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
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Abstract
Introduction
METHODS
RESULTS
DISCUSSION
References
Appendix

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/Delta TTR, where u is the infusion rate of (stable label) leucine tracer and Delta 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 alpha -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
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Abstract
Introduction
METHODS
RESULTS
DISCUSSION
References
Appendix

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 alpha -ketoisocaproic acid (alpha -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 alpha -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
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Abstract
Introduction
METHODS
RESULTS
DISCUSSION
References
Appendix

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)
F<SUB>in</SUB> = F<SUB>out</SUB> (1)
f<SUB>in</SUB> = f<SUB>out</SUB> + u (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 alpha -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
z<SUB>L</SUB> = f<SUB>in</SUB>/ F<SUB>in</SUB> (3)
z<SUB>K</SUB> = f<SUB>out</SUB>/ F<SUB>out</SUB> (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
F<SUB>in</SUB> = u/(z<SUB>L</SUB> − z<SUB>K</SUB>) (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 alpha -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 alpha -[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 alpha -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
R<SUB>a</SUB> = u/z<SUB>K</SUB> (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
z<SUB>K</SUB> = r<SUB>D</SUB>/R<SUB>D</SUB>
u = r<SUB>D</SUB>
R<SUB>A</SUB> = R<SUB>D</SUB>
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
RTR = F<SUB>in</SUB>/ L (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 alpha -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
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Abstract
Introduction
METHODS
RESULTS
DISCUSSION
References
Appendix

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 alpha -KIC TTR (see Fig. 2).


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Fig. 2.   Plasma leucine (top) and (bottom) tracer-to-tracee ratio of leucine () and alpha -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 alpha -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 alpha -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
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Abstract
Introduction
METHODS
RESULTS
DISCUSSION
References
Appendix

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 alpha -KIC in plasma is identical to intracellular TTR of leucine. Ever since the original proposal that during leucine infusion, alpha -KIC is a good surrogate of the true protein precursor labeling (22, 26), alpha -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 alpha -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 alpha -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 alpha -KIC enrichment and plasma alpha -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 alpha -KIC to be identical to relative outward transport of leucine across tissues. If relative outward transport of alpha -KIC differs from that of leucine, plasma enrichment of alpha -KIC is then biased toward intracellular leucine enrichment of tissues with higher relative outward transport of alpha -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 alpha -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 alpha -KIC) were indistinguishable after radioactive leucine tracer infusion (14). Chinkes et al. (9) reported identical leucine and alpha -KIC enrichments after a constant infusion of alpha -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
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Abstract
Introduction
METHODS
RESULTS
DISCUSSION
References
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
z<SUB>e</SUB> = (f<SUB>out1</SUB> + f<SUB>out2</SUB> + u)/(F<SUB>out1</SUB> + F<SUB>out2</SUB>) (A1)
With the assumption of tracer indistinguishability, the tracer and unlabeled leucine fluxes leaving intracellular compartments are related to the intracellular TTRs as
z<SUB>i1</SUB> = f<SUB>out1</SUB>/ F<SUB>out1</SUB> (A2)
z<SUB>i2</SUB> = f<SUB>out2</SUB>/ F<SUB>out2</SUB> (A3)
Expressing tracer fluxes fout1 and fout2 with Eqs. A2 and A3, and substituting these in Eq. A1, we obtain
z<SUB>e</SUB> = (z<SUB>i1</SUB>F<SUB>out1</SUB> + z<SUB>i2</SUB>F<SUB>out2</SUB> + u)/(F<SUB>out1</SUB> + F<SUB>out2</SUB>)
which can be written as a sum of two expressions
z<SUB>e</SUB> = (z<SUB>i1</SUB>F<SUB>out1</SUB> + z<SUB>i2</SUB>F<SUB>out2</SUB>)/(F<SUB>out1</SUB> + F<SUB>out2</SUB>) + u/(F<SUB>out1</SUB> + F<SUB>out2</SUB>) (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
z<SUB>l</SUB> = w<SUB>1</SUB>z<SUB>i1</SUB>+ w<SUB>2</SUB>z<SUB>i2</SUB> (A5)
The weights are defined as the tissue outward transport flux out of the total leucine flux Fout (where Fout = Fout1 + Fout2)
w<SUB>1</SUB> = F<SUB>out1</SUB>/ F<SUB>out</SUB>
(A6)
w<SUB>2</SUB> = F<SUB>out2</SUB> / F<SUB>out</SUB>
With the use of Eq. A5, Eq. A4 can be rewritten as
z<SUB>e</SUB> = z<SUB>i</SUB> + u/ F<SUB>out</SUB>
from which a similar formula to that used in the main text to calculate the transport can be derived
F<SUB>in</SUB> = F<SUB>out</SUB> = u/(z<SUB>e</SUB> − z<SUB>i</SUB>)
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 alpha -KIC (zK) is identical to the weighted TTRs of intracellular leucine (zi), i.e.
z<SUB>K</SUB> = w<SUB>1</SUB>z<SUB>i1</SUB> + w<SUB>2</SUB>z<SUB>i2</SUB> (A7)
the value Fin represents the sum of whole body inward transport in the presence of tissue heterogeneity. TTR of plasma alpha -KIC can be derived by employing similar principles, as
z<SUB>K</SUB> = w<SUB>K1</SUB>z<SUB>K1</SUB> + w<SUB>K2</SUB>z<SUB>K2</SUB>
where zK1 (zK2) represents intracellular TTR of alpha -KIC in tissue 1 (2), and wK1 (wK2) represents alpha -KIC outward transport in tissues 1 (2) out of the total outward alpha -KIC transport. Due to the reversibility of leucine intracellular conversion to alpha -KIC, the intracellular TTRs of leucine and alpha -KIC are guaranteed to be identical, i.e.
z<SUB>i1</SUB> = z<SUB>K1</SUB>
z<SUB>i2</SUB> = z<SUB>K2</SUB>
Thus, for Eq. A7 to hold, it is sufficient that the weights are equal
w<SUB>1</SUB> = w<SUB>K1</SUB>
w<SUB>2</SUB> = w<SUB>K2</SUB>
This means that alpha -KIC enrichment in plasma is identical to leucine intracellular enrichment if outward relative transport of leucine and alpha -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.


    REFERENCES
Top
Abstract
Introduction
METHODS
RESULTS
DISCUSSION
References
Appendix

1.   Altman, D. G., and J. M. Bland. Measurement in medicine: the analysis of method comparison studies. Statistician 32: 307-317, 1983.

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Am J Physiol Endocrinol Metab 276(3):E573-E579
0002-9513/99 $5.00 Copyright © 1999 the American Physiological Society




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