Hepatic uptake and metabolism of benzoate: a
multiple indicator dilution, perfused rat liver study
Andreas J.
Schwab1,2,
Lei
Tao3,
Tsutomu
Yoshimura3,
André
Simard1,
Ford
Barker3, and
K. Sandy
Pang3,4
1 McGill University Medical Clinic, Montreal General
Hospital and 2 Department of Medicine, McGill University,
Montreal, Quebec H3G 1A4; 3 Department of Pharmaceutical
Sciences, Faculty of Pharmacy, University of Toronto, Toronto,
Ontario M5S 2S2; and 4 Department of Pharmacology,
University of Toronto, Toronto, Ontario, Canada M5S 1A8
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ABSTRACT |
Multiple,
noneliminated references (51Cr-labeled erythrocytes,
125I-albumin, [14C]- or
[3H]sucrose, and [2H]2O),
together with [3H]hippurate or
[14C]benzoate, were injected simultaneously into the
portal vein of the perfused rat liver during single-pass delivery of
benzoate (5-1,000 µM) and hippurate (5 µM) to investigate
hippurate formation kinetics and transport. The outflow dilution data
best fit a space-distributed model comprising vascular and cellular
pools for benzoate and hippurate; there was further need to segregate
the cellular pool of benzoate into shallow (cytosolic) and deep
(mitochondrial) pools. Fitted values of the membrane
permeability-surface area products for sinusoidal entry of unbound
benzoate were fast and concentration independent (0.89 ± 0.17 ml · s
1 · g
1) and greatly
exceeded the plasma flow rate (0.0169 ± 0.0018 ml · s
1 · g
1), whereas both
the influx of benzoate into the deep pool and the formation of
hippurate occurring therein appeared to be saturable. Results of the
fit to the dilution data suggest rapid uptake of benzoate, with
glycination occurring within the deep and not the shallow pool as the
rate-determining step.
membrane permeability; mathematical models; mitochondria; glycine
conjugation
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INTRODUCTION |
BENZOATE (BENZOIC ACID)
is a monocarboxylate used as a food preservative and for the
treatment of hyperammonemia (5). Its metabolism in humans
and rats occurs exclusively by conjugation with glycine to form
hippurate (hippuric acid; N-benzoylglycine) in the liver and
kidney (1, 4, 6). The first step of this pathway is
activation by benzoyl-CoA ligase to form benzoyl-CoA; a similar
activation pathway also constitutes the first step of fatty acid
catabolism by
-oxidation. Compounds like benzoate that do not carry
hydrogen at the
- and
-positions, however, will not be degraded
by
-oxidation. Rather, substitution of CoA by an amino acid may
occur, such as the formation of a glycine conjugate by means of glycine
N-acyltransferase (26). Both steps have been
shown in rats and in cattle to proceed within the mitochondrial matrix,
and energy-dependent conversion of benzoate to hippurate has been
demonstrated in isolated rat and beef liver mitochondria (13).
Chiba et al. (8) suggested that hippurate synthesis from
benzoate in the perfused rat liver proceeded with an overall
Michaelis-Menten constant (Km) of 12 µM and
maximum velocity (Vmax) of 101 nmol · min
1 · g
1. The
relative importance of transport vs. metabolism of benzoate on the
overall glycination of benzoate in liver, however, has not been
studied. Metabolism of benzoate within hepatocytes requires the
bidirectional transport of substrate and metabolite across the
basolateral plasma (sinusoidal) membrane and the mitochondrial outer
and inner membranes. There exists information on carrier-mediated transport of benzoate across human erythrocyte (25) and
intestinal Caco-2 cell membranes (35). The metabolite
hippurate is not eliminated by the liver (8, 38), although
avid influx and efflux occur across the basolateral membrane. Transport
is most likely mediated by the hepatic monocarboxylate transporter 2 that appears to be inhibited by benzoate (12, 38). To
date, however, no systematic investigation on monocarboxylate transport
into mitochondria has been conducted, although the transport of
pyruvate across the mitochondrial inner membrane was found to be
mediated by specific carriers (7, 20). Previous studies
have revealed that benzoate and hippurate are not distributed into
erythrocytes, although binding to albumin exists (8, 38).
In this study, we applied the multiple indicator dilution (MID) method
to characterize the kinetics of hepatic transport and metabolism of
benzoate to understand the roles of sinusoidal and mitochondrial
transport in the overall glycine conjugation process.
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MATERIALS AND METHODS |
Materials.
Benzoic acid, hippuric acid, benzoyl chloride, and bovine serum albumin
(fraction V) were purchased from Sigma Chemical (St. Louis, MO).
[14C]benzoic acid (specific activity, 4.07 GBq/mmol) and
[2-3H]glycine (specific activity, 1,600 GBq/mmol) were
obtained from American Radiolabeled Chemicals (St. Louis, MO) and
DuPont Canada, (Markham, ON, Canada), respectively.
[3H]hippurate was synthesized from
[3H]glycine as described previously (15,
38). [51Cr]sodium chromate (specific activity
5,392 mBq/mg), 125I-labeled serum albumin (specific
activity 0.46 mBq/mg), and 2H2O (>99.98%
pure) were purchased from Merck Frosst, Montreal, QC, Canada.
