Introduction

Top Abstract Introduction Theoretical Models of Hepatic Drug... Experimental Procedures Results Discussion References

Enalapril is a prodrug that is hydrolyzed to yield the active diacid metabolite, enalaprilat. Three members of the type-B carboxylesterase family that are thought to be involved in hepatic xenobiotic metabolism, namely, hydrolases A (Robbi et al., 1990), B (Yan et al., 1994), and C (Yan et al., 1995) have been cloned from rat liver. The expressions of both hydrolases A and B are greater in the perivenous (PV)¹ than the periportal (PP) region of rat liver. Additionally, a 59-kDa carboxylesterase that exhibits a PV zonation has been purified from rat liver (Satoh et al., 1985; Pohl et al., 1991). Hydrolase B is expressed in rat kidney as well as liver (Yan et al., 1994) and is able to hydrolyze aspirin (Mentlein and Heymann, 1984) and the angiotensin converting enzyme inhibitor ester-prodrugs benazepril, delapril, and temocapril (Luan et al., 1997). Hydrolase A is involved in the hydrolysis of clofibrate and procaine (Mentlein and Heymann, 1984). Hydrolases A and B are both paraoxon-inhibitable, and are distinguished from each other by their affinity in catalyzing the hydrolysis of p-nitrophenol acetate (Morgan et al., 1994). The substrate specificity and role played by hydrolase C are, however, less well characterized (Yan et al., 1995).

The highest carboxylesterase activity toward enalapril exists in the liver, where metabolism is characterized by a K_m value of 710 µM (Tocco et al., 1982; Tabata et al., 1990). Rat liver perfusion studies showed that enalapril was highly removed with a steady-state extraction ratio (E_ss,HAPV) of 0.77 when arterially delivered enalapril was swept into the liver by the flow of blank perfusate through the portal vein in the antegrade direction (HAPV perfusion), whereas a much reduced E_ss,HAHV of 0.12 existed with HAHV perfusion when arterially delivered drug was confined to the PP end of the acinus with retrograde (hepatic venous) perfusion with blank perfusate. The observation inferred that hydrolysis of enalapril occurred predominantly in the PV region (Pang et al., 1991). However, the mechanism, whether transport or metabolism is responsible for the zonation, has not been identified.

The interplay of transport and metabolism and the rate-determining step are important considerations in the description of hepatic processing of drugs. Recently, uptake of enalapril was shown to be mediated by Oatp1, the organic anion transporting polypeptide 1 cloned from rat liver (Pang et al., 1998), and transport activities were found to be identical among zonal hepatocytes (K_m^uptake = 344 µM, V_max^uptake = 11 nmol/min/10⁶ cells) (Abu-Zahra et al., 2000). The definitive answer to the question of whether transport or metabolism is responsible for the zonated hydrolysis in perfused liver required the direct comparison of metabolic and uptake activities. In this communication, metabolic activities in the 9000g supernatant (S9) fractions of PV and PP rat hepatocytes were studied to test the hypotheses that metabolism and not transport is rate-determining in the overall hydrolysis of enalapril and that metabolism is greater in the PV region. A correlation was also sought between the in vitro and perfusion data with existing models of hepatic drug clearances.

	Theoretical

Top Abstract Introduction Theoretical Models of Hepatic Drug... Experimental Procedures Results Discussion References

