A surrogate measure of whole body leucine transport across the
cell membrane
Roman
Hovorka1,
Paul V.
Carroll2,
Ian J.
Gowrie1,
Nicola C.
Jackson2,
David L.
Russell-Jones2, and
A. Margot
Umpleby2
1 Metabolic Modelling Group,
Centre for Measurement and Information in Medicine, City
University, London EC1V 0HB; and
2 Department of Endocrinology,
St. Thomas' Hospital, London SE1 7EH, United Kingdom
 |
ABSTRACT |
Based on a mass-balance model, a surrogate
measure of the whole body leucine transport into and out of cells under
steady-state conditions was calculated as u/
TTR, where u is the
infusion rate of (stable label) leucine tracer and
TTR is the
difference between the tracer-to-tracee ratio of extracellular and
intracellular leucine. The approach was evaluated in ten healthy
subjects [8 males and 2 females; age, 31 ± 9 (SD) yr; body mass
index, 24.0 ± 1.6 kg/m2] who
received a primed (7.58 µmol/kg) constant intravenous infusion (7.58 µmol · kg
1 · h
1)
of
L-[1-13C]leucine
over 180 min (7 subjects) or 240 min (3 subjects). Five subjects were
studied on two occasions
1 wk apart to assess reproducibility. Blood
samples taken during the last 30 min of the leucine infusion were used
to determine plasma leucine concentration (129 ± 35 µmol/l), TTR
of leucine (9.0 ± 1.5%), and TTR of
-ketoisocaproic acid (6.7 ± 0.8%). The latter TTR was taken as the measure of the free
intracellular leucine TTR. The whole body inward and outward transport
was 6.66 ± 3.82 µmol · kg
1 · min
1;
the rate of leucine appearance due to proteolysis was 1.93 ± 0.24 µmol · kg
1 · min
1.
A positive linear relationship between the inward transport and plasma
leucine was observed (P < 0.01),
indicating the presence of the mass effect of leucine on its own
transport. The transport was highly variable between subjects
(between-subject coefficient of variation 57%) but reproducible
(within-subject coefficient of variation 17%). We conclude that
reproducible estimates of whole body transport of leucine across the
cell membrane can be obtained under steady-state conditions with
existing experimental and analytical procedures.
mathematical model; stable-label isotope tracer; steady-state
conditions; reproducibility
 |
INTRODUCTION |
AMINO ACIDS enter mammalian cells by employing several
transport systems, with system L being
the main transport system responsible for transport of leucine (10), an
essential amino acid. Activities of these systems are affected by the
amino acid availability, and some, but not system
L, are also hormonally regulated (23).
A method has been developed to measure amino acid transmembrane
transport in an organ and/or tissue under in vivo conditions by
Biolo et al. (4) to complement in vitro investigations (27), providing
novel insights into amino acid transport under, for example,
hyperinsulinemia (6) or resistance exercise (7). The
method employs as its principal experimental tool an arteriovenous balance technique of stable-label amino acid tracers and is therefore experimentally nontrivial.
The use of
-ketoisocaproic acid (
-KIC) plasma enrichment as a
marker of intracellular free leucine enrichment and thus tRNA precursor
pool enrichment has long been advocated (22) and regularly employed to
obtain estimates of whole body leucine turnover rates (19, 21). Leucine
is converted to
-KIC intracellularly by reversible
transamination, and the other routes of leucine
intracellular appearance are via transmembrane transport and proteolysis.
Matthews (17) suggested that whole body leucine transmembrane transport
can be quantified by employing the difference between the intracellular
and extracellular leucine enrichment after an infusion of leucine
tracer. Informal derivation of the principles of the method and
approximate calculations with "average" data were carried out.