[14C]sucrose (183 MBq/mmol) and [3H]sucrose
(455 GBq/mmol) were obtained from NEN Life Science Products (Boston,
MA). All reagents used were of glass-distilled, high-performance liquid
chromatographic grade or the highest purity available (Fisher Scientific, Mississauga, ON, Canada).
Rat liver perfusion.
Male Sprague-Dawley rats (Charles River Canada, St. Constant, QC,
Canada; 295-367 g; livers were 9.1-13.4 g) were used for single-pass liver perfusion studies. The animals were housed in accordance with approved protocols of the University of Toronto Animal
Committee, kept under artificial light on a 12:12-h light/dark cycle,
and were allowed free access to water and food ad libitum. In situ
single-pass liver perfusion was carried out at 37°C as previously
described (8) with perfusate (12 ml/min) entering via the
portal vein and exiting via the hepatic vein; the hepatic artery was
ligated. The perfusate contained bovine erythrocytes (20%), freshly
obtained and washed (Ryding Meats, Toronto, ON, Canada), 5% bovine
serum albumin, and 17 mM glucose (Travenol Labs, Deer Park, IL) in
Krebs-Henseleit bicarbonate solution. Constant concentrations of
hippurate (5 µM) and benzoate (one concentration, ranging from 5 to
1,000 µM) were used for each liver preparation. The perfusate was
oxygenated with 95% oxygen-5% carbon dioxide (Matheson, Mississauga,
ON, Canada) and oxygen (BOC Gases, Whitby, ON, Canada). The pH was
maintained at 7.4 by adjustment of the flow of gases and monitored by
an "on-line" flow-through pH electrode (Orion, Boston, MA). Inflow
and outflow perfusate samples, collected at 15, 25, 35, 45, and 55 min
after the onset of perfusion, were used for determination of the
average input (Cin) and output (Cout) plasma
concentrations of unlabeled hippurate and benzoate. Although both
benzoate and hippurate were excreted only minimally into bile
(8), bile samples were collected for the first 15 min and
at 5- to 10-min intervals thereafter up to 60 min to monitor the
excreted radioactivity and the bile flow.
MID.
Two consecutive MID injections (0.23 ml) were made within each liver
perfusion study: the first one was made between 10 and 15 min after the
initiation of perfusion, whereas the second injection was made at 35 min. The first injection mixture/dose contained 51Cr-labeled erythrocytes (2.35 ± 1.54 µCi),
125I-labeled albumin (1.25 ± 1.32 µCi),
[14C]sucrose (0.72 ± 0.36 µCi),
2H2O (0.106 ± 0.006 ml), and
[3H]hippurate (1.77 ± 0.32 µCi). The second dose
contained 51Cr-labeled erythrocytes (2.65 ± 1.67 µCi), 125I-labeled albumin (1.08 ± 0.97 µCi),
[3H]sucrose (1.46 ± 0.44 µCi), and
[14C]benzoate (0.91 ± 0.30 µCi). Each dose
contained the appropriate concentrations of unlabeled benzoate and
hippurate in a composition otherwise identical to that of the perfusate
and was introduced into the inflow system by an electronically
controlled injection valve (16). Simultaneously, a
fraction collector was activated to collect samples at successive 1-, 2-, and 3-s intervals for a total of 180 s for the first injection
and at 1-, 2-, and 3-, and 5-s intervals for a total of 280 s for
the second injection. The hematocrits of the blood perfusate and dose
were determined for each experiment by use of a hematocrit centrifuge
(Model MB Microhematocrit Centrifuge, IEC, Fisher Scientific). Sham
experiments (without liver) were conducted to characterize the
dispersion due to the injection device and the inflow and outflow catheters.
Quantitation of isotopes.
The 51Cr and 125I radioactivities in whole
outflow perfusate blood samples (25-200 µl) and in the 1:10
diluted dose were assayed by gamma counting (Cobra II,
Canberra-Packard Canada, Mississauga, ON, Canada); the
3H and 14C radioactivities in perfusate plasma
(50-200 µl) and in plasma from the 1:10 diluted dose were
assayed by liquid scintillation counting (LS5801, Beckman Canada,
Mississauga, ON, Canada) as previously described (16).
2H2O was assayed by Fourier transform infrared
spectrometry (FTIR, Model 1600, Perkin Elmer Canada, Rexdale, ON,
Canada) over the frequency interval between 2,300 and 2,700 cm
1 (28).
Plasma outflow and bile samples (25-100 µl), supplemented with
excess benzoate and hippurate, were assayed for the individual radiolabeled species by thin-layer chromatography (Silica Gel GF, 250 µm, Analtech, Newark, DE) with chloroform:cyclohexane:acetic acid
(80:20:10, vol/vol/vol); the values for the distance traveled relative
to the solvent front (Rf) for hippurate and
benzoate were 0.15 and 0.95, respectively, and labeled sucrose and
albumin did not interfere with the radiochromatograms. The
regions associated with the authentic standards were visualized under
ultraviolet light and scraped into scintillation vials. After the
addition of 0.5 ml of water and 10 ml of scintillation cocktail (Ready Protein, Beckman), the radioactivity of each sample was assayed by
liquid scintillation counting.
Assay of unlabeled benzoate and hippurate in plasma and bile.
The concentrations of unlabeled benzoate and hippurate in plasma
samples and bile were assayed by high-performance liquid chromatography, as previously described (8).
Data treatment.
