Total body water and the exchangeable hydrogen I. Theoretical calculation of nonaqueous exchangeable hydrogen in man

JESUS M. CULEBRAS AND FRANCIS D. MOORE Department of Surgery, Harvard Medical School at Peter Bent Brigham Hospital, Boston, Massachusetts 02115

CULEBRAS,JESUS M., AND FRANCIS D .MOORE .TotaZ body water and the exchangeable hydrogen. I. Theoretical calcula- tion of nonaqueous exchangeable hydrogen in man. Am. J. Physiol. 232(l): R54-R59, 1977 or Am. J. Physiol.: Regulatory Integrative Comp. Physiol. l(1): R54-R59, 1977. -A theoreti- cal calculation of the total nonaqueous exchangeable hydrogen in protein, carbohydrates, and fat in man has been made. It shows that of the total exchangeable hydrogen in the body 5.22% is located in biochemical components, soluble in body water, containing hydrogen that is exchangeable with the isotope. This value represents a maximum upward distortion of total body water measurements by isotope dilution, due to the maximum possible exchangeability in these molecular conformations. From comparative measurements reported in the literature it is clear that this maximum is not achieved during the short period of time during which tritium-dilution studies are performed. It is the authors’ belief that the hard-to- exchange amide hydrogens described by Blout in the protein conformations account for this failure of the isotope to achieve complete exchange in the short time allowed.

body composition; tritium space; protein conformation; isotope dilution

FOR THE PAST THIRTY YEARS, since first conceived by Hevesy and Hofer (7) and reported in laboratory ani- mals by Moore (10) total body water (TBW) has been measured by the dilution of isotopic water.

Both of the hydrogen atoms of water are fully ex- changeable with isotopic water tagged by substituting hydrogen with either deuterium or tritium. It is on this fact that the measurement of total body water is based. After injection of the tracer dose of tritiated or deuter- ated water, a period of equilibrium is allowed to pass. Samples of blood or other body fluids are then taken, appropriately treated by distillation or oxidation, and measured for isotope concentration. By this simple iso- tope-dilution formula, the equilibrium concentration being taken as the denominator, the total volume of dilution is calculated and reexpressed as total water. In practice an equilibrium time of approximately 2 h has been shown to be satisfactory for mixing and exchange in mammalian body water although over 95% of the exchange occurs much more rapidly than that. Losses in expired air and urine are negligible because of the long half-life of isotopic hydrogens in the body, approxi-

mately 11 days as determined by Schloerb et al. (12). A potential fault could lie in the existence of biologi-

cal compounds soluble in body water, containing hydro- gen that is exchangeable with the isotope. This ex- changeable hydrogen, other than water, we have termed “nonaqueous exchangeable hydrogen.” Were this to be a large fraction of the total exchangeable hydrogen of the body, the total body water would dis- play a systematic nonrandom error demonstrating a factitiously high value.

There is an impressive body of experimental data (9, 15-17, 20) to show that hydrogen exchange with an appropriate isotope does take place in the case of all organic compounds containing hydroxyl or amino groups in certain conformations. This recombination may not always be a direct substitution, but rather an exchange following ionization of the hydrogen or hy- droxyl component of the compound in solution, followed by alternative recombination with the isotope. Moore et al. (11) have estimated that this nonaqueous exchangea- ble hydrogen accounts for l-Z% of the total exchangea- ble hydrogen in the body, the remainder being water. In any event, the only true validation for the total body water method depends on measurement by isotope dilu- tion followed then by a desiccation measurement of the total water of the carcass or whatever other tissue is being considered.

In a recent series of experiments Tisavipat and Hug- gins (18) have reported systematic errors by which the isotope-dilution value exceeds the total body water as measured directly by desiccation, by amounts as great as 842% of the latter.

Although isotopic hydrogen is incorporated into a variety of molecules by synthetic processes, the half- time of these biosyntheses is so slow and the quantity so small as to consume trivial amounts of hydrogen during the first few hours that the isotope is present. Similarly, the appearance of new untagged water by the oxidation of fat and carbohydrate during the equilibrium period would add to the dilution of the injected isotope but, again, the total amounts involved during a l- or Z-h period would be trivial.

One is therefore left with the possibility that Huggins’ data demonstrate a much larger fraction of body hydro- gen as being in the “nonaqueous exchangeable hydro-

It54

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TOTAL BODY WATER AND THE EXCHANGEABLE HYDROGEN R55

gen” category, than previously considered possible. If corroborated, such findings would render suspect all of the prior data on body composition as based on total water, as well as a number of derived calculations in- cluding intracellular water, average intracellular po- tassium concentration, and body fat.

In this paper we endeavor to calculate an acceptable estimate for the theoretical maximum exchangeable hy- drogen in protein carbohydrate and fat as based on available data from molecular structural analysis.

