a study of the rate of protein synthesis in humans · a study of the rate of protein synthesis in...

A STUDY OF THE RATE OF PROTEIN SYNTHESIS IN HUMANS

II. MEASUREMENT OF THE METABOLIC POOL AND THE RATE OF PROTEIN SYNTHESIS*

BY ANTHONY SAN PIETROt AND D. RITTENBERG

(From the Department of Biochemistry, College of Physicians and Surgeons, Columbia University, New York, New York)

(Received for publication, June 3, 1952)

The view of the living cell as a dynamic system, elaborated in 1939 by Schoenheimer, Ratner, and Rittenberg (3), has been generally accepted. That tissue constituents interact with the diet at a rapid rate has been demonstrated for most components of the diet (4). It is important to differentiate clearly between an equilibrium and a steady or dynamic state (5). A system at equilibrium is a closed one; material neither enters nor leaves and the state is determined by thermodynamic quantities. A system in a stationary state is an open system; materials enter and leave and the state is determined by kinetic factors. The advantages which accrue to a living cell from this form of organization have been indicated by Rittenberg (6). The steady state of the organism is but a reflection of the equality of the rates at which these chemical reactions occur. Recently Sprinson and Rittenberg (7) have developed a method by which the ab- solute rate of protein synthesis in an intact animal can be estimated. The assumption underlying this method is that a dietary amino acid is either used for protein synthesis or is oxidized and its nitrogen excreted. Results of their experiments with N15-labeled glycine indicated that in a normal adult human about 1.3 gm. of protein per kilo of body weight were daily being synthesized. They were further able to estimate the size of the metabolic pool which was found to be about 0.5 gm. of nitrogen per kilo of body weight. Data similar to those obtained by Sprinson and Rittenberg have been reported by White and Parson (8) who fed N15-labeled glycine

* Some of the results given here have been presented by one of us at a Ciba Foun- dation conference in London (1) and at the 120th meeting of the American Chemical Society, New York, September, 1951 (2). We are indebted to J. and A. Churchill, Ltd., for permission to reproduce some material appearing in the published report of the Ciba conference. This work was supported in part by a grant from the Amer- ican Cancer Society on the recommendation of the Committee on Growth of the National Research Council.

t Life Insurance Medical Research Fund Fellowship, 1949-50. This report is from a dissertation submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy in the Faculty of Pure Science, Columbia University. Pres- ent address, McCollum-Pratt Institute, The Johns Hopkins University.

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458 RATE OF PROTEIN SYNTHESIS. II

and N’j-labeled yeast, by Wu and Snyderman (9) who fed N15-labeled L-aspartic acid, and by Bartlett and Gaebler (10) who fed N15-labeled glycine.

In the theoretical treatment of their data, Sprinson and Rittenberg tacitly assume that the excretion of urea is not a rate-determining step. We have reanalyzed this problem without making this assumption.

Theoretical Considerations

We assume the kinetic interrelationship of the amino acid and protein metabolism to be that illustrated by the accompanying scheme.

We define the metabolic pool, as did Sprinson and Rittenberg (7)) as that mixture of compounds, derived either from the diet or breakdown of tissues, that the body employs for the synthesis of tissue constituents, and which is assumed to be homogeneous. Urea is not a part of the metabolic pool.

Let the nitrogen content of the metabolic pool be P gm. of nitrogen. Dietary nitrc.gen enters the metabolic pool at the rate of D gm. of nitrogen per day. Some of the components are used for protein synthesis at the rate of S gm. of nitrogen per day; another part, E, gm. of nitrogen per day, is converted to urea and mixes with urea already present. The remainder of the nitrogen excreted is denoted by E, (gm. of nitrogen per day). We assume E, to be small as compared to E,. The total urea in the organism, U gm. of nitrogen, is the urea pool. Urea enters it at the rate of E, gm. of nitrogen per day and leaves it at the same rate via the urine. Since we assume that the animal is in the stationary state, the rate of protein breakdown, R, is equal to S.

If we define the total excretion of nitrogen in the urine to be ET, then

ET = E, t E,


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A. SAN PIETRO AND D. RITTENBERG 459

For the stationary state

D = ET; R=S

that is, for a subject in nitrogen balance, the rates of nitrogen intake and excretion are equal, and the rates of synthesis and breakdown of proteins are similarly equal.