For the MID data, the concentration of radiolabel in the outflowing
perfusate was normalized to the dose, yielding fractional recovery (or
concentration/dose) (16). The fractional recovery integral
[area under the curve (AUC)] was approximated by summing the products
of fractional recoveries and sample intervals with monoexponential
extrapolation to infinity; the integral of the product of fractional
recovery and time [at mid-intervals, area under the moment curve
(AUMC)] was calculated similarly (16, 30). The ratio of
AUMC to AUC yielded the mean transit time (MTT). Tracer recoveries were
obtained by multiplying AUCs with perfusate flow. The hippurate
synthesis rate was obtained as the difference between the inflow and
outflow plasma hippurate unlabeled concentrations multiplied by plasma
flow, or, alternatively, as the tracer recovery of
[14C]hippurate multiplied to the steady-state delivery
rate of unlabeled benzoate; the latter was calculated as the inflow
benzoate concentrations multiplied by plasma flow. Plasma flow was
calculated as perfusate flow × (1
hematocrit). These
calculations were based on the findings that benzoate and hippurate do
not enter erythrocytes and that biliary excretion and metabolism of
hippurate are negligible (38).
Modeling of hepatic benzoate disposition.
The kinetic events underlying the disposition of benzoate in the
perfused rat liver are displayed schematically in Fig.
1. Benzoate and hippurate are present in
the plasma space as protein-bound and nonprotein-bound (unbound) forms,
and it is assumed that only the unbound form in the plasma space
exchanges with that in the cellular space of hepatocytes. Furthermore,
rapid equilibrium between bound and unbound forms is assumed. Because
albumin is excluded from part of the interstitial space (the Disse
space), whereas unbound benzoate and hippurate, like sucrose, occupy
this space in an unrestricted fashion, the spaces of distribution of bound benzoate and hippurate are diminished accordingly
(18). The dependence of nonlinear benzoate and hippurate
binding to albumin on the total plasma concentration was calculated
using previously determined binding association constants
(KA of 8.37 × 103 M
1
and 1.9 equivalent sites for benzoate, and KA of
2.1 × 103 M
1 and 1.03 equivalent sites
for hippurate) (8, 38); these constants predicted
relatively poor and concentration-independent binding of the substrates
within the concentrations studied. Variants of the model
considered comprised either a single intracellular benzoate pool
(model A, Fig. 1A) or two intracellular benzoate pools: namely, a "shallow" cytosolic pool connected directly to the
plasma pool and a "deep" pool connected only to the shallow pool.
Irreversible metabolism of benzoate to form hippurate was assumed to
occur either in the shallow (model B, Fig. 1B) or
the deep (model C, Fig. 1C) pool.

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Fig. 1.
Schematic representation of the models used to interpret
benzoate uptake and biotransformation to hippurate at the level of a
single sinusoid. A: model A with a single
substrate intracellular pool. B and C:
models B and C with 2 substrate intracellular
pools and metabolite formation from shallow and deep pool,
respectively. Rapid equilibrium is assumed between protein-bound and
unbound forms of benzoate and hippurate in plasma and in the
interstitial space, resulting in lumped intravascular pools. Hatched
line: endothelial cells. See Fitting procedures for
definitions of terms.
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Fitting procedures.
The outflow profiles of the nonmetabolized indicators,
51Cr-labeled erythrocytes, 125I-labeled
albumin, [3H]- or [14C]sucrose, and
2H2O, were evaluated by linear superposition as
described previously (38). The fitted parameters
were the ratios of extravascular to vascular distribution spaces (
)
and the common large-vessel transit time (t0).
The optimized values of t0 were then assigned for modeling the outflow profiles of benzoate and hippurate.
The data obtained from the injection of [3H]hippurate
were first evaluated using a model with barrier limitation as described previously (38). Fitting furnished the transfer
coefficients for hippurate transport (k25 and
k52) and the parameter
rel,H derived from the ratio of interstitial to vascular distribution spaces
of hippurate (
H; see Eq. A10). The tracer
[3H]hippurate outflow profile was further resolved into
throughput and exchanging (returning) components.
The theoretical outflow profiles of [14C]benzoate and its
metabolite [14C]hippurate were calculated using the
procedures described in APPENDIX A. The values of the
[14C]hippurate transport parameters
(k25 and k52) and the
interstitial-vascular distribution space ratio for hippurate
(
H) were taken from the results of the
[3H]hippurate injection applied to the same liver.
Fitting of the [14C]benzoate and
[14C]hippurate profiles furnished the transfer
coefficients for benzoate transport (k13 and
k31) exchange parameters between intracellular pools (k34 and k43)
(where applicable for models B and C), the coefficient for metabolism (k35 or
k45) for models B and C,
and the parameter
rel,B derived from the ratio of the
interstitial to the vascular distribution space of benzoate
(
B; see Eq. A11). The tracer
[14C]benzoate outflow profile was further resolved into
throughput and exchanging (returning) components.
Transfer coefficients for cellular uptake are defined as the proportion
of tracer present in the source compartment (the sinusoid and the
adjacent part of the interstitial space) entering the cells per unit
time. The values of these coefficients depend on the volumes of the
source compartment, which vary with experimental conditions such as
flow rate, hematocrit, or binding proteins. A physiologically more
relevant parameter is the sinusoidal permeability-surface area product,
which is the amount taken up per unit time divided by the extracellular
concentration (source compartment) and has the same unit as clearance
(vol/time). Because only the portion of benzoate or hippurate not bound
to plasma proteins is assumed to enter cells, the pertinent
extracellular concentrations are those of unbound benzoate and
hippurate. The unbound concentrations are determined by the products of
the unbound fractions determined in vitro and the total sinusoidal
plasma concentration under the assumption that, within the sinusoid and
the interstitial space, the unbound and protein-bound benzoate or
hippurate species are close to equilibrium at all times.
