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11
Glucose and Short-chain
Fatty Acid Metabolism
R.P. Brockman
St. Peter’s College, Muenster, Saskatchewan, Canada
Introduction
The characteristic feature of ruminants is the fermentative nature of their
digestion. This feature of their digestive system allows them to survive on
high-fibre diets (Leng, 1970). The principal products of fermentation of dietary
fibre are short-chain fatty acids, the most important of which are acetate,
propionate and butyrate (Kristensen et al., 1998; Majdoub et al., 2003).
They account for more than 70% of the animals’ caloric intake (Bergman,
1990). Since the dietary carbohydrate is fermented, ruminant animals normally
absorb little or no dietary carbohydrate as hexose sugar (see Chapter 10), and
their glucose needs must be met by gluconeogenesis even in the fed state
(Bergman et al., 1970; Lomax and Baird, 1983). In animals consuming high
concentrate diets not all of the carbohydrate may be fermented, but even then
the absorption of hexose sugar from the gut accounts for less than one-third of
the whole-body glucose turnover (van der Walt et al., 1983). Unlike in simple-
stomached animals, in ruminants the liver is incapable of having a net uptake of
glucose (Brockman, 1983).
Metabolism of Glucose
Methodology
Any discussion of the quantitative aspects of metabolism requires a discussion
of the techniques used to obtain the information. Estimates of the rates of
production and utilization of metabolites in vivo have been made principally
using two techniques: isotope dilution and arteriovenous catheterization. Sev-
eral isotopes may be used simultaneously. In addition, isotope dilution has been
combined with the arteriovenous difference technique.
ß CAB International 2005. Quantitative Aspects of Ruminant Digestion
and Metabolism, 2nd edition (eds J. Dijkstra, J.M. Forbes and J. France)

the 2-label will show a loss of glucose, but the 6-label will not. Thus, the
14
C-
labelled isotope gives the lowest estimates of turnover rates and because of
recycling of the label underestimates the true rate of glucose production.
Glucose labelled in the 6-position with tritium gives estimates about 10% higher
and in 2 or 3 position about 15% higher than
14
C-labelled glucose (Bergman
et al., 1974). Because of the loss of label in the hexose phosphate isomerase
reaction, the latter probably overestimates the rate of turnover of glucose. The
best estimate is probably obtained with tritium label on the 6-carbon.
Double isotope techniques are useful to measure glucose turnover, sub-
strate turnover and incorporation of substrate into glucose simultaneously
(Brockman and Laarveld, 1986). Tritiated glucose may be used to measure
glucose turnover while the carbon label may be used to monitor the glucose
precursor. This approach eliminates the need to conduct separate experiments
to obtain data for two metabolites, thereby reducing inter-experimental error.
Measuring the appearance of the carbon label into glucose may assess the
fate of the metabolite. The specific radioactivities of the precursor and product
(glucose) are determined and the fraction of product produced is the ratio of
the specific radioactivities of product:precursor. A limitation of this method
is that the estimate of glucogenic potential is underestimated because the
calculation is based on blood or plasma specific radioactivity of the precursor.
292 R.P. Brockman
The intracellular activity and intracellular dilution of the isotope are ignored. For
example, crossing-over of isotopic carbons between metabolic pathways with
common intermediates, as between respiratory and gluconeogenic pathways
both of which involve oxaloacetate (see Fig. 11.1) may occur. This reduces
intracellular specific radioactivity (the exchange of oxaloacetate between the

in the gluconeogenic pool when
a glucose precursor is the source
of the label.
HO
C
COH
OH
OH
OH
OH
H
H
D
D
DC
C
C
C
D
HO
C
COH
OH
OH
OH
OPO
3
H
H
D