In vitro parameters obtained from studies in cellular and subcellular fractions may be scaled up to represent parameters for physiological variables such as transport and intrinsic clearances for the whole organ. The correlation between in vitro and whole organ/in vivo data is of interest in pharmacokinetics for the understanding of the physiological processes underlying the disappearance of a substrate and the formation of metabolites by the liver. Models of hepatic drug clearances have been proposed to interrelate the physiological variables. These models vary with respect to the description of how blood flow is channeled through the sinusoid as well as how a substrate is dispersed across the acinus, resulting in a concentration gradient in the acinus. Historically, the "well stirred" (or venous equilibration) model (Rowland et al., 1973), which assumes the liver as a single well mixed compartment receiving bulk flow, and the "parallel-tube" (or sinusoidal perfusion) model (Winkler et al., 1973), which describes enzymes being distributed evenly in single sheets of hepatocytes lining the flow path (plug flow), have been used widely. The models represent boundary conditions of perfectly mixed and nonmixed systems, respectively. According to the well stirred model, the concentration of drug in liver is constant and is in equilibrium with that in venous blood, whereas according to the parallel-tube model, drug concentration declines exponentially in the direction of flow. Other models exist and render predictions that are intermediate to those of the well stirred and parallel-tube models: the "dispersion" model (Roberts and Rowland, 1986); the "series-compartment" model (Gray and Tam, 1987); and the "zonal-compartment" model (Meijer and Groothuis, 1991; Tirona and Pang, 1996). The dispersion model describes nonideal blood flow through sinusoids of different lengths, whereas the series-compartment model describes well stirred subcompartments connected in series. Other combinations have also surfaced to depict the "enzyme-distributed" occurrence of enzymatic activities (Pang and Stillwell, 1983).

	Models of Hepatic Drug Clearances

Top Abstract Introduction Theoretical Models of Hepatic Drug... Experimental Procedures Results Discussion References

The models of drug clearances (Fig. 1) are simplified when viewed under first order conditions. Under these instances, the permeability surface area products (or transport clearances) into and out of the cell (PS_in and PS_out) as well as the metabolic (CL_int,liver^met) and biliary (CL_int,liver^bile) intrinsic clearances are independent of concentration; protein binding is also linear with concentration. The E_ss value for enalapril was predicted using the well stirred, parallel-tube, dispersion, and zonal-compartment models according to eqs. 1 to 6. 

View larger version (28K): [in this window] [in a new window]   Fig. 1.   Depiction of the well stirred, parallel-tube, and dispersion models, and their various degrees of mixing denoted by the dispersion number, DN.

Well Stirred Model. For the well stirred model, the value of E_ss for the whole liver is (Gillette and Pang, 1977):

(1)

where Q is the plasma flow rate through the liver and enalapril is confined to plasma; f_u is the unbound fraction of drug in the plasma, and CL_int,liver^total is the total intrinsic (metabolic plus biliary) clearance.

Parallel-Tube Model. For the parallel-tube model, E_ss is given by (Pang and Chiba, 1994):

(2)

Dispersion Model. For the dispersion model, E_ss is given by (Roberts and Rowland, 1986):

(3)

where D_N is the dispersion number relating to the degree of dispersion of the system and varied between 0.15 to 0.24 (Tirona et al., 1998). R_N, the efficiency number, is a composite parameter of the transport clearances, the intrinsic clearances, flow, and unbound fraction.

(4)

Zonal-Compartment Model. The zonal-compartment model, a version of the series-compartment model (Gray and Tam, 1987), described single cells being aligned in series along the sinusoidal flow path (Fig. 2). Three is the smallest number of units to denote the zonal regions, 1, 2, and 3, and both transport and metabolic activities are allowed to vary (Tirona and Pang, 1996). The mass balance rate equations describing the sinusoidal and cellular enalapril concentrations in each (i^th) of three compartments in series are:

View larger version (17K): [in this window] [in a new window]   Fig. 2.   Schematics of the zonal compartment model consisting of three ith subcompartments (1, 2, and 3); an expansion of any ith compartment is shown. See text for definition of the terms.

(5)

(6)

i1

	Experimental Procedures

Top Abstract Introduction Theoretical Models of Hepatic Drug... Experimental Procedures Results Discussion References

Materials. [³H]Enalapril, synthesized as described previously (Pang et al., 1998), was 98.5% pure, as judged by thin-layer chromatography (TLC) [1-propanol/1 M acetic acid/water, 10:1:1, v/v/v, with silica gel GF TLC plates]. Enalaprilat and unlabeled enalapril were obtained from Merck Sharp and Dohme Research Laboratories (West Point, PA). Collagenase A (clostridium histolyticum) was purchased from Boehringer Mannheim (Darmstadt, Germany). All other reagents and solvents were of HPLC grade.

