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

After 50 Years of Hepatic Clearance Models, Where Should We Go from Here? Improvements and Implications for Physiologically Based Pharmacokinetic Modeling

There is overwhelming preference for application of the unphysiologic, well-stirred model (WSM) over the parallel tube model (PTM) and dispersion model (DM) to predict hepatic drug clearance, CLH , despite that liver blood flow is dispersive and closer to the DM in nature. The reasoning is the ease in computation relating the hepatic intrinsic clearance ( CLint ), hepatic blood flow ( QH ), unbound fraction in blood ( fub ) and the transmembrane clearances ( CLin and CLef ) to CLH for the WSM. However, the WSM, being the least efficient liver model, predicts a lower EH that is associated with the in vitro CLint ( Vmax / Km ), therefore requiring scale-up to predict CLH in vivo. By contrast, the miniPTM, a three-subcompartment tank-in-series model of uniform enzymes, closely mimics the DM and yielded similar patterns for CLint versus EH , substrate concentration [S] , and KL / B , the tissue to outflow blood concentration ratio. We placed these liver models nested within physiologically based pharmacokinetic models to describe the kinetics of the flow-limited, phenolic substrate, harmol, using the WSM (single compartment) and the miniPTM and zonal liver models (ZLMs) of evenly and unevenly distributed glucuronidation and sulfation activities, respectively, to predict CLH For the same, given CLint ( Vmax and Km ), the WSM again furnished the lowest extraction ratio ( EH,WSM = 0.5) compared with the miniPTM and ZLM (>0.68). Values of EH,WSM were elevated to those for EH, PTM and EH, ZLM when the Vmax s for sulfation and glucuronidation were raised 5.7- to 1.15-fold. The miniPTM is easily manageable mathematically and should be the new normal for liver/physiologic modeling. SIGNIFICANCE STATEMENT: Selection of the proper liver clearance model impacts strongly on CLH predictions. The authors recommend use of the tank-in-series miniPTM (3 compartments mini-parallel tube model), which displays similar properties as the dispersion model (DM) in relating CLint and [ S ] to CLH as a stand-in for the DM, which best describes the liver microcirculation. The miniPTM is readily modified to accommodate enzyme and transporter zonation.

Hepatic clearance concepts and misconceptions: Why the well-stirred model is still used even though it is not physiologic reality?

The liver is the most important drug metabolizing organ, endowed with a plethora of metabolizing enzymes and transporters to facilitate drug entry and removal via metabolism and/or biliary excretion. For this reason, much focus surrounds the development of clearance concepts, which are based on normalizing the rate of removal to the input or arterial concentration. By so doing, some authors have recently claimed that it implies one specific model of hepatic elimination, namely, the widely used well-stirred or venous equilibration model (WSM). This commentary challenges this claim and aims to provide a comprehensive discussion of not only the WSM but other currently applied hepatic clearance models - the parallel tube model (PTM), the dispersion model (DM), the zonal liver model (ZLM), and the heterogeneous capillary transit time model of Goresky and co-workers (GM). The WSM, PTM, and DM differ in the patterns of internal blood flow, assuming bulk, plug, and dispersive flows, respectively, which render different degrees of mixing within the liver that are characterized by the magnitudes of the dispersion number (D_N), resulting in different implications concerning the (unbound) substrate concentration in liver (Cu_H). Early models assumed perfusion rate-limited distribution, which have since been modified to include membrane-limited transport. The recent developments associated with the misconceptions and the sensitivity of the models are hereby addressed. Since the WSM has been and will likely remain widely used, the pros and cons of this model relative to physiological reality are further discussed.

Physiologically-based pharmacokinetic modeling for absorption, transport, metabolism and excretion