)-Fructose-6-P
Fig. 11.2. A schematic representation of the loss of label from the 2-position, but not the 3 and
6 positions, of glucose during the isomerase reaction. In this reaction glucose-6-phosphate is
converted to fructose-6-phosphate.
Glucose and Short-chain Fatty Acid Metabolism 293
of the rate of blood flow, gives estimates of the net organ uptake or output.
While the error of individual determinations in the blood samples may be low,
the error of the net metabolism may be high, particularly when the concentra-
tion differences across the organ are low compared to the concentration of the
respective metabolite in the vessels. This is the case for glucose across the
portal-drained viscera and liver where the arteriovenous differences are less
than 5% of the concentration in each vessel (Bergman et al., 1970). The
analytical error for the arteriovenous differences may be more than 20 times
greater than the error in determining the concentrations in each vessel.
This technique cannot distinguish between different uses within the organ.
Thus, it represents a maximum estimate of utilization for a specific purpose and
overestimates the rate of utilization. For example, the net hepatic uptake of
lactate may be three times the incorporation of lactate into glucose (Brockman
and Laarveld, 1986). In those organs that are net producers of a metabolite,
this approach does not show what has been produced and used intracellularly
and underestimates the rate of production by the organ. Thus, the true rates of
production and utilization lie somewhere between the values obtained by
isotopic and arteriovenous difference techniques.
When the two techniques are combined, utilization and production within
specific organs can be determined simultaneously. In addition to giving better
estimates of organ production the dual approach allows the determination of
metabolic interconversions within individual organs (van der Walt et al., 1983).
Glucose-producing organs and glucose production
Many studies have estimated the rates of glucose production by ruminants
under varying dietary and physiological conditions. An adult sheep (50–

genesis, and glycerol from lipolysis becomes a more important glucose precur-
sor; its contribution may reach 40% during fasting (Bergman et al., 1968).
While many studies have shown that amino acids are glucogenic, the best
estimates of glucogenic potential are the differences after everything else is
accounted for. Not surprisingly, the rate of glucose production is linearly related
to the availability of its precursors in plasma (cf. Lindsay, 1978). That does not
mean that glucose synthesis is not subject to hormonal regulation. The output
of glucose by the sheep liver and uptake of some glucose precursors have been
shown to increase markedly during exercise (Brockman, 1987) and glucagon
administration (Brockman, 1985; Brockman et al., 1975) and decrease during
insulin administration (Brockman and Laarveld, 1986).
The organs that may release glucose into the blood are liver, gut and
kidney. The liver is the most important glucose-producing organ in the rumin-
ant. It accounts for 85–90% of whole-body glucose turnover in animals on a
roughage diet (Bergman et al., 1970). Since the rate of absorption of hexose
sugar from the gut is low, the ruminant animal has little need to remove glucose
from the portal blood. Not surprisingly, the ruminant liver has little or no
glucokinase and little hexokinase (Ballard et al., 1969). Experimentally, hyper-
glycaemia with high plasma insulin concentrations did not induce a net uptake
of glucose by the liver (Brockman, 1983). This indicates that physiologically the
Table 11.1. Summary of the fraction of glucose derived from various substrates in sheep
(data from Bergman et al., 1966, 1968; Lindsay, 1978).
% of Glucose turnover % of Hepatic extraction
Metabolite Fed Fasted Pregnant Fed Fasted Pregnant
Propionate
a
Blood 27–40 ÀÀ 85–90 85–90 À
Rumen 40–50 À 34–43 n.a. n.a. n.a.
Lactate/pyruvate 15–20 13 10–15 8–15 20–30 29
Glycerol 5 15–30 18–40