Isolation of Rat Hepatocytes. The isolation of rat hepatocytes from all zones and from zones 1 (PP) and 3 (PV) of the rat liver and from the whole liver was identical with that previously described (Abu-Zahra et al., 2000). The enrichment of PP or PV hepatocytes was routinely verified by marker enzymes (Tan et al., 1999). The activity of the PP marker enzyme, alanine aminotransferase, was 2.20 ± 0.09 times higher (ANOVA P < .05) in PP (461 ± 150 nmol/min/mg of protein) than in PV (210 ± 49 nmol/min/mg of protein) hepatocytes, whereas glutamine synthetase, an enzyme expressed exclusively in the distal PV hepatocytes, exhibited significantly lower activity in PP (0.52 ± 0.96 nmol/min/mg of protein) than in PV preparations (27.7 ± 11.6 nmol/min/mg of protein) (ANOVA P < .05); the PP/PV ratio was 0.018 ± 0.03.

Preparation of S9 Fraction from Homogeneous and Zonal Hepatocytes. Hepatocyte suspensions of >90% viability were centrifuged for 5 min at 850g. The incubation buffer supernatant was aspirated, and ice-cold Krebs-Henseleit bicarbonate buffer (containing 120 mM NaCl, 25 mM NaHCO₃, 4.75 mM KCl, 2.54 mM CaCl₂, 1.19 mM MgSO₄·7H₂O, and 1.19 mM KH₂PO₄) was added in an amount three times the volume of the hepatocyte pellet. The mixture was shaken by vortex, then homogenized for 1 to 2 min (Ultra Turrax T25 homogenizer; Janke and Kunkel, IKA-Labortechnik, Staufen i.m. Briesgau, Germany). Homogenates were centrifuged (Beckman J2-21 M centrifuge; Beckman Canada, Mississauga, ON) at 9000g at 4°C for 20 min. The resulting supernatant (S9 fraction) was either used immediately or stored at 70°C until use.

Metabolic Studies. Preliminary studies had shown that identical rates of enalapril hydrolysis were obtained with freshly prepared and thawed (frozen at 70°C) S9 preparations. Thawed S9 preparations were diluted to a concentration of approximately 2 mg of protein/ml then preincubated in a rotating water bath for 10 min at 37°C. Aliquots (100 µl) of S9 were added to 100 µl of enalapril (and tracer [³H]enalapril, about 200,000 dpm/ml) in Krebs-Henseleit bicarbonate buffer to result in concentrations of 50 to 4000 µM in 0.2 ml of incubation mixture. Samples (100-µl) were retrieved after 15 min, a predetermined time in which metabolic formation rates were found to be linear with time. The samples were placed into 1.5-ml microfuge tubes containing 300 µl of ice-cold CH₃CN to halt the reaction. The tubes were centrifuged, and the supernatants were stored at 20°C for later analysis by TLC. Fifty microliters of the remaining incubation mixture was removed for liquid scintillation counting (model 5801; Beckman Coulter, Mississauga, ON, Canada). Protein was measured by the method of Lowry et al. (1951).

Assays of Enalapril and Enalaprilat. [³H]Enalapril and [³H]enalaprilat were separated by TLC (Pang et al., 1991). Silica gel GF TLC plates (Analtech, Newark, DE) were initially prepared by placement of approximately 150 µl of a solution containing authentic standards of enalapril and enalaprilat in CH₃CN and H₂O. Two hundred microliters of the deproteinized sample in CH₃CN was spotted at the origin of the TLC plate, which was preloaded with the authentic standards. The plate was developed in a solvent system of 1-propanol/1 M acetic acid/water (10:1:1, v/v/v). After resolution, the standards, which had comigrated with their radiolabeled counterparts, were visualized under a UV lamp, and the bands were scraped off into 20-ml glass vials containing 0.5 ml of water and 10 ml of scintillation fluor (Ready Protein; Beckman Instruments). After mixing, the vials were stored in darkness for a minimum of 48 h before liquid scintillation counting. Additionally, 50 µl of sample was counted for determination of on-plate recovery. The relative amounts of radioactive enalapril and enalaprilat present on the TLC plates and the specific activity of the incubation mixture were used to calculate the amounts of metabolite formed per 15 min. The information provided the rate of metabolism, v (nanomoles of enalaprilat formed per min per milligram of protein), for each incubation mixture.

