Introduction

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Drug removal by the liver involves the microcirculation, binding-debinding, transport, metabolism, and excretion, and is a distributed-in-space phenomenon that is modulated by zonation. A common method for probing enzyme zonation in the absence of a transport barrier is single-pass prograde/retrograde perfusion of the rat liver preparation (Pang and Terrell, 1981; St-Pierre et al., 1989). With prograde perfusion, perfusate enters the portal vein and exits at the hepatic vein, first recruiting upstream and then downstream enzymes. With retrograde perfusion, flow enters the hepatic vein and exits the portal vein such that zonal distributions of enzymes appear reversed (Pang and Terrell, 1981; Pang et al., 1983). A more elaborate perfusion protocol is the dual perfusion of the hepatic artery (HA) and portal vein, or the hepatic vein (HV). If the substrate is delivered via HA single-pass to the liver with blank perfusate flowing retrogradely (HAHV), substrate will be confined to the periportal (PP) space. Conversely, with prograde flow of blank perfusate entering the portal vein (HAPV), substrate delivered from HA is swept across the entire liver (Pang et al., 1988). The removal rate constants for the respective regions may be obtained upon normalization of the metabolic activity to the cellular water spaces accessed (Chiba et al., 1994).

By contrast, assessment of metabolic heterogeneity behind a transport barrier in the intact liver is more complex. The metabolic rates will depend on the transport of the drug and metabolite and whether the enzyme distribution is periportal (PP) or perivenous (PV). It is known that if transport across the hepatocyte membrane is poor, the fate of formed and preformed metabolites may differ (Sato et al., 1986; deLannoy and Pang, 1987; Schwab and Pang, 1999). Although there exist a few reports on the use of metabolite data to assess enzyme zonation after pulse injection of drug to the perfused rat liver preparation (Mellick et al., 1994; Ballinger et al., 1995), the basis for estimation has not been rigorously developed theoretically. A recent theoretical treatise had examined the influence of enzyme zonation on the AUC and MTT of drugs and metabolites and the transmembrane transport when the liver is viewed as two half-parallel tubes arranged in series, or the tubes-in-series model (Schwab and Pang, 1999). Not unexpectedly, the mean residence time of the formed metabolite (MTT_M) depended on both transporter activities and localization of enzymes.

In this communication, we hypothesized that moment analysis of the metabolite is useful for examination of enzyme heterogeneity. Benzoate metabolism by glycine conjugation was chosen to illustrate the principle. A perivenous (zone 3) predominance of glycine conjugation has been inferred from HAPV and HAHV liver perfusion studies (Chiba et al., 1994). The metabolite, hippurate, undergoes saturable, barrier-limited transport into the rat liver, and is neither metabolized nor excreted into bile (Yoshimura et al., 1998). Benzoate also undergoes barrier-limited transport but is transported linearly and rapidly into hepatocytes at concentrations below 1 mM (Schwab et al., 2001). Transport is likely attributed to the monocarboxylic acid transporter 1 (Tamai et al., 1999) that transports L-lactate and is evenly distributed in the acinus (Staricoff et al., 1995). Although the mitochondria space for metabolism constitutes an added, intracellular compartment (Chiba et al., 1994; Schwab et al., 2001), the attributes are ideal for the testing of the principles of moment analysis on enzyme zonation. In this study, a bolus containing tracer preformed [³H]hippurate (PM) was injected rapidly into the hepatic vein of the rat liver at 20 min postperfusion to characterize the hippurate transfer coefficients. This was followed by a second injection containing [¹⁴C]benzoate at 30 min to characterize the transfer and metabolic coefficients of benzoate. Both injected doses also contained noneliminated reference indicators (⁵¹Cr-labeled RBCs, ¹²⁵I-labeled albumin, [¹⁴C]- or [³H]sucrose, and ²H₂O). The derived retrograde outflow data (17 ± 1 µM benzoate) were analyzed according to the barrier-limited, variable transit time model of Goresky (Goresky et al., 1973) and were compared with those observed previously for prograde flow under first-order conditions (<200 µM benzoate) (Schwab et al., 2001). However, due to our inability to encompass heterogeneity into the Goresky model, the previously developed tubes-in-series model (Schwab and Pang, 1999) was extended to encompass heterogeneity in mitochondrial metabolism behind transport barriers. The expectations were the unchanged area under the curve for preformed (PM) and formed (M) hippurate, an unchanged MTT_PM for PM, but a smaller MTT_M for formed hippurate for retrograde flow, since metabolic activity is distributed in the perivenous region. We further studied zonal transport and metabolism of benzoate with enriched, zonal rat hepatocytes.