(Krebs and Yoshida, 1963; Faulkner, 1980). However, the amount of propi-
onate reaching the kidney is small compared to that reaching the liver (Berg-
man and Wolff, 1971). The concentration of propionate in arterial plasma is
12–30 mM (Bergman and Wolff, 1971; Baird et al., 1980). If the kidney
extracts propionate as efficiently as the liver, the arteriovenous difference
across the kidney would be 10–25 mM, which is 20–55% of the arteriovenous
difference for glucose (Table 11.2). Thus, propionate could account for 10–
25% of net renal glucose production. That is equivalent to the glucogenic
potential of pyruvate, glycerol or alanine (Table 11.2). It seems that as a
fraction of organ production it may be equal to the contribution of propionate
to glucose synthesis in the liver (see above).
Table 11.2. Arterial concentrations, arteriovenous concentration differences (A–V) and net
renal uptake (negative values are production) of glucose, lactate, glycerol and alanine in sheep
(data from Kaufman and Bergman, 1974; Heitmann and Bergman, 1980).
Artery (mM) A–V (mM) Uptake (mmol/h)
Metabolite Fed Fasted Pregnant Fed Fasted Pregnant Fed Fasted Pregnant
Glucose 2700 2600 2900 À45 À55 À53 À2.5 À3.0 À4.3
Lactate 761 892 848 52 54 56 2.9 2.8 4.6
Pyruvate 53 76 56 7 13 3 0.4 0.7 0.3
Glycerol 67 149 41 11 13 14 0.5 0.8 1.0
Alanine 87 96 À 13 10 À 0.5 0.4 À
296 R.P. Brockman
Glucose Utilization
Not all organs and tissues use glucose at the same rate (Table 11.3). The
muscle, as reflected by the hind limb, extracts 3% of the glucose, which passes
through in blood. However, because of the muscle mass, muscle utilization may
account for 20–40% of the glucose turnover (Oddy et al., 1985). Moreover,
glucose uptake by muscle is subject to hormonal regulation (Jarrett et al.,
1976). Insulin appears to be able to increase the uptake as much as fivefold
at high concentrations (Table 11.3; Jarrett et al., 1974; Hay et al., 1984;

a
6.6 1.60 2.28 0.25 0.35
Tail fat pad 3.7
b
2.2 0.39 0.83 0.11 0.38
Uterus 3.3 3.3 1.15 1.19 0.35 0.36
Mammary gland 3.1 3.3 0.72 0.70 0.23 0.22
a
These values are from the perfused fat pad.
b
These values are from the intact animal.
Glucose and Short-chain Fatty Acid Metabolism 297
yield, in other words according to the organs’ needs. Studies in sheep, which
were about 20 weeks pregnant, showed a strong correlation between blood
glucose concentration and uterine uptake of glucose (Leury et al., 1990). As
the blood glucose concentrations decreased during underfeeding (from
2.65 + 0.10 to 1.42 + 0.12 mM), uterine uptake of glucose went from
15.0 + 1.6 to 7.8 + 0.6 mmol/h.
The sheep fetus relies on placental transport to meet about half of its glucose
needs (Hodgson et al., 1981). The glucose uptake by the pregnant uterus is
greater than the glucose utilization by the fetus. The glucose used by the fetus
accounts for 28% of the glucose taken up by the uterus (Meschia et al., 1980).
Another 20% of glucose removed by the uterus is taken up by the fetus as lactate.
Thus, the fetus uses about half the glucose, which is removed by the uterus from
the blood. This is discussed in greater detail in Chapter 20.
The major use of glucose in the mammary gland is for the production of
lactose. This accounts for 50–60% of the glucose uptake by the bovine mam-
mary gland (Bickerstaffe et al., 1974; Baird et al., 1983). In sheep, glucose
uptake by the mammary gland is equivalent to 70% of lactose in the milk (Oddy
et al., 1985). The fractional extraction of glucose by the mammary gland