Let X0 m.eq. of N15, as amino acid, be introduced into the metabolic pool at zero time. This nitrogen will partly be excreted and partly be used for protein synthesis. The relative distribution of the N15 between the protein and the urea pools will be a function of the values of E, and 8. A high rate of excretion will be correlated with a low rate of protein synthesis and vice versa. If one excretory pathway can be completely defined, it should be possible to calculate the values of both P and S.

The complexity of the system is such that an exact treatment of this problem is almost impossible. However, on the basis of certain assumptions and approximations explicitly given below, it is possible to obtain a mathematical solution of some simplicity which is susceptible to experimental test.

Let A, = milliequivalents of N15 remaining in the metabolic pool at any time t. A, = milliequivalents of N15 in the urea pool at any time t. X, = milliequivalents of N15 excreted as urea nitrogen in the time t. t = time in days.

Then, assuming X0 to be small relative to both P and F, the protein pool,

-dx, = 2 (ET + S) dt - & dt (1)

where the first quantity, A,/P(E T + S) d2, represents the amount of Nl5 leaving the metabolic pool in the interval dt for excretion and protein synthesis, and the second quantity, Q dt, represents the amount of N15 that is delivered to the metabolic pool as a result of breakdown of proteins which, during the course of the experiment, had incorporated N15. We shall for the moment disregard this second quantity, for, when XO is much smaller than the total nitrogen content of the subject, Q will be negligible with respect to either ET or X.

It is to be noted that either ET or S can have many components; i.e., nitrogen from the metabolic pool may be used for many synthetic processes having rates ~1, sz . . . s, or excretory /processes having rates el, ez . . . e,. Under these conditions X = Zs, and ET = Ze,.

Equation 1 can be integrated to yield

A, = he-Bt (2)


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where

(2, a)

Equation 2 represents the amount of N15 remaining in the metabolic pool at any time t. The rapidity with which N15 is lost from the metabolic pool will be determined by B.

The rate at which the amount of N15 present in the urea pool changes will be determined by the rates at which N15 is delivered to this pool from the metabolic pool and is lost from the urea pool as excretion of urea nitrogen. Thus,

(3)

On substituting for X, from Equation 2 a first order linear differential equation is obtained of which the solution (11) is

L =

b&U P[E,, - BU]

e[(EulW-~l f + constant 1 e-(E,IU) t

The constant of integration in Equation 4 is equal to - (XoE,U/PIE, - BU]), for at t = 0, X, is 0. By making this substitution and factoring one obtains

MLLU AU = P[E, - BU]

[e-Bt _ e-L%I~) ‘I

Equation 5 represents the amount of N15 present in the urea pool at any time t. The isotope concentration of the urea pool, C,, at any instant is

c, = kl x 100 = 1400kjE,

HE, - BU] [e-Bt _ e-W,/~)tl (6)

Differentiating Equation 6 yields an expression for the rate at which the isotope concentration of the urea pool is changing.

dCu -= dt

- Be-t 1 (7)

The rate of. excretion of N15 as urea nitrogen will be determined by the amount of N15 present in the urea pool. Thus,

dx, -= dt (8)


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Substituting for X, from Equation 5 yields

x0&?

dXe = P[E,, - BUI e-~t _ e-G%JU) t 1 & (9)

The amount of N15 excreted as urea nitrogen in any interval of time t is obtained by integrating Equation 9 between the limits of t = 0 and t = t.

h= t

s 0 dxe = P[E, - BUI XoEu2 [I’ e-Bt& _ s,’ ,-(Eu/u)t&] (lo)

This integration yields

x0-W x6 = P[E, - BUI

Equation 11 represents the amount of N15 which has been excreted as urea nitrogen up to time t.

The maximal fraction of N15 that would be excreted as urea nitrogen, A,, provided there was no return of isotope from the proteins, is obtained by evaluating Equation 11 at infinite time (t,) .

E2 = P[E, - BUI C 1

?i r1 _ e-~tm] - f$ [l _ e--(EJu) L] 1 021

u :m

Substituting for B from Equation 2, a yields

EUZ P u A, = ---

PE, - [ET+ SlU ET+ ifi E, 1 03)

Equation 13 is equivalent to

-Cl A, = -

ET + 6’ 04)

Solution of Equations

For illustration the shapes of the curves obtained when Equations 2, 5, and 11 are plotted against time are shown in Fig. 1. Constants were arbitrarily chosen.

