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Article

A Model of Whole-Body Protein Turnover Based on Leucine Kinetics in Rodents¹

Animal Science Department, University of California at Davis, Davis, CA 95616 and ^* The University of Reading, Department of Agriculture, Earley Gate, Reading RG6 6AT, UK

	ABSTRACT

TOP ABSTRACT INTRODUCTION THE MODEL MODEL EVALUATION DISCUSSION REFERENCES

 
The measurement of fractional synthesis rate is based on the following assumptions: amino acids for protein synthesis are supplied by an intracellular pool; amino acids from protein degradation are not recycled preferentially to protein synthesis; and proteins turn over at a homogeneous rate. To test these assumptions, a mechanistic, theoretical model of protein turnover for a nongrowing 26-g mouse was developed on the basis of data from the literature. The model consisted of three protein pools turning over at fast (102 µmol Leu, t_1/2= 11.5 h), medium (212 µmol Leu, t_1/2 = 16.6 h) or slow (536 µmol Leu, t_1/2 = 71.5 h) rates and extracellular (1.69 µmol Leu), leucyl-tRNA (0.0226 µmol Leu) and intracellular (5.72 µmol Leu) amino acid pools that exchanged amino acids. The flow of amino acids from the protein pools to the leucyl-tRNA pool determined the amount of recycling. The flow of amino acids from the extracellular pool to aminoacyl tRNA determined the amount of channeling. Two flooding dose data sets were used to evaluate specific radioactivity changes predicted by the model. Predictions of specific radioactivities using flooding dose, pulse dose or continuous infusion methods indicated that the model can be a useful tool in estimating the rates of channeling and recycling. However, it was found that use of data from flooding dose experiments might cause inaccurate predictions of certain fluxes.

KEY WORDS: • rodents • protein synthesis • protein degradation • mathematical model • tracer kinetics

	INTRODUCTION

TOP ABSTRACT INTRODUCTION THE MODEL MODEL EVALUATION DISCUSSION REFERENCES

 
Fractional synthesis rate (FSR)⁴ is used as an estimate of the synthesis rate of protein in a tissue or in the whole body. FSR estimates can be used to measure differences in protein metabolism and to determine partitioning of amino acids among tissues or cell compartments resulting from treatment effects such as feeding, genotype or disease. Three methods, flooding dose, pulse dose and continuous infusion, are used to estimate FSR by measuring the incorporation of radiolabeled amino acids into protein relative to the specific radioactivity of an amino acid found in the precursor pool (extracellular, intracellular or aminoacyl tRNA) per unit time. Each method is based on similar assumptions about the process of protein turnover in cells, tissues or whole-body systems. Three of the assumptions are that the protein pool is homogeneous (one pool), the amino acid pool is homogeneous (one pool) and amino acids from protein degradation are not preferentially reused for protein synthesis (no recycling). If any of these assumptions were not valid, FSR may not be representative of the true protein synthesis rate. In addition, how each of the assumptions affects the estimation of FSR has never been examined quantitatively. The overall objectives of this research were to quantitate the effects of each assumption on estimates of FSR and to determine if the model could be used to estimate FSR, channeling and recycling. In this paper, a dynamic, mechanistic whole-body rodent (rat or mouse) model, based on leucine kinetics, was developed and evaluated to determine if the model could represent protein turnover.

	THE MODEL

TOP ABSTRACT INTRODUCTION THE MODEL MODEL EVALUATION DISCUSSION REFERENCES

 
General description.

The model is a dynamic representation of leucine kinetics in a nongrowing rodent. The model traces the turnover of leucine from the free amino acid pools to oxidation or the protein pools (Fig. 1 A).Leucine can remain in the protein pools, be released through protein degradation to be converted back into protein or be oxidized. Similarly, if radiolabeled leucine is flooded, pulsed or continuously infused into the extracellular pool, it can pass to the leucyl-tRNA pool and be used for protein synthesis or enter the intracellular pool. In the intracellular pool, leucine can be oxidized, remain as a reserve or be transported to another pool (Fig. 1 B). Thus amino acids for protein synthesis can arise from several sources, i.e., the intracellular pool, the extracellular pool (channeling) or protein degradation (recycling). Because the rodent is nongrowing, protein is always in steady state; protein synthesis is always equal to protein degradation (Waterlow et al. 1978 ). Definitions and units of the symbols used in the model are listed in Table 1 .Conservation of mass principles give the differential equations for the model for unlabeled and radiolabeled amino acid, respectively (Table 2 ).