pregnancy and lactation. The uteroplacental unit is a net producer of lactate,
whereas the mammary gland is a net user of lactate. In pregnant sheep
extrahepatic production of lactate may be 75% of the whole-body turnover
compared to about 55% of production by the portal-drained viscera in non-
pregnant animals (van der Walt et al., 1983). Lactate released into the maternal
blood may account for 15–20% of the glucose utilization by the uteroplacental
unit (Meschia et al., 1980); an equivalent amount of lactate goes to the fetus.
Thus, lactate production may account for one-third of the glucose taken up by
the uterus, another third is taken up by the fetus as glucose.
The net uptake of lactate by the mammary gland of lactating animals is
equal to about 20% of its glucose uptake on a molar basis (Oddy et al., 1985).
The liver uses more of the lactate, and is normally a net user of lactate (Table
11.4). About one-third of the lactate is removed by the liver and appears as
glucose in fasted sheep (Brockman and Laarveld, 1986). The extraction of
lactate by the liver varies with the dietary intake or physiological status (Brock-
man and Laarveld, 1986; Brockman, 1987) and is subject to hormonal regu-
lation, the most important of which is insulin. While in the pregnant animal
75% of the lactate is used by the liver, presumably for gluconeogenesis, in the
lactating animal about 40% of lactate turnover is used by the liver. The effects
observed by changes in dietary status may also be influenced by metabolites.
Propionate, for example, appears to reduce the hepatic removal of lactate
independent of any effect of hormones (Baird et al., 1980). It seems that
when propionate is available, which means during feasting, the liver uses
propionate preferentially as a substrate for glucose production, thereby sparing
lactate and other glucose precursors for other uses.
Table 11.4. Insulin concentrations, lactate extraction by the liver and net hepatic uptake
(NHU) and turnover rate (TR) of lactate in sheep under various physiological states and during
glucagon and insulin infusion (data from van der Walt et al., 1983; Brockman and Laarveld,
1986; R.P. Brockman, unpublished results).
Status

amounts of lactate are used by the mammary gland (Oddy et al., 1985) and
lactate accounts for only about 6% of glucose synthesis.
Metabolism of Short-chain Fatty Acids
Propionate
A sheep on a maintenance diet of 800 g of lucerne pellets per day produces
30–45 mmol propionate per hour in its rumen (Judson and Leng, 1973a;
Steel and Leng, 1973b). Of this, 18–24 mmol/h is absorbed (Bergman et al.,
1966; Bergman and Wolff, 1971; Noziere et al., 2000). Since absorption
accounts for only 40–60% of ruminal production, a substantial amount of
ruminal propionate is metabolized or converted to other metabolites before
and/or during absorption. In studies with washed reticulorumens almost all the
propionate, which was infused into the rumen, was recovered in the portal
blood (Kristensen et al., 2000; Kristensen and Harmon, 2004), indicating
that propionate is not metabolized to a significant degree by the ruminal
epithelium during absorption. This is consistent with the results of earlier
studies in cattle that indicated that little propionate is metabolized during
absorption (Weigland et al., 1972). Thus, half of the ruminal propionate is
metabolized within the gut.
Table 11.5. Summary of the interconversions of lactate and glucose in sheep (data from
Reilly and Chandrasena, 1978; van der Walt et al., 1983; Brockman and Laarveld, 1986).
% Glucose
from lactate
% Lactate
to glucose
% Lactate
from glucose
% Glucose
to lactate
Recycling
(%)

cose production and the proportion of glucose derived from propionate with-
out changing the proportion of propionate appearing in glucose (Bergman
et al., 1966). In studies in cows the intravenous infusion of propionate at rates
which doubled the entry rate of propionate only marginally reduced the hepatic
extraction of propionate, from 80–85% to 70–75%, while the hepatic uptake
of propionate doubled (Baird et al., 1980). Similar results were obtained in
sheep during intraruminal infusion of propionate at 58 mmol/h (Berthelot
et al., 2002). Thirdly, the hepatic extraction efficiency and incorporation of
propionate into glucose do not appear to be influenced by glucoregulatory
hormones, e.g. insulin (Baird et al., 1980; Brockman, 1990). Finally, glucose
infusion sufficient to cause hyperglycaemia and hyperinsulinaemia in cows did
not appear to affect the net hepatic uptake of propionate while the hepatic
output of glucose decreased (Baird et al., 1980). Another study showed that
this occurred without a change in the amount of propionate converted to
glucose (Amaral et al., 1990).
Propionate may influence the utilization of other substrates for glucose
synthesis. First, propionate is a known substrate for lactate production (Leng
and Annison, 1963), with perhaps half of the blood lactate being derived from
ruminal propionate (Leng et al., 1967). Secondly, the infusion of exogenous
propionate in cows was associated with a decrease in the hepatic extraction of
lactate in the absence of changes in plasma insulin concentrations (Baird et al.,
1980). In studies where propionate was infused at 40 mmol/h into a mesen-
teric vein in fasted sheep, whole-body lactate production went from 16 + 1to
29 + 3 mmol/h while hepatic production of lactate increased less than
Glucose and Short-chain Fatty Acid Metabolism 301
5 mmol/h (1.3 + 0.7 vs. 5.9 + 1.6 mmol/h) (R.P. Brockman, unpublished
data). Thus, the change in hepatic production accounted for less than half of
the increase in whole-body production of lactate during propionate infusion.
The relationship between lactate and propionate and the differential hor-
monal response between lactate/pyruvate and propionate in the liver, are