Curve A shows the fraction of isotope remaining in the metabolic pool at any time t. It is an exponential curve, the initial slope of which is determined by the value of the constant B. The larger the magnitude of B, the greater will be the initial slope of this curve and the more rapid the loss of N15 from the metabolic pool.

Curve B shows the fraction of N15 excreted as urinary urea nitrogen in the time t. This curve exhibits an initial lag period during which the isotope concentration of the urea pool is building up, followed by an in-


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creased rate of excretion; the curve finally approaches the value A, as an asymptote.

Curve C shows either the fraction of N15 in the urea pool or the isotope concentration of the urea pool at any time t. Prior to the time of the maximum, t,,,., N15 is being delivered to the urea pool from the metabolic pool at a rate faster than that at which it is being lost from the urea pool for the excretion of urinary urea nitrogen. Beyond the time of the

I\ CURVE A

tmax TIME

CURVE A- FRACTION REMAINING IN METABOLIC POOL

hP

h,=e -Bt

CURVE B-FRACTION EXCRETED AS UREA NITROGEN

I

CURVE C -FRACTION REMAINING IN UREA POOL

Au EUU h, = pcEu-suJ

,-B&t

I

lOOho Eu c u”P-1

-Bt --B-#t x 14 5 1 FIG. 1. Representative curves showing distribution of isotope following intra-

venous injection of labeled amino acid.

maximum, the reverse is the case. At the time of the maximum, these two rates will be equal; i.e., neither the fraction of N16 in the urea pool nor the isotope concentration of the urea pool is changing.

The time of the maximum can be employed to calculate the value of B. Equation 7 denotes the rate at which the isotope concentration of the urea pool is changing, i.e. the slope of Curve C at any time t. At the maximum, the slope of this curve is zero and acu - [ 1 =*= 14**hE,

P[E, - BUI Eu eG%Iu) Gxmx. _ Be-Bfmax.

dt U tmsx. 1 (15)

For this expression to be zero,

EU _ e-(E,/U)tmsx. = Be-Btm=.

u 06)


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B can be calculated from Equation 16 if the values of E,, U, and t,,,, are known.

The magnitude of the metabolic pool, P, can be calculated from Equa- tion 6 provided the isotope concentration of the urea pool at any time is known. For this calculation, the isotope concentration of the urea pool at the time, t,,,., was used.

(17)

The rate of protein synthesis, S, can be calculated from Equation 2, a if ET, B, and P are known.’

ET + S B=- P (2, d

or

S=BP-ET 08)

It should be noted that the experimental procedures used for some of these measurements are such that an average value for the isotope concentration of the urea pool rather than an instantaneous value is obtained. These isotope values were then plotted at the mid-point of the collection interval, assuming they were the instantaneous value for this time. The time of the maximum is taken as the center of that collection period during xvhich the average isotope concentration of the urea pool was at its maximal value. That this assumption does not introduce any serious error in the calculations is shown in Appendix I.

A sample calculation is given in Appendix II.

EXPERIMENTAL’

The N15-labeled glycine and aspartic acid were prepared by methods previously reported (12, 13).

The N15-glycine was prepared in sterile saline solution and filtered through a sterile Seitz bacterial filter, and a measured aliquot of this solution was injected intravenously. In Experiment DR-1, 715 mg. of glycine (32.9 atom per cent excess N15) in a volume of 19 ml. were injected over a period of 3 minutes. For Experiment AGS-1, 805 mg. of glycine (32.9 atom per cent excess N15) in a volume of 20 ml. were injected over a

1 We assume that all of the Nr5 excreted is in the urine. Actually a small per cent of the NrS is excreted in the feces (3). This will tend to make our values for total nitrogen excretion low and our value for the rate of protein synthesis, S, a little high.

* The quantitative nitrogen values were a measure in terms of milliequivalents of nitrogen. These were converted to a mg. basis by neglecting the difference in mass between normal and heavy nitrogen and multiplying all the values by 14.


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period of 2 minutes. In a case of aspartic acid, 2.02 gm. of the amino acid (29.7 atom per cent excess N15) were neutralized with sodium bicar- bonate and administered orally. The volume of solution given was 300 ml.