View larger version (23K): [in this window] [in a new window]   Figure 1. The six-pool model of leucine turnover: (A) unlabeled material (tracee); (B) radiolabeled material (tracer). QE, QI and QT are leucine in the extracellular (plus plasma), intracellular and aminoacyl-tRNA pools, respectively; QF, QM, QS are leucine in the fast, medium and slow turnover protein pools, respectively; FIT is flux of leucine from intracellular pool to aminoacyl-tRNA pool; FTI is flux of leucine from aminoacyl-tRNA pool to intracellular pool; FIO is flux of leucine oxidized from intracellular pool; FOE is intake flux of leucine to extracellular pool; FET is flux of leucine from extracellular pool to aminoacyl-tRNA pool (channeling); FEI is flux of leucine from extracellular pool to intracellular pool; FIE is flux of leucine from intracellular pool to extracellular pool; FTF, FTM,FTS are fluxes of leucine from aminoacyl-tRNA pool to fast, medium and slow protein turnover pools; FFT, FMT, FST are fluxes of leucine from protein degradation in fast, medium and slow protein turnover pools, respectively, to aminoacyl-tRNA pool (recycling). The symbols q and f are similarly defined for radiolabeled material.

The whole-body free leucine pool is divided among an extracellular pool (Q_E), an intracellular pool (Q_I), and an aminoacylated tRNA pool (Q_T). All three free leucine pools interchange fully. Because whole-blood data are not available for the rodent, the extracellular pool is assumed to be homogenous and representative of the free amino acid in the extracellular space and plasma. The influx of amino acid into the extracellular pool (F_0E) is absorption; the efflux from the intracellular pool (F_IO) is oxidation. The aminoacylated tRNA pool represents amino acids covalently bound to tRNA and can be derived from the extracellular pool (channeling, F_ET), the intracellular pool (F_IT) or protein degradation (F_FT, F_MT, F_ST). Flux from the extracellular to the intracellular pool (F_EI) represents the transport of leucine into the intracellular compartment. Intracellular leucine can be oxidized (F_IO), transported back to the extracellular pool (F_IE) or undergo acylation (F_IT).

Estimation of initial size of free amino acid pools.

Initial pool sizes provide a starting value for differential equations. The differential equations describe the inflow and outflow of leucine. Calculation of initial leucine in the extracellular, intracellular and aminoacyl tRNA pools was based on body weight. Therefore the model can be used easily to represent protein turnover in rodents of different sizes. Equations and values for the initial amino acid pools are listed in Table 3 .To calculate the extracellular leucine content, it was assumed that the concentration of leucine in plasma was the same as that in the extracellular space and that there was rapid equilibration between the two spaces. Therefore the amount of leucine in the extracellular pool was the amount in the extracellular space (first term) plus the amount in the plasma (second term). To calculate the leucyl-tRNA pool size, total tRNA from liver was used to estimate the amount of tRNA in fast protein turnover tissue and total tRNA from muscle for slow and medium protein turnover tissues. The number of leucine codons (6) was divided by the number of total codons (60) to estimate that 10% of the total tRNA was leucyl tRNA. Therefore the total charged leucyl tRNA was 0.88 (Palmiter 1975 ) times 0.1 (Table 3) .

Whole-body protein is divided into pools with fast (Q_F), medium (Q_M) or slow (Q_S) turnover rates. Each pool is assumed to be homogenous. The rates of turnover of the three pools are used to account for the nonhomogeneity of total protein. Amino acids from degradation can go to the intracellular or aminoacyl-tRNA pools. Fluxes from the protein pools to aminoacyl tRNA (F_FT, F_MT, F_ST) represent recycling of amino acids from degradation to synthesis without mixing with the intracellular pool. Protein synthesis can occur only via the aminoacyl-tRNA pool.

