## Abstract

Phenylalanine (Phe) kinetics are increasingly used in studies of amino acid kinetics, because the metabolic fate of Phe is limited to incorporation into protein (protein synthesis, S_{p}) and catabolism via hydroxylation (*Q*
_{pt}) to tyrosine (Tyr). Besides an infusion of labeled Phe to measure Phe flux (*Q*
_{p}), a priming dose of Tyr and an independent Tyr tracer are used to measure Tyr flux (*Q*
_{t}) and*Q*
_{pt}. Alternatively,*Q*
_{t},*Q*
_{pt}, and S_{p} can be approximated by using equations, based on Phe and Tyr concentrations in body proteins, that eliminate the need for a Tyr tracer. To evaluate the accuracy of this approach, data were obtained from 12 type I diabetic patients and 24 nondiabetic control subjects who were studied with the full complement of tracers both with and without insulin infusion. S_{p} approximations closely matched measured values in both groups (mean difference <2%, all values <5%), but the agreement was poor for*Q*
_{pt} (error range = −8 to +43%) and*Q*
_{t} (error range −22 to +41%). Insulin status had no effect on these comparisons. The lower approximation error for S_{p} vs.*Q*
_{pt} is due to the small contribution (∼10%) of*Q*
_{pt} to*Q*
_{p}. Approximation error for *Q*
_{pt}(*r* > 0.99) can be explained by variability in the ratio of Tyr to Phe coming from protein breakdown, (*Q*
_{t} −*Q*
_{pt})/*Q*
_{p}. Ideally, all fluxes should be directly measured, but these data suggest that whole body S_{p} can be approximated with an acceptably small margin of error. However, the same equations do not yield reliably accurate values for*Q*
_{pt} or*Q*
_{t}.

- protein metabolism
- stable isotopes

the use of stable isotopes has become an invaluable tool for measuring whole body protein synthesis rates in humans. Among the useful tracers for such studies is isotopically labeled phenylalanine (Phe), as proposed by Clarke and Bier (3) and further developed by Thompson et al. (16). Phe is an ideal tracer because it is not synthesized endogenously and has only two fates in the body: incorporation into protein (protein synthesis, S_{p}) and conversion to tyrosine (Tyr) through hydroxylation. As described by Thompson et al., Phe-to-Tyr hydroxylation (*Q*
_{pt}) can be determined from *1*) incremental Tyr enrichment derived from a Phe tracer during an infusion of labeled Phe and *2*) Tyr flux (*Q*
_{t}) by use of an independent Tyr tracer. Both Phe and Tyr enrichment in plasma can be determined by use of established gas chromatography-mass spectrometry methods.

As an alternative to directly measuring*Q*
_{t} and*Q*
_{pt}, Thompson et al. (16) developed equations to approximate both of these parameters and, therefore, whole body S_{p}. Using this indirect approach does not require the independent Tyr tracer infusion. It was originally proposed that excluding the Tyr infusion had both practical and financial benefits (16). From a practical standpoint, tyrosine’s low solubility can necessitate large infusion volumes, which may be difficult in some patients, i.e., children or subjects with renal complications. At least four investigations involving newborns or young children have used the approximation equations, presumably for these reasons (4, 7, 15, 17). However, Tyr infusions have been successfully performed in premature infants (5). In many clinical conditions, such as renal and cardiac failure, however, there is obvious advantage if the volume of the infusion can be restricted.

Regardless of the reason for using the approximations, the method has yet to be adequately tested for its validity. The assumptions of the model are that Phe and Tyr appear only from protein breakdown in the fasted state and that the ratio of their appearance should resemble the proportional content of Tyr and Phe in whole body proteins. For their calculations, Thompson et al. (16) selected a Tyr-to-Phe ratio of 0.73 on the basis of animal studies (10). The validity of their approximation equations was originally demonstrated in four healthy adults (16). In this small group approximated and measured averages differed by only 1% for both*Q*
_{pt} and S_{p}. Subsequent comparisons have been less consistent, however. In six type I diabetic patients, approximated S_{p} was only 5% lower than measured, but*Q*
_{pt}approximations averaged 51% higher (14). Likewise,*Q*
_{pt}approximations in six premature infants ranged from 11% under to 25% over the measured values (15). In contrast, less than 2% variation between the approximated and measured parameters was reported in three pediatric cancer patients (4).