Normal male adults in nitrogen balance, on a diet of their own choosing, were used in these experiments. Just prior to the administration of the amino acid, the bladder was emptied and urine samples were collected at various time intervals for a period of 2 days. The volume of urine voided during each collection period was measured and the samples then made up to a definite volume with distilled water. Aliquots of the diluted urine samples were ana.lyzed for total nitrogen and N15 concentration of the ammonia, urea, and total nitrogen fractions (14, 15). When glycine was

TABLE I

Size of Metabolic Pool and Rate of Protein Synthesis in Human Subjects

For Experiments DR.1 and DR-2, the subject’s age was 44 years, and for Experi- ment AGS-I,28 years. Experiment AGS-2 was done on the same subject as Experi- ment AGS-1, 2 years later.

Experiment No. Body weight

kg. DR-1 68 DR-2 6S AGS-1 / 72 AGS-2 ) 69

I

-1

Amino acid administered I p

Glycine (intravenous) Aspartic acid (orally) Glycine (intravenous)

I‘ ‘I

w. gm. N per day

0.61 39.4 0.84 29.0 3.40 91.8 1.8 59

s

administered, a measured aliquot of the injection solution was similarly analyzed for total nitrogen and N15 concentration.

RESULTS AND DISCUSSION

The size of the metabolic pool, P, and the rate of protein synthesis, S, for these experiments are given in Table I. These values were calculated as previously described. A sample calculation for Experiment DR-1 (Table II) is shown in Appendix II. The time of the maximal N15 concentration of the urea pool is 0.049 day. By using Equation 16, a value for B of 83.2 per day was calculated. P was calculated from Equation 17 to be 0.61 gm. of nitrogen. A value for S of 39.4 gm. of nitrogen per day was obtained with Equation 18.

The size of the metabolic pool resembles the total amount of free amino acid nitrogen in the body. Assuming an average value for free amino acid nitrogen concentration in the blood of 6.5 mg. per cent, the free amino acid nitrogen contents for Subjects DR and AGS are 2.2 and 2.3 gm. of nitro-


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gen3 respectively. The values reported (7, 9) earlier for the magnitude of the metabolic pool were actually some unknown combination of both the metabolic pool and the urea pool. It is apparent that the time of the maximal isotope concentration of the urea pool is of utmost importance in investigations of this nature. At the time of the maximum, almost com- plete distribution of the injected N16 between the protein pool and the urea pool has occurred. The amount of N15 remaining in the metabolic pool, at the time of this maximum, is negligible compared to the amount initially introduced into this pool. Hence, the rate of excretion of N’5 as urinary urea nitrogen, after the time of the maximal isotope concentration of the urea pool, is a measure of the rate of excretion of isotope from the urea pool and not from the metabolic pool as was originally assumed to be the case. The maximal fraction of N15 excreted as urinary urea nitrogen will be given by Equation 14. However, the actual observed fraction of W5 excreted as urinary urea nitrogen is in excess of this maximal fract.ion because of feed-back of N15 from the protein pool. If this feed-back is not taken into account, then the value assumed for the maximal fraction of N15 excreted as urinary urea nitrogen, A,, will be too large. This value is used to calculate the rat.e of protein synthesis, S, and, if it is too high, then the calculated value for S will be too small. The values p,eviously reported for the rate of protein synthesis following administration of glycine or aspartic acid are too low for this reason.

It is evident from the data presented (Tables II to IV) that the original assumption of no return of N15 to the metabolic pool from the protein pool is erroneous. In each experiment, the fraction of N15 excreted as urea nitrogen is in excess of the maximal fraction that should have been excreted as urea nitrogen, provided there had been no return of N15 from the protein pool during the course of the experiment. From the data of Ex- periment DR-1 (Table II), it is seen that 24.9 per cent of the N15 was excreted as urea nitrogen in the time of 2.13 days, whereas the maximal percentage of N15 which should have been excreted, calculated from Equa- tion 14, is 17.6 per cent. Theoretically, only 17 per cent of the W5 should have been excreted as urea nitrogen during the course of the experiment. This is not too serious a complication if it is assumed that a constant additional amount of N15 is being excreted as urea nitrogen due to feed- back of N’s from the protein pool. If the observed values are corrected for this feed-back as follows:

Correction = 17 - 24.9 ~ = -3.70y0 per day

2.13

3 The total body water of these subjects was assumed to be 50 per cent of the body weight as measured in Paper I (16).


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a set of corrected values is obtained; these approximate very closely the calculated data. The observed values for Experiments DR-2 and AGS-1 were similarly corrected and are shown in Tables III and IV. In each case, this type of correction has been applied to all of the observed values independent of the time of collection of the urine samples. By using these corrected values for A,, the rate of protein synthesis, X, was calculated from Equation 14. These values are given in Table I.