	Materials and Methods

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Benzoic acid, hippuric acid, and bovine serum albumin (fraction V) were obtained from Sigma-Aldrich (St. Louis, MO). [¹⁴C]Benzoic acid (specific activity, 110 mCi/mmol) and the [2-³H]glycine (specific activity, 43.4 Ci/mmol) used for the synthesis of hippurate (Yoshimura et al., 1998) were obtained from American Radiolabeled Chemicals, Inc. (St. Louis, MO) and DuPont Canada, Inc. (Markham, ON, Canada), respectively. [⁵¹Cr]Sodium chromate (specific activity 5392 mBq/mg), ¹²⁵I-labeled serum albumin (specific activity 0.46 mBq/mg), and ²H₂O (>99.98% pure) were procured from Merck Frosst (Montreal, QC, Canada). [¹⁴C]Sucrose (4.95 mCi/mmol) and [³H]sucrose (12.3 Ci/mmol) were purchased from PerkinElmer Life Sciences (Boston, MA). Digitonin was obtained from Fluka (Buchs, Switzerland). Collagenase was purchased from Roche Diagnostics (Oakville, ON, Canada). All reagents used were of glass-distilled, high-performance liquid chromatographic grade, or the highest purity available (Fisher Scientific, Mississauga, ON, Canada).

Transport and Metabolic Studies in Isolated and Zonal Rat Hepatocytes

Isolation of Homogeneous, Periportal (PP), and Perivenous (PV) Rat Hepatocytes. Enriched PP and PV hepatocytes and homogeneous hepatocytes from male, Sprague-Dawley rats (304 ± 28 g; Charles River Canada, St. Constant, QC, Canada) were prepared according to the digitonin/collagenase perfusion method of Lindros and Pentïlla (1985), with modifications (Tan et al., 1999). The rats were housed in accordance with approved protocols of the University of Toronto Animal Committee, kept under artificial light on a 12:12-h light/dark cycle, and allowed free access to water and food ad libitum. Hepatocyte viability was assessed by Trypan blue exclusion, and averaged 93 ± 1.4% for the transport studies and 94 ± 2.8% for the metabolism studies. Zonal enrichment was defined with respect to the activities of alanine aminotransferase and glutamine synthetase, assayed by a commercially available kit (Sigma-Aldrich) and by a standard UV method (Tan et al., 1999; Tirona et al., 1999), respectively; the PP/PV ratio was 1.5 for alanine aminotransferase and 12 for glutamine synthetase. Protein was assayed by the method of Lowry et al. (1951).

Uptake of Benzoate by Isolated and Zonal Rat Hepatocytes. Uptake studies were conducted as outlined previously (Tirona et al., 1999). All buffers were pregassed with Carbogen [95% O₂, 5% CO₂ (v/v); Canox Gas, Mississauga, ON, Canada). After preincubation in an atmosphere of Carbogen for 10 min at 37°C, uptake of [¹⁴C]benzoate (1 and 400 µM with 215,000 ± 102,000 dpm/ml) and [³H]sucrose (383,000 ± 301,000 dpm/ml), an interstitial space marker, by PP (n = 3) and PV hepatocytes (n = 3) and isolated (homogeneous) hepatocytes (n = 4) was examined over the course of 1 min in 1.67 × 10⁶ cells. Samples were removed at 15, 30, 45, and 60 s for rapid centrifugation through a layer of silicon oil (100 µl, density 1.02 g/ml) into the lowest layer of 50 µl of 3 N NaOH. After removal of the tips into a 20-ml glass scintillation vial and left overnight, 50 µl of 3 N H₂SO₄ was added to neutralize the sample. After the addition of scintillation fluor (Ready Safe; Beckman Coulter, Canada, Mississauga, ON, Canada), the radioactivity of the cell and the supernatant (25 µl) were quantified in a liquid scintillation spectrometer (LS5801; Beckman Coulter Canada). The extracellular volume entrapped in the cellular compartment was found by the [³H]sucrose content, and a correction was made in the determination of cellular contents on [¹⁴C]benzoate uptake.

Metabolism of Benzoate in Zonal Rat Hepatocytes. Cell suspensions of PP or PV hepatocytes, preincubated at 37°C for 10 min, were added to mixtures of [¹⁴C]benzoate and unlabeled benzoate to result in concentrations of 480,000 ± 136,000 dpm/ml and 1 µM in 1.6 to 1.7 × 10⁶ cells/ml. Duplicate samples (100 µl) were retrieved simultaneously at various times (0.5-7.5 min) directly into a 1.5-ml microcentrifuge tube containing 0.5 ml of acetonitrile (and internal standard, methoxybenzoic acid) for HPLC analysis using a reverse-phase Beckman Ultrasphere column as previously described (Chiba et al., 1994; Cong et al., 2001; Schwab et al., 2001). The samples were mixed well and stored at 20°C until analysis. After thawing and centrifugation, 200 µl of the sample was injected directly onto the HPLC column. Standards of known, different counts were processed in an identical fashion for construction of the calibration curve.