The seminal paper on the liver physiologically-based pharmacokinetic (PBPK) model by Rowland et al. (J Pharmacokinet Biopharm 1:123-136, 1973) that described the influence of blood flow, intrinsic clearance, and binding on hepatic clearance had inspired further development of PBPK modeling of the liver, kidney and intestine as well as whole body. Shortly thereafter, a series of papers from Pang and Rowland compared the well-stirred and parallel-tube liver models and sparked further development on clearance concepts in the liver, including those described by the dispersion model. From 2005 onwards, several seminal papers by Rodgers and Rowland, in their recognition of the binding of molecules to tissue acidic and neutral phospholipids, improved the methodology in providing estimates of the tissue-to-plasma coefficient and rendering easy calculation of these hard-to-get constants. The improvement has strongly consolidated the basic premise on PBPK modeling and simulations and these basics have allowed scientists to focus on other important variables: membrane barriers, and transporter and enzyme and their heterogeneities that further impact drug disposition. In particular, the PBPK models have delved into sequential metabolism and futile cycling to illustrate how transporters and enzymes could affect the metabolism of drugs and metabolites. PBPK models that are especially pertinent to metabolite kinetics are being utilized in drug studies and risk assessment. These types of PBPK modeling reveal differences in kinetics between the formed vs. preformed metabolite, showing special considerations for membrane barriers, and the influence of competing pathways and competing organs.

Formed and preformed metabolites: facts and comparisons

The administration of metabolites arising from new drug entities is often employed in drug discovery to investigate their associated toxicity. It is expected that administration of metabolites can predict the exposure of metabolites originating from the administration of precursor drug. Whether exact and meaningful information can be obtained from this has been a topic of debate. This communication summarizes observations and theoretical relationships based on physiological modelling for the liver, kidney and intestine, three major eliminating organs/tissues. Theoretical solutions based on physiological modelling of organs were solved, and the results suggest that deviations are expected. Here, examples of metabolite kinetics observed mostly in perfused organs that did not match predictions are provided. For the liver, discrepancies in fate between formed and preformed metabolites may be explained by the heterogeneity of enzymes, the presence of membrane barriers and whether transporters are involved. For the kidney, differences have been attributed to glomerular filtration of the preformed but not the formed metabolite. For the intestine, the complexity of segregated flows to the enterocyte and serosal layers and differences in metabolism due to the route of administration are addressed. Administration of the metabolite may or may not directly reflect the toxicity associated with drug use. However, kinetic data on the preformed metabolite will be extremely useful to develop a sound model for modelling and simulations; in-vitro evidence on metabolite handling at the target organ is also paramount. Subsequent modelling and simulation of metabolite data arising from a combined model based on both drug and preformed metabolite data are needed to improve predictions on the behaviours of formed metabolites.

Safety testing of metabolites: Expectations and outcomes

Metabolites arising from chemical entities, old or new, are often mediators of toxicity. Frequently, metabolites are investigated in test animals, with the expectation that the resultant toxicity or activity will mimic the exposure of their formed counterparts. This communication described observations that showed discrepant kinetics between formed and preformed metabolites in the liver, intestine, and kidney, major drug removal organs. Differences in the observed areas under the curve (AUCs) or the extraction ratios (Es) of formed and preformed metabolites in the liver had been attributed to zonal, enzyme heterogeneity, membrane barriers, or transporters. Preformed and formed metabolite also differed in their handling by the kidney; only the preformed and not the formed metabolite would be filtered. In the intestine, differences in the absorption of the precursor and the metabolite and the flow pattern in the intestine would bring about discrepancy in the time-courses of the formed vs. preformed metabolites. Analytical solutions of the AUCs of the metabolites and extraction ratios, based on physiological modeling of the liver, kidney, and intestine, showed that the AUC of the preformed, administered metabolite was dependent only on metabolite parameters, whereas the AUC of the formed metabolite was modulated additionally by the metabolic, secretory and intestinal absorptive intrinsic clearances of the precursor drug. Hence, administration of the synthetic metabolite would not reflect the toxicity associated with the metabolite formed via bioactivation. However, data on preformed metabolite may be used for simultaneous fitting by a combined model of drug and metabolite. Such a strategy is shown to be successful in risk assessment of environmental chemicals. Upon refinement of the resultant model with data on metabolite transport and handling by modeling and simulations, the resultant model would be more robust to provide improved predictions on metabolite toxicity pursuant to drug administration.

