An understanding of the role of enzyme localization of the liver on metabolite kinetics: a computer simulation

Systems toxicology from genes to organs

This unique overview of systems toxicology methods and techniques begins with a brief account of systems thinking in biology over the last century. We discuss how systems biology and toxicology continue to leverage advances in computational modeling, informatics, large-scale computing, and biotechnology. Next, we chart the genesis of systems toxicology from previous work in physiologically based models, models of early development, and more recently, molecular systems biology. For readers interested in further details this background provides useful linkages to the relevant literature. It also lays the foundations for new ideas in systems toxicology that could translate laboratory measurements of molecular responses from xenobiotic perturbations to adverse organ level effects in humans. By providing innovative solutions across disciplinary boundaries and highlighting key scientific gaps, we believe this chapter provides useful information about the current state, and valuable insight about future directions in systems toxicity.

An integrated approach to model hepatic drug clearance

It has been well accepted that hepatic drug extraction depends on the blood flow, vascular binding, transmembrane barriers, transporters, enzymes and cosubstrate and their zonal heterogeneity. Models of hepatic drug clearances have been appraised with respect to their utility in predicting drug removal by the liver. Among these models, the "well-stirred" model is the simplest since it assumes venous equilibration, with drug emerging from the outflow being in equilibrium with drug within the liver, and the concentration is the same throughout. The "parallel tube" and dispersion models, and distributed model of Goresky and co-workers have been used to account for the observed sinusoidal concentration gradient from the inlet and outlet. Departure from these models exists to include heterogeneity in flow, enzymes, and transporters. This article utilized the physiologically based pharmacokinetic (PBPK) liver model and its extension that include heterogeneity in enzymes and transporters to illustrate how in vitro uptake and metabolic data from zonal hepatocytes on transport and enzymes may be used to predict the kinetics of removal in the intact liver; binding data were also necessary. In doing so, an integrative platform was provided to examine determinants of hepatic drug clearance. We used enalapril and digoxin as examples, and described a simple liver PBPK model that included transmembrane transport and metabolism occurring behind the membrane, and a zonal model in which the PBPK model was expanded three sets of sub-compartments that are arranged sequentially to represent zones 1, 2, and 3 along the flow path. The latter model readily accommodated the heterogeneous distribution of hepatic enzymes and transporters. Transport and metabolic data, piecewise information that served as initial estimates, allowed for the unknown efflux and other intrinsic clearances to be estimated. The simple or zonal PBPK model provides predictive views on the hepatic removal of drugs and metabolites.

Vascular binding, blood flow, transporter, and enzyme interactions on the processing of digoxin in rat liver

The roles of vascular binding, flow, transporters, and enzymes as determinants of the clearance of digoxin were examined in the rat liver. Digoxin is metabolized by Cyp3a and utilizes the organic anion transporting polypeptide 2 (Oatp2) and P-glycoprotein (Pgp) for influx and excretion, respectively. Uptake of digoxin was found to be similar among rat periportal (PP) and perivenous (PV) hepatocytes isolated by the digitonin-collagenase method. The Km values for uptake were 180 +/- 112 and 390 +/- 406 nM, Vmax values were 13 +/- 8 and 18 +/- 4.9 pmol/min/mg protein, and nonsaturable components were 9.2 +/- 1.3 and 10.7 +/- 2.5 microl/min/mg for PP and PV, respectively. The evenness of distribution of Oatp2 and Pgp was confirmed by Western blotting and confocal immunofluorescent microscopy. When digoxin was recirculated to the rat liver preparation in Krebs-Henseleit bicarbonate (KHB) for 3 h in absence or presence of 1% bovine serum albumin (BSA) and 20% red blood cell (rbc) at flow rates of 40 and 10 ml/min, respectively, biexponential decays were observed. Fitted results based on compartmental analyses revealed a higher clearance (0.244 +/- 0.082 ml/min/g) for KHB-perfused livers over the rbc-albumin-perfused livers (0.114 +/- 0.057 ml/min/g) (P < 0.05). We further found that binding of digoxin to 1% BSA was modest (unbound fraction = 0.64), whereas binding to rbc was associated with slow on (0.468 +/- 0.021 min(-1)) and off (1.81 +/- 0.12 min(-1)) rate constants. We then used a zonal, physiologically based pharmacokinetic model to show that the difference in digoxin clearance was attributed to binding to BSA and rbc and not to the difference in flow rate and that clearance was unaffected by transporter or enzyme heterogeneity.

