bile are related to the products of bile flow rate and their concentrations in bile in compartment I at the outlet
<FR><NU><UP>d</UP>A<SUP><UP>E<SUB>1</SUB>S</UP></SUP><SUB><UP>bile</UP></SUB></NU><DE><UP>d</UP>t</DE></FR>=Q<SUB><UP>bile</UP></SUB>[<UP>E<SUB>1</SUB>S</UP>]<SUP><UP>I</UP></SUP><SUB><UP>bile</UP></SUB>

<FR><NU><UP>d</UP>A<SUP><UP>E<SUB>1</SUB>G</UP></SUP><SUB><UP>bile</UP></SUB></NU><DE><UP>d</UP>t</DE></FR>=Q<SUB><UP>bile</UP></SUB>[<UP>E<SUB>1</SUB>G</UP>]<SUP><UP>I</UP></SUP><SUB><UP>bile</UP></SUB>

    References
Top
Abstract
Introduction
Experimental Procedures
Results
Discussion
Appendix
References


0022-3565/01/2971-0423-0436$03.00
THE JOURNAL OF PHARMACOLOGY AND EXPERIMENTAL THERAPEUTICS
Copyright © 2001 by The American Society for Pharmacology and Experimental Therapeutics



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