However, the performance of the method with individual data was not
assessed. The present study describes, in detail, the principles of
this approach and its application in normal subjects under fasting
conditions. The intrasubject variability (reproducibility) of this
surrogate measure of leucine transport was also evaluated by repeating
the study in one-half of the subjects.
 |
METHODS |
Model of leucine transport under steady-state
conditions. The conceptual model of unlabeled and
labeled leucine transport across the cell membrane during a constant
infusion of leucine tracer is shown in Fig.
1.

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Fig. 1.
Conceptual model of leucine kinetics during a constant infusion of
leucine tracer (u) under fasting conditions shows inward transport of
unlabeled leucine (Fin) and
labeled leucine (fin), outward
transport (Fout and
fout), net leucine disposal
(Rd and
rd; both protein synthesis and
leucine oxidation are included), and net leucine appearance
(Ra; protein breakdown).
Tracer-to-tracee ratios of extracellular leucine and intracellular
leucine are denoted by ze and
zi. There is no intracellular
appearance of leucine tracer from protein breakdown based on the
assumption that tracer is not recycled.
|
|
At steady-state conditions when there is no appearance of leucine due
to food intake, the total amount of unlabeled leucine (leucine
originating from endogenous supplies) transported to the extracellular
fluid from inside the cells
(Fout) is equal to the total
amount transported in the opposite direction
(Fin); a similar zero mass
balance is maintained for labeled leucine (leucine originating from the
tracer infusion) with the inclusion of the labeled leucine infusion (u)
|
(1)
|
|
(2)
|
where
fin and
fout are the inward and outward
transport of labeled leucine across the cell membrane, respectively.
The tracer-to-tracee ratio of leucine (TTR; the ratio of labeled to
unlabeled leucine) in the extracellular fluid
(ze) is assumed identical to TTR
of plasma leucine (zL). The
intracellular TTR of leucine
(zi) is assumed equal to TTR of
-KIC in plasma (zK). Under
the assumption of tracer indistinguishability, the ratios of labeled to
unlabeled leucine leaving and entering cells are related to these two
TTRs
|
(3)
|
|
(4)
|
Equations 3 and 4 result from the assumption of
tracer indistinguishability. With the assumption of an ideally mixed
extracellular compartment, which consists of unlabeled and labeled
leucine, the transport fluxes of unlabeled and labeled leucine from the extracellular to the intracellular pools (inward transport) will be
proportional to the availability of these species in the extracellular pool. Thus the ratio of these fluxes will be identical to the ratio of
the amount of these species in the extracellular pool (TTR of the
extracellular pool). Similarly, the outward fluxes will be proportional
to the availability of the unlabeled and labeled leucine in the
intracellular pool (TTR of the intracellular pool).
Solving Eqs.
1-4
for Fin with simple algebraic
manipulations (4 equations with 4 unknowns:
Fin,
Fout,
fin, and
fout) we obtain that
|
(5)
|
The
formula given by Eq. 5 calculates leucine inward
transport from the infusion rate of labeled leucine and the difference of two TTRs. It is independent from plasma leucine concentration.
Subjects and experimental protocol.
Ten healthy subjects [8 males and 2 females; age, 31 ± 9 (SD) yr;
body mass index, 24.0 ± 1.6 kg/m2] were studied. The
experiments were approved by the Ethics Committee, Guy's & St.
Thomas' National Health Service Trust, and all subjects provided written informed consent. Five subjects were studied on two
occasions
1 wk apart.
Data were obtained from experiments originally designed for other
purposes. This resulted in details of gas chromatography-mass spectrometry (GC-MS) analysis to be different in five subjects who
participated in the reproducibility study. All other procedures, including data processing, were identical. It was unjustified to repeat the experiments because of ethical and resource reasons when the data were already available.