Membrane transport in hepatic clearance of drugs. II: Zonal distribution patterns of concentration-dependent transport and elimination processes

PURPOSE

The objective of the present simulation study was to investigate the effects of hepatic zonal heterogeneity of membrane transporter proteins and intrinsic elimination activities on hepatic clearance (CL) and drug concentration gradient profiles in the sinusoidal blood and hepatocytes.

METHODS

The model used in the simulations assumes an apparent unidirectional carrier-mediated transport and a bidirectional diffusion of substrates in the hepatic sinusoidal membrane as well as a nonlinear intrinsic elimination. Three different distribution patterns of the transporter and the metabolizing enzyme along the sinusoidal flow path were used for the simulations. The effects of changes in the Michaelis-Menten parameters for those nonlinear processes, and in the unbound fractions of the drug in blood and tissue components were investigated.

RESULTS

Significant differences in CL occurred when the distribution patterns of the transporter and/or the metabolizing enzyme activities were altered under nonlinear conditions. The highest CL values were observed when the transporter and the metabolizing enzyme had similar distribution patterns within the liver acinus, while opposite distribution patterns produced the lowest CL values. Tissue concentration profiles were significantly affected by the distribution patterns of the transporter, but the changes in blood concentration profiles were relatively small. Altering protein binding in blood produced significant changes in CL, and blood and tissue concentration gradients, while altering protein binding in tissue affected only drug accumulation patterns within hepatocytes, regardless of the distribution patterns of the transporter or the metabolizing enzyme.

CONCLUSIONS

The present simulations demonstrate that hepatic zonal heterogeneities in the transporter and the metabolizing enzyme activities can significantly influence hepatic clearance and/or drug concentration gradient profiles in the sinusoidal blood and hepatocytes.

Physiologic models of hepatic drug clearance: influence of altered protein binding on the elimination of diclofenac in the isolated perfused rat liver

The single-pass perfused rat liver preparation was used to assess the influence of binding to human serum albumin on the steady-state hepatic extraction of diclofenac (n = 8). In the absence of binding protein, the extraction ratio of diclofenac approached unity (range, 0.975-0.992), such that its clearance was perfusion-rate limited. As the binding of diclofenac to protein was increased by the addition of human serum albumin to the perfusion medium, its extraction ratio decreased dramatically, and clearance eventually became capacity limited. The relationship between diclofenac availability and fraction unbound was analyzed with various physiologic models of hepatic drug clearance. The dispersion model, which contains a parameter (the dispersion number) that quantifies the axial spreading of a substrate as it passes along the liver length, provided a significantly better description of the data (p < 0.05) than the undistributed parallel-tube model, which assumes that an eliminated substrate travels through the liver as an undispersed plug, and the well stirred (venous equilibrium) model, which assumes that substrate undergoes infinite mixing as soon as it enters the liver. The dispersion number estimated for diclofenac (mean, 3.03; range, 0.89-7.56) was significantly greater than that predicted from considerations of the transverse heterogeneity of blood flow within the hepatic sinusoidal bed, suggesting that additional factors influenced the relationship between availability and fraction unbound for this compound. Such factors may include transverse heterogeneity of the metabolizing enzyme system(s), axial flux of substrate created by diffusion within hepatic tissue, and protein-facilitated transfer of substrate across an unstirred fluid layer adjacent to the hepatocyte surface.

