Download Assessment of the mathematical issues involved

Clinical Science (1993) 84,
177-183 (Printed in Great Britain)
I77
Assessment of the mathematical issues involved in
measuring the fractional synthesis rate of protein using
the flooding dose technique
David L. CHINKES, Judah ROSENBLATT and Robert R. WOLFE
Metabolism Unit, Shriners Burns Institute, and University of Texas Medical Branch, Galveston,
Texas, U.S.A.
(Received 24 September 1991/20 July 1992; accepted 19 O c t o b e r 1992)
1. The fractional synthesis rate of protein is commonly measured by either the constant infusion
method or the flooding dose method. The two methods often give different results.
2. An underlying assumption of the traditional flooding dose formula is that the protein synthesis rate is
not stimulated by the flooding dose. A new formula
for calculation of the fractional synthesis rate is
derived with the alternative assumption that the
protein synthesis rate is stimulated by an amount
proportional to the change in the intracellular concentration of the infused amino acid. The alternative
formula is:
Fractional synthesis rate - EB( t, - EB( O)
j: EFlCdt
where E B and EF are the enrichments of bound and
free amino acid, respectively (atom per cent excess),
and C=l-(E,/E,), where EI is the enrichment of
the infusate. This approach defines the lowest possible
value for the fractional synthesis rate. The traditional
equation gives a maximal value for the fractional
synthesis rate.
3. When data from the literature are considered, the
fractional synthesis rate of muscle protein as calculated by the constant infusion technique falls between
the values of fractional synthesis rate calculated by
the two flooding dose formulae when leucine is the
tracer, suggesting that a flooding dose of leucine
exerts a stimulatory effect on the rate of protein
synthesis, but that the increase is not as great as the
increase in the intracellular concentration of leucine.
4. The precision of the formula for the calculation of
fractional synthesis rate is limited by the accuracy of
the underlying assumptions regarding the effect of the
flooding dose on the fractional synthesis rate. At
present, the best approach would appear to be the use
of both equations to calculate the upper and lower
bounds of the true fractional synthesis rate.
INTRODUCTION
Difficulty in identifying the true precursor enrichment for the calculation of protein synthesis by the
constant tracer infusion method limits the accuracy
of the calculated values. The so-called ‘flooding
dose’ technique was designed to overcome this
limitation. The rationale of the method is to inject
simultaneously boluses of both tracer and tracee
amino acid, thereby ‘flooding’ the entire precursor
pool (extracellular and intracellular components) to
such an extent that the enrichment is the same
everywhere. The fractional synthesis rate (FSR) of
the specific protein is then determined by dividing
the rate of increase in the product enrichment in a
given amount of time by the average precursor
enrichment over that time.
There are several practical advantages to the
flooding dose technique. Theoretically, it should
eliminate uncertainty regarding precursor enrichment, since the precursor is at the same enrichment
in all compartments. Furthermore, because of this
flooding of the precursor pool, it should be possible
to use only plasma enrichment measurements to
quantify the true precursor enrichment. Another
advantage is that it is possible to give enough tracer
to enable sufficient tracer incorporation for accurate
measurement in a short period of time. This is
particularly important in the measurement of the
FSR of proteins that turn over slowly, such as
muscle, which may require 4 h or more of constant
tracer infusion to achieve a comparable level of
protein-bound amino acid enrichment. The ability
to complete the determination in a short time is not
only a logistical advantage (i.e. a shorter experimental time for subject and experimenter), but may
enable specific questions to be answered that otherwise could not be addressed. For example, the
response of protein synthesis to a hormone infusion
may be short-lived (due to a counter-regulatory
response), yet physiologically important. Because of
Key words: amino acids, constant infusion, flooding dose, fractional synthesis rate, leucine, metabolism, modelling, muscle, protein degradation, protein synthesis, tracer.
Abbreviations: APE, atom per cent excess; FSR, fractional synthesis rate.
Correspondence: Dr Robert R. Wolfe, Metabolism Unit, Shriners Burns Institute, 610 Texas Avenue, Galveston, T X 77550, U.S.A.
I78
D. L. Chinks et al.
these practical advantages, the flooding dose technique has become widely popular over the past ten
years. In particular, the recent modification of the
technique for the use of stable isotopic tracers [l],
instead of the original use of radioactive tracers [2],
represents a potentially important new advance in
methodology.