CO
2
CH
3
CH
2
C
O
O
PC
O

O
O

C
C
Pyruvate
Oxaloacetate
Propionate
PEP Glucose
PEPCK
Fig. 11.3. A summary of the entry of propionate and pyruvate to the pyruvate carboxylase (PC)
and phosphoenolpyruvate carboxykinase (PEPCK) reactions in gluconeogenesis.
302 R.P. Brockman
Acetate
Production
Quantitatively, acetate is the most important short-chain fatty acid in the
ruminant. About 70% of the intraruminal turnover or production of acetate
can be accounted for by portal absorption of acetate (Bergman and Wolff,

utilization rate by the organ.
Utilization
Acetate is metabolized rapidly by the body. Estimates of acetate’s half-life range
from 3 to 4 min (Annison and Lindsay, 1961) to 13 min (Jarrett et al., 1974).
Acetate extraction by the hind limb is 50–60%, where the net uptake accounts
for 20% of the oxygen uptake (Jarrett et al., 1976). Acetate extraction is lower
during fasting and exercise when ketone bodies and long-chain free fatty acids
make up the major energy sources (Jarrett et al., 1976). At these times acetate
extraction efficiency may be as low as 15%.
Glucose and Short-chain Fatty Acid Metabolism 303
The brain also removes acetate from the blood. The net uptake may
account for about 3% of acetate turnover, about 3 mmol/h (Pell and Bergman,
1983). On a molar basis this is equivalent to about 10% of the glucose uptake
by the brain, so that the brain is not a major user of acetate. In lactating animals
up to 20% of the acetate turnover is accounted for by mammary gland utiliza-
tion (Pethick and Lindsay, 1982; King et al., 1985). It removes about half the
acetate presented to it (Bickerstaffe et al., 1974; Laarveld et al., 1985), and
17–29% of the organ’s fatty acid synthesis is attributable to acetate (King et al.,
1985). Obviously, the absolute amount removed is a function of milk yield.
Acetate turnover is reduced during insulin deficiency (Jarrett et al., 1974)
and the uptake by the hind limb is increased by insulin (Table 11.6). In
untreated diabetic sheep the extraction of acetate by the hind limb may be as
low as 5% (Knowles et al., 1974), compared to 50–60% when insulin is
available as in normal animals and treated diabetics (Knowles et al., 1974;
Pethick et al., 1981). In contrast, the uptake of acetate by the mammary gland
is not influenced by insulin (Laarveld et al., 1985). Typically insulin concentra-
tions are lower in lactating animals than in non-lactating animals and the
difference in the responses to insulin allows the body to direct acetate to the
mammary gland by reducing uptake by insulin-responsive organs.
Acetate is a major source of energy for the ruminant. About 25% of