Fitting. Fitting of the in vitro metabolic data was performed by an iterative, nonlinear least-squares procedure (Scientist, v.2; Micromath Scientific Software, Salt Lake City, UT). A weighting scheme of 1/(observation)² was used because this provided the best optimization of the data. The best fit was described by the simple Michaelis-Menten equation:

(7)

where K_m^met represents the Michaelis-Menten constant and the V_max^met denotes the maximal velocity.

In Vitro Data Scale-Up for Use in Models of Hepatic Clearances. Values for plasma flow [12·(1  hematocrit) ml/min], the input enalapril concentration (C_in), liver weight, and unbound fraction of drug in plasma (f_u) were taken from the literature (Pang et al., 1991). Other parameters were derived from in vitro data. The maximal velocity for uptake, V_max^uptake, determined in vitro from isolated hepatocytes in the presence of sodium (Abu-Zahra et al., 2000) was scaled up by multiplication with the scaling factor or 1.25 × 10⁸ cells/g of liver (Lin et al., 1980), and the ratio V_max^uptake/K_m^uptake provided the sinusoidal influx clearance, PS_in. Analogously, the maximal velocities for metabolism determined from S9 of PP, homogeneous, and PV hepatocytes (Table 1) were scaled up to per gram of tissue by multiplication with the scaling factor, 100 mg of S9 protein/g of liver (Mahler and Cordes, 1966). Because HAHV perfusion revealed perfusion volumes of about one-third those for whole liver (Pang et al., 1991), the volume and weight, and the associated intrinsic clearances for transport and metabolism for the PP region were taken as one-third the whole liver; a similar assumption was made for the midzonal (MZ) and PV regions. The metabolic intrinsic clearances CL_int,i^met for each zonal region (where subscript i = PP, MZ, or PV) were estimated from the ratios of V_max,i^met/K_m,i^met, with the assumption that each zonal region is one-third the liver weight (or 12.8/3 g). The parameters derived from homogeneous hepatocytes were used to represent those in the MZ region of the liver (Table 2).

(8)

(9)

(10)

The Alternative, Zonal-Compartment Model. A model of three zonal compartments in series (repeated sets of eqs. 5 and 6; Tirona and Pang, 1996) was used to describe the segregated, metabolic activities in different zones of the liver (Fig. 2). Within each zone, the metabolic intrinsic clearance, CL_int,i^met, was varied and ascribed various values according to the observations (Table 2), whereas the transport clearances were kept constant (Table 4). Three possible scenarios were presented: in the first instance, the total metabolic and biliary intrinsic clearances were divided evenly into three equal portions for zones 1, 2, and 3 (set 1); in the second case (set 2), the metabolic intrinsic clearances were calculated from the scaled-up mean (V_max,i^met/K_m,i^met) in vitro parameters of each zone (see Table 2); and in the third case, a modified, zonal distribution (set 3) was adopted to encompass variability of the data. For the PP zone, the value V_max,PP^met was given by the value of (mean  S.D.) whereas the K_m,PP^met was given the value (mean + S.D.). For the PV zone, V_max,PV^met and K_m,PV^met were modified to yield the highest V_max,PV^met (mean + S.D.) and lowest K_m,PV^met (mean  S.D.), whereas parameters for the MZ region were not modified. This manipulation provided a much steeper activity gradient of metabolic activities.

Simulations. Simulations for the zonal-compartment model (three scenarios) were performed on Scientist (v.2; Micromath Scientific Software) with the differential equations presented previously (eqs. 5 and 6) and values shown in Table 4.

Statistics. The data were presented as mean ± S.D. The means were compared by use of ANOVA or the paired t-statistic accordingly, with P = .05 denoting the level of significance.