Estimation of initial size of protein pools.

All pool size calculations were based on a 26-g reference mouse. A 26-g reference mouse was used because 26 g was the average weight of mice in which protein content was determined. The ratio of organ protein to whole-body protein in the mouse was used to calculate organ protein content in the rat (Table 4 ).To determine Q_F, Q_M and Q_S, organs were classified as fast, medium or slow protein turnover organs (Table 4) . Organ protein was assumed to contain 6% leucine on a dry basis (Waterlow et al. 1978 ). Therefore the percentage of leucine in protein was 2% when corrected for water content. Initial leucine in protein pool sizes are also scaled to body weight to represent protein turnover in rodents of different sizes. The estimates of leucine bound to protein are listed in Table 4 .

Some literature values were available to estimate leucine fluxes among the free amino acid pools. If literature values were not available, assumptions about relationships among fluxes were used. Estimates with the flooding dose method were based on the assumption that the rodent is essentially not growing over the 15–30 min experimental time period. Therefore there is no accretion of protein, and oxidation (F_IO) was set equal to intake (F_OE) (Waterlow et al. 1978 ). Equations for F_IE and F_TI (Table 2 , Eq. 1.2a and 2.5) are balance equations that are based on the assumptions that the intracellular pool and leucyl-tRNA pools, respectively, are in steady state. Table 2 lists the equations and assumptions and Table 5 lists the values for the free leucine fluxes (µmol/min).

View this table: [in this window] [in a new window]   Table 5. Steady-state parameter values based on literature values for fluxes under two different scenarios: aminoacyl tRNA charging from extracellular or from intracellular sources and predicted parameter values for data from Bernier and Calvert (1987) and Obled et al. (1991) fit to the model using Simusolv (Dow Chemical 1990)e

Because literature values were unavailable for F_ITand F_TI, fluxes were calculated on the basis of two scenarios (Table 5) . In the first, leucyl tRNA was charged solely from the extracellular pool (Q_E) of leucine directly (channeling). Therefore, the net flow of leucine was from Q_T to Q_I and F_IT was assumed to equal zero. F_TI (Eq. 2.5) could be calculated by a balance equation for Q_I on the basis of the assumption that Q_I was in steady state. If the assumption is made that all amino acids in the cell arise from extracellular channeling, intracellular amino acids are the result of "spillover" of the protein synthetic machinery, and the difference between F_IT and F_TI should be very close to 0.221 mol/min (i.e., F_IT = 0). The second scenario was that leucyl tRNA was charged primarily from the intracellular pool (Q_I). The net flow of leucine was from Q_I to Q_T; therefore F_TI (Eq. 2.5) was assumed to equal zero. F_IT (Eq. 2.7b) could be calculated by a balance equation for Q_I on the basis of the assumption that Q_I was in steady state. If the assumption is made that all amino acids in the cell used for protein synthesis arise from the intracellular pool, the difference between F_IT and F_TI should be very close, 0.233 mol/min (i.e., F_TI = 0). Therefore, the estimated values for F_IT and F_TI are the net fluxes of leucine for the different scenarios and do not represent the total flow of leucine between Q_I and Q_E. All of the estimates of fluxes are based on the assumptions that the model is balanced (pool sizes do not change) and that no recycling is occurring. In reality, charging from both the extracellular and intracellular pools probably occurs and pool sizes (extracellular and intracellular) do change.

Estimation of protein synthesis and degradation rates in steady state (nongrowing).