Rat Liver Perfusion

Male Sprague-Dawley rats (n = 8; 296 ± 9 g; livers were 11 ± 2.2 g) served as liver donors. In situ single-pass liver perfusion under retrograde flow was carried out as previously described (St-Pierre et al., 1989) with perfusate (12 ml/min) at 37°C entering via the hepatic vein and exiting via the portal vein; the hepatic artery was ligated. Perfusate consisted of bovine erythrocytes (20%), freshly obtained and washed (kind gift of Ryding-Regency Meat Packers, Toronto, ON, Canada), 5% bovine serum albumin, and 17 mM glucose (Baxter Travenol Laboratories, Deerpark, IL) in Krebs-Henseleit bicarbonate solution (pH 7.4). Perfusate was gassed simultaneously with 95% oxygen/5% carbon dioxide (Matheson, Mississauga, ON) and oxygen (BOC Gases, Whitby, ON, Canada), and the pH, monitored by an "on-line" flow-through pH electrode (Thermo Orion, Boston, MA), was maintained at 7.4 by adjusting the proportion of the two gas supplies. Three to five inflow and outflow perfusate samples, collected during steady state, were used for determination of the average input (C_In) and output (C_Out) perfusate concentrations of unlabeled benzoate and hippurate; both benzoate and hippurate do not distribute into red blood cells (Yoshimura et al., 1998; Schwab et al., 2001). Bile samples were collected for the first 15 min and at 5- to 10-min intervals thereafter up to 60 min to monitor the excreted radioactivity and the bile flow; the total recovery relative to the injected dose was found to be minimal.

Multiple Indicator Dilution (MID). Two consecutive injections (0.23 ml) were made within each liver perfusion study with retrograde flow at 20 and 30 min, respectively, after the initiation of perfusion, as described previously (Goresky, 1963; Schwab et al., 2001). The first injection mixture contained ⁵¹Cr-labeled erythrocytes (0.34 ± 0.034 µCi), ¹²⁵I-labeled albumin (2.3 ± 0.16 µCi), [¹⁴C]sucrose (0.34 ± 0.09 µCi), ²H₂O (0.09 ± 0.0056 ml), and [³H]hippurate (1.36 ± 0.16 µCi) to define the transport parameters pertaining to the preformed metabolite. The second mixture contained ⁵¹Cr-labeled erythrocytes (0.28 ± 0.023 µCi), ¹²⁵I-labeled albumin (2.3 ± 0.26 µCi), [³H]sucrose (0.30 ± 0.1 µCi), and [¹⁴C]benzoate (1.14 ± 0.21 µCi). Each injected mixture contained a constant concentration of unlabeled benzoate (17 ± 1.3 µM) in a composition otherwise identical to that of the perfusate and was introduced into the inflow system by an electronically controlled injection valve; subsequent outflow samples were continuously being collected for a total of 180 and 280 s, respectively, for the first and second injections, as described previously (Schwab et al., 2001). The hematocrits of the injection mixture and the perfusate were determined for each experiment by use of a hematocrit centrifuge (model MB Microhematocrit Centrifuge, IEC; Fisher Scientific). Sham experiments (without liver) were conducted to characterize the dispersion due to the injection device and the inflow and outflow catheters, and for estimation of the mean transit time of the catheters.

Quantitation of Radioisotopes in MID Study and Assay of Unlabeled Benzoate and Hippurate in Perfusate and Bile

The ⁵¹Cr and ¹²⁵I radioactivities in outflow blood perfusate samples and the injected dose were assayed by gamma counting (Cobra II;0 Canberra Industries Canada, Mississauga, ON, Canada). Perfusate plasma was separated from red blood cells by centrifugation, and the contained [³H] and [¹⁴C] radioactivities in outflow perfusate plasma (25-200 µl) and the plasma dose (1:10 dilution, 25 µl) were made up to 200 µl with blank perfusate plasma. After the addition of 800 µl of acetonitrile for deproteinization, 800 µl of the supernatant was removed for liquid scintillation counting (LS5801; Beckman Coulter Canada). ²H₂O in perfusate plasma was assayed by Fourier transform infrared spectrometry as previously described (Pang et al., 1991). To the perfusate plasma sample (100 or 200 µl) from the second injection was added acetone (4:1, v/v) for deproteinization, and the supernatant fraction containing the [¹⁴C]benzoate and [¹⁴C]hippurate was removed and spotted onto the origin of the Silica Gel GF thin-layer chromatography plate (250 µm; Analtech, Newark, DE) that was prespotted with unlabeled benzoate and hippurate. The outflow perfusate and bile samples were developed in a solvent system of chloroform/cyclohexane/acetic acid (80:20:10, v/v/v), as described previously (Schwab et al., 2001). The scraped fractions after thin-layer chromatography development were added to 0.5 ml water, mixed, and subjected to liquid scintillation counting as described earlier (Schwab et al., 2001).