At 8:00 AM after an overnight fast, a cannula (Venflon, Vigo,
Helsinborg, Sweden) was inserted retrogradely into a hand vein under
local anesthesia, and two basal blood samples were taken. The hand was
heated to obtain arterialized samples. A primed (7.58 µmol/kg)
constant intravenous infusion (7.58 µmol · kg
1 · h
1)
of
L-[1-13C]leucine
(99% atom percent excess; MassTrace, Woburn,
MA) was given over a period of 180 min (7 subjects) or 240 min (3 subjects; to test informally the attainment of the steady-state
conditions within 3 h, data not shown). Four to six samples
approximately equidistantly spaced were taken during the last 30 min of
the leucine infusion to assess the steady state and limit the effect of
the measurement error on the results. The samples were analyzed for the
enrichment of
-KIC and leucine and the plasma leucine concentration.
Analytical methods. Plasma
L-[1-13C]leucine
was measured as the
t-butyldimethylsilyl derivative under
selected ion monitoring by GC (Hewlett-Packard 5890 series II, Woking,
UK)-MS (subjects 1-5:
VG Trio II, Biotech, Cheshire, UK;
subjects
6-10:
Hewlett-Packard 5971A MSD) monitoring the ions 302 and 303 representing the [m-57] natural abundance and (m-57)+1
enriched fragments, respectively. Leucine concentration was measured
with an internal standard of norleucine. Plasma
-[1-13C]KIC
enrichment was measured as (A:
subjects
1-5)
quinoxalinol-trimethylsilyl derivative and
(B:
subjects
6-10)
t-butyldimethylsilyl derivative under
selected ion monitoring by GC (Hewlett-Packard 5890)-MS (Hewlett-Packard 5971A MSD) monitoring
(A) the ions 232 and 233 representing the [m-42] natural
abundance and [m-42]+1 enriched fragments and (B) the ions 259 and
260 representing the
[m-57] natural abundance
and [m-57]+1 enriched
fragments, respectively.
Data analysis. TTRs of leucine and
-KIC were calculated from raw peak isotope ratios of individual
samples on the basis of work by Cobelli et al. (12) to
correct for spectra overlap (15, 20). Leucine appearance
due to proteolysis Ra was
calculated with the standard formula
|
(6)
|
The
derivation of Eq.
6 can be also obtained from Fig. 1
with a mass balance analysis and by realizing that because of
steady-state conditions the following equalities hold
Inward
transport of leucine Fin was
calculated with Eq.
5.
The amount of plasma cleared of leucine due to leucine inward
transport [relative transport rate (RTR)] was defined
as
|
(7)
|
where
L is plasma leucine concentration. RTR normalizes the inward transport
by plasma leucine and removes the potential first-order effect of
leucine (mass effect) on its own transport. In the presence of
the mass effect, RTR can be used more effectively to compare
leucine transport between subjects with different plasma leucine
concentrations. The values zL,
zK, and L used in
Eqs. 5-7
were obtained by averaging TTRs of leucine, TTRs of
-KIC, and plasma
leucine concentration during the last 30 min of the leucine infusion, respectively.
Statistical analysis. The
reproducibility was assessed from indexes measured in five subjects on
two separate occasions. In each case, indexes were analyzed by ANOVA,
allowing for effects due to subject. The method calculates the total
variance that includes components due to intersubject and intrasubject
variance (1). This gave an estimate of the intrasubject subject
reproducibility of the duplicate responses [within-subject
coefficient of variation (CV) and within-subject variation as % of
total variation]. Mean values from two occasions were used in the
remaining calculations and for visualization purposes. For
visualization purposes, three subjects who received a 4-h infusion were
treated as if receiving a 3-h infusion. The values are represented as
means ± SD unless stated otherwise.
 |
RESULTS |
Plasma leucine increased from a prestudy level of 111 ± 32 to 125 ± 40 µmol/l at the end of the study
(P < 0.05, paired
t-test). However, during the final 30 min of the
L-[1-13C]leucine
infusion, no significant alteration was detected in plasma leucine,
leucine TTR, and
-KIC TTR (see Fig. 2).

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Fig. 2.
Plasma leucine (top) and
(bottom) tracer-to-tracee ratio of
leucine ( ) and -ketoisocaproic acid ( ) during a constant 7.58 µmol · kg 1 · h 1
infusion of
L-[1-13C]leucine.