In a subsequent paper a comparison between TBW measured by desiccation and by tritium in the rat will be described.

NONAQUEOUS EXCHANGEABLE HYDROGEN IN PROTEIN

It is known (9,12,20) that the exchangeable hydrogen atoms are those located in carboxyl, hydroxyl, amino, imino, sulfhydryl, and other groups in which hydrogen is bound to atoms other than carbon. Hydrogen bound directly to carbon is not exchangeable with isotopic hydrogen. Isotopic hydrogen is placed in those linkages only during synthesis, a process whose net effect is negligible over the short term of isotope equilibration by exchange.

We have calculated the percentage of hydrogen ex- changeability in each amino acid, as based on the fore- going considerations. From this it is possible to calcu- late the percentage of the exchangeability of hydrogen in several representative proteins naturally occurring in mammals.

In Table 1 are shown the amino acids naturally occur- ring in mammalian protein, with their formulas, molec- ular weights, the number of theoretically exchangeable hydrogen atoms in each molecule, as well as the percent of the total molecular weight represented by the ex- changeable hydrogen fraction.

In Table 2 the composition of collagen, the most ubiq- uitous protein in mammals, is shown; the percentages of

TABLE 1. Percentage of exchangeable H+ in amino acids

Amino Acid Formulas Molecular Exchangeable H+ wt No.ofH %bywt

atoms

Alanine Lysine Arginine Threonine

CH&HNH&O,H H,N(CH,),CH(NH,)CO,H H2NC(NH)NH(CH2)&HNH2C02H CH,CHOHCH(NH,)CO,H

89.09 146.19 174.21 119.12

2.2449 2.7362 3.4441 1.6790

Tyrosine HOC)-CH,CH(NH,)C02H 181.19 2 1.1038

Tryptophan G,KJW, 204.22 Valine (CH3)$HCH(NH&0,H 117.15 Leucine (CH,),CHCH,CH(NH&O,H 131.80 Aspartic HO,CCH&H(NH,) CO,H 133.10 Glutamic HO,CCH,CH,CH(NH,)CO,H 147.13 Proline C,H9N0, 115.13

1.4690 1.7072 1.5175 1.5026 1.3593 0.7626

Hystidine - a- CH,CH(NH,)CO,H

N NH 155.16 3 1.9335

Phenylalanine Hydroxyproline Serine Methionine Cystine Cysteine Isoleucine Glycine

C,H,CH,CH(NH,)CO,H WW& HOCH,CH(NH2) CO,H CH,SCH2CH2CH(NH2)C0,H [HOzCCH(NH2)CH2S12 HSCH,CHtNH&JO,H (Same as leucine) NHzCHzCOOH

165.19 131.13 105.09 149.22 240.29 121.15

1.2107 0.7826 1.9031 1.3403 1.6647 1.6508

75.00 2 2.6667

The hydrogen atom that shows in the -COOH radical of each amino acid would be exchangeable. However, this hydrogen disappears with the peptide bond formation. There- fore, we did not reflect it in the calculations of this table.

TABLE 2. Collagen (whole protein)

Amino Acid/100 “,i~~$‘[~ng~~- cha?gzb?tH x g Protein* Acid, % by Wtt Amino Acid/100

g Protein

Amino Acid

Alanine 8.04 2.24 0.1801 Arginine 7.20 3.44 0.2477 Aspartic 5.26 1.50 0.0789 Glutamic 9.47 1.36 0.1288 Glycine 22.76 2.67 0.6077 Histidine 0.62 1.93 0.0120 Hydroxylysine 0.83 2.74 0.0227 Hydroxyproline 11.73 0.76 0.0891 Leucine and isoleucine 4.72 1.52 0.0717 Lysine 3.75 2.74 0.1028 Methionine 0.67 1.34 0.0090 Phenylalanine 2.10 1.21 0.0254 Proline 14.40 0.76 0.1094 Serine 2.84 1.90 0.0540 Threonine 1.91 1.68 0.0321 Tyrosine 0.83 1.10 0.0091 Valine 2.86 1.71 0.0489

ASH 2% CARBOHY ORATE 1 ‘!b

n

FAT 20%

PROTEIN IS’!/.

WATER 59%

NON-AQUEOUS 5.2”/.

AQUEOUS 94.8 ‘/.

Total 100.00 1.8294 Average exchangeable hydrogen by weight = 1.83%.

from Tristam (19). t From Table 1, last column. * Data

H exchangeability from the previous table have been applied to this protein; the last column shows the total exchangeable hydrogen calculated for each amino acid. The total sum of this column represents the theoretical percentage of exchangeable H by weight found in colla- gen.

In Tables 3, 4, and 5, similar calculations have been made for other mammalian proteins, actin, myosin, and

BODY COMPOSITION EXCHANGEABLE HYDROGEN

FIG. 1. Theoretical model of exchangeable hydrogen in living ver- tebrate.