A comparative investigation of hepatic clearance models: predictions of metabolite formation and elimination

Liver clearance models serve to improve our understanding of the relationships between the physiological determinants and hepatic clearance and predict changes in the disposition of substrates when homeostasis of the organ is perturbed. Their ability to describe metabolism was presently extended to the sequential formation and elimination of primary (M1), secondary (M2), and tertiary (M3) metabolites during a single passage of drug (P) across the liver, under steady state and first-order conditions. The well-stirred model is distinct from other models in that metabolite formation and elimination is independent of enzymic distributions, the number of steps involved in metabolite formation, and the intrinsic clearances of the precursors. This model predicts that the extraction ratio of a formed primary metabolite derived from drug (E[M1, P]) is identical to that for the preformed primary metabolite (E[M1]), and that the extraction ratios of a secondary metabolite derived from drug (E[M2, P]) and primary metabolite (E[M2, M1]) or preformed secondary metabolite (E[M2]) are identical. For the more physiologically acceptable, parallel-tube and dispersion models, metabolite sequential elimination is highly influenced by the intrinsic clearances of the precursors and the enzymic distributions that mediate removal of precursor species and the metabolites. Furthermore, the extent of sequential metabolism recedes as the number of steps involved for metabolite formation increases. These models predict that E[M1, P] less than E[M1], and E[M2, P] less than E[M2, M1] less than E[M2], with the magnitude of the changes being less for the dispersion model than for the parallel-tube model. Competing pathways that divert substrate from entering the sequential pathway were found to exert only minimal influence on the sequential pathway.

Availability predictions by hepatic elimination models for Michaelis-Menten kinetics

Numerical methods have been used to compare the availability predictions of a number of hepatic elimination models when Michaelis-Menten kinetics is operative. Propranolol and galactose were used as model compounds. Lower availabilities were predicted by the dispersion model than by a segregated distribution model for both compounds. The differences in the predictions were most pronounced for models corresponding to a large variation in solute residence times in the liver. The predictions of the tank-in-series, dispersion model with mixed boundary conditions and dispersion model with Dankwerts boundary conditions were similar over all concentrations studied. Changes in blood flow and protein binding provided little discrimination between the model predictions. It is concluded that micromixing of blood between sinusoids and the anatomical sites of mixing are important determinants of availability when liver eliminating enzymes are partially saturated.

Hepatic modeling of metabolite kinetics in sequential and parallel pathways: salicylamide and gentisamide metabolism in perfused rat liver

Previous data on salicylamide (SAM) metabolism in the perfused rat liver had indicated that SAM was metabolized by three parallel (competing) pathways: sulfation, glucuronidation, and hydroxylation, whereas sequential metabolism of the hydroxylated metabolite, gentisamide (GAM), was solely via 5-glucuronidation to form GAM-5G. However, under comparable conditions, preformed GAM formed mainly two monosulfate conjugates at the 2- and 5-positions (GAM-2S and GAM-5S); 5-glucuronidation was a minor pathway. In the present study, the techniques of normal (N) and retrograde (R) rat liver perfusion with SAM and mathematic modeling on SAM and GAM metabolism were used to explore the role of enzymic distributions in determining the dissimilar fates of GAM, as a generated metabolite of SAM or as preformed GAM. Changes in the steady-state extraction ratio of SAM (E) and metabolite formation ratios between N and R perfusions were used as indices of the uneven distribution of enzyme activities. Two SAM concentrations (134 and 295 microM) were used for single-pass perfusion: the lower SAM concentration exceeded the apparent Km for SAM sulfation but was less than those for SAM glucuronidation and hydroxylation; the higher concentration exceeded the apparent Km's for SAM sulfation and glucuronidation but was less than the Km for hydroxylations. Simulation of SAM metabolism data was carried out with various enzyme distribution patterns and extended to include GAM metabolism. At both input concentrations, E was high (0.94 at 134 microM and 0.7 at 295 microM) and unchanged during N and R, with SAM-sulfate (SAM-S) as the major metabolite and GAM-5G as the only detectable metabolite of GAM. Saturation of SAM sulfation occurred at the higher input SAM concentration as shown by a decrease in E and a proportionally less increase in sulfation rates and proportionally more than expected increases in SAM hydroxylation and glucuronidation rates. At both SAM concentrations, the steady-state ratio of metabolite formation rates for SAM-S/SAM-G decreased when flow direction changed from N to R. An insignificant decrease in SAM-S/SAM-OH was observed at the low input SAM concentration, due to the small amount of SAM-OH formed and hence large variation in the ratio among the preparations, whereas at the high input SAM concentration, the decrease in SAM-S/SAM-OH with a change in flow direction from N to R was evident. The metabolite formation ratio, SAM-G/SAM-OH, however, was unchanged at both input concentrations and flow directions.(ABSTRACT TRUNCATED AT 400 WORDS)