olized in the ruminal epithelium during absorption (Kristensen et al., 2000;
Kristensen and Harmon, 2004). Only about one quarter of the butyrate which
was infused into a washed reticulorumen preparation was recovered in the
portal blood (Kristensen et al., 2000).
During absorption butyrate is largely converted to ketone bodies in the
ruminal epithelium (Emmanuel, 1980). In sheep on a maintenance diet the net
production of ketone bodies by the portal-drained viscera has been reported to
be 15–20 mmol/h (Katz and Bergman, 1969), although estimates of net portal
production of ketone bodies as low as 3 mmol/h have been reported (Noziere
et al., 2000; Majdoub et al., 2003). Studies with cattle suggest that the net
production of ketone bodies by the portal-drained viscera may be two to three
times more than the net portal production of butyrate (Lomax and Baird,
1983; Lozano et al., 2000). Kristensen et al. (2000) cited unpublished studies
in which 40% of the intraruminally infused butyrate was accounted for by the
release of 3-hydroxybutyrate into the portal-drained viscera. Ketone body
production by the portal-drained viscera decreases during fasting, when butyr-
ate production is decreased (Noziere et al., 2000).
Studies in sheep indicate that more than 80% of the butyrate that is
absorbed from the gut is removed in a single pass through the liver (Bergman
and Wolff, 1971). It may be lower in cattle where hepatic extraction of butyrate
was about two-thirds (Lozano et al., 2000). Only 20–33% is used by the
peripheral tissues. Thus, while the sheep hind limb appears to be able to remove
about one-third of the butyrate presented to it (Majdoub et al., 2003), quanti-
tatively utilization by muscle is small. In contrast, the liver is a net producer of
ketone bodies (Katz and Bergman, 1969; Majdoub et al., 2003) and appears to
be able to use butyrate as a substrate (Annison et al., 1963b). It appears that at
least in cattle the production of ketone bodies by the liver may exceed hepatic
uptake of butyrate in fed animals (Lozano et al., 2000). Ketone body produc-
tion by the liver is greatest when free fatty acids rather than butyrate are
available as substrates (Katz and Bergman, 1969). Hepatic ketone body pro-

about 0.25 mmol/h in the same animals. Studies with the washed reticuloru-
men preparation indicated that net portal production may account for about
one-third of the ruminal production of valerate and half that of isovalerate
(Kristensen et al., 2000; Kristensen and Harmon, 2004), which suggests that
there is substantial metabolism of these metabolites during absorption. All of
the valerate and about 85% of the isovalerate that is absorbed into the portal
blood is removed by the liver so that essentially little or no valerate and
isovalerate pass through the liver into the general circulation (Kristensen and
Harmon, 2004).
Conclusions
Due to the fermentative nature of their digestion, ruminant animals normally
absorb little dietary carbohydrate as hexose sugar, and short-chain fatty acids
account for up to 70% of their energy needs. Acetate is the major substrate for
lipogenesis and oxidation. Propionate is a major substrate for gluconeogenesis.
The fed animal appears to use propionate as the major glucose precursor,
thereby sparing other glucose precursors, such as amino acids, for synthetic
functions in other parts of the body. When propionate is less abundant, lactate,
glycerol from fat and amino acids from extrahepatic tissues are used to a
greater extent to produce glucose. Similarly, during fasting fatty acids from
lipolysis may replace butyrate and acetate as energy sources.
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1
Division of Nutritional Sciences, School of Biosciences, University of
Nottingham, Sutton Bonington Campus, Loughborough, Leicestershire LE12
5RD, UK;
2
Department of Animal Sciences, The Ohio State University,
OARDC, 1680 Madison Avenue, Wooster, OH 44691-4096, USA
Introduction
Viscera whose blood supply drains into the portal vein include most of the
alimentary tract, the spleen and the pancreas. In addition, mesenteric and
omental fat depots, which can be substantial, contribute portal venous blood.
Since it is the large expansion of the stomach that characterizes ruminants, it is
understandable that special attention is devoted to metabolism in this region.
Many metabolic peculiarities of ruminants stem from this. Most blood flowing
into the liver is portal and since the metabolism of the liver is linked with that of
the gastrointestinal (GI) tract, some features of its metabolism are also included.
This chapter emphasizes the quantification of nutrient and hormonal flows
in the splanchnic region. Several techniques have been used to study ruminant
metabolism. Among the most recent techniques available for use in intact
animals is that of nuclear magnetic resonance (NMR), e.g. glycogen metabolism
in human liver (Morris et al., 1994). However, the high cost of equipment for
this has rendered it unavailable for large animals such as sheep, goats and
cattle. Thus only the arteriovenous (A–V) difference technique is considered
here. This involves implantation (under general anaesthesia) of plastic catheters
in an artery and in the mesenteric, portal and hepatic veins (see Fig. 12.1). Any
artery may be used since the concentration of metabolites is virtually the same
in all arteries. After adequate recovery from the operation, sampling of blood
through these catheters together with some means of estimating blood flow is
used to estimate net inflow/outflow (typically referred to as ‘net flux’) of
metabolites across the whole of the portal-drained viscera (PDV) and liver. It