Permeability-surface-area products per unit wet weight of the liver
were calculated by multiplying the transfer coefficients
k13 and k25 based on
unbound concentrations with the extracellular space of distribution
(see Eq. A6).
For analysis of the nonmetabolized as well as metabolized indicators,
transport functions (impulse responses) of the liver were obtained by
numerical deconvolution of experimental outflow profiles with the
transport function of the combined injection and collection devices
(the catheter transport function), using an algorithm obtained from the
National Simulation Resource in Mass Transport and Exchange (University
of Washington, Seattle, WA). Conversely, theoretical outflow profiles
of nonmetabolized indicators were obtained by convolution of calculated
transport functions with the catheter transport function
(38), using an algorithm for numerical integration (QDAG
from IMSL, Visual Numerics, Houston, TX). Optimal parameters and their
uncertainties were estimated by using the classic weighted least
squares approach (23) with algorithms obtained from IMSL.
The data were weighted assuming an error variance proportional to the
magnitude of the observation as appropriate for radioactivity count
data (10, 23). Parameter uncertainties and independence
among parameters were verified using standard deviations and
correlations obtained from the fitting procedure (23).
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RESULTS |
Hepatic uptake and metabolism of benzoate.
The total recoveries of the 51Cr, 125I,
14C, and 3H radiolabels and of
2H2O in the venous outflow samples were
virtually complete (Table 1). This
suggests that all of the injected benzoate returned to the vasculature
either as unchanged benzoate or as hippurate, confirming that benzoate
and hippurate were not significantly excreted and that benzoate was
metabolized exclusively to hippurate that was not further metabolized.
Tracer [14C]hippurate recoveries decreased with
increasing unlabeled benzoate concentrations, indicating saturation of
benzoate conjugation. Upon fitting of hippurate formation rates to the
Km equation, with the logarithmic average
unbound concentration of benzoate taken as the substrate concentration
(Fig. 2), the optimized maximal rate of
the overall conjugation of 78 ± 6 nmol · min
1 · g
1 was found
to be similar to that (101 nmol · min
1 · g
1)
determined previously in steady-state rat liver perfusions
(8). However, the unbound benzoate concentration at
half-maximal conjugation (Km,overall of 2.6 ± 1.0 µM) was slightly lower than previously reported (12 µM).
This small discrepancy was probably due to interanimal variations.
Nevertheless, these values of the Km,overall
were of the same order of magnitude. Rates of hippurate formation based on recoveries from the injection of [14C]benzoate
furnished similar parameters (Vmax,overall of 68 ± 5 nmol · min
1 · g
1 and
Km,overall of 3.8 ± 1.2 µM).

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Fig. 2.
Rates of bulk and tracer hippurate syntheses at different
benzoate concentrations. Benzoate concentrations are the unbound
logarithmic average concentrations u = fu(Cin Cout)/ln(Cin/Cout), where
Cin and Cout are inflow and outflow benzoate
concentrations, respectively, and fu is fraction unbound in
plasma. Lines are calculated rates v according to
Michaelis-Menten kinetics (Km):
v = Vmax/(1 + Km/ u), with maximum velocity
(Vmax) = 78 nmol · min 1 · g 1 and
Km = 2.6 µM for bulk and
Vmax = 68 nmol · min 1 · g 1 and
Km = 3.8 µM for tracer.
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Outflow profiles.
Representative outflow profiles of tracer [3H]hippurate
(first injection), of tracer [14C]benzoate and its
metabolite [14C]hippurate (second injection), and of the
noneliminated indicators are shown in Figs.
3 and 4,
respectively, for low and high concentrations of unlabeled benzoate and
of 5 µM hippurate in perfusate.

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Fig. 3.
Outflow profiles of the preformed metabolite
[3H]hippurate and the noneliminated references. Two
representative multiple indicator dilution (MID) studies are shown
conducted at 5 µM hippurate but 2 steady-state input plasma
concentrations of benzoate. Data are fractions of recovered dose per
milliliter of perfusate and are plotted in linear (top) and
semilogarithmic (bottom) formats.
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Fig. 4.
Outflow profiles of [14C]benzoate, its metabolite
[14C]hippurate, and the noneliminated references. Two
representative MID studies are shown conducted at 2 steady-state input
plasma concentrations of benzoate and a constant hippurate
concentration of 5 µM. Data are fractions of recovered dose per
milliliter of perfusate and are plotted in linear (top) and
semilogarithmic (bottom) formats.
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Linear superposition by use of the delayed-wave model.
The outflow profiles of the noneliminated indicators for the first and
the second injection (labeled erythrocytes, albumin, sucrose, and
2H2O) in hepatic venous blood were increasingly
dampened in magnitude and prolonged in time, but their shapes were
otherwise similar (16, 17). MTTs of the noneliminated
indicators (Table 1) and values of t0 and
(Table 2) were virtually identical for both of the injections made at 15 and 35 min, and the values were similar to those obtained in previous perfused rat liver MID studies (16, 17, 27, 28, 30, 38). This observation attests to the
stability of the liver preparation and strongly suggests constancy of
the transfer constants for hippurate during the experiment.