With the increasing use of labeled Phe in human metabolic studies, it is important that the models and equations employed are rigorously tested to determine the validity of the approximation equations. Previous reports raise the possibility that use of approximations could produce variable results. It is uncertain whether the variability in these earlier studies is due to shortcomings in the model and equations, limited sample sizes, or differences in the metabolic state of the subjects studied. The current study was performed with these concerns in mind. We have evaluated the accuracy of the indirect method for determining whole body Phe kinetics by using a much larger study population than has previously been reported. Furthermore, the data were obtained from studies of patients with type I diabetes and nondiabetic control subjects, each studied with and without administration of exogenous insulin, so that the influence of metabolic status could be assessed.

## METHODS

#### Materials.

l-[^{15}N]Phe,l-[*ring*-^{2}H_{5}]Phe,l-[*ring*-^{2}H_{2}]Tyr, andl-[*ring*-^{2}H_{4}]Tyr were purchased from Cambridge Isotope Laboratories (Andover, MA).l-[^{15}N]Tyr and additionall-[*ring*-^{2}H_{4}]Tyr were purchased from Isotec (Miamisburg, OH). All isotopes were 99 atom percent excess. The chemical, isotopic, and optical purities of these compounds were confirmed before use. Sterile solutions were prepared and shown to be bacteria and pyrogen free before use in human subjects.

#### Subjects.

Data from 72 studies were obtained from a total of 36 men and women who provided informed written consent to participate in three different institutionally approved protocols (Table1). Subjects were classified as either having type I diabetes or as being nondiabetic controls. All diabetic volunteers were studied in the insulin-treated and insulin-deprived states on separate occasions at least 3 wk apart. Results from six members of the diabetic group (referred to here as*subgroup A*) have already been published (12). Data from the other six diabetic subjects, referred to as *subgroup B*, have not previously been published. The control group was composed of 24 young healthy men and women. Control studies were performed in two phases (basal and insulin infusion) on a single day, as described below. Additional results from the control group appear elsewhere (9).

#### Protocol.

For 3 days preceding each study, participants received a weight-maintaining diet. All subjects were admitted to the hospital 24–48 h before each investigation. No food or caloric beverages were consumed after the evening meal the night before the study. All of the type I diabetic subjects were switched from long- or intermediate-acting insulin to regular insulin 72 h before the study to avoid the carry-over effects of the longer-acting insulin (12). Their subcutaneous regular insulin injections were discontinued at 6:00 PM, and either saline or insulin was infused overnight and throughout the duration of the protein turnover measurements on the following morning. During insulin treatment, insulin dosage was regularly adjusted to maintain blood glucose within the normal range.

Isotope infusions were started at ∼7:00 AM via forearm vein catheters. Members of the control group and diabetic*subgroup B* received primed, continuous infusions ofl-[^{15}N]Phe (3.9 μmol ⋅ kg^{−1} ⋅ h^{−1}, 3.9 μmol/kg prime) andl-[*ring*-^{2}H_{4}]Tyr (2.9 μmol ⋅ kg^{−1} ⋅ h^{−1}, 2.9 μmol/kg prime), and a priming dose ofl-[^{15}N]Tyr (1.4 μmol/kg). Diabetic *subgroup A*received primed, continuous infusions ofl-[*ring*-^{2}H_{5}]Phe (4.6 μmol ⋅ kg^{−1} ⋅ h^{−1}, 4.6 μmol/kg prime) andl-[*ring*-^{2}H_{2}]Tyr (3.5 μmol ⋅ kg^{−1} ⋅ h^{−1}, 3.5 μmol/kg prime), and a priming dose ofl-[*ring*-^{2}H_{4}]Tyr (1.5 μmol/kg) (12). Isotope infusions were maintained for up to 5 h. Arterial blood samples were collected from either brachial or femoral lines, immediately before the isotope infusion was started and then at 10- to 20-min intervals after isotopic plateau had been reached (2–3 h after start of the infusion). The protocol for controls included a second study phase on the same day. Immediately on conclusion of the basal period, insulin was infused at either 0 (saline), 0.25, 0.50, or 1.00 mU ⋅ kg body weight^{−1} ⋅ h^{−1}for 2.5 h (9). Six subjects were assigned to each insulin dose. Four arterial blood samples were collected at 10-min intervals beginning 2 h after the start of insulin in this group.