The multiple-indicator dilution technique for characterization of normal and retrograde flow in once-through rat liver perfusions

The technique of normal and retrograde rat liver perfusion has been widely used to probe zonal differences in drug-metabolizing activities. The validity of this approach mandates the same tissue spaces being accessed by substrates during both normal and retrograde perfusions. Using the multiple-indicator dilution technique, we presently examine the extent to which retrograde perfusion alters the spaces accessible to noneliminated references. A bolus dose of 51Cr-labeled red blood cells, 125I-albumin, 14C-sucrose and 3H2O was injected into the portal (normal) or hepatic (retrograde) vein of rat livers perfused at 10 ml per min per liver. The outflow perfusate was serially collected over 220 sec to characterize the transit times and the distribution spaces of the labels. During retrograde perfusion, red blood cells, albumin and sucrose profiles peaked later and lower than during normal perfusion, whereas the water curves were similar. The transit times of red blood cells, albumin and sucrose were longer (p less than 0.005), whereas those for water did not change. Consequently, retrograde flow resulted in significantly larger sinusoidal blood volumes (45%), albumin Disse space (42%) and sucrose Disse space (25%) than during normal flow, whereas the distribution spaces for total and intracellular water remained unaltered. The distension of the vascular tree was confirmed by electron microscopy, by which occasional isolated foci of widened intercellular recesses and spaces of Disse were observed. Cellular ultrastructure was otherwise unchanged, and there was no difference found between normal and retrograde perfusion for bile flow rates, AST release, perfusion pressure, oxygen consumption and metabolic removal of ethanol, a substrate with flow-limited distribution, which equilibrates rapidly with cell water (hepatic extraction ratios were virtually identical: normal vs. retrograde, 0.50 vs. 0.48 at 6 to 7.4 mM input concentration). These findings suggest that the functional and metabolic capacities of the liver remain unperturbed during retrograde perfusion, rendering the technique suitable for the investigation of zonal differences in drug-metabolizing enzymes.

Competing pathways in drug metabolism. II. An identical, anterior enzymic distribution for 2- and 5-sulfoconjugation and a posterior localization for 5-glucuronidation of gentisamide in the rat liver

Gentisamide (2,5-dihydroxybenzamide, GAM), a substrate that forms two monosulfates at the 2 and 5 positions (GAM-2S and GAM-5S) and a monoglucuronide at the 5 position (GAM-5G), was delivered at 8 or 80 microM by normal (N) and retrograde (R) flows to the once-through rat liver preparation. At the lower (8 microM) input concentration, ratios of conjugate formation rate, GAM-5S/GAM-5G and GAM-2S/GAM-5G, were decreased significantly (4.01 +/- 1.42 to 2.93 +/- 0.99, and 1.13 +/- 0.65 to 0.66 +/- 0.41, respectively) whereas a small but significant increase in the steady-state extraction ratio, E (0.89 +/- 0.029 to 0.94 +/- 0.016), was observed upon changing the flow direction from N to R. At the higher input GAM concentration (80 microM), conjugate formation rate ratios were relatively constant for GAM-5S/GAM-5G (1.18 +/- 0.08 to 1.11 +/- 0.12) and GAM-2S/GAM-5G (0.33 +/- 0.05 to 0.31 +/- 0.05) upon changing flow direction from N to R, despite a slight increase in E from 0.87 +/- 0.023 to 0.91 +/- 0.016 was observed. These results suggest that the sulfotransferase activities responsible for 2- and 5-sulfoconjugations are identically distributed and localized anterior to 5-glucuronidation activities during a normal flow of substrate into the rat liver (entering the portal vein and exiting the hepatic vein), and that the presence of uneven distribution of conjugation activities is discriminated only at the lower input drug concentration. At high concentration (greater than Km for all systems), saturation of all pathways occurs, and other anteriorly/identically distributed competing pathways would fail to perturb downstream intrahepatic drug concentrations and the resultant conjugation rates. The lack of change in metabolic profiles renders the condition unsuitable for examination of uneven distribution of enzymes in the liver. These observations were generally predicted by theoretical enzymic models of consistent distribution patterns. Because 2- and 5-sulfation were mediated by systems of similar Km but different Vmax values, two possibilities, the same isozyme of sulfotransferase being involved in the formation of two enzyme-substrate complexes to form two distinctly different products or two isozymes of sulfotransferases of identical distribution, were discussed.