TABLE II

Rate of Utilization of Glycine Nitrogen by Human Subject (Experiment DR-1)

Tiie Urea nitrogen excreted

mg.

0 -0.017 100 0.017-0.038 246 0.038-0.059 257 0.059-0.081 247 0.081-0.101 196 0.101-o. 127 310 0.127-o. 156 300 0.156-0.229 647 0.229-0.485 2500 0.485-0.827 2620 0,827-l. 23 3330 1.23 -1.54 2945 1.54 -1.83 2540 1.83 -2.13 2840

-

-

N’S concentration

-7

Urea Ammonia -

atom per cent atom fier tent ezcess ezce.w

0.094 3.940 0.107 1.354 0.129 0.558 0.117 0.336 0.122 0.233 0.112 0.185 0.103 0.146 0.101 0.125 0.100 0.091 0.071 0.050 0.047 0.054 0.040 0.034 0.034 0.036 0.023 0.040

-

T

ger cent

0.21 0.73 1.25 1.83 2.32 2.92 3.58 5.11 9.26

12.7 15.0 16.0 16.6 17.0

2 x 100

-

1

- -

-

Observed ( --

hrrectedt

per cent

0.21 0.15 0.80 0.66 1.54 1.32 2.18 1.89 2.72 2.34 3.49 3.02 4.18 3.60 5.64 4.79

11.2 9.61 15.4 12.3 18.9 14.3 21.5 15.8 23.4 16.7 24.9 17.0

- Weight of subject = 68 kilos. * Calculated by Equation 11. E, = 8.95 gm. of N per day, B = 83.2 per day, ET

= 11.5 gm. of N per day, U = 5.65 gm. of N, P = 0.61 gm. of N, A,, = 3.20m.eq. of Nl5.

t Correction, (17 - 24.9)/2.13 = -3.70 per cent per day.

That the size of the metabolic pool is small seems to be indicated by the high value for the isotope concentration of the urinary ammonia. This ammonia can be considered to arise by deamination of the constituent amino acids of the metabolic pool. The isotope concentration of the ammonia would then be equal to the average isotope concentration of the metabolic pool. The isotope concentration of the urinary ammonia does, in fact, decrease very rapidly, almost parallel to the decrease of the isotope concentration of the metabolic pool. Whenever a labeled amino acid is administered, the isotope concentration of the urinary ammonia is greater


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than that of the urea for a short time following administration of the amino acid. This would be consistent with the hypothesis that the isotope concentration of the urinary ammonia is indicative of the size of the metabolic pool, whereas the isotope concentration of the urea is indicative of the amount of urea nitrogen present in the subject for dilution of the newly formed isotope-containing urea. When ammonia is administered, the reverse is the case; the isotope concentration of the urea is greater than that of the ammonia. This would indicate that the isotopic ammonia initially

TABLE III

Rate of Utilization of Glycine Nitrogen by Human Subject (Experiment AGX-1)

Time

days %-.

0 -0.048 878 0.048-0.148 1190 0.148-0.295 2045 0.295-o. 465 1664 0.4650.844 3970 0.844-1.00 1950 1.00 -1.27 2130 1.27 -1.46 2050 1.46 -1.91 4460 1.91 -2.06 1650

Urea nitrogen excreted

N’s concentration

Urea Ammonia C :alculated* Observed hrrectedt

atom ger cent atom per cent ezces* excess

0.057 1.366 0.070 0.256 0.068 0.130 0.068 0.100 0.059 0.051 0.056 0.048 0.052 0.036 0.043 0.033 0.037 0.026 0.036 0.036

per cent per cent *er cent

0.41 1.00 0.69 1.86 2.67 1.73 3.72 5.45 3.57 5.35 7.63 4.67 7.68 12.3 6.98 8.24 14.5 8.13 8.97 16.7 8.60 9.26 18.5 9.20 9.75 21.8 9.59 9.84 23.0 9.88

-

k x 100

Weight of subject = 72 kilos. * Calculated by Equation 11. E, = 10.6 gm. of N per day, B = 31 per day, ET

= 13.7 gm. of N per day, U = 6.06 gm. of N, P = 3.4 gm. of N, xo = 3.57 m.eq. of N’5.

t Correction, (9.84 - 23.0)/2.06 = -6.38 per cent per day.

introduced is being converted to urea and is not identical with the ammonia which is being excreted in the urine. The urinary ammonia arises from unlabeled amino acids of the body.