Concomitant with the advantages of the flooding
dose technique, there are potential problems stemming from the requisite assumptions. The most
crucial assumption is that the bolus injection of an
amount of amino acid well in excess of the total
body free pools of that amino acid does not stimulate the rate of protein synthesis. The available
physiological evidence pertaining to this assumption
will be discussed below. However, if this assumption
is not correct, then one could still conclude that the
traditional formula serves as the upper bound for
the true FSR. This is because all observed synthesis
is ascribed to the rate pre-existent before the flooding dose. To obtain a lower bound for the true
FSR, we will derive, for the first time, an alternative
flooding dose formula with the assumption that the
stimulation of the protein synthesis rate will be, at
most, proportional to the increase in the intracellular concentration of the infused amino acid (see
Fig. 1). For example, if the leucine intracellular
concentration was doubled as a consequence of
giving a leucine flooding dose, then we will assume
that the protein synthesis rate would be at most
doubled.
The calculation of the upper and lower bounds of
the true FSR has two advantages. First, if the
bounds are sufficiently close, then one can conclude
that the true FSR has been obtained. Second, when
one compares the calculation of the upper and
lower bounds of the FSR of two different physiological states, then if the bounds of the FSRs of the
two states do not overlap, one can conclude that
there is a difference in the FSRs, regardless of the
uncertainties of the relationship between the precursor enrichment and the synthesis rate.
We will also show that when stable-isotope flooding doses are given, the free amino acid enrichments
in the traditional formula need to be expressed as
atom per cent excess (APE) rather than as the
tracer/tracee ratio. Since the free amino acid enrichment has been in some cases as high as 20 APE [l],
the difference between the APE and the tracer/
tracee ratio is as great as 20%.
ASSUMPTIONS NECESSARY FOR THE
TRADITIONAL DERIVATION
The usual equation used to calculate the FSR
after giving a constant infusion or a flooding dose of
labelled amino acid is:
Normal
li
Before After
Before After
u-
lntracellular precursor Synthesis rate
concn. (mmol of free (g of protein h - ' k g - ' )
precursor amino
acid/kg)
Before After
w
Before After
u
intracellular precursor Synthesis rate
concn. (mmol of free (g of protein h - ' kg-')
precursor amino
acid/kg)
Fig. I. Differences in the assumptions of the two models used to
estimate FSR from a flooding dose. In the traditional model (a), it is
assumed that increasing the intracellular concentration of the amino acid
being infused causes no change in the protein synthesis rate. The alternative
model (b) assumes that the increase in protein synthesis rate is proportional
to the increase in the intracellular concentration of the amino acid infused.
The purpose of looking at these two models is to obtain upper and lower
bounds for FSR, for presumably the true response is not outside of these
two boundaries.
where E , and E , are the enrichments of free and
bound amino acid, respectively. (Enrichment in the
case of radioisotopes is the specific activity and, in
the case of stable isotopes, is APE throughout the
paper, except where noted. Tracer is the labelled
infused amino acid and tracee is the endogenous
amino acid and the unlabelled infused amino acid.
As we shall see, APE is the proper way to express
enrichments in the specific case of measuring protein
incorporation.) A correct derivation of an equation
similar to eqn. (1) is given by Zilversmit [3].
Zilversmit's formula was not derived with the flooding dose technique in mind, so we will review in
detail the assumptions necessary for the derivation
of Zilversmit's formula to apply.
Assumption (1) of the traditional derivation is
that the rate of incorporation of amino acid (both
labelled and unlabelled) is constant and at its
normal value over the duration of the experiment.
This is reasonable in the constant tracer infusion
method. In the flooding dose method, however, a
bolus of amino acid of 50mg/kg body weight or
more is given. Assessing the physiological effects of
Mathematical validity of the flooding dose method
administering a large quantity of a specific amino
acid on protein synthesis is a difficult task. There is
a large body of literature, which has recently been
reviewed in [4], indicating that leucine flooding
doses promote protein synthesis in vitro when other
amino acids are plentiful. One should be cautious,
however, when extrapolating from these results to
the situation in vivo, where the availability of other
amino acids might be limiting. If stimulation of
protein synthesis does occur from the addition of
only leucine, then one would have to presume that
there is a reservoir of the other amino acids needed
to produce the protein and that the stimulation
occurs either because leucine might be the amino
acid which is in shortest supply or because of a
regulatory effect of leucine. It is not clear whether
leucine alone stimulates muscle protein synthesis.