Carrier-mediated entry of 4-methylumbelliferyl sulfate: characterization by the multiple-indicator dilution technique in perfused rat liver

The hepatocellular entry of 4-methylumbelliferyl sulfate (4MUS) a highly ionized and highly bound anion capable of futile cycling, was examined in the single-pass albumin-free perfused rat liver preparation. Desulfation of 4MUS to 4-methylumbelliferone (4MU) was verified in vitro to be a low-affinity, high-capacity process (Km = 731 micromol/L; Vmax = 414 nmol min(-1) g(-1) liver). With 4MUS given to the perfused rat liver, sulfation of 4MU, the formed metabolite, was attenuated in the presence of 2,6-dichloro-4-nitrophenol (DCNP), a sulfation inhibitor, and when sulfate ion was substituted by chloride ion. 4MU sulfation, being a high-affinity system, was reduced most effectively at the lowest 4MUS concentration (15 micromol/L) used, evidenced by the increased (24%) net hepatic extraction ratio of 4MUS and reduced utilization (72%) of infused tracer 35SO4(2-) by 4MU for 4MU35S formation. Single-pass multiple indicator dilution (MID) studies were thus conducted under identical conditions (DCNP and absence of inorganic sulfate), with injection of [3H]4MUS and a set of noneliminated vascular and cellular reference indicators into the portal vein (prograde) or hepatic vein (retrograde), against varying background bulk concentrations of 4MUS (5 to 900 micromol/L). The steady-state removal rate of 4MUS and formation rates of 4MU and its glucuronide conjugate (4MUG) were not altered with perfusion flow direction, suggesting the presence of even or parallel distributions of 4MUS desulfation and 4MU glucuronidation activities. When the outflow dilution profile of [3H]4MUS was evaluated with the barrier-limited model of Goresky, a slight red cell carriage effect was found for 4MUS. The permeability surface area product for cellular entry for prograde showed a dramatic concentration-dependent decrease (from 0.13 to 0.01 mL sec(-1) g(-1), or 7.4 to 0.56 times the blood perfusate flow rate) and was resolved as saturable and nonsaturable components, while data for retrograde were more scattered, varying from 2.8 to 1 times the blood perfusate flow rate. Efflux (coefficient = 0.0096 +/- 0.0024 and 0.0088 +/- 0.0062 mL sec(-1) g(-1), respectively) was relatively insensitive to concentration and flow direction. The same was observed for the removal capacity for metabolism and excretion (sequestration coefficient: for prograde, 0.0056 +/- 0.0017 mL sec(-1) g(-1); for retrograde, 0.0056 +/- 0.003 mL sec(-1) g(-1)). The decrease in the apparent partition coefficient (ratio of 4MUS concentration estimated in tissue to unbound plasma concentration) and the increase in relative throughput component with concentration further substantiate the claim on the presence of concentrative processes at the sinusoidal membrane.

Availability and mean transit times of phenol and its metabolites in the isolated perfused rat liver: normal and retrograde studies using tracer concentrations of phenol

Phenolic compounds are frequently detoxified by the formation of sulphate and glucuronic acid conjugates in the liver. These conjugates are formed in the hepatocytes and then either transported into the bile or back into the blood. In this study, we examined the transport kinetics of phenol and its metabolites in the isolated perfused rat liver by monitoring the outflow profiles of these compounds after a bolus input in a single pass preparation. Phenol was almost exclusively metabolized to phenyl sulphate (97%) at the trace concentrations used, with the amount of phenol and metabolites excreted into the bile being minimal (3.5%). The metabolite formed was rapidly transported back into the perfusate, with mean transit times of 17.4 and 12.3 s anterograde and 24.9 and 24.2 s retrograde at flow rates of 15 and 30 mL min-1 respectively, which were intermediate between those of Evans blue and water. The outflow concentration-time profile for phenyl sulphate formation was unaffected by the addition of another organic anion (bromosulphophthalein). The effect of enzyme zonation on outflow concentration-time profiles was also investigated using retrograde perfusions. The transit time ratios for generated metabolite to water for anterograde perfusions (0.6) was found to be more than twice that for retrograde perfusions (0.23) at 15 mL min-1 and approximately 1.6 times greater at 30 mL min-1, being 0.58 and 0.37 respectively. The relative ratios obtained are consistent with previous findings that normalized variance of solutes in the retrograde perfusions is greater than that for anterograde perfusions.