Membrane-limited hepatic transport of the conjugative metabolites of 4-methylumbelliferone in rats

The hepatic transports of 4-methylumbelliferone (4-MU) and its conjugative metabolites, the glucuronide (4-MUG) and sulfate (4-MUS), were investigated in rats with various methods. The extraction ratio (E) was estimated with the multiple indicator dilution (MID) method using isolated perfused rat liver. The values of E for 4-MUG and 4-MUS were much lower (less than 0.2) than that for the parent compound, 4-MU (0.89). In addition, we examined the simulation of the outflow curves of conjugates based on the "distributed" model in which we varied the permeability between the blood and hepatocytes. When the permeability was much smaller relative to the hepatic blood flow, the simulated curve was superimposed on the dilution curve. These results suggest that the influx permeabilities of these conjugates are so low that little extraction occurs during the passage through the liver. Measuring the unidirectional uptake of these conjugates into the liver with the in vitro centrifugal filtration method using isolated hepatocytes, we determined the influx permeabilities (PSinf(total] for the total ligands. The value of PSinf(total) determined with the in vitro method was extrapolated to that per gram of liver, assuming 1 g of liver has 1.3 X 10(8) cells. The values of PSinf(total) for 4-MU, 4-MUG, and 4-MUS were 4.8, 0.06, and 0.11 mL/min/g liver, respectively. Thus, the influx permeabilities for 4-MUG and 4-MUS were much smaller than the hepatic blood flow (1.6 mL/min/g liver), confirming the results of MID method.

Models of hepatic elimination: comparison of stochastic models to describe residence time distributions and to predict the influence of drug distribution, enzyme heterogeneity, and systemic recycling on hepatic elimination

The residence time distribution of noneliminated solutes in the liver can be represented by a variety of stochastic models. The dispersion model (closed and mixed boundary conditions), gamma distribution, log normal distribution and normal distribution models were used to describe output concentration-time profiles after bolus injections into the liver of labeled erythrocytes and albumin. The dispersion model and log normal distribution model provide the best representation of the data and give similar estimates of relative dispersion and availability for varying hepatocellular enzyme activity. The availability of solutes eliminated from the liver by first-order kinetics is determined by the residence time distribution of the solute in the liver and not on events occurring in the liver when a uniform enzyme distribution is assumed. Both enzyme heterogeneity (axial or transverse) and hepatocyte permeability may affect solute availability. A more complex model accounting for enzyme distribution and the micromixing of solute within the liver is required for solutes undergoing saturable kinetics.

Competition between two enzymes for substrate removal in liver: modulating effects due to substrate recruitment of hepatocyte activity