On the one hand, data in uitro suggest a stimulatory
role for leucine [4]. O n the other hand, McNurlan
et al. [5] found that a flooding dose of phenylalanine gave the same results as a flooding dose of
leucine. They concluded that a leucine flooding dose
did not stimulate protein synthesis in vivo, since
studies in vitro have not indicated that phenylalanine flooding doses stimulate protein synthesis
[ 6 ] . Also, the addition of a large amount of leucine
did not affect muscle FSR calculated by using a
flooding dose of phenylalanine [SJ. O n the other
hand, studies in which a constant infusion of
another amino acid was simultaneously given with a
flooding dose of leucine have produced conflicting
opinions as to whether protein synthesis was promoted [7, 81. However, interpretation of results
from this type of experimental protocol is made
difficult by the fact that the transport rate between
plasma and tissue of many amino acids changes
when a single amino acid is infused [9], thereby
potentially confounding the results from the constant infusion technique when a flooding dose is
simultaneously administered. Thus the extent to
which a flooding dose of leucine stimulates muscle
protein synthesis in humans is unclear.
Assumption (2) is that the enrichment or specific
activity of the free amino acid pool at any time t is
equal to the rate that labelled amino acids are
incorporated into protein at time t divided by the
rate that amino acids (both labelled and unlabelled)
are incorporated into bound protein at time t.
Assumption (2) may be criticized in that there may
be a significant delay between the time when amino
acids are no longer ‘free’, i.e. are bound to transfer
RNA, and the time when amino acids are ‘bound’,
i.e. are measurable as bound proteins. The delay
time in liver cells is usually around 1-2min [lo]. In
other systems, the delay may be longer, and may
involve other factors. Failure to account for the
delay causes an underestimation of the true value of
FSR when the flooding dose technique is used, so
that the fact that there may be an important delay
factor can not explain the differences in the computed muscle FSR values in humans using the
I79
constant infusion and flooding dose methods. On
the contrary, an important delay factor would only
amplify the differences.
Assumption ( 3 ) is that none of the protein into
which tracer is incorporated is degraded before the
experiment ends. This assumption might be of slight
concern during a prolonged tracer infusion for
slowly turning over pools, because there may be
some recycling of tracer. This assumption is reasonable in the flooding dose situation for muscle
because all sample collection is complete within 2 h.
For tissues with faster turnover rates than muscle,
the sampling interval is proportionally shorter as
well. Furthermore, it should be emphasized that
eqn. (1) is valid for tissues that satisfy assumption
( 3 ) even if other tissues do not satisfy assumption
( 3 ) . In other words, if, for example, liver tissue fails
to meet this requirement, then calculations involving
the calculation of FSR in muscle are not
invalidated.
Assumption (4) is that amino acids can enter the
bound amino acid pool only by incorporation from
the free amino acid pool. This presumably is not
controversial.
Assumption (5) is that the pool size of bound
protein (both labelled and unlabelled) is constant
and at its normal value throughout the experiment.
Some consideration may be necessary in long studies in small, young animals, since rats have been
shown to grow at a rate of 5%/day [ll].
It is also of interest to point out the assumptions
that are not needed for this calculation. N o assumptions are made about irreversible loss of free amino
acid by routes other than incorporation into protein, whether the rate of this loss changes over the
course of the experiment, or what the interactions
are between free amino acids and tissues not being
sampled. Since the kinetics of the free amino acids
Tracee kinetics
n
4
€FS
{
Bound pool
k-
Bound pool
u
Tracer kinetics
Fig. 2. Model of amino acids needed to derive the formula to
estimate FSR by the flooding dose technique. The only assumptions
needed about the free amino acid pool are that the enrichment is known
(EF) and the incorporation rate (S) (derived solely from the free amino acid
pool) is constant.
D. L. Chinkes et al
180
play no role in the traditional calculation of FSR, it
is perhaps simpler to think in terms of a single-pool
model (shown in Fig. 2), where the single pool
represents bound protein. We see in this model that
the only information that we need to know about
the free amino acid pool is the enrichment of the
free amino acid pool and the rate at which it
delivers tracee to the bound amino acid pool.
Some misconceptions should be cleared up about
the misleading notation in more recent derivations
of the FSR formula. For instance, in the derivation
in [ll], the starting assumption is that k,, the FSR,
is equal to k,, the fractional degradation rate.