#### Sample analysis and calculations.

Plasma enrichment of Phe and Tyr were determined using gas chromatography-mass spectrometry, as described (9).*M*-4 mass abundance of [^{2}H_{2}]Tyr was adjusted for *m*-2 mass distribution by use of a matrix correction. The reproducibility and stability of the measurements were determined for each isotope measured. Interassay coefficients of variation, determined from replicates of a representative plasma sample, were between 3.8 and 6.0%. Isotopically enriched standards were used to calculate the intra-assay coefficients of variation, which ranged from 2.7 to 6.7%.

Whole body kinetics for Phe and Tyr were calculated using the equations described by Thompson et al. (16) and outlined below. Infusion and flux rate units are micromoles per kilogram per hour. The rates of flux (*Q*) of Phe and Tyr (measured) were obtained from isotope dilution
Equation 1where i is the rate of tracer infusion and E_{infusate} and E_{plasma} correspond to the enrichments of infusate and plasma amino acids, respectively. Conversion rate of Phe to Tyr (*Q*
_{pt}) in the measured model was calculated as
Equation 2where*Q*
_{t} and*Q*
_{p} are the flux rates for Tyr ([^{2}H_{4}]Tyr or [^{2}H_{2}]Tyr) and labeled Phe, respectively. E_{t}and E_{p} are the Tyr ([^{15}N]Tyr or [^{2}H_{4}]Tyr) and labeled Phe enrichments in plasma, respectively, and i_{p} is the infusion rate of the Phe tracer.

The approximations of*Q*
_{t} and*Q*
_{pt} were obtained from the following equations
Equation 3
Equation 4where P_{t} and P_{p} refer to the protein contents of Tyr and Phe, respectively, and the other quantities are as previously described. *Equation 3
* is a mathematical combination of *Eqs. 2
* and *
4
*. The molar ratio of P_{t} to P_{p}, according to Thompson et al. (16), was assumed to be 0.73 on the basis of measurements in animal studies (10). When*Q*
_{t} was calculated with *Eq. 4
*, the approximated value for*Q*
_{pt}(*Eq. 3
*) was used.

The rate of whole body incorporation of Phe into proteins, S_{p}, was calculated as the difference between*Q*
_{p} and*Q*
_{pt}. Measured and approximated S_{p} values were determined by using either the measured or approximated*Q*
_{pt}, respectively.

To determine the agreement of approximated values with measured values, comparisons between means of each treatment were first performed, as shown in Figs. 1-3. The graphic method of Bland and Altman (1) was also used, with slight modification. Differences between measured and approximated values were plotted against the measured values in Figs. 4-6, with the assumption that the measured value was accurately determined. Approximation error was calculated as the percent deviation of the approximated value from the measured value. Analysis of variance was used for comparisons within and between groups. Pearson product correlations were used to determine the strength of association for selected variables. Significant effect for all tests was accepted at*P* < 0.05.