In a nongrowing rodent, protein synthesis and degradation are equal; therefore ,F_TF + F_TM + F_TS = (F_FT + F_MT + F_ST) + (F_FI + F_MI + F_SI) (Eqs. 2.2, 2.3, & 2.4 and 3.0, 3.1 and 3.2). Values for F_TF, F_TM and F_TS for the reference mouse were calculated from estimates of average FSR (K_s) for different tissues of mice and rats from flooding dose experiments and continuous infusion experiments separately (Tables 6 and7).Because FSR was relative to the total leucine in protein, it was expected that it would be approximately the same for rats and mice; thus no adjustment was made for different body weights. There were not enough estimates in the literature of whole-organ or mouse FSR using a pulse dose to calculate average FSR. Organs were classified as fast, medium or slow protein turnover organs and assigned to an appropriate protein pool. The estimates of protein synthesis rates were used to simulate two data sets from flooding dose experiments.

Flooding dose. Calculations of FSR from flooding dose experiments are based on the average specific activity of the precursor pool and the specific activity of the protein pool at the end of the experiment (15 or 30 min). The method assumes one amino acid and one protein pool that are homogeneous and well mixed (Garlick et al. 1980 ). Terms used the in equations are defined in Table 1 .

Pulse dose. FSR estimates from pulse dose experiments can be calculated using the equation of Peters and Peters (1972) .

where s_p and s_i are calculated based on data collected at the end of the experiment (60 min). In the original equation, s_p was the disintegrations per minute of leucine in protein, multiplied by the time length of the measurement (60 min) and divided by the leucine concentration in protein to obtain the final protein specific radioactivity. The denominator (s_i) was the disposal rate of the amino acid injected or the dose of amino acid given divided by the area under the curve for disappearance of the radiolabeled amino acid over time.

    Continuous infusion. FSR estimated by the continuous infusion experiments are calculated using the following equations (Waterlow et al. 1978 ):

where K_s is found by plotting K_s vs. s_p/s_i at a fixed tand B. Definition of terms in equations are listed in Table 1 .

Fractional synthesis and degradation rates estimated by different experimental methods.

K_S values estimated by the continuous infusion method were lower than estimates by the flooding dose method. This was expected because continuous infusion experiments obtain measurements over a longer period of time, i.e., 6 h for continuous infusion compared with 15–30 min for a flooding dose. The longer experimental period allows for a greater recycling of radiolabel; therefore the specific radioactivity of the precursor pool (intracellular, extracellular or aminoacyl tRNA) will decrease over time. Data compiled by Waterlow et al. (1978) indicated that FSR estimates obtained by continuous infusion were between 11 and 24%/d for the slow turnover protein pool, between 48 and 55%/d for the medium turnover protein pool and between 50 and 68%/d for the fast turnover protein pool.

	MODEL EVALUATION

TOP ABSTRACT INTRODUCTION THE MODEL MODEL EVALUATION DISCUSSION REFERENCES

 
In the previous section, all pools in the model were in steady state. The equations for two fluxes, F_IE and F_TI, were based on the assumptions that the intracellular and leucyl RNA pool sizes do not change (Table 5 , columns 1 and 2). Protein synthesis rate was assumed to equal protein degradation rate and the protein pools were in steady state. In this section, these assumptions were tested. Two data sets were fit to the model using the maximum log likelihood method according to Simusolv (Dow Chemical 1990 ) to find the most likely combination of fluxes that would cause the model to reproduce the experimental data sets. The combination of fluxes predicted by the model to reproduce the specific radioactivity data of Bernier and Calvert (1987) and Obled et al. (1991) is listed in columns 3 and 4 of Table 5 .

Nongrowing rodent model.

Protein synthesis was assumed to equal degradation; therefore Equations 2.2, 2.3 and 2.4 were used to represent protein synthesis and Equations 3.0, 3.1 and 3.2 (Table 2) were used to represent recycling from protein degradation. The only pools that remained constant in size were the aminoacyl-tRNA pool (Q_T) and the protein pools (Q_S, Q_M, Q_F). Therefore Equation 2.5 was used to represent F_TI.. F_IT reflects the relative amounts of channeling and recycling (Eq. 2.7a). Equations for F_FI, F_MI, F_SI, F_ET, F_TE and F_EI are those listed in Table 2 .

Data sets 1 and 2.