The concentrations of unlabeled benzoate and hippurate in perfusate plasma samples and bile were assayed by high-performance liquid chromatography, as previously described (Chiba et al., 1994; Schwab et al., 2001). Perfusate plasma (500 µl) was added to the internal standard, methoxybenzoic acid (50 µl of a 16 µg/ml solution in water), and was deproteinized with 800 µl of acetonitrile, dried under nitrogen, and reconstituted for injection into the HPLC column. A solvent gradient, consisting of 0.5% acetic acid and acetonitrile, was utilized. Standards for calibration curves (varying amounts of unlabeled benzoate) were processed under identical conditions.

Theory

The theory pertaining to fits to the hippurate and benzoate outflow data according to the Goresky model is based on homogeneous enzyme and transporter functions but heterogeneous flow behavior (Fig. 1). The equations that have been described in detail for prograde flow are presently utilized but will not be repeated here (Schwab et al., 2001). The fit to the Goresky model will provide the transport parameters for hippurate (first dose) and benzoate (second dose) as well as the mitochondrial transfer and metabolic rate constants. However, we have not yet found a consistent way to model enzyme zonation in the Goresky-type model. Hence, we had adopted an alternate approach for the detection of enzyme zonation from prograde and retrograde MID data by extending the existing theory on the tubes-in-series model (Schwab and Pang, 1999; Fig. 1A). However, with the present precursor-product pair, benzoate and hippurate, glycine conjugation occurs within the mitochondria (Gatley and Sherratt, 1977), evoking consideration of an extra pool (Fig. 1B). Results of MID studies by Schwab et al. (2001) indeed confirmed the involvement of a deep compartment for metabolism. Hence, the theory was extended to reflect this (see Appendix 1). Moments may then be calculated for this model, and the results are summarized in Table 1.

View larger version (16K): [in this window] [in a new window]   Fig. 1.   Theoretical models of metabolism. Model A, metabolism in the cytosol according to Schwab and Pang (1999). k13 and k31 are coefficients for influx of tracer precursor into, and efflux from, parenchymal cells; k24 and k42 are the corresponding coefficients for the metabolite; k34 is the coefficient for enzymic conversion of parent to metabolite; k30 is that for sequestration (removal) of the parent drug (other than formation of the metabolite); and k40 is that for sequestration of the metabolite. Model B, metabolite formation in a deep compartment (compartment 4), with k13 and k31 as above. k25 and k52 are the coefficients for influx and efflux for the metabolite; k45 is the coefficient for glycine conjugation of benzoate; k30 (coefficient for additional sequestration of benzoate) and k50 (coefficient for sequestration of the metabolite) are set to zero.

Enzyme Zonation within the Tubes-in-Series Model. The rate constant for metabolic transformation is again treated as a function of the relative position within the acinus, denoted by  (where  = 0 represents a position adjacent to the portal venule, and  = 1 represents one adjacent to the central venule) to represent enzyme zonation. Conversely, rate constants for transmembrane transport (k₁₃, k₃₁, k₂₅, k₅₂, k₃₄, and k₄₃) are treated as constants to represent homogeneously distributed transporter activity. This assumption is validated, at least for k₁₃, in the zonal-hepatocyte uptake study of benzoate. For the formulation of Laplace transforms and moments of outflow profiles, the sinusoid was considered as two half-sinusoids arranged in series, each with a transit time of 0.5 MTT_ref. A stepwise change of k₄₅ at  = 0.5 was assumed such that

(1)

(2)

where ₄₅ is the length-averaged value of k₄₅(), the metabolic rate constant, and r is a heterogeneity parameter with values between 1 and 1. As defined previously, positive values of r denote a predominantly periportal enzymic distribution and negative values of r denote a predominantly perivenous enzymic distribution (Schwab and Pang, 1999). Special cases include exclusively periportal (PP) enzyme distribution (r = 1) and exclusively perivenous (PV) enzyme distribution (r = 1); for r = 0, the enzyme distribution is even or uniform. Various values of r ranging from 1 to +1 were used to explore the impact of intermediate enzyme zonation on the moments of drugs and metabolites. As shown previously, the overall unit impulse response of subsystems connected in series is given as the convolution of the individual unit impulse responses (Lassen and Perl, 1979; Bronikowski et al., 1987; Schwab et al., 2001). Laplace transforms and AUCs are obtained as the products of those of the outflow profiles of the subsystems, whereas MTTs are their sums.

(3)

(4)

Data Treatment

For the multiple indicator dilution data, the concentrations of radiolabels in the outflow perfusate were normalized to the respective doses, yielding fractional recoveries (or concentration/dose). The fractional recovery-integral (or area under the curve, AUC) and area under the moment curve (AUMC, or the integral of the product of fractional recovery and time at mid-intervals) of the outflow data of benzoate and hippurate were estimated by the spline function of IMSL (Visual Numerics, Houston, TX). The ratio of AUMC/AUC furnished the mean transit time, MTT. Tracer recoveries were obtained by multiplying AUCs with perfusate flow and were virtually complete for the noneliminated reference indicators and the [³H]hippurate and [¹⁴C]benzoate doses; the latter recovery was assessed as the summed recoveries for [¹⁴C]benzoate and [¹⁴C]hippurate.