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Table 2.
Parameters obtained by linear superposition of the sucrose outflow
profiles on the data of the red blood cell, albumin, and
2H2O profiles
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Model fits to outflow profiles of [3H]hippurate.
Outflow profiles obtained after injection of
[3H]hippurate (Fig. 3) were similar to those obtained
previously in the absence of benzoate (38). The rising
upslope of [3H]hippurate was slightly delayed with
respect to that of labeled albumin, but it preceded slightly that of
the labeled sucrose curve (Fig. 3), as expected due to binding of
hippurate to albumin and entry into hepatocytes. The
[3H]hippurate profile crossed over and then peaked lower
and earlier than the labeled sucrose curve and exhibited a more delayed
downslope. As the bulk benzoate concentration was increased, relatively
little change was observed in the tracer [3H]hippurate
curve (see Fig. 3) in relation to the curves for labeled albumin and
labeled sucrose. The calculated outflow profiles showed a good fit to
the [3H]hippurate data (Fig.
5). The optimal interstitial-to-sinusoid distribution ratio (
H) was slightly larger than the
value of 1.08 ± 0.37 calculated after consideration of binding of
hippurate to albumin in plasma perfusate (27, 37, 38). The
transfer coefficients for transport of hippurate between plasma and
hepatocytes (k25 and k52;
Table 3), the ratio of
k25 and k52, or the
equilibrium partitioning ratio (1.2 ± 0.27), the influx
permeability surface area product (P25S of 0.052 ± 0.019 ml · s
1 · g
1), and
the throughput component (48.8 ± 6.3% of dose; Table 3) remained
constant against the various unbound plasma concentrations of benzoate
but were significantly smaller than those previously obtained when
benzoate was absent in the perfusion fluid (P < 0.05)
(38). The combined observations can tentatively be
interpreted as an inhibitory influence of benzoate.

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Fig. 5.
Optimal calculated first injection outflow profiles of
[3H]hippurate. Data are the same as those in Fig. 3.
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Model fits to outflow profiles of [14C]benzoate and
of formed [14C]hippurate.
Outflow profiles of tracer [14C]benzoate showed a peak
that roughly coincided in time with the [3H]sucrose peak
but was much lower in magnitude, followed by a prolonged tail (Fig. 4).
Those of tracer [14C]hippurate were much lower in
magnitude and showed a peak that was considerably delayed relative to
the sucrose profiles. At high benzoate concentrations, the tail of the
[14C]benzoate outflow profiles was increased in
magnitude, whereas the [14C]hippurate outflow profiles
were reduced. This can be interpreted as saturation of the overall
conjugation process, but the specific step or steps where this
saturation occurs were not immediately apparent from inspection of the
curves. A more detailed assessment of the kinetics of benzoate
conjugation was obtained by modeling analysis of the experimental data.
A minimum of two intracellular benzoate pools, a shallow and a deep
intracellular pool, were needed to fit the benzoate data, as can be
clearly discerned by visual inspection of the fits obtained with the
various models (Fig. 6). When the deep
intracellular pool (compartment 4) was omitted from the model
(model A, Fig. 1A), the calculated outflow
profiles of benzoate and hippurate could not be fitted to the outflow
data collected later than 50 s after injection (Fig.
6A). Similarly, the model denoting conversion of benzoate to
hippurate in the shallow intracellular pool (model B, Fig.
1B) did not allow a good fit to the data. With this model (model B), the [14C]hippurate profile was
predicted to exhibit a peak that was much earlier than that of the
experimental data (Fig. 6B). By contrast, the model that
described metabolism from the deep intracellular pool (model
C, Fig. 1C) allowed an improved fit to the experimental outflow profiles of benzoate and hippurate (Fig. 6C).
However, models B and C were indistinguishable
when only benzoate data were fitted and the metabolite data were
ignored (results not shown), as expected from theory (APPENDIX
B). In the latter case, the optimized coefficients for benzoate
transfer between the plasma and shallow intracellular pools were
identical for both models and close to those listed in Table
4, whereas those representing the
transfer between the shallow and the deep intracellular pools and
benzoate metabolism to hippurate were altered according to
Eqs. B1-B3 in APPENDIX
B. The proper selection of the optimal model of benzoate
metabolism (model C) was thus dictated by the fit of the
metabolite data. A much lower sum of squared residuals was obtained
with model C than with models A and B
(30× that of model C). Model C is the simplest
model consistent with bidirectional transport of benzoate and hippurate
between plasma and hepatocytes, irreversible metabolism, and the
inclusion of a deep pool.

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Fig. 6.
Optimal calculated second
injection outflow profiles of [14C]benzoate and its
metabolite, [14C]hippurate. Data are the same as those in
Fig. 4. Models A, B, and C are those represented
in Fig. 1A, B, and C, respectively.
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Kinetics of benzoate glycine conjugation.