Modulating effects of competing pathways, exemplified by sulfation (high affinity-low capacity) and glucuronidation (low affinity-high capacity), on drug disappearance and metabolite formation were investigated in a simulation study. The phenomenon of substrate recruitment of hepatocyte activity in drug removal and metabolite formation was shown with respect to inlet substrate concentration, and drug processing from inlet to outlet by enzyme systems localized differentially along the sinusoidal flow path in liver. Three enzymic distribution models: (A) sulfation and glucuronidation evenly distributed in liver, (b) sulfation occurring exclusively in the first half of the liver and glucuronidation in the second half, and (C) glucuronidation solely in the first half and sulfation in the second half, were described. The influence of Km and Vmax of the competing pathway, including enzyme induction (increase in Vmax), on any given pathway was also explored. Competing pathways exert their effects on other given pathways by modulating intrahepatic drug concentration from the inlet to outlet of the liver. When a competing pathway is similarly distributed or is at an anterior location to another pathway, the former pathway effectively reduces intrahepatic drug concentrations which reach downstream hepatocytes for recruitment of activity. For example, when glucuronidation activity is anterior to sulfation activity (defined with respect to flow direction), sulfation is without an effect on glucuronidation, but glucuronidation exerts a maximal influence over sulfation rates (Model C). When glucuronidation is in direct competition with sulfation (Model A) or is posteriorly distributed to sulfation (Model B), saturation of the high-affinity sulfation pathway leads to greater fluxes of substrate available downstream for glucuronidation. This results in an apparent compensatory increase in glucuronidation with reduced sulfation capacity, which occurs at input concentrations greater than the Km for sulfation but less than the Km for glucuronidation. This compensation pattern is more prominent for highly extracted compounds where both sulfation and glucuronidation are effective pathways in drug removal, and where large intrahepatic drug concentration gradients are expected. Since the physiologic description of intrahepatic drug concentration is often described by a concentration gradient from the inlet to outlet of the liver, the logarithmic average concentration has been used to estimate the mean liver concentration in the determination of kinetic constants for enzymic reactions.(ABSTRACT TRUNCATED AT 400 WORDS)

Effect of a diffusional barrier to a metabolite across hepatocytes on its kinetics in "enzyme-distributed" models: a computer-aided simulation study

The effect of a diffusional barrier to a metabolite between the blood and hepatocytes on elimination kinetics of formed and preformed metabolites was predicted under various enzymic distributions in the liver by computer-aided simulation. Sequential metabolism by which the primary metabolite (MI) is generated from the parent drug (D) and further metabolized to the terminal metabolite (MII) by enzymes A and B, respectively, was chosen for the simulation. Moreover, four models of enzyme distribution patterns were defined with regard to the hepatic blood flow path. The extraction ratios for the preformed and formed metabolites (designated as Em and Ep----m, respectively) were simulated by varying both the average intrinsic clearance of enzyme B (CLint,B) and the permeability of hepatocytes for MI (Pm), while keeping the average intrinsic clearance of enzyme A (CLint,A) equal to hepatic blood flow (Q). When a rapid equilibrium of MI between the blood and hepatocytes held, i.e., Pm was large relative to Q, Em was equal to or higher than Ep----m for all models, as previously shown by Pang and Stillwell. By contrast, it was found that when a diffusional barrier for MI existed, i.e., Pm was small relative to Q, Em was equal to or lower than Ep----m. Furthermore, it was observed that the smaller Pm became, the larger the difference between Em and Ep----m became. We further simulated the effect of the intrinsic clearance (CLint,C) for a metabolic pathway, which competes for that by enzyme A, on the Ep----m value. In the model assuming even distribution of all the enzymes along the flow path, irrespective of the CLint,C value, a similar effect of Pm on Ep----m was observed when the Pm value was relatively small (Pm less than Q). By contrast, in the case of uneven enzymic distributions of enzymes A and B, the effect of the CLint,C value on the relationship between Pm and Ep----m occurred to some extent. From these simulations, it was concluded that lower membrane permeability (Pm) both diminishes the entry of preformed metabolite into the hepatocytes and accelerates the removal of intracellularly formed metabolite (through sequential metabolism) by diminishing its efflux, yielding lower Em than Ep----m. When Pm becomes small (Pm less than 1/10Q), these mechanisms for lower Em than Ep----m predominate over other mechanisms such as the presence of a competing metabolic route and uneven distribution of enzymes.

An enzyme-distributed system for lidocaine metabolism in the perfused rat liver preparation