Modeling of Hepatic Hippurate and Benzoate Disposition. The outflow profiles of the nonmetabolized indicators, ⁵¹Cr-labeled erythrocytes, ¹²⁵I-labeled albumin, [³H]- or [¹⁴C]sucrose, and ²H₂O, were evaluated by linear superposition as described previously (St-Pierre et al., 1989; Xu et al., 1990; Schwab et al., 2001). The kinetic model for the transport and metabolism of benzoate in the perfused rat liver has previously been validated (Schwab et al., 2001). In the absence of an established whole-organ model that includes enzyme zonation, the data were fitted to the homogeneous-enzyme model of Goresky, as done previously for the prograde experiments (Schwab et al., 2001). The outflow profiles (impulse responses) were calculated using an algorithm based on an approximation of the reference indicator curves by exponential sums as previously described (Schwab, 1984; Schwab et al., 2001).

Statistics

All data were presented as mean ± S.D. Analysis of variance was used to compare differences in the mean values. A P value of < 0.05 was viewed as significant.

	Results

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Uptake and Metabolism of Benzoate by Zonal Hepatocytes. The amounts of benzoate accumulated within hepatocytes, estimated as the radioactivity in cell pellets, were linear with time within 1 min of sampling. The regression slopes yielded similar uptake rates for the PP, PV, and homogeneous isolated rat hepatocytes at the low BA (1 µM) and high (400 µM) concentrations tested (Fig. 2). The results paralleled those for the uptake of L-lactate, the model substrate of monocarboxylic acid transporter 2, in zonal rat hepatocytes (Staricoff et al., 1995). The disappearance of benzoate (1 µM) in the incubation mixture upon incubation was similar for both PP and PV hepatocytes (n = 4 preparations each). The rate of formation of hippurate was linear up to 5 min of incubation, and interpretation was based on data gathered up to 3 or 5 min (Fig. 3). No difference was found for hippurate formation from PP (5.86 ± 1.88% initial concentration/min) and PV (5.25 ± 1.46% initial concentration/min, P > 0.05) hepatocytes, nor for the decay rate constants of BA (0.0676 ± 0.0220 min¹ for PP cells and 0.0563 ± 0.0162 min¹ for PV cells) in the incubation system (P > 0.05).

View larger version (20K): [in this window] [in a new window]   Fig. 2.   Uptake of benzoate by periportal (n = 3), homogeneous (n = 4), and perivenous (n = 3) isolated rat hepatocytes for 1 and 400 µM benzoate. Data are mean ± S.D.

View larger version (16K): [in this window] [in a new window]   Fig. 3.   Lack of zonal difference in metabolism of benzoate (1 µM) by PP and PV hepatocytes (1.6-1.7 × 106 cells/ml) in formation of hippurate. The disappearance of benzoate from PP () and PV () cells was accounted for by formation of hippurate in PP () and PV () cells. Data are mean ± S.D. of four preparations each.

AUC and MTT For the Tubes-in-Series Model. The solutions for AUC and MTT are shown in eqs. 3 and 4. For a drug such as benzoate, which entails metabolism within a sequestered pool (see Fig. 1B), the apparent tissue to plasma partitioning of drug was given by (k₁₃/k₃₁)(1 + k₃₄/k₄₃) due to the additional mitochondrial pool, whereas that for the preformed metabolite was given by k₂₅/k₅₂, and the ratio of these values yields the relative permeability characteristics of the drug and metabolite (Table 1). The area under the curve of the formed metabolite, AUC_M, was found to be constant for prograde and retrograde flow directions regardless of whether (k₁₃/k₃₁)(1 + k₃₄/k₄₃) > k₂₅/k₅₂ or (k₁₃/k₃₁)(1 + k₃₄/k₄₃) < k₂₅/k₅₂. By contrast, the MTT_M would change according to the values of (k₁₃/k₃₁)(1 + k₃₄/k₄₃) versus k₂₅/k₅₂ and the flow direction (Table 1). These relationships were similar to those found in an earlier treatise when the tubes-in-series model was first developed in the absence of the mitochrondrial compartment (Schwab and Pang, 1999).