The concept of a single metabolic pool for the whole body is obviously an oversimplification. From animal experiments (17) it is known that the rates of protein synthesis in various organs are different and so presumably are the rates of turnover of the metabolic pools in the individual organs. The rate of protein synthesis calculated by these measurements is the sum of all of the synthetic rates for the total body. It seems reasonable that, in the main, the measured synthetic rate is related to those proteins, such as the serum proteins and visceral proteins, which have fairly short half


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lives. That this is the actual case can only be inferred from the data presented. However, Borsook et al. (18), working with mice, have found the same time relationships followin, v the intravenous injection of Ci4- labeled amino acids. Within less than 10 minutes, nearly all of the amino acid had disappeared from the blood into the carcass. After 1 hour, both the incorporation into the visceral proteins and the initial burst of oxidation of the amino acid had attained nearly their maxima.

TABLE IV Rate of Utilization of Aspartic Acid Nitrogen by Human Subject (Experiment DR-2)

Time

days

0 -0.014 0.014-0.039 0.039-0.095 0.09&0.251 0.251-o. 470 0.470-0.867 0.867-1.11 1.11 -1.26 1.26 -1.51 1.51 -1.89 1.89 -2.09

Urea nitrogen excreted

w. 286‘ 272 530

1590 2190 4530 2830 1640 2610 3300 2400

N’s concentration

-- I. c

atom per cent atom ger ce ezce*s cscess

0.040 0.431 0.186 1.267 0.241 0.475 0.238 0.195 0.204 0.090 0.143 0.063 0.113 0.104 0.093 0.056 0.074 0.035 0.056 0.031 0.047 0.027

AlIlIIlOIlti

:nt

2 x 100

:&&ted* Observed hrectedt

gev cent per cmt per celzt

0.19 0.18 0.06 0.96 0.98 0.65 3.16 3.00 2.19 8.50 9.00 6.87

13.8 16.1 12.1 19.4 26.3 18.9 21.2 31.3 21.9 22.0 33.7 23.0 22.9 36.8 24.0 23.6 39.7 23.7 23.8 41.5 23.8

Weight of subject = 68 kilos. * Calculated by Equation 11. E, = 10.5 gm. of N per day, B = 51.4 per day,

ET = 13.3 gm. of N per day, U = 5.65 gm. of N, P = 0.84 gm. of N, X0 = 4.52 m.eq. of N’s.

t Correction, (23.8 - 41.5)/2.09 = -8.5 per cent per day.

It is impossible to determine accurately either the size or the character of the protein pool, F, from these considerations. However, it is reasonable to assume that the protein pool is not homogeneous. Were this the case, the feed-back of Nib from the protein pool to the metabolic pool during the course of a 48 hour experiment would be negligible. That this feed-back does occur would indicate that the metabolically active part of the protein pool is much smaller than the total protein nitrogen content of the subject. It is possible to estimate roughly the size of this fraction of the protein pool, F,, from the rate at which the feed-back of N*5 from the protein pool is occurring. From the data for Experiment DR-1 (Table II) it is seen that this feed-back resulted in the excretion of an additional 7.9 per cent of the N15 (0.25 m.eq. of N15) as urinary urea nitrogen in 2.13 days.