Two data sets with whole-body protein and amino acid–specific radioactivities were simulated to determine whether the model could predict specific radioactivity changes over time and whole-body FSR. The first data set was a flooding dose experiment in 30-g mice given 370 MBq ¹⁴C leucine and 100 µmol leucine per 100 g body weight (Bernier and Calvert 1987 ). Whole-body specific radioactivity measurements were taken at 2, 5, 10, 15, 20 and 30 min in the free amino acid pool (acid supernatant) and protein pool (acid precipitate). The second data set was a flooding dose experiment in 70-g rats given 877 MBq ¹⁴C leucine and 140 µmol leucine per 70 g body weight (Obled et al. 1991 ). The 70-g rat was assumed to be nongrowing because the amount of protein the rat would gain in 15 min would be within 10–15% of the experimental error in measuring specific radioactivity changes of the leucine in protein and free amino acid pools. Whole-body specific radioactivity measurements were taken at 5, 7, 9, 11, 13 and 15 min in blood plasma, free amino acid pool (acid supernatant) and protein pool (acid precipitate). Free leucine in the extracellular space was also estimated. The plasma specific radioactivity was assumed to equal the extracellular specific radioactivity. The intracellular specific radioactivity was obtained by correcting the free amino acid specific radioactivity for the extracellular contribution. Both C. Obled (Institut National de la Recherche Agronomique) and C. C. Calvert (University of California, Davis) graciously supplied raw specific radioactivity data from the papers by Bernier and Calvert (1987) and Obled et al. (1991) to test the model.

Fluxes (F_IO, F_OE, F_IE), the percentages of protein synthesized (K_SF, K_SM, K_SS), PC and PR were fitted using Simusolv (Dow Chemical 1990 ) to have the model produce specific radioactivities as close to the data as possible (Tables 8 and 9).Because changes in data on specific radioactivity over time were not available in the continuous infusion experiments, only fits using the flooding dose method could be obtained. FSR represented the total fractional synthesis rate predicted by the model based on K_SS, K_SM and K_SF using the flooding dose method. The resulting fluxes were compared with steady-state model fluxes for scenarios 1 and 2 in Table 5 .

View this table: [in this window] [in a new window]   Table 8. Observed specific radioactivity (Obs) from Bernier and Calvert (1987) and predicted specific radioactivity (Pred) by the model using parameters from Table 5 h

Protein synthesis rates from the fits of the data given by Obled (Obled et al. 1991 ) and Bernier (Bernier and Calvert, 1987 ) for individual protein pools were lower than synthesis rates calculated from the literature (Table 6) . In the Obled and Bernier data sets, the protein pools were not divided into fast, medium and slow turnover pools. To fit the protein specific radioactivity data, therefore, only the slow pool turnover rate was allowed to vary (K_SS). Thus all of the error associated with fitting the data is in the turnover rate for the slow protein pool. But, the estimated rates (K_SF, K_SM, K_SF) from fitting to each data set were close. FSR calculated from the model simulations of the data were close to the FSR published by Obled and Bernier, i.e., 31 and 33 %/d, respectively. Because true FSR was relative to the total leucine in protein, it was expected that it would be approximately the same for rats and mice. FSR was calculated on the basis of a 2.5-min measurement of the specific radioactivity of the free leucine pools for the Bernier data and was based on a 5-min measurement for the Obled data.

Fits of free amino acid fluxes.

The fluxes determined from the Bernier and Obled data sets were fairly close to each other. If the F_ij were adjusted by the body weight of the rodent, F_EI, F_IE, and F_ET were fairly close. However, intake was higher and oxidation was lower in the Bernier data compared with the Obled data set. To fit the data from Bernier, dietary intake (5 g/d) had to be increased to 1202 µmol leucine (or 11g/d) to decrease the specific radioactivity of the free leucine pool. As a result, oxidation was lowered because a greater (and quicker) dilution of the free leucine pools could be achieved by increasing intake instead of increasing oxidation. The estimate of intake would be expected to be the most accurate because it was the easiest to measure. The percentage of error was very low for the Bernier data (<5%); thus much of the error associated with the free amino acid pools was probably taken up by the intake value. The predictions of oxidation rates from both data sets were at least four times greater than if intake was truly equal to oxidation as assumed for the literature values (scenarios 1 and 2 in Table 5 ). In the Obled solution, however, intake was fixed at that expected for a 70-g rat (14 g/d). Therefore, in both data sets, a dilution of the specific radioactivity of the free amino acid pools was necessary to fit data. The dilution could arise from increased oxidation, a recent meal, experimental error, a differential use of radiolabeled leucine over unlabeled leucine or another source that was not accounted for in the model.