Moment Analysis of Hippurate and Benzoate in MID Studies. The steady-state extraction ratio of benzoate (0.6) for retrograde flow (Table 2) was similar to that observed previously for prograde flow (data of Schwab et al., 2001). Representative outflow profiles of tracer [³H]hippurate (first injection), of tracer [¹⁴C]benzoate and its metabolite, [¹⁴C]hippurate (second injection), and of the noneliminated indicators are shown in Figs. 4 and 5, respectively, for 17 µM benzoate in the inflow perfusate. The outflow profiles of the noneliminated indicators (labeled erythrocytes, albumin, sucrose, and ²H₂O) for the first and the second injections in outflow (portal venous) perfusate were increasingly dispersed. The total recoveries of the ⁵¹Cr-, ¹²⁵I-, ¹⁴C-, and ³H-radiolabels and of ²H₂O in the venous outflow samples were virtually complete (Table 3). All of the injected [³H]hippurate returned to the vasculature as [³H]hippurate, and the [¹⁴C]benzoate returned as unchanged [¹⁴C]benzoate or [¹⁴C]hippurate, suggesting that benzoate was metabolized exclusively to hippurate and that both benzoate and hippurate were not significantly excreted.

View this table: [in this window] [in a new window]   TABLE 2 Steady-state data for retrograde perfusion of benzoate in the present studies were compared with those for prograde perfusion at similar concentrations of benzoate (data from Schwab et al., 2001)a

View larger version (20K): [in this window] [in a new window]   Fig. 4.   Outflow profiles of the preformed metabolite, [3H]hippurate, and the noneliminated references, pursuant to first MID injection. The representative single-pass study was conducted at a 17 µM concentration of the precursor, benzoate. Data are presented as fractions of dose recovered per milliliter of perfusate and are plotted in linear (top) and semilogarithmic (bottom) formats. The continuous line in the bottom panel represents the fitted outflow profile.

View larger version (22K): [in this window] [in a new window]   Fig. 5.   Outflow profiles of [14C]benzoate, its metabolite, [14C]hippurate, and the noneliminated references. The representative single pass study was conducted at 17 µM benzoate. Data are presented as fractions of dose recovered per ml of perfusate and are plotted in linear (top) and semilogarithmic (bottom) formats. The continuous and broken lines in the bottom panel represent the fitted outflow profiles for parent drug and metabolite, respectively.

View this table: [in this window] [in a new window]   TABLE 3 Recoveries of noneliminated reference indicators and labeled hippurate and benzoate after injection of MID doses of [3H]hippurate and [14C]benzoate during retrograde perfusion were compared with those published by Schwab et al. (2001) for retrograde perfusiona

View this table: [in this window] [in a new window]   TABLE 4 Transit times of outflow profiles for the noneliminated reference indicators and preformed hippurate and benzoate during retrograde perfusion were compared with those of Schwab et al. (2001) for prograde perfusion of benzoatea

View larger version (16K): [in this window] [in a new window]   Fig. 6.   Distention of the vascular spaces during retrograde perfusion (light bar) over prograde perfusion (dark bar). , significantly different, with P < 0.05.

Model Fits to Outflow Profiles of [³H]Hippurate According to Goresky's Model. The outflow profile of hippurate obtained after injection of [³H]hippurate during retrograde flow (Fig. 4) was similar to that described for prograde flow (Schwab et al., 2001). The optimal interstitial to sinusoid distribution ratio _H (0.30 ± 0.43) obtained after consideration of binding of hippurate to albumin in perfusate fluid, was smaller than the value of 1.08 ± 0.33 reported by Schwab et al., (2001) due to distention of the vasculature. The transfer coefficients (k₂₅ and k₅₂, Table 5) differed for the influx coefficient (k₂₅) but not for the permeability surface area or PS product (0.049 ± 0.036 ml sec^-1 g^-1) for the influx of hippurate between perfusate and hepatocytes. The ratio of k₂₅ and k₅₂, or the equilibrium, partitioning ratio was 0.26 ± 0.07 and differed from that (0.82 ± 0.17) for prograde flow (Schwab et al., 2001).

View this table: [in this window] [in a new window]   TABLE 5 Fitted parameters obtained for preformed hippurate and benzoate (see Fig. 1 for definition of terms) from MID studies with retrograde perfusion versus those obtained from Schwab et al. (2001) for prograde perfusion For BA, k13/ k31was 1.68 for prograde and 0.7 for retrograde; for HA; k25/ k52was 0.81 for prograde and 0.26 for retrograde. Values for prograde and retrograde were statistically different. Data were mean ± S.D.

Model Fits to Outflow Profiles of [¹⁴C]Benzoate According to Goresky's Model. The outflow profile of benzoate obtained after injection of [¹⁴C]benzoate during retrograde flow (Fig. 5) was similar to that described for prograde flow (Schwab et al., 2001). The optimal interstitial to sinusoid distribution ratio _B (0.45 ± 0.04), obtained after consideration of binding of benzoate to albumin in perfusate fluid (Chiba et al., 1994), was significantly smaller than the value of 0.97 ± 0.46 reported by Schwab et al. (2001) due to distention of the vasculature. Two of the coefficients (k₃₁ and k₃₄, Table 5) differed from those for prograde flow, and the permeability surface area product of benzoate was slightly greater, with the metabolic coefficient being smaller than those for prograde flow (Table 5). The ratio of k₁₃ and k₃₁, or the equilibrium partitioning ratio, was 0.7 ± 0.20 and differed from that for prograde flow (1.68 ± 0.75) (Schwab et al., 2001). However, for these fits, k₁₃/k₃₁ > k₂₅/k₅₂ for both retrograde and prograde flows.