## RESULTS

Isotopic enrichment values are shown in Table2. All subjects studied achieved isotopic plateau for plasma amino acid enrichments during the study period (9,12). To increase the sample size in the diabetic group, data from*subgroups A* and*B* were pooled, despite the fact that they received differentially labeled (^{15}N or deuterated) Phe and Tyr tracers as described in methods. Data pooling was performed only after it was confirmed that there were no systematic differences in any of the outcome variables of interest between the two data sets. For the sake of clarity, no distinction between *subgroups A* and*B* is made in the remainder of the text. However, to demonstrate the overlap of the results, different symbols are used in Figs. 4-6 to denote the two diabetic subgroups. Agreement between [^{15}N]Phe and [^{2}H_{5}]Phe kinetics has been demonstrated previously by others (8).

As previously reported and shown in Fig. 1, insulin infusion decreased S_{p} in both the diabetic (12) and control groups (9). A slight dose-dependent effect was evident in controls receiving insulin, but this was not statistically significant. The agreement between measured and approximated S_{p} was not affected by insulin status (see Fig. 4 and Table 3). Correlational analysis indicated excellent agreement between measured and approximated S_{p} values in both the control (*r* = 0.99) and diabetic (*r* = 0.98) groups. Approximated values tended to be lower than measured S_{p}, especially in the control subjects, but the average error for the S_{p} approximations was <2%, and the range was 4.8% below to 1.1% above the measured value (Table 3). However, Fig. 4 reveals a tendency for greater separation between measured and approximated values as measured values increase.

Agreement between the direct and indirect models was not as strong for*Q*
_{pt} as it was for S_{p}. Exogenous insulin reduced*Q*
_{pt} in controls but not diabetics (Fig. 2), although there was no systematic effect of insulin on the relationship between measured and approximated values (Fig. 5 and Table 3). The correlation coefficients between the measured and approximated*Q*
_{pt} values were high in each subject group and treatment (*r* = 0.89). By comparing Figs. 4 and5, it is clear that the absolute differences between measured and approximated *Q*
_{pt}are the same as for S_{p} (±2 μmol ⋅ kg^{−1} ⋅ h^{−1}). The percent error of the approximations is an order of magnitude higher for *Q*
_{pt} than S_{p}, however. The range of*Q*
_{pt} approximation error in all subjects was −8% to +43%, with all of the control data and one-half of the diabetic data higher than measured. Unlike S_{p}, the differences between measured and approximated*Q*
_{pt} were evenly distributed (Fig. 5).

Diabetics and controls both had reductions in Tyr flux in response to the insulin administration (Fig. 3). Again, there was no effect of insulin on the agreement between measured and approximated values (Fig.6, Table 3). Correlations between approximated and measured values were lower than for S_{p} or*Q*
_{pt}(*r* < 0.77, controls;*r* < 0.45, diabetics). The range of error was −22% to +41%, and the approximated values were most likely to be overestimates of the measured values (Table 3). Mean differences between measured and approximated*Q*
_{t} were statistically significant in controls but not diabetics.

Flux ratios are shown in Table 4.*Q*
_{pt} and*Q*
_{t} data for these calculations were obtained from the measured model with all three of the Phe and Tyr isotopes. The ratio of*Q*
_{pt} to*Q*
_{p} indicates the relative contribution of Phe hydroxylation to total*Q*
_{p}. It can be seen that *Q*
_{pt}accounted for 9–11% of total*Q*
_{p} in all cases, with no differences between groups or treatments. The ratio (*Q*
_{t}−*Q*
_{pt})/*Q*
_{p}in Table 4 represents the ratio of Tyr and Phe flux coming from whole body protein breakdown (16). Theoretically, this ratio should approximate 0.73, which is the value used for P_{t}/P_{p}in *Eqs. 3
* and *
4
*. The results show that the control group value was significantly lower than 0.73 in both study phases. Diabetic subjects were evenly distributed above and below the 0.73 value, although the average was <0.73 in both conditions.