	Results

Top Abstract Introduction Theoretical Models of Hepatic Drug... Experimental Procedures Results Discussion References

Enalapril Metabolism in S9 Fraction of Homogeneous and Zonal Hepatocytes. In the S9 fractions of homogeneous, PP, or PV hepatocytes, metabolism of enalapril was linear within 30 min (data not shown). Other preliminary studies failed to show loss of activity in thawed versus fresh preparations (data not shown). Metabolism was concentration-dependent among all preparations (Fig. 3), and the fit was best with eq. 7, which described simple Michaelis-Menten kinetics with a single saturable component. The fitted V_max,PP^met was 5.5 ± 3.1 nmol/min/mg of S9 protein, and the corresponding K_m,PP^met was 1049 ± 335 µM for PP hepatocytes. These values were not statistically different from those obtained from the S9 of homogeneous hepatocytes: V_max,HO^met of 8.0 ± 2.99 nmol/min/mg of S9 protein and K_m,HO^met of 1308 ± 419 µM (Table 1; P > .05, ANOVA), and the K_m^met values were generally similar to the value of 710 µM reported by Tabata et al. (1990). However, the fitted V_max,PV^met (21.0 ± 6.0 nmol/min/mg of S9 protein) and K_m,PV^met (2612 ± 236 µM) for the S9 of PV hepatocytes were both significantly higher than those observed for the S9 of either homogeneous or PP hepatocytes (Table 1; P < .05, ANOVA).

View larger version (18K): [in this window] [in a new window]   Fig. 3.   Metabolism of enalapril by S9 obtained from PP, whole liver (HO), and PV hepatocytes (mean ± S.D., n = 4).

Comparison of Scaled-Up Transport and Metabolic Intrinsic Clearances. Although no difference was observed for transport among zonal cells (Abu-Zahra et al., 2000), differences were obtained for metabolic intrinsic clearance within zonal hepatocytes CL_int,i^met. The metabolic intrinsic clearance of the PV region was 1.5 times that of the PP region (Table 2). The scaled-up data revealed a high PS_in (4 ml/min/g of liver) in relation to the metabolic intrinsic clearances (0.52-0.8 ml/min/g) among the zonal regions (Table 2). The PS_in was 5 to 7.7 times the metabolic intrinsic clearances. The data suggest that metabolism and not transport is the rate-limiting step in the removal of enalapril.

Predictions of PS_out and E_ss,HAHV with the Well Stirred, Parallel-Tube, and Dispersion Models. Values of PS_out, based on the scaled-up PS_in and intrinsic clearances and the observed E_ss,HAPV value of 0.77 (Pang et al., 1991) were different among the well stirred, dispersion, and parallel-tube models (Table 3). Varying from a total mixing model to a nonmixing model, the estimated PS_out values decreased with increased mixing (1.93 < 9.2 < 15.5 ml/min), giving rise to predicted E_ss,HAHV values of the reverse rank order (0.53 > 0.44 > 0.39) (Table 3). The lower PS_out rendered higher extraction ratios due to entrapment of drug in the cell. The predicted values of E_ss,HAHV were 3.3 to 4.5 times the observed value, as were the ratios E_ss,HAHV:E_ss,HAPV.

Predictions of the Series-Compartment Model of Three Subcompartments. Because three different PS_out values resulted with the well stirred, parallel-tube, and dispersion models, simulations were performed with each of the PS_out values for each of the enzyme distributions (sets 1-3; zonal-compartment models of even-enzyme distribution, zonal-enzyme distribution based on observed data, and modified, zonal-enzyme distribution incorporating variability; Table 4), yielding a total of nine different simulations of enalapril removal with the zonal-compartment model (Table 5). Among the simulations based on similar intrinsic clearances, values for E_ss,HAPV were generally similar, regardless of the enzyme distribution due to the high transport clearance of drug, rendering enzymic distribution unimportant for whole organ removal of the unienzyme substrate (Pang and Stillwell, 1983)._, Again, the lower PS_out rendered higher extraction ratios due to entrapment of drug in the cell. E_ss,HAPV and E_ss,HAHV were greatest with the lowest PS_out of 1.93 ml/min/liver, and both parameters were progressively diminished with increasing PS_out (9.2 and 15.5 ml/min/liver). Although the E_ss,HAPV values were generally similar for all three scenarios of the zonal-compartment model (Table 5), values of E_ss,HAHV began to diverge due to differences in enzyme content with increasing PS_out. The best correspondence existed for the PS_out of 9.2 or 15.5 ml/min/liver with the modified zonal-enzyme system (sets 2 and 3, Table 5).

