L. Bass

Enzymatic elimination of substrates flowing through the intact liver

Enzymatic elimination of a class of substrates by the liver is analyzed in terms of a convective model of the microcirculation carrying the substrates. The elimination generates concentration gradients of the substrates which in turn affect the elimination rate through Michaelis-Menten saturation kinetics. The interplay of biochemical, anatomical and haemo-dynamic factors results in a variety of limiting regimes of elimination which are given a quantitative discussion and classification. The kinetic parameters of the enzymatic elimination reaction are expressed in terms of quantities observable on the intact liver. An overall elimination efficiency is defined by comparison with a homogenous process and evaluated for all elimination regimes, with clinical implications. Examples of two types of experiments supporting the validity of the model are presented.

Hepatic elimination of flowing substrates: The distributed model

An earlier model of hepatic elimination with functionally identical sinusoids is extended by introducing statistical distributions of enzyme contents per sinusoid and of blood flow per sinusoid, these being either uncorrelated or closely correlated. The steady-state theory of the resulting distributed model is developed, including methods of determining experimentally the coefficients of variation of the distributions. Such determinations are made on an illustrative experimental example. Quantitative predictions of expected effects of changes in blood flow are given, including one for which the undistributed model predicts a null effect. Shapes of the postulated distributions are discussed only in relation to observable effects. Effects of the distributions are compared with maximum possible effects of incomplete equilibration of substrate within each sinusoidal cross-section, and methods for distinguishing these effects from each other are outlined.

The Puzzle of Rates of Cellular Uptake of Protein-Bound Ligands

The rates of hepatic and cerebral uptake of physiologically important ligands, such as fatty acids, drugs and dyes, have long been known to be surprisingly high when most ligand is bound to plasma proteins (Baker & Bradley, 1966, Pardridge & Landaw, 1984). The magnitudes of these rates, as well as the unexpected forms of their dependence on protein concentration, have motivated the hypothesis of specific albumin receptors on the hepatocyte (Weisiger, Gollan & Ockner, 1981) helping to translocate the ligand from albumin into the cell; and the hypothesis of a catalytic mechanism of dissociation of ligand from protein at the cellular surface (for example, Baker & Bradley, 1966; Forker & Luxon, 1981). We shall refer to both proposals as facilitation hypotheses. We do not include in this term facilitation of cellular uptake of unbound ligands (see for example Stremmel, Strohmeyer & Berk, 1986).

A stochastic model of hormesis

In order to describe the life-prolonging effect of some agents that are harmful at higher doses, ionizing radiations in particular, a stochastic model is developed in terms of accumulation and progression of intracellular lesions caused by the environment and by the agent itself. The processes of lesion repair, operating at the molecular and cellular level, are assumed to be responsible for this hormesis effect within the framework of the proposed model. Properties of lifetime distributions, derived for analysis of animal experiments with prolonged and acute irradiation, are given special attention. The model provides efficient means of interpreting experimental findings, as evidenced by its application to analysis of some published data on the hormetic effects of prolonged irradiation and of procaine on animal longevity.

On the Relation Between Extended Forms of the Sinusoidal Perfusion and of the Convection Dispersion Models of Hepatic Elimination

Two models of hepatic elimination, the distributed sinusoidal perfusion model, and the convection-dispersion model, are extended and then compared for first order kinetics in the steady-state. The sinusoidal perfusion model is extended by the inclusion of intrahepatic sites of mixing between sinusoids. The degree of such mixing is estimated for taurocholate elimination by isolated perfused rat livers by a comparison of anatomical and kinetic estimates of uptake heterogeneity, using previously published data. The dispersion model is generalized by the inclusion of distributions of enzyme activity along the flow. Direct comparison of the two models in the limit in which the degree of dispersion is small, allows the flow-dependence of the dispersion coefficient to be determined, thereby greatly extending the explanatory power of the convection-dispersion model. Finally, the effect of intrahepatic mixing sites on uptake by Michaelis-Menten kinetics is quantified in terms of the distributed sinusoidal perfusion model, with results which may be applicable to capillary beds in general.