The influence of enzymic distribution on lidocaine metabolism was investigated in the once-through perfused rat liver preparation. Low input concentrations of 14C-lidocaine (1-2 microM) and preformed monoethylglycine xylidide (MEGX; 2.3-2.8 microM) were delivered by normal and retrograde flow directions to the liver preparations at 10 ml/min per liver. Upon reversal of normal to retrograde delivery of lidocaine, the rates at which lidocaine, MEGX, and glycine xylidide (GX) left the liver almost doubled, whereas the rates of appearance of (total) hydroxylated lidocaine and MEGX in bile and perfusate increased to lesser extents. Upon reversal of normal to retrograde delivery of preformed MEGX, the rates of appearance of MEGX and GX were virtually unchanged. Computer simulations on lidocaine and preformed MEGX metabolism were performed on both evenly distributed ("parallel tube" model) and enzyme-distributed systems. An even or parallel distribution of N-deethylation and hydroxylation activities for lidocaine metabolism failed to predict the observed increased hepatic availability of lidocaine. Rather, the distribution of a low-affinity, high-capacity N-deethylation system anterior to a high-affinity, low-capacity hydroxylation system for lidocaine metabolism adequately predicted the increased hepatic availability of lidocaine. Further extension of these consistent enzyme-distributed models on the metabolism of lidocaine metabolites suggests that the N-deethylation and hydroxylation activities for the metabolism of lidocaine, MEGX, 3-hydroxyidocaine, and 3-hydroxy MEGX are not identically distributed. When these enzyme-distributed models were appraised with reference to the "parallel tube" and "well-stirred" models of hepatic drug clearance, predictions from these enzyme-distributed models proved to be superior to the "parallel tube" and "well-stirred" models for the present data on lidocaine metabolites with normal and retrograde perfusions. Previously published data on lidocaine and MEGX metabolism after inputting 4 micrograms/ml (17 microM) lidocaine at flow rates of 10, 12, 14, and 16 ml/min were reexamined with respect to the adequacy of these enzyme-distributed models. They were found to be superior to the evenly-distributed or "parallel tube" model in predicting hepatic availability of lidocaine and the rate of appearance of MEGX. However, the enzyme-distributed systems were not as consistent as the "well-stirred" model in predicting lidocaine hepatic availability in these flow experiments.

A simulation study on the effect of a uniform diffusional barrier across hepatocytes on drug metabolism by evenly or unevenly distributed uni-enzyme in the liver

The effect of a uniform diffusional barrier on hepatic extraction of the parent drug by evenly or unevenly distributed uni-enzyme was quantitatively determined by the present simulation study. Five models of enzymic distribution were defined with regard to the hepatic blood flow path, and the extraction ratios were calculated or simulated under the various conditions of average intrinsic clearances and diffusion clearances across hepatocytes. Differences in the extraction ratios among the five models were evaluated by the "relative extraction ratios," which are the extraction ratios in each model divided by that in the model where the enzymatic activity is evenly distributed. It was found that when a diffusion clearance was high compared to the intrinsic clearance, enzymic distribution was not an important determinant of the extent of hepatic extraction. By contrast, when a diffusional barrier across hepatocytes exists, i.e., the diffusion clearance is low or intermediate compared to the intrinsic clearance, extraction ratios differed widely among the models of enzymic distribution, especially at intermediate average intrinsic clearances. In the presence of a diffusional barrier, the more skewed the distribution of the enzymatic activity is, the lesser the amount of drug eliminated at steady state. The most efficient metabolism occurred when the enzymatic activity was evenly distributed.

A review of metabolite kinetics

The importance of metabolites as active and toxic entities in drug therapy evokes the need for an examination of metabolite kinetics after drug administration. In the present review, emphasis is placed on single-compartmental characteristics for a drug and its primary metabolites under linear kinetic conditions. The determination of the first-order elimination rate constants for drug and metabolite are also detailed. For any ith primary metabolite mi formed solely in liver, kinetic parameters with respect to primary metabolite formation under first-order conditions require a comparison of the areas under the metabolite concentration-time curve after drug and preformed metabolite administrations. These area ratios hold regardless of the number of noneliminating compartments for the drug and metabolite. These parameters include fmi and gmi, the fractions of total body clearance that respectively furnishes mi to the general circulation and forms mi, and hmi, the fraction of hepatic clearance responsible for the formation of mi. Moreover, the fraction of dose dmi converted to form mi is defined with respect to the route of drug administration. The inherent assumption of these estimates, however, requires that the extent of sequential elimination of the generated mi be identical to the extent of metabolism of preformed mi. Discrepancies have been found, and may be attributed mostly to the uneven distribution of drug-metabolizing activities as well as to the presence of diffusional barriers. Other linear systems that involve mi formation from multiple organs are briefly described.