Optimal parameters obtained with model C are summarized in
Table 4. The parameters were only weakly to moderately correlated to
each other, thus excluding complications of overparametrization of the
model. The optimal interstitial to sinusoid distribution ratio of
benzoate (
B) was slightly larger than the one calculated from the binding to plasma albumin (0.85 ± 0.40), as observed for
hippurate (see Model fits to outflow profiles of
[14C]benzoate and of formed
[14C]hippurate). According to model
C, the optimized permeability-surface products for uptake of
unbound benzoate into the intracellular space (P13S = 0.89 ± 0.17 ml · s
1 · g
1) were not
significantly dependent on benzoate concentration (Fig. 7) and greatly exceeded the plasma flow
rate (0.017 ± 0.002 ml · s
1 · g
1). However,
those for uptake into the deep intracellular pool (k34) and for irreversible metabolism of
benzoate (k45) decreased with increasing
benzoate concentration (Table 4; Fig. 7). This trend was also seen with
the ratio of the transfer coefficients for uptake into the deep
intracellular pool and return into the shallow intracellular pool
(k34/k43; Fig. 7).
Because of metabolic sequestration, the steady-state ratios of the
benzoate content in the deep intracellular pool to that in the shallow
intracellular pool, calculated as
k34/(k43 + k45), were smaller than the corresponding equilibrium partition ratios for benzoate between these pools, calculated as the ratios of transfer coefficients
(k34/k43) (Fig. 7). The
throughput component against the various unbound concentrations of bulk
benzoate used for experimentation was 11.7 ± 5.2% of the dose.

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Fig. 7.
Derived kinetic parameters at various benzoate plasma
concentrations. P13S, permeability-surface area product for
influx of nonprotein-bound benzoate into hepatic parenchymal cells;
k34/k43, equilibrium
partitioning ratio between deep (mitochondrial) and shallow (cytosolic)
intracellular pools;
k34/(k43 + k45), calculated ratio between the contents of
the deep (mitochondrial) and shallow (cytosolic) intracellular pools;
k45, transfer coefficient for metabolic
conversion of benzoate to hippurate. Unbound benzoate
concentration is the logarithmic average unbound
concentration u = fu(Cin Cout)/ ln(Cin/Cout).
|
|
 |
DISCUSSION |
MID experiments are typical input-output experiments that
can be quantitatively interpreted with concepts originating from linear
systems theory. The models that are applied to these systems resemble
black boxes, and the information obtained on the processes underlying
the observations is, by nature, limited. However, proper interpretation
of data is possible if certain restrictions, based on reasonable
assumptions about the nature of the underlying physiological processes,
are obeyed.
The additional data on metabolite outflow profile greatly strengthened
the stance for a more detailed kinetic analysis of MID experiments,
especially when the metabolite is characterized for its transport and
sequestration coefficients, as in this and other studies. In MID
experiments with [2-3H]lactate in perfused rat liver, the
metabolite (3H2O) was found to be formed from a
deep intracellular pool connected in series to a shallow intracellular
pool. The deep pool was considered to be composed of several
intermediate metabolites exchanging 3H with the two
position of lactate (such as malate, fumarate, and NAD+)
(29, 32). Conversely, sulfation of acetaminophen was found to occur from the shallow and not the deep intracellular acetaminophen pool (27).
Based on the present additional data on [3H]hippurate and
formed [14C]hippurate, the model with only one
intracellular pool (model A) was found inadequate in
describing the composite data on [14C]benzoate and
[14C]hippurate at postinjection times longer than 50 s. The observation suggests that tracer benzoate present inside the
hepatocyte is not represented by a single moiety that is instantly and
evenly distributed throughout the hepatocyte. For
[14C]benzoate, the model with two intracellular pools was
found satisfactory, and the delayed appearance of the metabolite
corroborates the conclusion that formation of metabolite involved a
deep intracellular pool. However, in addition to this local
heterogeneity of intracellular distribution of substrate, the outflow
profile could be interpreted by various physiological phenomena, such
as binding to intracellular proteins or other cellular binding sites
(17), intracellular diffusion (24),
reversible metabolism (29, 32), or subcellular compartmentalization. Similar outflow dilution profiles that were incompatible with a single intracellular pool were found with enalaprilat and sulfobromophthalein-glutathione conjugate (17, 30, 32), substances that are only excreted into bile. For these
substrates, the power of discrimination of whether sequestration occurs
from a shallow or from a deep pool is curtailed in the absence of
additional metabolic data.
For benzoate metabolism in the rat liver, glycination occurs in the
deep intracellular, pool. We propose that this pool represents the
mitochondrial compartment and that the shallow intracellular pool
represents the cytosolic space, a conjecture that is consistent with
the presence of enzymes for hippurate synthesis (benzoyl-CoA ligase and
glycine N-acyl transferase) in the mitochondria of rat and
bovine livers (13, 14, 22, 36). The mitochondrial content
of benzoyl-CoA in cells exposed to benzoate is unknown; however,
because the maximal activity of the transferase was found to largely
exceed that of the ligase, synthesis of benzoyl-CoA is expected to be
rate limiting, and the concentration should be very low (13,
36).
The spatial distribution of solutes such as benzoate and hippurate
within the cell is uncertain due to the multitude of potential subcellular compartments and cellular binding sites. To appropriately estimate the apparent permeabilities and partition coefficients from
transfer coefficients, the volumes of the various spaces involved have
to be known. For a tentative interpretation of the intracellular
benzoate kinetics, only the cytosolic and mitochondrial spaces were
presently considered. The cytosol and the mitochondria occupy 58% and
18%, respectively, of the volume of hepatocytes (3). The
mitochondrial-to-cytosolic concentration ratios are therefore
approximately three times higher than the content ratios shown in Fig.