Values are means ± SD (n = 10).
|
|
TTRs of
-KIC and leucine and the transport indexes are detailed in
Table 1.
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Table 1.
Leucine inward transport, relative transport rate of leucine, leucine
appearance, plasma concentration of leucine, TTR of
-KIC, and TTR of leucine after a 3- or 4-h
L-[1-13C]leucine infusion
|
|
A positive linear relationship between leucine transport and plasma
leucine was observed (y = 0.086x
4.450, P < 0.01; Fig. 3).

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Fig. 3.
Linear relationship between plasma leucine and leucine inward transport
under fasting conditions.
|
|
Results of the reproducibility analysis are given in Table
2. Small absolute differences in
within-subjects CV were observed; plasma leucine demonstrated the
lowest, and relative transport rate the highest within-subject CV.
Large differences in within-subject variation were present.
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Table 2.
Reproducibility of leucine inward transport, relative transport rate of
leucine, leucine appearance, and plasma concentration of leucine after
L-[1-13C]leucine infusion
|
|
 |
DISCUSSION |
The present study provides novel insights about a surrogate measure of
the whole body leucine transport across the cell membrane during a
constant
L-[1-13C]leucine
infusion with a method originally proposed by Matthews (17). The
results demonstrate that a reproducible estimate of whole body
transport can be obtained with the use of existing techniques and
measurement procedures.
The approach is of potential value in the assessment of abnormalities
and control of transport of leucine, an essential amino acid, across
the cell membrane in normal and disease states. Although our
understanding of the role and the regulation of amino acid transporters
is increasing, as yet we have no reliable, applicable method for the
assessment of in vivo transporter activity, and the proposed method has
the potential to complement in vitro techniques.
The method does not introduce new assumptions. It relies on the
existing assumptions of tracer indistinguishability and that TTR of
-KIC in plasma is identical to intracellular TTR of leucine. Ever
since the original proposal that during leucine infusion,
-KIC is a
good surrogate of the true protein precursor labeling (22, 26),
-KIC
enrichment (or specific activity in the case of radioactive leucine
tracer; i.e., the reciprocal pool model) has been used in numerous
studies to measure protein breakdown, synthesis, and oxidation (19).
Experimental evidence suggests that in human skeletal muscle, plasma
-KIC enrichment overestimates free intracellular leucine enrichment
by ~20-30% (2, 9, 25), although in dogs identical enrichments
were observed in all tissues except in the kidney (14). The difference
could be attributed to tissue enrichment heterogeneity (differences in
protein synthesis and protein breakdown across tissues). During
fasting, a net flow of essential amino acids from skeletal muscle to
the gut is present, enabling the maintenance of the gut protein
synthesis (13, 18). Therefore, lower enrichment levels of leucine are
expected to be present in the muscle (higher appearance of
intracellular unlabeled leucine from protein breakdown) than in the
gut. Plasma
-KIC enrichment results from mixing (averaging) these
different enrichments, overestimating muscle and underestimating gut
intracellular leucine enrichments.
A recent study by Ljungqvist et al. (16) studied in great detail the
relationship between precursor enrichment in muscle leucyl-tRNA, tissue
fluid, and plasma in the vastus lateralis muscle. The valuable results
suggest functional heterogeneity in intracellular leucine pools, e.g.,
preferential use of extracellular leucine compared with intracellular
leucine (due to protein breakdown) for leucine deamination. It was
suggested that tissue fluid leucine enrichment is the best precursor of
the true tRNA enrichment. However, when whole body turnover rates are
estimated and the arteriovenous balance technique is not used, the
tissue fluid enrichment such as that measured in the muscle tissue will
not be identical to enrichment in all tissues because of tissue
heterogeneity, which is also confirmed by Ljungqvist et al. on the
basis of differences between tissue fluid
-KIC enrichment and plasma
-KIC enrichment. Using the leucine tissue fluid enrichment in the
(primary) model would result in an overestimation of whole body leucine
turnover (biased toward muscle tissue turnover rates). Similar
reasoning applies to the measurement of a surrogate measure of leucine
transport. The lack of difference in enrichment between leucyl-tRNA and
tissue fluid leucine during fasting is concordant with the presence of a net flow of leucine from the muscle to the gut. However, the lack of
the difference in these enrichments during mixed-meal feeding is
difficult to explain given the expected net incorporation of leucine
into proteins during the absorptive state.