When the measured (*Q*
_{t} −*Q*
_{pt})/*Q*
_{p}ratios were plotted against the*Q*
_{pt} approximation errors (Fig. 7), a wide range of (*Q*
_{t} −*Q*
_{pt})/*Q*
_{p}values (0.52–0.81) was evident, and the relationship between the two variables was very strong (*r* > 0.99). In Fig. 7 all 72 data points are pooled to illustrate that a single line can be used to describe the relationship between (*Q*
_{t} −*Q*
_{pt})/*Q*
_{p}and the *Q*
_{pt}approximation error, regardless of metabolic status. The line of best fit was slightly curvilinear, as denoted by the equation (*y* = 266*x*
^{2} − 527*x* + 244) in Fig. 7.

## DISCUSSION

The purpose of the current study was to determine the accuracy of the approximation equations for whole body Phe kinetics by use of a previously developed model. Several studies in the literature have used the approximation equations (4, 6, 7, 15, 17), but to date a limited amount of data has been presented that addresses their accuracy. For the purpose of analysis, we have evaluated the approximated values by using the measured values as a benchmark, assuming that the measured values are accurate.

The results show that whole body S_{p} approximations differed from measured values by <2%, or <0.75 μmol ⋅ kg^{−1} ⋅ h^{−1}, on average. The error was biased toward underapproximation in all of the control subjects. Values for subjects with diabetes, however, were equally under- and overapproximated. There was also a slight tendency for the size of error to increase with the absolute value of S_{p}. In practical terms, however, the discrepancies between measured and approximated values are negligible. Figure 1 demonstrates that the variability among subjects within groups is typically equal to or greater than that of the approximation errors. A natural concern when the indirect model of Phe kinetics is used is that agreement between the measured and approximated outcomes could change among treatments or patient groups. Our data show no effect of insulin on accuracy of approximations in either the group with type I diabetes or the group without diabetes. There was a small difference in average approximation error between the diabetic and nondiabetic groups, but, again, in practical terms this difference should not prevent the identification of physiologically important effects in similar patients. Other metabolic states or treatment conditions need to be examined, but in general these results suggest that in studies in which whole body S_{p} is the variable of interest, the indirect model provides acceptable results.

In contrast, the approximation equations provided unacceptably variable results for *Q*
_{pt}and *Q*
_{t}. As shown in Table 3, the error rates for these two parameters were 10-fold higher than for S_{p}. The indirect model produced*Q*
_{pt} values that were significantly higher than the measured approach, which in turn caused the underapproximation of S_{p}. S_{p} is calculated as the difference between *Q*
_{p} and*Q*
_{pt}, so any error associated with approximating*Q*
_{pt} will be reflected in the S_{p} value. However, *Q*
_{pt} was only 10% of the total*Q*
_{p}, so it makes only a minor contribution in the final S_{p} calculation. Other authors tend to report higher hydroxylation rates, i.e., 15–25% of*Q*
_{p} (2-4,13-16), so there is potential for*Q*
_{pt} approximation error to make a greater impact on S_{p}, but the contribution should still remain fairly small. Approximations of*Q*
_{t}, on the other hand, give the same relative error as*Q*
_{pt} because of the method of calculation. In absolute terms,*Q*
_{t} approximations were as much as 8 μmol ⋅ kg^{−1} ⋅ min^{−1}above to 11 μmol ⋅ kg^{−1} ⋅ min^{−1}below the measured values in these subjects, which is too high to be of use in nearly any study.

A closer look at the*Q*
_{pt} approximation error showed that it was clearly related to the ratio of*Q*
_{t} and*Q*
_{p} coming from protein breakdown, (*Q*
_{t} −*Q*
_{pt})/*Q*
_{p}(Fig. 7). When Thompson et al. (16) developed the equation for estimating Phe hydroxylation (*Eq.3
*), it was assumed that Tyr and Phe appeared from catabolism in the same ratio as their relative distributions in whole body proteins (P_{t}/P_{p}= 0.73). The data in Fig. 7 show that this ratio did not accurately fit the subjects in this study, particularly the control group, because the majority of values were lower than 0.73.