7. This is in agreement with considerable accumulation of benzoate
inside isolated mitochondria as reported previously (14)
and may reflect energy-dependent uptake of benzoate into the
mitochondrial matrix and/or saturable binding of benzoate to
intramitochondrial sites. A judicious examination of benzoate uptake
into isolated mitochondria would be needed to elucidate the mechanism
of intramitochondrial accumulation.
Saturation of overall benzoate conjugation was noted, as observed
previously (8). From the present analysis, it may be concluded that sinusoidal transport of benzoate is not a controlling factor. From model analysis, saturation at the levels of mitochondrial benzoate uptake and metabolism is postulated to exist, and the observation is in agreement with saturation of benzoate conjugation in
the isolated rat liver mitochondria (14) and the very low Km values (between 1.1 and 7.4 µM) of beef
liver mitochondrial carboxylic acid:CoA ligases toward benzoate
(36). In fact, the value of Km is
similar to that of the overall glycination reaction of benzoate
observed in the perfused rat liver preparation (2.6-3.8 µM for
this study and 12 µM from previous studies; Ref. 8). At
low benzoate concentration, a considerable proportion of benzoate entering the mitochondria appears to be metabolized, as indicated by a
high k45-to-k43 ratio. In
contrast, metabolism of benzoate at higher concentrations is limited by
the maximal velocity of benzoate CoA ligase. No saturation, however,
was observed for transport of benzoate across the basolateral membrane
of hepatocytes in the concentration range studied. Therefore, a
carrier-mediated mechanism could not be confirmed. Nonsaturable
transport has also been observed for D-lactate or
L-lactate in similar experiment with perfused rat livers,
although carrier-mediated transport was assumed in these cases
(31, 32). Notably, tracer experiments under nonisotopic
steady-state conditions like the ones described here provide parameters
of near-equilibrium exchange that frequently result in higher
Km than experiments under zero-trans conditions (34).
The MTT of preformed hippurate (28 ± 3 s) and hippurate
formed from benzoate (114 ± 32 s) differed (Table 1). The
MTT of the formed hippurate is strongly influenced by the
transport and metabolic (formation) coefficients and tissue binding of
its precursor, benzoate, in addition to its influx and efflux transport
and tissue binding parameters (33). The formation of
hippurate in a deep, sequestered pool representing the mitochondria
increased the residence time of the metabolite in liver and the MTT of
formed hippurate.
Interpretation of MID experiments in the perfused rat liver by modeling
analysis revealed rapid and nonsaturable uptake but saturable
metabolism of benzoate. The approach further corroborated the
mitochondrial localization of the benzoate conjugation reaction, as
previously observed from in vitro experiments. Formation of hippurate
in the deep pool greatly delayed the appearance of the metabolite and
increased the MTT in relation to the MTT of preformed hippurate.
Transport of benzoate across plasma and mitochondrial membranes of
hepatocytes was found to occur in both directions simultaneously,
whereas the first step of benzoate metabolism catalyzed by the
benzoyl-CoA ligase reaction was saturable and appeared to be the
rate-limiting step of the overall process. The present analysis thus
confirms and expands the concepts previously established with in vitro experiments.
 |
APPENDIX A. MATRIX APPROACH TO MID EQUATIONS |
Labeled material is contained in various pools, as shown in Fig.
1C for model C. Benzoate and hippurate in blood
plasma form mobile pools, with concentrations c1
and c2, respectively. The intracellular
(presumably cytosolic) benzoate and hippurate pools, with
concentrations c3 and c5,
respectively, and the deep (mitochondrial) benzoate pool, with
concentration c4, are stationary pools. The behaviors of tracer benzoate and hippurate inside a single sinusoidal flow path and adjacent parenchymal cells (hepatocytes) are described by
the following system of partial differential equations
|
(A1)
|
|
(A2)
|
|
(A3)
|
|
(A4)
|
|
(A5)
|
where t is time, x is the position along
the length of the path, vF is the linear
velocity of flow within the sinusoidal lumen,
B and
H are the ratios of the interstitial distribution spaces
of benzoate and hippurate, respectively, to the sinusoidal plasma
space, and
is the hepatocyte-to-sinusoidal plasma volume ratio. The
ratios of vascular to extravascular distribution volumes of benzoate
and hippurate (
B and
H) are equivalent to
ref as defined previously (38). Exchange
between pools is determined by transfer coefficients, with the
dimension of reciprocal time, related to permeabilities and enzymatic
activities. Under saturating conditions, transfer coefficients depend
on the concentrations of unlabeled substrates or metabolites that may
vary along the flow path due to sequestration. To simplify the
analysis, however, we will neglect variations in concentrations and
treat transfer coefficients as constants (19).
The following equations relate the transfer coefficients for
hepatocellular membrane passage to membrane permeabilities
|
(A6)
|
|
(A7)
|
where P13S and P31S are the
permeability-surface area products for exchange of nonprotein-bound
benzoate across the hepatocyte cell membranes in the inward and outward
direction, respectively, VP is the sinusoidal plasma
volume, fu and ft are the fractions of
non-protein-bound benzoate in plasma and cytosol, respectively, and
Vcell is the hepatocellular volume. Similar expressions
hold for the hippurate permeabilities P25S and
P52S. The transfer coefficient k45
represents the irreversible hepatic biotransformation activity and,
when this is multiplied to the amount of intracellular precursor, yields the reaction rate.