Transport, binding, and metabolism of sulfate conjugates in the liver

Sulfate conjugates are a heterogeneous class of polar, anionic metabolites that result from the conjugation of endogenous and exogenous compounds. Sulfate conjugates exhibit a high degree of binding to albumin, the extent of which usually exceeds those of their parent compounds. Preponderant direct and indirect evidence suggests that sulfation activity is slightly higher in the periportal than in the perivenous (centrilobular) region of the liver, but recent immunohistochemical studies imply that specific isoforms of the sulfotransferases may also be preferentially localized in the perivenous region. Entry of sulfate conjugates into the liver cell is poor unless discrete carriers are present. Although known transport carriers exist for the sulfated bile acids, the specificity of the carriers for drug sulfate conjugates is presently unknown. The removal of sulfates is usually by way of biliary excretion while, on occasion, sulfates can be desulfated and participate in futile cycling with their parent compounds. The binding, transport, and hepatic elimination of various drug sulfate conjugates are examined. Non-recirculating studies carried out in the perfused rat liver with the multiple indicator dilution technique under varying input sulfate conjugate concentrations have provided essential information on the effects of vascular (red blood cells and plasma protein) binding on transport and removal of the conjugates. These studies clearly demonstrate the need to study protein binding, transmembrane transfer characteristics across the liver basolateral (sinusoidal) and canalicular membranes, and enzyme zonation in a distributed-in-space fashion in order to properly define the handling of sulfate conjugates in the liver.

Moment analysis of hepatic local disposition of allopurinol and oxipurinol: metabolism kinetics from allopurinol to oxipurinol in the rat isolated perfused liver

Drug metabolism in the liver was examined by the rat isolated perfused liver using the single-pass bolus-input technique. The test compounds, allopurinol and its metabolite oxipurinol, were independently introduced into the liver from the portal vein, and the concentration profiles in the venous outflow were monitored and kinetically analysed by moment theory. The recovery ratios of allopurinol and oxipurinol after the individual administration of each drug were estimated to be 0.17 (+/- 0.08 s.d.) and 1.03 (+/- 0.02 s.d.), respectively. The outflow recovery ratio of oxipurinol as the metabolite after allopurinol administration was estimated to be 0.80 (+/- 0.07 s.d.). These results indicate that the combined outflow recovery of the precursor and the metabolite after allopurinol administration is almost 100% in the rat liver.

Nonlinear protein binding and enzyme heterogeneity: effects on hepatic drug removal

The kinetics of substrate removal by the liver and the resulting nonlinear changes in unbound fraction along the flow path at varying input drug concentrations were examined by a model simulation study. Specifically, we varied the binding association constant, KA, and the Michaelis-Menten constants (Km and Vmax) to examine the steady state drug removal (expressed as hepatic extraction ratio E) and changes in drug binding for (i) unienzyme systems and (ii) simple, parallel metabolic pathways; zonal metabolic heterogeneity was also added as a variable. At low KA, E declined with increasing input drug concentration, due primarily to saturation of enzymes; only small differences in binding were present across the liver. At high KA, a parabolic profile for E with concentration was observed; changes in unbound fraction between the inlet and the outlet of the liver followed in parallel fashion. Protein binding was the rate-determining step at low input drug concentrations, whereas enzyme saturation was the rate-controlling factor at high input drug concentration. Heterogeneous enzymic distribution modulated changes in unbound fraction within the liver and at the outlet. Despite marked changes in unbound fraction occurring within the liver for different enzymic distributions, the overall transhepatic differences were relatively small. We then investigated the logarithmic average unbound concentration and the length averaged concentration as estimates of substrate concentration in liver in the presence of nonlinear drug binding. Fitting of simulated data, with and without assigned random error (10%), to the Michaelis-Menten equation was performed; fitting was repeated for simulated data obtained with presence of a specific inhibitor of the high-affinity, anteriorly distributed pathway. Results were similar for both concentration terms: accurate estimates were obtained for anterior, high affinity pathways; an overestimation of parameters was observed for the lower affinity posteriorly distributed pathways. Improved estimations were found for posteriorly distributed pathways upon inhibition with specific inhibitors; with added random error, however, the improvement was much decreased. We applied the method for fitting of several sets of metabolic data obtained from rat liver perfusion studies performed with salicylamide (SAM) (i) without and (ii) with the presence of 2,6-dichloro-4-nitrophenol (DCNP), a SAM sulfation inhibitor. The fitted results showed that SAM sulfation was a high-affinity high-capacity pathway; SAM glucuronidation was of lower affinity but comparable capacity as the sulfation pathway, whereas SAM hydroxylation was of lower affinity and lower capacity.

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.