Simulations Based on Tubes-in-Series Theory. Simulations were made based on the analytical solutions for the MTT_M (eq. 4) for prograde and retrograde flows and the values of k₁₃,, k₃₁, k₃₄, k₄₃, and k₄₅ for benzoate, and of k₂₅ and k₅₂ in Table 5. The condition for simulation was identical to the experimentally obtained, fitted parameters that revealed that the partition ratio for benzoate (ratio of influx/efflux rate constants) k₁₃/k₃₁ (1 + k₃₄/k₄₃) was greater than that for hippurate (k₂₅/k₅₂). The resulting PP/PV ratio of MTT_M was plotted against r, the heterogeneity parameter. The simulations (Fig. 7) predicted that the PP/PV ratio of MTT_M exceeds unity for negative values of r and was less than unity for positive values of r for the tubes-in-series model. Both the simulation with the tubes-in-series model and the observed data suggest the perivenous abundance of benzoate glycine conjugation activity, as found by Chiba et al. (1994).

View larger version (15K): [in this window] [in a new window]   Fig. 7.   Effect of the heterogeneity factor (r) on the PP/PV ratio of MTTM with the tubes-in-series or tube model. The fitted parameters k13, k31, k25, k52, k34, and k45 (Table 5) were used in the simulation. The value of r = 1 indicates exclusive PP metabolic zonation (enzyme present in first half of liver); the value of r = 1 represents exclusive PV metabolic zonation (enzyme present in second half of liver); r = 0 indicates evenly distributed metabolic activity. Further simulation was performed with the parameters, based on a two-compartment tanks-in-series model. Similar trends were obtained.

	Discussion

Top Abstract Introduction Materials and Methods Results Discussion Appendix References

Metabolite behavior is highly complex and may differ from the kinetic behavior of a preformed metabolite entering an organ. Although the same transport function and enzyme(s) are involved in metabolite removal, perceptive differences exist due to the presence of a transport barrier for metabolite, barring the PM from entering and preventing M from leaving (deLannoy and Pang, 1987). The kinetic behavior of the formed metabolite (M) is highly dependent on the model of hepatic drug clearance: whether the well stirred model, the parallel tube model, or the dispersion model (St-Pierre et al., 1992; Pang, 1995) applies, and depending on whether the permeability of drugs and metabolite is high or poor.

According to the well stirred model, the kinetics of M is independent of drug behavior, and the MTT_M is the sum of the MTTs for highly permeable drug and preformed metabolite (Chan et al., 1985; St-Pierre et al., 1992; Mellick et al., 1997). For both the parallel tube and dispersion models, however, the kinetic behavior of M is predicated on drug kinetic behavior (St-Pierre et al., 1992). The difference on metabolite formation between the dispersion model (dispersive flow and some mixing) and the parallel tube model (plug flow, nondispersive and no mixing) for flow-limited substrates in the absence of enzyme heterogeneity is, however, small, and a similar trend persists when enzyme heterogeneity is added (St-Pierre et al., 1992). For these reasons, lower values for MTT_M are predicted for the parallel tube and dispersion models in comparison with the well stirred model for highly permeable drugs and metabolites (Roberts et al., 1988; St-Pierre et al., 1992; St-Pierre and Pang, 1993a,b; Mellick et al., 1997). When permeabilities of the drug and the metabolite are low, however, MTT_M will exceed the sum of the mean transit times of the drug and the preformed metabolite (Mellick et al., 1997), since poor permeability of the metabolite retards entry of preformed metabolite but extends the sojourn time of the metabolite formed in the organ. This is confirmed by calculations that show that barrier limitation of transport of the metabolite may increase MTT_M beyond the sum of the mean transit times of the drug and the preformed metabolite, even when the transport of the precursor is not barrier-limited.

The presence of an additional precursor pool such as the mitochondrial space, where conjugation of benzoic acid takes place (Fig. 1B), will extend the mean transit times of the drug and the formed metabolite but will not affect that of the preformed metabolite. However, the presence of the additional mitochondrial pool would not affect the trends of the expected changes on the AUC_M and MTT_M with enzyme zonation (Table 1). Our observation that MTT_M for formed hippurate greatly exceeded the sum of the MTTs of benzoate and preformed hippurate is only suggestive of the poor permeability of hippurate. This finding is in agreement with the present transfer constants for hippurate, as well as those found in previous MID experiments (Yoshimura et al., 1998; Schwab et al., 2001), showing that the influx clearance of hippurate (P₂₅S) was less than the perfusate flow rate.