Differences in leucine transport across tissues are likely to be
present. It would be valuable to establish, on both a theoretical and a
practical basis, the physiological meaning of the transport rate
calculated by the proposed model under the condition of tissue heterogeneity. Ideally, the calculated value should represent the sum
of transport rates in all body tissues. Our theoretical analysis given
in the APPENDIX indicates a condition
under which this assertion would hold. The condition states that it is
sufficient for the relative outward transport of
-KIC to be
identical to relative outward transport of leucine across tissues. If
relative outward transport of
-KIC differs from that of leucine,
plasma enrichment of
-KIC is then biased toward intracellular
leucine enrichment of tissues with higher relative outward transport of
-KIC. It is currently unclear whether this essential assumption is
satisfied because of the lack of experimental data. Further studies and
a different experimental design are needed.
It is clear that the presented method is unable to discriminate between
transmembrane transport in individual tissues. It is also unable to
detect changes in transport rates due to treatment and/or
stimuli when simultaneous changes in tissues result in a net zero
transport difference. In this respect, the method has similar drawbacks to the primary or reciprocal model in the measurement of whole body leucine turnover. The potential of the method is to
assess changes in transmembrane transport on the whole body level and
to suggest further investigations that are more detailed.
A method to measure the bidirectional transmembrane transport of amino
acids in muscle has been developed by Biolo and colleagues (4, 5). The
method employs the traditional arteriovenous balance technique with or
without the muscle biopsy and estimates the inward and outward
transmembrane transport with a three-compartment model under
steady-state conditions. The method has been employed successfully
to assess the effect of resistance exercise (7) and
hyperinsulinemia (6) on transmembrane transport of amino acids in human skeletal muscle. The method by Biolo and co-workers is
superior to the presented method because it allows transmembrane transport of a range of amino acids to be measured. However, in comparison, it is experimentally more complicated and confined to the
measurements in a particular organ or tissue.
Currently, no other method exists that would provide a similar whole
body measurement, and therefore no comparison with independent measurements can be made. It is therefore currently impossible to
evaluate the accuracy of the method. However, the method is expected to
provide a useful surrogate measure of leucine transport benefiting (and
also suffering) from the same "averaging" properties as the
standard measures of whole body leucine turnover derived by the
primary, reciprocal, or other whole body models (11, 19, 21). The
benefits of the surrogate measures were confirmed in various clinical
studies, although the drive for more accurate, tissue-specific measures
is clearly present (3). It is natural to expect that a similar trend
regarding the (surrogate) measures of leucine transport will follow.
The present study suggests that the amount of leucine transported
across the cell membrane is about three times higher than intracellular
appearance due to protein breakdown. An identical value was calculated
by Matthews (17) with average data. A nearly identical ratio was found
in the human small intestine (8). The ratio was reversed in the human
skeletal muscle (8), indicating tissue heterogeneity.
The higher transport rate compared with leucine incorporation into
protein and leucine appearance due to protein breakdown suggests that
the transport is not the rate-limiting step of leucine metabolism. The
supply of intracellular leucine from the extracellular fluid is rapid
compared with the speed of intracellular metabolic processes. The
intracellular metabolic processes are therefore well supplied by
leucine, subject to the availability of leucine in the extracellular
space (interstitial fluid).
The reproducibility assessment employs two critical measures. The
within-subject CV indicates the expected variability when replicate
measurements are made in one subject. The within-subject variation as a
percentage of total variation puts the within-subject variability
within the context of the overall variability. For a variable to be
highly reproducible and able to discriminate between subjects, both
measures should attain a low value (say <20%).