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The major part (X/E. + X) of the N15 fed back will be reutilized for protein synthesis; the smaller fraction (ET/ET + 8) will be lost as excretory nitrogen. This would mean that a total of 1.4 m.eq. of N15 had to be returned from the protein pool to the metabolic pool during this time. The rate at which nitrogen is being returned to the, metabolic pool from the breakdown of tissue proteins is equal to the rate of protein synthesis, i.e. 39.4 gm. of nitrogen per day. Let us assume an average isotope concentration, C p, for the metabolically active fraction of the protein pool during the experimental period. This value can be estimated since we know the rate at which nitrogen is being returned to the metabolic pool from the metabolically active fraction of the protein pool and the amount of N15 returned to the metabolic pool in 2.13 days. Therefore,

1.4 X 14 = CF X 39.4 X lo3 X 2.13

CF = 0.23 X 10-a

We know that originally 2.48 m.eq. of N15 (3.20 X X/(E, + 8)) had been incorporated into the metabolically active fraction of the protein pool. At the end of 2.13 days there remains only 2.16 m.eq. of N15 in the metabolically active fraction of the protein pool. The size of the metabolically active fraction of the protein pool, FR, is then given the expression

FR = 2.32 X 14 2.32 X 14 X 103 =

CF 0.23 mg.

FR = 141 gm. of nitrogen

This value is close to that of the nitrogen content of the proteins of the plasma, liver, and the internal organs for a man weighing 70 kilos (19).

The half life of the metabolically active fraction of the protein pool is estimated to be 2.5 days.

ktt = 0.693

(0.693) tt = (3g,4,141) = 2.5 days

This is somewhat lower than the generally accepted values for the half lives of these total organ proteins. However, values similar to this have been reported (20).

The rapidity with which nitrogen is lost from the metabolic pool may prove to be the explanation for the r81e of the time factor in protein synthesis (21). It is known from experiments in which rats are kept on a diet deficient in an essential amino acid that to produce growth the essential amino acid must be fed at the same time as the deficient protein. If any


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considerable time elapses between the feeding of the amino acid and the deficient diet, the supplement will be destroyed before the incomplete protein enters the system. It can be seen from our data that this time interval is about 2 to 4 hours,

The time of the maximal isotope concentration of the urea pool occurs very shortly after the administration of the amino acid, usually within 3 hours. As in previously reported experiments, the time of this maximum has been ascertained from an average value of the isotope concentration of the urinary urea nitrogen. In light of the rapidity with which these reactions are taking place, it might be better to ascertain the time of this maximum from the isotope concentration of the blood urea nitrogen. In this way, instantaneous sampling of the isotope concentration of the urea pool could be achieved. This would allow for a more accurate measure of both the time of the maximum and the isotope concentration of the urea pool at that time. This type of approach would eliminate the possibi1it.y of dilution due to incomplete clearing of the bladder at the start of the experiment. We have carried out an experiment of this nature (Experiment AGS-2, Table I). The time of the maximal N15 concentration of the blood urea nitrogen was 0.092 day. The size of the metabolic pool, P, and the rate of protein synthesis, X, calculated as described above, were 1.8 and 59 gm. of nitrogen per day, respectively.

We are indebted to Mr. Irving Sucher for the mass spectrometric anal- yses and to Miss Laura Ponticorvo for technical assistance.

SUMMARY

1. The size of the urea pool is basic to an evaluation of the interrelationships between the amino acids and protein metabolism. Previously reported measurements of these interrelationships did not take account of the fact that the rate of urea nitrogen excretion was a rate-determining step.

2. A theoretical system describing the interrelationships between the amino acids and protein metabolism in man is presented. The approximations and assumptions necessary for a mathematical treatment of this theoretical system are discussed.

3. The size of the metabolic pool and the rate of protein synthesis in normal human subjects have been calculated. The results indicate that the size of the metabolic pool is small and that this pool is turning over at a rapid rate. It appears that the immediate impact of an injected amino acid is largely dissipated within several hours; from then on redistribution of the amino acids released from the proteins dominates the picture.


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A. S.4N PIETRO AND D. RITTENBERG 471

APPENDIX I

Justijication for Use of Average Isotope Concentration of Collection Interval As Instantaneous Value at Middle Point of Interval

Consider the collection interval t - At to t + At. The average isotope concentration,C,, of the urea pool for this interval is

-

cu = P[E, - BU]

1400bE, [ S,zt ‘;e-;v’t ‘“1

Carrying out the indicated operations, we obtained Equation 20.

(19)

F, = 1400&E, re-Bt

PIE, - BU]2At 1 B (,BAt- ,--Bat) -

[J~-GW-‘) t (20)

&A

(,(E,/V)At _ ,-W,/U)At) 1 By expanding [eBA ’ - emBA “1 and [e(EU’v)A ’ - e- (E~‘v)At] into series, Equation 20

reduces for small values of At to Equation 22.