Drug Removal within Zonal Regions of the Zonal Compartment. Because the zonal-compartment model with the modified zonal-enzyme distribution best described the data, simulation was performed to determine the effects of the metabolic intrinsic clearance CL_int,i^met at the given influx transport clearance (PS_in,i) on the removal within each zone (E_ss,i), whereas all other parameters were held constant. The overall availability of the liver (F_liver) was given by the product of the individual availability of each zone (F_i), as expected of the relation for compartments in series (Table 6).

	Discussion

Top Abstract Introduction Theoretical Models of Hepatic Drug... Experimental Procedures Results Discussion References

The correlation of in vitro data to whole organ/in vivo is a widely investigated topic in drug metabolism. Varying successes have been encountered (Lin et al., 1980; Houston, 1994; Pang and Chiba, 1994; Iwatsubo et al., 1997; Ito et al., 1998). Poor correlations have been blamed on neglect of a transport barrier at the sinusoidal membrane and lack of consideration of metabolic zonation (Pang and Chiba, 1994). It was shown that the membrane barrier poses a major source of discrepancy when transport and not metabolism/excretion is the rate-limiting step (de Lannoy and Pang, 1987; Geng et al., 1995; Tirona and Pang, 1999). In such an instance, the overall removal rate mimics the transport rate. Moreover, zonal transport and zonal metabolism are important for whole organ removal (Meijer and Groothuis, 1991; Kwon and Morris, 1997). The in vitro and in vivo correlation should be stratified when such zonal data exist.

In vitro data now exist for enalapril, whose uptake by rat hepatocytes was homogeneously distributed (Abu-Zahra et al., 2000). The S9 fraction from PV hepatocytes, however, exhibited a significantly higher V_max^met and K_m^met than those for homogeneous or PP hepatocytes (Table 1). If there were a greater expression of a single enzyme, differences in V_max^met would be expected but the K_m^met should remain constant. Hence, it is likely that the V_max^met and K_m^met represent apparent values of pooled activities of multiple enzymes rather than those of an individual enzyme despite the good fit of data to a single saturable component. The condition exists if there is a lack of resolution to discern individual systems of similar K_m^met values. As it is known that the carboxylesterases are in greater abundance in the PV region (Pohl et al., 1991; Yan et al., 1995) and that these enzymes have overlapping substrate specificities and varying affinities, it is highly probable that the greater maximal velocity in S9 of PV is due to greater expression of multiple and not a single carboxylesterase.

Due to differences observed for both V_max^met and K_m^met in the S9 of PP and PV, the intrinsic metabolic clearance under first-order conditions (CL_int^met or V_max^met/K_m^met) was highest for PV hepatocytes, followed by that for the homogeneous, then PP hepatocytes (Table 2). These values were much lower than the PS_in for transport, suggesting that metabolism and not transport is rate-limiting in the overall removal of enalapril in the intact organ. Hence, the higher metabolic intrinsic clearance in the PV region dictates the higher removal in the intact organ, an inference that is consistent with the findings of Pang et al. (1991). Through comparison of the in vitro data, it could be concluded that zonal metabolism and not transport constitutes the observations of Pang et al. (1991).

The test remains, however, whether the in vitro transport and metabolic activities, when scaled up, would adequately reflect activities of the whole organ. Cellular uptake by the rat liver has been found to correlate closely with that in isolated rat hepatocytes (Yamada et al., 1997; Tirona and Pang, 1999), and there is demonstrable success in correlating metabolic data in vitro to in vivo (Lin et al., 1980; Houston, 1994; Ito et al., 1998). The simplistic modelswell stirred, parallel-tube, and dispersion models that do not account for transport or metabolic heterogeneityare, however, inept in predicting the associated E_ss,HAHV values (Table 3). All of the E_ss,HAHV values predicted by these models were much higher than the observed E_ss,HAHV, suggesting that these idealized and simplified models of hepatic drug clearances were unable to predict the hepatic removal of enalapril in the absence of zonation (Table 3). Not unexpectedly, the parallel-tube and well stirred models, representing boundary conditions for the degree of mixing for drug removal in the liver, were found associated with extreme values of the PS_out (1.93 and 15.5 ml/min), with an intermediate value (9.2 ml/min) for the dispersion model.