To derive the 0.73 P_{t}/P_{p}value, Thompson et al. (16) used the whole body protein amino acid composition from a hen (P_{t}/P_{p}= 0.68) and extrapolated from multiple tissue analyses in rat (0.75) and pig (0.75), which were published in the monograph of Munro and Fleck (10). There is a lack of similar data for humans, so most subsequent authors have opted to use the 0.73 ratio in their calculations of Phe hydroxylation. However, for their study on Phe kinetics in infants, Kilani et al. (7) used a ratio of 0.71 to estimate Phe hydroxylation, citing previous work on the human fetus (18). On closer examination, however, the ratio appears to have been miscalculated by those authors (7). The original report of Widdowson et al. (18) presented the amino acid content of fetal bodies in relative mass units (g/g N), which would yield a Tyr-to-Phe mass ratio of 0.71. The number that should be used in the flux equations should be the Tyr-to-Phe molar ratio, which would be 0.64 when the data of Widdowson et al. (18) are used.

In light of the different ratios available, two important points about using them in the approximation equations should be made clear. First, the ratio of amino acids in whole body proteins (P_{t}/P_{p}) is not likely to match the ratio of those amino acids coming from whole body protein breakdown (*Q*
_{t} −*Q*
_{pt})/*Q*
_{p}. This discrepancy stems from the fact that there are multiple protein pools in the body that have different amino acid ratios (10), different pool sizes, and different turnover rates (11, 12). For example, skin and muscle have a high P_{t}/P_{p}and large protein pools but slow turnover, whereas liver and gut have a low P_{t}/P_{p}, smaller pool size, and high turnover. The P_{t}/P_{p}estimate greatly oversimplifies the complexity of factors determining (*Q*
_{t}−*Q*
_{pt})/*Q*
_{p}. To further complicate matters, changing physiological conditions could affect the (*Q*
_{t}−*Q*
_{pt})/*Q*
_{p}ratio if some protein pools respond differently than others.

Second, in view of the current results, selecting a “better” ratio to use in the approximation equations is not really possible. The main reason is the high variability of (*Q*
_{t} −*Q*
_{pt})/*Q*
_{p}among subjects (range = 0.52–0.81). The cause of this variability is not apparent. Given the high degree of precision for measuring isotopic enrichment in plasma, the variability is more likely physiological than methodological. Whatever the explanation, this variability among patient groups and studies is common. Pacy and colleagues (13, 14) reported average values between 0.52 and 0.59 irrespective of nutritional state or diabetic status. In three pediatric cancer patients (4) and four healthy adults (16), the average ratio was 0.76, whereas in nine healthy infants, the average was 0.88 (2). These differences help explain why previous attempts to validate the approximation equations have met with mixed success. In the studies of young cancer patients and healthy adults, (*Q*
_{t}−*Q*
_{pt})/*Q*
_{p}averaged 0.76, and estimate error for Phe hydroxylation was <2% (4,16). However, in six type I diabetics, the average ratio was 0.53 under both insulin-treated and insulin-deprived states, leading to an average hydroxylation estimation error of 51% (14). These results are compatible with those shown in Fig. 7.

In conclusion, use of the approximation equations for Phe kinetics can provide reasonably accurate rates of whole body protein synthesis, but approximation of Phe hydroxylation and Tyr flux is associated with unacceptably high and variable levels of error. We have demonstrated that the approximation errors are closely related to the ratio of Tyr to Phe coming from protein breakdown and that this parameter varies widely among subjects. It is unclear why that ratio is so different among subjects, but it underscores the need to use the full measured model in all studies, if possible.

## Acknowledgments

We gratefully acknowledge the skillful technical assistance of G. C. Ford, M. Persson, M. Bigelow, and the Clinical Research staffs of the Mayo Clinic and the Karolinska Hospital.

## Footnotes

Address for reprint requests and other correspondence: K. S. Nair, Endocrine Research Unit, 5–194 Joseph, Mayo Clinic and Foundation, Rochester, MN 55905 (E-mail: nair.sree{at}mayo.edu).

This work was supported in part by National Institutes of Health Grant DK-41973 and General Clinical Research Center Grant RR-00585.

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked “

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- Copyright © 1999 the American Physiological Society