1400XoE, e, = pjE,gBU] . ..I -

e-:-,v)t[l +E$+g3+ . ..]I c, = p;yo;u, [e-B’ [l + GE21 - e-%lv)t (22)

The instantaneous isotope concentration of the urea pool for the mid-point of the collection interval is

1400XoE,

‘, = P[E, - BUl [e-Bt _ e-wv) t] (6)

The ratio of the average value to the instantaneous value for the isotope concentration of the urea pool is

c Y= e-B t _ ,--b%/U) t

c u e-Bt _ e-(Eu/U) t

(23)

(24)

(25) CA (BA@ -- c , “1 = l + ($[e[B=(Eth) I t _ 1,


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The fraction on the right side of Equation 25 represents the error in the original assumption. For Experiments DR-1, DR-2, and AGS-1, it is 0.22 per cent, 1.23 per cent, and 2.40 per cent, respectively.

APPENDIX II

Sample Calculation of B, P, and S The data presented in Table II are used for these calculations. Calculation of B (Equation 16); time of maximum = 0.049 day.

~~-Bhnsx. = + e-(Eu/U) hmx.

ffe-B tmax. = ;$ (0.926) = 1.47

B = 83.2 per day

Calculation of P (Equation 17).

1400@,

’ = C&E, - BU) (em Bhmx. _ e -(-%IW hmx.)

’ = 0.129(8.95 - 83.2(5.65))

1400(3.20)8.95 X lo+ (o.018 _ o.g26)

P = 0.61 gm. nitrogen

Calculation of S (Equation 18).

S = BP - E,

S = 83.2(0.61) - 11.5

S = 39.4 gm. nitrogen per day

BIBLIOGRAPHY

1. Rittenberg, D., Ciba Foundation conference on isotopes in biochemistry, Lon- don, 190-201 (1951).

2. Rittenberg, D., Abstracts, American Chemical Society, New York, Sept., 8P (1951).

3. Schoenheimer, R., Ratner, S., and Rittenberg, D., J. Biol. Chem., 130,703 (1939). 4. Rittenberg, D., and Schoenheimer, R., Physiol. Rev., 20, 218 (1940). 5. von Bertalanffy, L., Science, 111, 23 (1950). Burton, A. C., J. Cell. and Comp.

Physiol., 14, 327 (1939). Denbigh, K. G., Hicks, M., and Page, F. M., Tr. Faraday Sot., 44, 479 (1948).

6. Rittenberg, D., Harvey Lectures, 44, 200 (1948-49). 7. Sprinson, D. B., and Rittenberg, D., J. Biol. Chem., 180, 715 (1949). 8. White, A. G. C., and Parson, W., Arch. Biochem., 26, 205 (1950). 9. Wu, H., and Snyderman, S. E., J. Gen. Physiol., 34, 339 (1950).

10. Bartlett, P. D., and Gaebler, 0. H., J. Biol. Chem., 196, 1 (1952). 11. Phillips, H. B., Differential equations, New York, 3rd edition, 38 (1934). 12. Schoenheimer, R., and Ratner, S., J. Biol. Chem., 127, 301 (1939).


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13. Wu, H., and Rittenberg, D., J. Biol. Chem., 179, 847 (1949). 14. Van Slyke, D. D., and Cullen, G. E., J. Biol. Chem., 19, 211 (1914). 15. Sprinson, D. B., and Rittenberg, D., J. Biol. Chem., 180, 707 (1949). 16. San Pietro, A., and Rittenberg, D., J. Biol. Chem., 201, 445 (1953). 17. Borsook, H., Physiol. Rev., 30, 206 (1950). 18. Borsook, H., Deasy, C. L., Haagen-Smit, A. J., Keighley, G., and Lowy, P. H.,

J. Biol. Chem., 187, 839 (1950). 19. Vierordt, H., Anatomische, physiologische, und physikalische Daten und Tabel-

len, Jena (1906). 20. Kosterlitz, H. W., Nature, 164, 207 (1944). 21. Geiger, E., Science, 111, 594 (1950).


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Anthony San Pietro and D. RittenbergSYNTHESIS

POOL AND THE RATE OF PROTEIN MEASUREMENT OF THE METABOLIC

SYNTHESIS IN HUMANS: II. A STUDY OF THE RATE OF PROTEIN

1953, 201:457-473.J. Biol. Chem.

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