Fits of the Bernier and Obled data predicted that F_TI was zero. A small F_TI (as with the flux estimates from the Bernier and Obled data) makes sense energetically and structurally because once an amino acid was bound to the leucyl-tRNA-elongation factor 1 -GTP complex it would be difficult to escape protein synthesis and a waste of the energy used to charge the leucyl tRNA. However, tRNA may have other uses in the cell such as for protein degradation through the ubiquitin system (Deshpande et al. 1996 ). Therefore F_TI might have been occurring, but it was probably so small that it was essentially zero.

Comparison of fits to a two-pool model of protein turnover.

To check the solution from the fitting of the Bernier data, a two-pool model of protein synthesis created by Waterlow et al. (1978) was used to fit the data (Table 5) . The model was created for continuous infusion experiments with one free amino acid pool with an intake flux, an oxidation flux and one protein pool. The two pools exchanged amino acids; the flux from the amino acid pool to the protein pool represented protein synthesis and the flux from the protein pool to the amino acid pool represented protein degradation. Synthesis was assumed to equal degradation and intake equaled oxidation. Although the model was created for continuous infusion experiments in which data for specific radioactivity changed over time were not available, the model was adapted for a flooding dose experiment by assuming that even if the animal was not growing, intake and oxidation were not equal. The percentage of error for specific radioactivities of the amino acid pool were higher (26%) but about the same for the protein pool (6%). K_S was very close to the FSR from the six-pool model (32 vs. 33 %/d), but intake was higher than the previous estimate (1.69 vs. 0.84 µmol Leu/min) and oxidation was closer to the value for intake (0.27 vs. 0.34 µmol Leu/min). Therefore the solutions from the Bernier data implied that there was probably another source of dilution for the amino acid pools.

Comparison of changes in pool sizes.

Specific radioactivity in a pool could change only if there was an influx of leucine from a pool with a different specific radioactivity. The greater the change in specific radioactivity over time, the greater the difference in specific radioactivity must be between the two pools that were exchanging amino acids. Because specific radioactivity is the ratio of radiolabeled leucine to unlabeled leucine, only information about dilutions of radioactivity and not actual pool size changes can be derived. For instance, there was no way to tell if the change in specific radioactivity was due to an influx of unlabeled amino acid such as from intake or protein degradation or from a source with a very low specific radioactivity such as the intracellular pool. Therefore more estimates of changes in pool size for Q_E and Q_I are required to determine how much the pools change in size and would aid in determining if the intake and oxidation fluxes from the Bernier and Obled data were accurate. Figure 2 shows the estimates for pool sizes for Q_E and Q_I from the Bernier (A) and Obled (B) solutions from Table 5 .

View larger version (22K): [in this window] [in a new window]   Figure 2. Changes in unlabeled leucine in the extracellular pool (QE) and intracellular pool (QI) predicted by the model from the fluxes determined using the data of (A) Bernier and Calvert (1987) and (B) Obled et al. (1991) .

Comparison of predicted specific radioactivities to the Bernier data.

The Bernier data were difficult to fit because the model is overparameterized relative to the data set. Overall specific radioactivity changes in the protein and free amino acid pools did not yield enough information to give "good" estimates of individual fluxes between pools. Several possible combinations of F_IT, F_TI, F_EI and F_IE could yield the same overall specific radioactivity change for the amino acid pool and K_SF, K_RF, K_SM, K_RM, K_SS and K_RS for the overall specific radioactivity of the protein pool. In general, as the number of pools and therefore fluxes to fit increase, more combinations of estimates will yield the same results. However, because more solutions are possible, the algorithms used to fit the data have more difficulty converging, i.e., have more difficulty solving. Therefore only general conclusions about overall rates could be deduced from the Bernier data. More data on changes in specific radioactivities and pool sizes for individual amino acid and protein pools over the experimental period would lead to better predictions of fluxes among pools.