Because zonation was detected for metabolic activities among zonal rat hepatocytes, the data could be viewed with respect to a zonal-compartment model that describes the liver as three subcompartments or zonal regions consisting of different transport or metabolic activities or both (Tirona and Pang, 1996). Improved correlation was attained between data in vitro and in vivo with the zonal-compartment model. The low PS_out value associated with the well stirred model (1.93 ml/min) was inconsistent with the observed E_ss,HAPV and E_ss,HAHV values in the perfused liver preparation (Pang et al., 1991). Absence of metabolic zonation (even enzyme case) was also incongruent with the observations. By contrast, the PS_out value predicted by both the dispersion and parallel-tube models, together with zonal metabolic heterogeneity (parameter set 2, PV/PP = 1.5 from observations; and parameter set 3, PV/PP activity of 6.6 for the steeper distribution of esterase activity-gradient) better correlated with the observed data (Table 5). The closeness between the in vitro zonation patterns with perfusion data validates the model of HAPV-HAHV perfusion in determining the preponderance of zonal activity of the liver (Pang et al., 1991).

However, the predicted values of E_ss for HAHV remained higher than observed. This is partially attributed to a lesser volume reached by HAHV perfusion (< one-third liver) as inferred by the intracellular water space accessed (Pang et al., 1991). Also, the gradient in metabolic activity, increasing from the PP to the PV zone, is underestimated by the present extrapolation with in vitro data. The same artifact was observed for the gradient of glutathione S-transferase activity for ethacrynic acid within zonally enriched hepatocytes although a steeper activity gradient was obtained with lysates from the farthest cells of the PP and PV zones prepared by dual-pulsing of digitonin (Tirona et al., 1999). Unfortunately, accurate patterns of metabolic zonation could not be determined from the present zonal hepatocyte studies (Kera et al., 1987), and the preparation of lysates is not applicable to the study of enalapril metabolism because membrane-associated proteins, such as the microsomal esterases thought to be involved in enalapril metabolism, are not present in a functional form in lysates (Witters et al., 1993; Fang et al., 1998). It is likely that the shape of the actual gradient is continuous as would be expected for gradient-type distribution of an enzyme (Oinonen and Lindros, 1998), rather than stepwise as modeled presently. Gradient distributions of cytochrome P450 isoforms have been estimated from mRNA distributions in lysates that exist evenly (CYP2C12) across the acinus or increased from PP to PV regions (CYP3A1), to exclusively PV expression (CYP2B1/2) (Oinonen and Lindros, 1998). It is also surmised that the correlation may improve with optimization of a better definition of the enzymic distribution and PS_out. A simulation with a zonal-compartment model of six subcompartments (two equal subcompartments within each zonal region) was also performed (data not shown). However, the results were less compliant with the observations.

Notwithstanding the above comments, it appears that the parameters for metabolism and transport determined in various zones in vitro reflect the total intrinsic metabolic and transport activities in the whole organ, albeit the gradient is less shallow than in reality. The metabolic intrinsic clearance of the liver could be approximated by the sum of the metabolic intrinsic clearances of the zonal regions. Moreover, drug extraction among zonal regions occurs successively, and the product of the zonal bioavailabilities determines the overall bioavailability of the liver (Table 6). By modeling the liver as a series of subcompartments with different zonal transport/metabolic intrinsic clearances, a more complete description of the hepatic removal is attained, as shown in this first exercise on the removal of the enalapril in the perfused liver. Metabolism and not transport was found to be rate-determining for hydrolysis. The zonation observed in perfused liver is attributed to a greater PV metabolism, as verified by the in vitro data. Modeling along similar strategies should improve future efforts in in vitro and in vivo correlation.