The dose is introduced at the origin (x = 0) of the
initially tracer-free sinusoid. The system of differential equations
therefore needs to be solved with the following initial condition, at
t = 0
|
(A8)
|
where q0 is the amount of tracer
initially applied to the entrance of the sinusoid,
Fs is sinusoidal blood flow, and
is the
impulse function. All other concentrations are set to 0 at x = 0.
We use an eigenvalue method previously developed by Schwab et al.
(27, 29) for our calculations. For this purpose, the transfer coefficients are collected into the compartmental matrix A
|
(A9)
|
Because benzoate and hippurate show extracellular distribution
spaces similar to that of sucrose due to the low vascular protein
binding, the latter is used as a reference tracer. In accordance with
this, the average relative velocity along the sinusoids is defined to
be 1 for sucrose and 0 for hepatocytes. The average velocity of
benzoate in plasma contained in the combined sinusoidal and the
interstitial spaces relative to sucrose is (1 +
Suc)/(1 +
B), and that of total
hippurate is (1 +
Suc)/(1 +
H).
Analogous to what was previously developed (37, 38), we
introduce the derived parameters
|
(A10)
|
and
|
(A11)
|
such that the value of
Suc is not
needed for this evaluation. The relative velocities are collected in
the diagonal matrix W
|
(A12)
|
Concentration terms are collected in a vector, u, whose
elements are amounts per unit sucrose distribution space, normalized to
the injected dose
|
(A13)
|
With these definitions, the system of partial differential
equations can then be written concisely as
|
(A14)
|
where
' = (1 +
Suc)x/vF.
The initial conditions become
|
(A15)
|
where
|
(A16)
|
These equations are used to calculate the response of the whole
liver to an impulse input, as explained in detail elsewhere (27,
29). We used an algorithm that is based on the representation of
the impulse response of the reference indicator (labeled sucrose) by a
sum of exponentials. The observed sucrose outflow profile CSuc(t) is the convolution of the
impulse response with the catheter transport function
hcath(t)
|
(A17)
|
where F is hepatic perfusate flow and * is the
convolution operator. The parameters
i and
i are obtained by the method of moments with
exponential depression (11, 21) after numerical
deconvolution (2).
The outflow profiles of the substrate (benzoate) and metabolite
(hippurate) are then the first and second elements of the vector
|
(A18)
|
The use of a matrix as an exponent has been explained elsewhere
(27). Approximating the catheter transport
function as a piecewise polynomial of third degree
(9), each element of C(t) is a sum of terms
obtained by convolution of a piecewise polynomial with an exponential
function. An algorithm for analytical evaluation of the convolution
integrals was developed (not shown).
The transfer coefficients for influx and efflux at the basolateral
membrane, metabolism, and exchange between shallow and deep
intracellular pools were varied until an optimal simultaneous fit for
benzoate and hippurate was found. The hepatocyte influx permeability
surface area product is obtained by multiplying the value obtained for
k13 with the space of distribution of benzoate in plasma
|
(A19)
|
where F is blood flow, Hct is hematocrit,
Suc is sucrose MTT, and
cath is the MTT of the combined injection
and sample collection devices.
Similar schemes were used for the other models (Fig. 1, A
and B) and for hippurate injections, with smaller matrices A
and W, omitting the rows and columns pertaining to metabolism.
 |
APPENDIX B. EQUIVALENCE OF SUBSTRATE-ONLY MODELS |
Consider the following substitutions
|
(B1)
|
|
(B2)
|
|
(B3)
|
|
(B4)
|
or analogously
|
(B5)
|
|
(B6)
|
|
(B7)
|
|
(B8)
|
Eqs. A2 and A3 then become
|
(B9)
|
|
(B10)
|
Together with Eq. A1, these equations represent a
system with a deep intracellular pool and benzoate sequestration from
the shallow intracellular pool (Fig. 1B). The coefficients
for transfer between the plasma and shallow intracellular pools remain
unchanged, whereas those representing transfer between the shallow and
the deep intracellular pools are altered. The predicted amount in the
shallow intracellular benzoate pool is decreased. The two models are
indistinguishable from each other if only plasma
concentrations of the substrate (benzoate) are used for purposes of fitting.
 |
ACKNOWLEDGEMENTS |
This study was supported by the Medical Research Council of Canada
(MT-15657, MT-11228), the National Institutes of Health, the U.S.
Public Health Service (GM-38250), and the Fast Foundation. The
algorithm used for deconvolution was obtained from the National Simulation Resource, Department of Bioengineering, University of
Washington, Seattle, WA.
 |
FOOTNOTES |
Present address of Tsutomu Yoshimura: Department of Drug Metabolism and
Pharmacokinetics, Eisai Tsukuba Research Laboratories, Tsukuba, Ibaraki
300-2635, Japan.
Address for reprint requests and other correspondence: K. S. Pang, Faculty of Pharmacy, Univ. of Toronto, 19 Russell St., Toronto, ON M5S 2S2, Canada (E-mail:
ks.pang{at}utoronto.ca).
The costs of publication of this
article were defrayed in part by the
payment of page charges. The article
must therefore be hereby marked
"advertisement"
in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Received 7 August 2000; accepted in final form 22 January 2001.
 |
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