True physiological variation but also measurement errors contribute to
the calculations of the intersubject and also intrasubject variation.
Because of the form of the calculation formulas, the measurement error
increases to a greater extent the variability of leucine transport than
the variability of leucine appearance. Our calculations based on the
error propagation method and the Taylor series expansion of
Eqs.
5 and 6 suggest that the variation of
leucine transport is increased by ~18%, whereas the variability of
leucine appearance is increased by ~3% due to the measurement error.
The calculations (details not shown) assume a 5% measurement error
associated with individual measurements of
zL and
zK and average values of
zL and
zK as given in Table 1.
The results of the reproducibility analysis indicate that leucine
transport is highly reproducible in healthy subjects, especially when
consideration is taken of the variability due to measurement error.
Relative transport rate was also reproducible, although to a slightly
lesser extent. A striking comparison can be made between intrasubject
and intersubject variability of transport and leucine appearance. When
expressed as a CV, the intersubject variability of leucine appearance
is four times lower than that of leucine transport (13 vs. 57%). This
trend is maintained when the contribution in variability due to
measurement error is removed (10 vs. 39%). Thus it seems that
physiological mechanisms are in place, limiting intersubject
variability of protein breakdown and maintaining it at a similar rate
in our homogenous group of healthy subjects. This is also confirmed by
the high value of the within-subject variation as a percentage of total
variation (97%; see Table 2). Protein breakdown does not differ in a
single subject on different occasions to any great extent. However,
this small variability is comparable (or even much greater in the 5 subjects participating in the reproducibility study) to the variability between subjects. This makes the assessment of differences in leucine
breakdown between different subjects experimentally very difficult.
The control of leucine transport and also of plasma leucine is relaxed
with a higher intrasubject variability (between-subject CVs of 57 and
27%, respectively). This suggests that, at least in fasting healthy
subjects, protein breakdown is a tightly regulated process, and various
other processes are up- and downregulated to achieve this objective.
For example, the differences in leucine transport between subjects are
considerable and may control the supply of leucine for intracellular
protein synthesis and breakdown.
The observed linear relationship between plasma leucine and leucine
transport indicates that leucine promotes its own transport. Thus the
transport can be characterized, on the whole body level, as a
first-order process. This is in concordance with the observation that
acid transporters, principally system
L, are stimulated by the availability of substrate
(10). We also investigated the relationship between plasma leucine and
relative transport rate and failed to detect reduced relative transport
rate with elevated plasma leucine levels. This suggests that leucine
transport across a cell membrane is not attaining its saturation level
at fasting plasma leucine concentrations in healthy subjects.
We employed an infusion rate of leucine tracer that resulted in ~7
and ~9% TTR of
-KIC and leucine, respectively. This enrichment level compares with that used by others (19) and is expected to have
little or no effect on tracee or protein metabolism (24). In our study,
the plasma leucine concentration increased by ~13% from its prestudy
level. This is largely explained by the additional leucine appearance
due to the constant tracer infusion.
We used arterialized plasma samples to determine enrichment levels.
Detailed investigations in dogs indicated that calculations of leucine
turnover based on venous or arterial samples were identical when the
reciprocal pool model was used and, after data were pooled, arterial
and venous specific activities of leucine (and
-KIC) were
indistinguishable after radioactive leucine tracer infusion (14).
Chinkes et al. (9) reported identical leucine and
-KIC enrichments
after a constant infusion of
-KIC stable-label tracer. This suggests
that sampling site (venous vs. arterial) has little effect on the
calculations of transport. However, we did not confirm this expectation
as no venous samples were taken.