m
> A
m
net flux of
m is positive (there is net release or absorption into venous blood). If
P
m
< A
m
net flux of m is negative (there is net uptake or removal from arterial
blood).
RUMEN
Small
intestine
Large
intestine
and caecum
Mesenteric
c
Gastro-
splenic
c
Gastro
duodenal
v
Splenic
v
Hepatic
c
Vena

E
am
) (12:3)
Fractional uptake of isotopic m ¼ Eq:(12:2)=Eq:(12:3)
¼ [(P
m
E
pm
)=(A
m
E
am
)] À 1 (12:4)
where E
pm
¼ enrichment (APE ¼ atom per cent excess) of m in portal vein;
and E
am
¼ enrichment of m in artery.
The true (gross) uptake ¼ input of m
:
Eq: (12:4)
¼ PBFA
m
[(P
m
E
pm
=A
m

E
pm
)=(A
m
E
am
)]
(12:6)
Oxidation
Measurement of oxidation of m by measuring production of
3
Hor
2
H across
the GI tract is impracticable because of the large flux of water across it. If
13
C-m
is used, letting P
CO
2
and E
P
CO
2
be the concentration and enrichment of CO
2
in portal and A
CO
2
, E

)PBF (12:8)
To express the fraction of CO
2
derived from m this is divided by the enrichment
of precursor m. This requires an assumption as to the enrichment of m in the
tissues being studied. It is usually taken as the venous-specific activity although
the value is perhaps more likely to lie between arterial and venous. For further
discussion of this point, see also France et al. (1999).
Metabolism of the Portal-drained Viscera and Liver 313
Fraction of CO
2
derived from
m ¼ [(P
CO
2
E
P
CO
2
À A
CO
2
E
A
CO
2
)PBF]=E
pm
(12:9)
The fraction of m uptake oxidized by the site studied is given as Eq. (12.8)/

and R
20
can be determined experi-
mentally from glucose and lactate concentrations and enrichments and
3
Glucose
sink
R
31
R
13
R
12
R
21
R
24
R
02
R
42
1
Glucose
2
Lactate
4
Lactate
sink
(a) (b)
R

21
þ R
31
¼ R
10
þ R
12
þ R
13
) and with
13
C-glucose infused, isotope
balance for the glucose and lactate pools supplies a further two equations.
Thus where A and V represent the arterial and venous input (and assuming
the latter reflects the tissue pools) we have:
AE
gluc
R
01
þ VE
lact
R
21
¼ (R
13
þ R
12
þ R
10
)VE

that gluconeogenesis from lactate does not occur in the GI which is almost
certainly true. With this simplified model it is not necessary to use two labelled
compounds since there are only three unknown rates; the two carbon balance
equations, plus the two for isotope balance obtained from use with
13
C-glucose
are more than sufficient to solve for the unknowns. Indeed it is possible to
solve without matrix analysis since first R
12
may be obtained from isotope
balance (R
12
þ R
02
¼ R
20
); then R
13
¼ R
01
À (R
10
þ R
12
), since R
31
does not
contribute label. Finally R
31
is obtained from carbon balance.

)=A
m
E
am
(12:12)
A different isotope (I
2
) of the amino acid is also infused into the duodenum (or
the same isotope could be infused on a separate occasion), and its fractional
Metabolism of the Portal-drained Viscera and Liver 315


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