In Table 8 , the observed specific radioactivities of the free amino acid pools showed linear incremental decreases of 66.6 Bq/(µmol · min), whereas the observed specific radioactivities of the protein pools increased at a decreasing rate. Therefore the decrease in specific radioactivity of ¹⁴C leucine in the free amino acid pools could be estimated by constant outflows and inflows of leucine between the amino acid pools, i.e., linear flux equations between amino acid pools (first-order equations). However, the nonlinearity of the increase of specific radioactivity in the protein pool implies that equations to predict protein synthesis fluxes should be dependent on the concentration of substrates (second-order equations). The curvilinear rise in the specific radioactivity of the protein pool was probably due to decreasing amounts of radiolabel passing from the amino acid pools to the protein pool because the specific radioactivities of the amino acid pools were decreasing and a constant amount of amino acid was being incorporated into protein.

Comparison of predicted specific radioactivities to the Obled data.

The Obled data (Table 9) provided much more information about individual pool specific radioactivity changes. The predictions of the specific radioactivities of the protein pools were <4% in error and the predicted specific radioactivities of the free leucine pools were within 10% of the observed values. Because the data were collected over only 15 min, the changes in specific radioactivities for all of the pools were constant except for the intracellular pool, which decreased at a decreasing rate. Because the model was created using linear equations to estimate fluxes, better fits for the linear data would be expected. This suggests that the model can make fairly accurate predictions of fluxes (FSR) when changes in specific radioactivity are constant (data are collected over a short period of time); more long term data about changes in specific radioactivities of amino acid and protein pools are required before better estimates of the fluxes can be made.

View this table: [in this window] [in a new window]   Table 9. Observed (Obs) specific radioactivity (14C leucine as tracer) from Obled et al. (1991) and predicted specific radioactivity (Pred) by the model using parameters from Table 5 i

	DISCUSSION

TOP ABSTRACT INTRODUCTION THE MODEL MODEL EVALUATION DISCUSSION REFERENCES

The lack of data available to define the free amino acid pool sizes and kinetics made it difficult to compare the fitted fluxes to the values derived from the literature. Because the amount of extracellular space seems to be relatively constant (Hider et al. 1969, 1971a and 1971b , Khairallah et al. 1977 , Roberts and Morelos 1965 ) and Q_T should not change over a short period of time, the weakest estimate of free leucine is the value for Q_I. In the flooding dose method, Q_I (5.72 µmol) is relatively small compared with the influx of unlabeled leucine; because the initial Q_I is much larger than Q_E and Q_T, however, an inaccurate estimate of their size could alter the specific radioactivity predicted by the model. In addition, Q_I is likely to be affected by the previous metabolic state of the animal and is the most difficult pool size to determine. In cell culture, Q_I is distinctly different and fairly simple to separate from Q_E. However, on whole-tissue or whole-body bases, Q_I is usually assumed to be the tissue homogenate that also includes Q_E and thus must be corrected for Q_E. The difference in changes in Q_I from predictions based on the Obled and the Bernier data (Fig. 2) could be due to problems associated with estimating Q_I, differences between the Bernier and Obled experimental protocols or differences between the metabolisms of mice and rats. Waterlow et al. (1978) stated that the interperitoneal dosing technique that was used by Bernier caused the amino acid infused to be absorbed more slowly than an intravenous dose as used by Obled. The Obled data may not represent the spike in leucine concentration in Q_I if it occurred before the 5-min measurement. Therefore Q_I decreases. The increase in Q_I observed in the Bernier data may be the slower absorption of leucine resulting from the use of an interperitoneal dose. For the purposes of this model, it has been assumed that the metabolism of the rat and mouse are essentially the same when comparisons are based on body size. If the fluxes are changed to micromole per gram, F_EI, F_ET, F_IT, F_TI and the micromoles of protein synthesized per minute are very close for the Bernier and Obled data fits. However, F_IE from the Bernier data is closer to the literature value (Table 5) for charging from Q_E, and the Obled value is closer to the literature value (Table 5) for charging from Q_I. The literature value for F_IE is based on the assumption that Q_I does not change over time, which is untrue for the fits from both data sets (Fig . 2). Because there are no data for determining F_IE, more information on pool size changes between Q_I and Q_E is required before F_IE can be determined. F_IO and F_OE were dissimilar among the literature, and the Bernier and Obled predictions. The assumptions that, for a nongrowing rodent, synthesis should equal degradation and intake should equal oxidation (Waterlow et al. 1978 ) may be true for a continuous infusion or pulse experiment in which the kinetics of fluxes between pools are close to physiologic levels. But the large bolus of amino acid given with the flooding dose method probably perturbs the system (Toffolo et al. 1993 ). Therefore synthesis probably still does equal degradation in a nongrowing rodent, but intake may not necessarily equal oxidation. The effect of a large dose of amino acid on the system is unknown. Q_E may expand, Q_I may increase or oxidation may increase. It is unlikely that protein synthesis is increased by excess leucine (Tovar et al. 1992 ). However, excess leucine may increase the competition for transport of other amino acids that use the L system, and the oxidation enzymes may be able to adjust to the large influx of amino acid in a short period of time (Calvert et al. 1982 ).