In conclusion, we have evaluated an approach to quantify a surrogate
measure of leucine transport across the cell membrane on the whole body
level by employing existing experimental procedures. Under fasting
conditions in healthy subjects, whole body inward transport of leucine
is a reproducible, mass-controlled process at a rate of about three
times that of leucine appearance due to proteolysis.
 |
APPENDIX |
This APPENDIX considers the effect of
tissue heterogeneity, i.e., differences in leucine transport and
leucine turnover between tissues, on the calculation of leucine
transport. For simplicity, we consider two heterogeneous tissues (see
Fig. 4). However, the results are
applicable to any number of heterogeneous tissues; the same principles
as described below apply.

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Fig. 4.
Conceptual model of leucine kinetics during a constant infusion of
leucine tracer (u) under fasting conditions. Model includes 2 tissues
with differing kinetic properties of leucine transport
(Fin,
Fout), intracellular leucine net
appearance (Ra), and net
disappearance (Rd). Symbols
denoted by lower case letters indicate tracer fluxes. There is no
intracellular appearance of leucine tracer from protein breakdown based
on the assumption that tracer is not recycled.
|
|
Under steady-state conditions, the TTR ratio in a compartment is equal
to the amount of tracer vs. tracee leucine entering the compartment.
Thus the extracellular leucine TTR
(ze) is identical to the sum of
tracer leucine influxes divided by the sum of unlabeled leucine
influxes entering the extracellular compartment
|
(A1)
|
With
the assumption of tracer indistinguishability, the tracer and unlabeled
leucine fluxes leaving intracellular compartments are related to the
intracellular TTRs as
|
(A2)
|
|
(A3)
|
Expressing
tracer fluxes fout1 and
fout2 with
Eqs.
A2 and A3, and substituting these in
Eq. A1, we obtain
which
can be written as a sum of two expressions
|
(A4)
|
The
first expression on the right side of Eq. A4 is
the ratio of tracer leucine mass that leaves intracellular space and
enters the extracellular compartment (i.e., the tracer infusion taken out of the total amount of tracer leucine entering extracellular space)
over the total amount of unlabeled leucine entering the extracellular
space. We denote this ratio zi not only for convenience but
because it represents the weighted intracellular TTR
|
(A5)
|
The
weights are defined as the tissue outward transport flux out of the
total leucine flux Fout (where Fout = Fout1 + Fout2)
(A6)
With
the use of Eq.
A5,
Eq.
A4 can be rewritten as
from
which a similar formula to that used in the main text to calculate the
transport can be derived
where
Fin is the total amount of
unlabeled leucine transported into cells, and the equality
Fin = Fout is due to
the steady-state conditions.
Thus under the provision that TTR of plasma
-KIC
(zK) is identical to the weighted TTRs of
intracellular leucine (zi), i.e.
|
(A7)
|
the
value Fin represents the sum of
whole body inward transport in the presence of tissue
heterogeneity. TTR of plasma
-KIC can be derived by employing
similar principles, as
where
zK1
(zK2) represents intracellular
TTR of
-KIC in tissue
1 (2), and
wK1
(wK2) represents
-KIC outward
transport in tissues
1 (2) out of the total outward
-KIC
transport. Due to the reversibility of leucine intracellular conversion
to
-KIC, the intracellular TTRs of leucine and
-KIC are
guaranteed to be identical, i.e.
Thus,
for Eq. A7 to hold, it is
sufficient that the weights are equal
This
means that
-KIC enrichment in plasma is identical to leucine
intracellular enrichment if outward relative transport of leucine and
-KIC are identical in each tissue.
 |
ACKNOWLEDGEMENTS |
The work was supported in part by the Economic & Social Research
Council, Swindon, UK, and the Special Trustee's
(Endowments) of St. Thomas' Hospital.
 |
FOOTNOTES |
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. §1734 solely to indicate this fact.
Address for reprint requests: R. Hovorka, Metabolic Modelling Group,
Centre for Measurement and Information in Medicine, City Univ.,
Northampton Square, London EC1V OHB, UK.
Received 5 June 1998; accepted in final form 9 November 1998.
 |
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