Confusion arises because in compartmental modelling the usual definition of k , in this case would be
the incorporation rate into protein divided by the
pool size of free amino acid. What is meant
(although not stated) instead in reference [11] is
that k , is the incorporation rate into protein divided
by the pool size of bound amino acid. In the case of
muscle, the magnitude of difference in these two
definitions is great, since there is a large difference
in the bound and free amino acid pool sizes.
DERIVATION OF THE TRADITIONAL FSR
FORMULA
In this section we will go through a derivation of
the traditional FSR formula using the set of
assumptions discussed above.
There are two ways of expressing enrichment
commonly used in stable-isotope studies. In flooding
dose experiments, it is common to express enrichment as APE, which is defined as the number of
mols of tracer divided by the number of mols of
tracer and tracee combined. Enrichment can also be
expressed as the tracer/tracee ratio, which is defined
as the number of mols of tracer divided by the
number of mols of tracee. The use of tracer/tracee
ratios has been generally advocated over the use of
APE because in most tracer applications the formulae are less complex when expressed in terms of
tracer/tracee ratio [12]. In the specific case of
measuring protein synthesis rates, however, expressing enrichment in terms of APE results in less
complex formulae. Conversion of tracer/tracee ratio
to APE can be easily accomplished by the formula:
APE =
(1
(tracer/tracee ratio)
+ tracer/tracee ratio)
Therefore, the formulae discussed below can be used
if the tracer/tracee ratio is measured, provided that
the above conversion is performed first.
If we combine assumptions (3) (no release of
tracer from protein) and (4) (entrance to bound pool
only via incorporation from free pool), we can
conclude that the rate of increase in the pool size of
bound labelled amino acid at time t [qB(t)] is equal
to the rate at which that labelled amino acid is incorporated into the bound pool at time t [S,(t)], i.e.
Assumption (2) (enrichment of free pool =rate of
labelled incorporation of amino acids into bound
pool divided by rate of incorporation of amino
acids into bound pool) states that the relationship
between the rate at which labelled amino acid is
incorporated into the bound pool at time t , the rate
that amino acid is incorporated into the bound pool
at time t [ S ( t ) ] and the enrichment or specific
activity of free amino acid at time t [&(t)] is:
If we combine eqns. (2) and (3), we get:
If we divide both sides of eqn. (4) by the pool size of
bound amino acid (qB+QB) we get:
Assumption (5) states that the pool size of bound
amino acid ( q B + Q B ) is constant, so the left-hand
side of eqn. (5) is equal to the rate of change of
enrichment or specific activity of the pool size of
amino acid bound to protein. By definition, FSR is
equal to the rate of incorporation of amino acid
divided by the pool size of bound amino acid.
Therefore, eqn. (5) can be written as
It is assumed that FSR is constant, which is true if
assumptions (1) (incorporation rate is constant) and
(5) (bound pool size is constant) are true, Hence, if
eqn. (6) is integrated from time zero, we find:
Solving for FSR yields:
Mathematical validity of the flooding dose method
181
which is the traditional formula.
Note that this derivation of FSR is valid for both
the constant infusion method and the flooding dose
method, and any other incorporation method, given
that the discussed assumptions are true.
CALCULATION OF FSR IF THE PROTEIN
SYNTHESIS RATE IS STIMULATED BY AN
AMOUNT PROPORTIONAL TO THE INCREASE IN
THE INTRACELLULAR FREE AMINO ACID POOL
SIZE
Assumption (1) of the traditional calculation is
that the incorporation of free amino acids into
protein does not change over the course of the
experiment. The uncertainties involved with this
assumption were enumerated in a previous section.
The specific issue which will be addressed in this
section is how the calculation of FSR is affected if
assumption (1) is changed to assumption (1'): the
incorporation rate of amino acids into protein is
stimulated by an amount proportional to the intracellular concentration of free amino acids (see Fig.
3). In other words, the rate of incorporation of the
endogenous tracee would not be affected by the
flooding dose, and any tracee or tracer from the
flooding dose incorporated into protein would
therefore represent an increased rate of incorporation. This alternative assumption would require
that endogenous amino acids other than the amino
acid being traced would be incorporated into the
protein at an increased rate, i.e. that protein synthesis is stimulated.