Protein synthesis rates predicted from the data for each individual pool are in fairly close agreement among data sets (Table 5) . Both the Obled and Bernier specific radioactivity data for the protein pool (Tables 8 and 9) show a linear increase in protein synthesis expected with a first-order process (Waterlow et al. 1978 ). Synthesis rates predicted from the Bernier and Obled data fitting are lower for the slow turnover pool than the rates predicted by the organ data (Table 5) . However, because the specific radioactivities of the individual protein pools were not available in the Bernier or Obled data, the predicted FSR for each pool may not be accurate. For example, a slight increase in K_SS could be balanced by a larger decrease in K_SF and still predict the same number of micromoles of protein synthesized, FSR and true FSR. The same overall FSR could be predicted from several possible combinations of K_SS, K_SM and K_SF. Increasing recycling (in the fitting solutions in Table 5 , no recycling was allowed) could also increase K_SS, K_SM and K_SF without increasing FSR or true FSR and increasing the micromoles of leucine into protein per minute only slightly. In addition, the K_SS, K_SM and K_SF predicted by the continuous infusion method are proportionally lower than those predicted by the flooding dose method. The decrease in specific radioactivity of the protein pool is too great to be caused by the heterogeneity of proteins at a 15-min measurement vs. a 3-h measurement. However, recycling could account for the lower FSR values because increasing recycling decreases the specific radioactivity of the protein pools. In addition, with a longer experimental time period, more recycling is probably taking place. To quantitate recycling or predict if recycling is more likely in a faster turnover tissue, the individual specific radioactivities in the fast, medium and slow turnover protein pools must be known.

The six-pool model of protein turnover in a rodent was able to duplicate data (Bernier and Calvert 1987 , Obled et al. 1991 ) of changes in specific radioactivities in free amino acid and protein pools over time. The model was also able to predict FSR, channeling and recycling rates. Therefore, if specific radioactivity data, including changes in protein and free amino acids over time are available, the model can predict FSR in nongrowing rodents of different sizes. The model also has the potential to represent protein turnover in individual tissues; however, it must be evaluated with tissue-specific radioactivity data.

	FOOTNOTES

 
² To whom correspondence should be addressed.

¹ The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked "advertisement" in accordance with 18 USC section 1734 solely to indicate this fact.

³ To whom reprint requests should be addressed.

⁴ Abbreviations used: FSR, fractional synthesis rate; PC, percentage channeling; PR, percentage recycling. For the definitions of other abbreviations, see Table 1 .

Manuscript received March 26, 1998. Initial review completed August 7, 1998. Revision accepted December 1, 1998.

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