Flow dependence of first-order uptake of substances by heterogeneous perfused organs

Abstract A commonly accepted model of steady first-order uptake of substances by a perfused organ consisting of capillaries acting in parallel assumes that the capillaries are functionally identical. The model predicts the constancy of the quantity F 1n (ci/co), where F is the rate of flow of perfusate through the organ, and c1 and co are the inlet (arterial) and outlet (venous) concentrations, respectively, of the substance being taken up. The failure of that constancy under variations of F at constant values of physiological control data, as observed in liver and in muscle, is explained here in its general features in terms of a narrow statistical distribution of the relevant properties of individual capillaries. The coefficient of variation ϵ of that distribution is a measure of the functional heterogeneity of the organ. A detailed quantitative interpretation of published data on the uptake of colloidal CrP04 by the Kupffer cells of perfused isolated rat livers is carried through. The resulting value of e is found to be smaller than the upper limit for the corresponding value of e pertaining to the elimination of galactose by the hepatocytes of isolated perfused rat livers, estimated earlier by different experimental and theoretical methods. Transformation of bolus flow into Poiseuille flow by the removal of erythrocytes from the perfusate is shown to increase significantly the value of ϵ.

CAPILLARY PERMEABILITY OF HETEROGENEOUS ORGANS: A PARSIMONIOUS INTERPRETATION OF INDICATOR DIFFUSION DATA

1. Calculations of capillary permeability of perfused organs from indicator diffusion data are reviewed, and reconsidered in terms of two kinds of organ heterogeneity of capillary extraction.

How small is the functional variability of liver sinusoids

Published experimental results on steady elimination of galactose by isolated rat livers perfused at different flow rates, predicted earlier from a model of hepatic elimination with functionally identical sinusoids, are assessed in terms of a more general model. An upper limit on the functional variability (heterogeneity) of liver sinusoids is deduced from the experimental results, and conditions for the detection of the actual variability by the same type of experiment are discussed quantitatively.

Hepatic uptake and metabolism of galactose can be quantified in vivo by 2-[18F]fluoro-2-deoxygalactose positron emission tomography

Metabolism of galactose is a specialized liver function. The purpose of this PET study was to use the galactose analog 2-[(18)F]fluoro-2-deoxygalactose (FDGal) to investigate hepatic uptake and metabolism of galactose in vivo. FDGal kinetics was studied in 10 anesthetized pigs at blood concentrations of nonradioactive galactose yielding approximately first-order kinetics (tracer only; n = 4), intermediate kinetics (0.5-0.6 mmol galactose/l blood; n = 2), and near-saturation kinetics (>3 mmol galactose/l blood; n = 4). All animals underwent liver C15O PET (blood volume) and FDGal PET (galactose kinetics) with arterial and portal venous blood sampling. Flow rates in the hepatic artery and the portal vein were measured by ultrasound transit-time flowmeters. The hepatic uptake and net metabolic clearance of FDGal were quantified by nonlinear and linear regression analyses. The initial extraction fraction of FDGal from blood-to-hepatocyte was unity in all pigs. Hepatic net metabolic clearance of FDGal, K(FDGal), was 332-481 ml blood.min(-1).l(-1) tissue in experiments with approximately first-order kinetics and 15.2-21.8 ml blood.min(-1).l(-1) tissue in experiments with near-saturation kinetics. Maximal hepatic removal rates of galactose were on average 600 micromol.min(-1).l(-1) tissue (range 412-702), which was in agreement with other studies. There was no significant difference between K(FDGal) calculated with use of the dual tracer input (Kdual(FDGal)) or the single arterial input (Karterial(FDGal)). In conclusion, hepatic galactose kinetics can be quantified with the galactose analog FDGal. At near-saturated kinetics, the maximal hepatic removal rate of galactose can be calculated from the net metabolic clearance of FDGal and the blood concentration of galactose.

Effects of capillary heterogeneity on rates of steady uptake of substances by the intact liver

Steady elimination of substances by a heterogeneous perfused organ is investigated for general uptake kinetics, with special reference to saturation kinetics. In the case of uptake of substances by hepatocellular enzymes according to Michaelis-Menten kinetics, the theory is brought to bear on published data on the elimination of galactose by isolated perfused pig livers. Using a statistical sample-splitting method, it is shown that the data are inconsistent with functional homogeneity of liver sinusoids (P < 0.002), and a reinterpretation of the pooled data is carried through in terms of a model incorporating capillary heterogeneity. The limitations of such analyses in the case of several parallel biochemical pathways of uptake are discussed.