It is important to note that this model is based
on the rate of incorporation of the endogenous
tracee, not the total rate of incorporation of tracer
and tracee. The traditional model is based on the
rate of incorporation of exogenous and endogenous
tracer and tracee. Stated mathematically, suppose
that:
where SBo,(t)is the rate of incorporation of the
bolus at time t, s , , d ( t ) is the rate of incorporation
of the endogenous free amino acid not from the
bolus, and S ( t ) is the total incorporation rate of
unlabelled free amino acid. The consequence of
choosing assumption (1') rather than assumption (1)
is that sE,d(t) is constant, not S(t).
We wish to define FSR as &,,d/(qB
QB), since we
are interested in the FSR that would have occurred
if we had not given a flooding dose.
Another assumption [assumption (6)] that is
needed is that E,, the ratio of the labelled bolus size
to the total bolus size, is equal to the rate at which
the labelled bolus is being incorporated into bound
protein divided by the rate at which all of the bolus
is being incorporated into protein. In other words,
an injected labelled amino acid molecule has the
+
Total incorporation
Endogenous
Before After
-+
Before After
'rate (S)
Endogenous
SE"
'incorporation rate
when bolus given
lntracellular Drecursor IncorDoration rate
concn. (mmoi of free (minil of tracee and tracer amino
precursor amino
acid incorporated h - ' kg -I)
acid/ kg)
Total incorporation
rate (S)
Endogenous
+bolus
Endogenous
I I
Belore After
incorporation rate
when bolus given
Before After
u lntracellular precursor Incorporation rate
concn. (mmol of free (mmol of tracee and tracer amino
acid incorporated h - l kg - I )
precursor amino
acid/ kg)
Fig. 3. Detailed look a t the assumptions underlying the t w o models.
In the traditional model (a), the total incorporation rate of amino acids is
unchanged. In the new model (b), the rate that amino acids are incorporated (S) is divided into the rate at which amino acids from the bolus are
incorporated (Seal) and the rate at which endogenous unlabelled amino acids
are incorporated (SEnd). Finding the relative proportions of these two rates
at any given time so that the endogenous incorporation rate can be found is
accomplished using the enrichment of the infusate (El) and the ratio of
labelled to total unlabelled amino acids at that given time [EF(t)].
Endogenous; 0,
unlabelled bolus; N, labelled bolus.
..
same odds of being incorporated into a particular
protein as an unlabelled amino acid molecule
injected at the same site. There should be no
problems with this assumption.
From this last assumption we have:
(9)
where SL is the rate of incorporation of the labelled
bolus.
The incorporation of endogenous amino acid is
the difference between the total incorporation rate
and the rate at which the bolus is being incorporated, i.e.
SEnd =s(t)
-s ~ 3 o d t )
(10)
Substituting eqn. (9) and then eqn. (3) into eqn. (10)
yields:
D. L. Chinkes et al.
I82
[ y]
7
=S(t) 1-
*t
Solving eqn. (1 1) for S(t) yields:
S(t ) =
*
*
SEnd
~~
By assumption (l'), S E n d is constant, so if we
substitute eqn. ( 2) into eqn. ( 5 ) and go through the
same reasoning sed to get the traditional equation,
we get:
45
90
I20
Constant infusion
Time that bound enrichment is sampled (min)
(m)
jb
[#]
dt
where
Fig. 4. Comparison of new (0)
and old
flooding dose formulae
(with a flooding dose of 27% enriched [I,2-13C]leucine) at different
sampling times with constant infusion results (using [U-"C]leucine)
using data from a comparative study in muscle of anaesthetized
postabsorptive dogs. *, indicates that the difference in the FSR computed
by the old and new formulae is statistically different from zero (P<O.OI);
7. indicates that the FSR computed by the old formula is statistically
different from the FSR computed by the old formula at either 90 or 120min
(P<O.Ol). Data are from [El.
If physiological evidence proves that protein synthesis is stimulated by the flooding dose in proportion
to the increase in the free intracellular amino acid
pool, then the traditional equation can be corrected
by using eqn. (14).
RESULTS
A comparison in muscle of results obtained by
using the two flooding dose formulae and the
constant infusion technique in muscle tissue in
anaesthetized postabsorptive dogs using a flooding
dose of 50mg of 27% enriched [1,2-'3C]leucine/kg
and a constant infusion of [U-'4C]leucine is shown
in Fig. 4, using the data from [S]. Using the new
formula based on assumption (l'), the results from
the constant infusion study (1.8 fO.l%/day) were
not statistically different from the results obtained in
the flooding dose study (ranging from 2.0f0.2 to
2.2 f0.3%/day). The old flooding dose formula
[based on assumption (l)] gave values significantly
in excess of those obtained with the new flooding
dose formula and the constant infusion technique
( P <0.01). The old formula applied to the samples
taken at 45 min (FSR = 5.0 k0.43%/day) gave values
which were statistically different ( P < 0.01) than were
obtained by applying the old formula to the
samples taken at 90 and 120min (3.410.4 and
3.5 f0.4"/,/day).