Interpretation of the AUC and MTT data of the present study depends on verifying the viability of the preparation at the times of both injections during retrograde flow. In previous experiments with retrograde perfusion of rat livers under similar conditions, measured rates of bile flow or oxygen consumption were not different from values obtained with prograde perfusion (St-Pierre et al., 1989; Xu et al., 1990), and inflow venous pressures were unchanged (St-Pierre et al., 1989) or only increased minimally (Xu et al., 1990). The observed difference in the hematocrit (Table 2) should not impact on liver viability or processing of benzoate and hippurate since both are not bound to red blood cells. However, distention was a hallmark of retrograde perfusion (St-Pierre et al., 1989; Xu et al., 1990), and this was evident from the blebbing of the curve form (shifting of maximum concentration to a lower value and at a later time) with retrograde flow. Of note, the MTT and the volumes of the vascular indicators were enlarged, and cellular water space, estimated by difference, was reduced for retrograde flow when compared with prograde data (Fig. 5), as found previously (St-Pierre et al., 1989; Xu et al., 1990). However, vascular volume distention during the second injection was much less severe than that for the first injection, indicating an adaptation process. The AUC and MTT of preformed species (hippurate or "PM" and benzoate) remained unchanged with both perfusion directions (Tables 3 and 4), and this finding strongly suggests that parameters pertaining to the formed metabolite, AUC_M and MTT_M, are not influenced by the changes in the vasculature. The AUC_M was unchanged, with reversal of flow direction (Table 3). The MTT_M for retrograde flow was significantly shorter than that for prograde flow (Table 4; P < 0.05), and the partition ratio (influx/efflux) of benzoate exceeded that for hippurate. The data are consistent with the theoretical prediction for a perivenous distribution of benzoate conjugation activity (Table 1). This metabolic heterogeneity suggested by moment analysis reflects that there is zonation of the enzyme, benzoyl CoA ligase (Schwab et al., 2001). Moreover, due to the rapid transport of benzoate, transport would not affect the overall conjugation rate of benzoate since it is not the rate-determining step (Schwab et al., 2001).

The investigations on uptake corroborated with previous evidence on the lack of zonal transport of benzoate (Fig. 2), but the metabolic studies with zonal hepatocytes failed to provide the expected higher perivenous distribution of benzoate conjugation activity (Fig. 3). A lack of in vitro substantiation was also observed for the glutathione S-transferase (GST) activities toward 1-chloro-2,4-dinitrobenzene (CDNB) and ethacrynic acid, both in incubation studies and Western blotting of immunoreactive Ya and Yb2 GSTs with zonal rat hepatocytes (Tirona et al., 1999). The observations were explained by the cross-contamination of the zonal hepatocytes by cells from other regions and the lack of a steep gradient for conjugation activity despite the fact that the activities are higher in the perivenous region. Indeed, the speculation was confirmed with use of PP and PV lysates for incubation studies and Western blotting when these provided a sharper enrichment and less cross-contamination between PP and PV cells; the higher GST activity in PV cells became apparent (Tirona et al., 1999). Hence, the lack of metabolic zonation for glycine conjugation within zonal hepatocytes in the present study is not definitive of a lack of zonation in the intact organ. This is primarily due to a limitation of the method for the preparation of enriched cells.

The tubes-in-series model, although less quantitative than the Goresky approach in incorporating flow heterogeneity, was nonetheless useful for the study of metabolic heterogeneity in the intact liver with the indicator dilution technique in progradely and retrogradely perfused livers. Although it is well known that the sinusoidal transit time is heterogeneous (Pang et al., 1994), the predictions afforded by the tubes-in-series model on the ranking of transit times should be preserved. In addition to the tubes-in-series model, another model, the tanks-in-series model (Gray and Tam, 1987; Saville et al., 1992) exists and may be another useful representation, since the impulse function resulting from an injection was similar to that for Goresky's model. However, the tanks-in-series- model is an empirical model, and the number of compartments (N) necessary to describe the data would vary according to the drug (Gray and Tam, 1987). It was found that N approached a value of 2 for red blood cells, albumin, and lidocaine (Gray and Tam, 1987; Saville et al., 1992), and a similar, tanks-in-series model with N = 2 was able to fit the data of estrone sulfate and estrone in the recirculating perfused rat liver preparation (Tan et al., 2001). In fact, our simulations based on the preliminary development of this model with two compartments (one for upstream and one for downstream) showed that characteristics exceedingly similar to the tubes-in-series model were obtained (see Fig. 7). The predictions on the changes of the AUC_M and MTT_M for the tanks-in-series model with permeability and flow direction (data not shown) were similar to that of the tubes-in-series model (Table 1). These models may be useful approaches and further developed as a zonal model (Abu-Zahra and Pang, 2000) to encompass enzyme and transport heterogeneity for the description of zonal drug metabolism.