When eqn. (13) is used in a comparative study in
muscle in postabsorptive man (with a flooding dose
of 50mg of 20% enriched ~-[l-'~C)leucine/kgand a
constant infusion of ~-['~C]valine)[7], the average
calculated FSR is 0.025 0.0027Jh as compared
with 0.043kO.O02%/h as measured by the constant
infusion method and 0.063 1O.OOS%/h as measured
-
0.08 i
0.06
..-..
E.
e 0.04
2
r,
0.02
0.00
1
2
3
4
5
Subject no.
6
1
(m)
Fig. 5. Comparison of new (H)
and old
flooding dose formulae
with constant
(with flooding dose of 20% enriched ~-[~["C]leucine)
using data from a comparainfusion results (using ~-["C]valine, 0)
tive study in muscle of postabsorptive man. Data are from [7].
by the traditional FSR formula. These values are all
statistically different ( P <0.01). The results for the
individual subjects are shown in Fig. 5. In all seven
cases of this experiment, FSR as computed by the
constant infusion method was between the values
calculated from the two flooding dose formulae. The
bound protein samples were measured 90min after
the flooding dose was given.
DISCUSSION
In this paper we have for the first time correctly
derived the traditional flooding dose equation for
Mathematical validity of the flooding dose method
the calculation of the FSR of a product when a
stable-isotope bolus dose of tracer is administered,
with assumptions appropriate for the application of
the formula to the flooding dose technique, showing
that the enrichments in the formula should be
expressed as the APE (as they commonly are) rather
than as the tracer/tracee ratio. In this traditional
approach it is assumed that protein synthesis is not
stimulated by the flooding dose. We have also
derived a new, alternative equation. In this case, the
alternative assumption is made that FSR is
increased by a rate in proportion to the change in
the intracellular concentration of the amino acid.
Use of these two equations provides the upper and
lower bounds around the true value of FSR calculated with a flooding dose in human and dog
muscle. The choice of the most appropriate equation equation depends on the extent to which the
flooding dose stimulates FSR. This latter question
has not been completely resolved.
In the case of the study in the dog, the new
formula corresponds well with the constant infusion
data, suggesting a stimulation of protein synthesis in
accord with assumption (1’).
The human data suggest that there is an increase
in protein synthesis, although not in proportion
with the increase in intracellular free leucine concentration. The bounds given by the two flooding dose
formulae are reasonable, although they are not very
‘tight’. Taking into account a delay factor may
cause the new formula to be a better predictor of
the true value, but it can only cause the old formula
to be a poorer predictor.
It is not possible to account for the discrepancies
between the results obtained with the traditional
flooding dose FSR formula and those determined by
the constant infusion method by errors in calculating FSR when using the constant infusion method.
It was pointed out in the derivation of the traditional flooding dose FSR formula that the underlying
assumptions and resulting formulae were identical
for the two methods. The advantage of the constant
infusion technique is that there is no doubt that the
protein synthesis is not significantly affected by a
constant infusion of tracer. The advantage of the
flooding dose technique is that there is little doubt
as to the proper precursor (free amino acid) enrichment. The true precursor enrichment (transfer RNA
enrichment) is not readily measurable, and it is not
certain what substitute for that value is optimal.
I83
However, none of the candidates commonly used
(i.e. intracellular and extracellular free amino acid,
or a marker of intracellular enrichment such as GIketoisocaproate) result in calculated values that can
explain the difference between the constant infusion
technique and the traditional flooding flooding dose
FSR calculation.
A common convention to deal with the uncertainties in constant infusion studies is to state that
the FSR lies between the bounds determined by the
intracellular and extracellular enrichments. We suggest that the two flooding dose formulae described
here can be used as bounds of the true FSR value in
muscle in humans, keeping in mind that if there is a
significant delay in the labelling of the transfer RNA
pool, the values from both equations will be too
high.
ACKNOWLEDGMENTS
This work was supported in part by grants from
the National Institutes of Health (DK 33952, 38010)
and a grant from the Shriner’s Hospital.
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