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R56 J. M. CULEBRAS AND F. D. MOORE

tropomysin. It should be noted that while in the compo- sition of collagen the total sum of the percentages of each amino acid is 100 in the other three tables the total sum of this column exceeds this value by 11.22-12.45%.

This anomaly is accounted for by the fact that the material in Table 2 (based on Tristam (19)) is corrected for the loss of water weight in amino acids involved in peptide bond formation. The same correction is not made by Kominz et al. (8). These latter data are the basis for the composition of actin, myosin , and tropo- myosin as shown in Tables 3, 4, and 5. The appropriate

correction is shown at the bottom of these tab1es.l When averaging the weight of exchangeable hydrogen for these four proteins we obtain a value equivalent to 1.49% of the total weight of the proteins themselves.

NONAQUEOUS EXCHANGEABLE HYDROGEN IN CARBOHYDRATES

Quantitative isotopic exchange reactions were carried out with free hexoses, their methyl glycosides, and other derivatives by Hamill and Freudenberg (4). They reported that the exchange number of hydrogen agreed closely with the number of hydroxyl groups in the sam- ple. For sucrose, Bonhoeffer and Brown (2) had previ- ously found that approximately one-half of the hydrogen atoms were exchangeable, but no precise value was shown. On the other hand, when glucose or glycogen is isolated from the body of an animal whose body fluids have been enriched with isotopic water, the isotope is invariably found in the product isolated, and it is pre- cisely located in the carbon bound positions (16).

TABLE 3. Actin (hydrolyzed protein)

Amino Acid Amino Acid/ 100 g Protein*

H Exchangeability/ Total Exchangea- AminoG;id, % by ble H x Amino

Acid/ 100 g Protein

Cystine Aspartic Threonine

1.34 1.66 0.0222 10.90 1.50 0.1635

7.02 1.68 0.1179 5.88 1.90 0.1117

14.85 1.36 0.2020 5.06 0.76 0.0385 5.02 2.66 0.1335 6.31 2.24 0.1413 4.92 1.71 0.0841 4.47 1.34 0.0599 7.46 1.52 0.1134 8.25 1.52 0.1254 5.80 1.10 0.0638 4.78 1.21 0.0578 2.94 1.93 0.0567 7.60 2.74 0.2082 6.61 3.44 0.2274 2.04 1.47 0.0300

Based on these findings we have calculated the hydro- gen exchangeability in saccharides. In them, depending on the number of hexoses entering in their composition, the percentage of exchangeable hydrogen varies: in a monohexose like glucose with a formula

Serine Glutamic Proline Glycine Alanine Valine Methionine Isoleucine Leucine Tyrosine Phenylalanine Histidine Lysine Arginine Tryptophan

H-+=0

H-C-OH I

HO-C-H

H--C--OH

H-C-OH

~H,oH

Total 111.25 1.9573

Correction for hydrogen loss in peptide bond formation: 0.625; 1.9573 - 0.625 = 1.3323. Average exchangeable hydrogen by weight = 1.3323. * Data from Kominz et al. (8). t From Table 1 last column.

the molecular weight is 180 and the number of ex- changeable hydrogen atoms is 5, giving a percentage of exchangeable hydrogen by weight of 5 x 100/180 = 2.78%. In the case of a disaccharide TABLE 4. Tropomyosin (hydrolyzed protein)

HO-C-H Amino Acid

H Exchangeability/ Total Exchangea- Amino Acid/ 100 g Protein*

Amino Acid % by

wtt ’ bility H x Amino

Acid/ 100 g Protein

I 0 HO-C-H 1 HO-C-H

I HO-C-H

I H--C----

Cystine Aspartic Threonine

0.78 11.84

3.33 4.20

31.00 0.00 0.94 9.78 4.45 2.38 3.80

12.44 2.72 0.58 0.85

16.01 7.30 0.00

1.66 1.50 1.68 1.90 1.36 0.00 2.66

0.0129 0.1776 0.0559 0.0798 0.4216 0.0000 0.0250 0.2191 0.0761 0.0319 0.0578 0.1891 0.0299 0.0070 0.0164 0.4400 0.2511 0.0000

Serine Glutamic Proline Glycine Alanine Valine Methionine Isoleucine Leucine Tyrosine Phenylalanine Histidine Lysine Arginine Tryptophan

I

H-C- OH H-C-OH 2.24 1.71 H 1.34

out of a molecular weight of 342 only 8 hydrogen atoms are exchangeable, rendering a percen .ta .ge of exchangea- bility of 8 x 1001342 = 2.33 %.

In a nonbranched polysaccharide with a general for- mula of

1.52 1.52 1.10 1.21 1.93 2.74 3.44 1.47 l The formation of a peptide bond between two amino acids in-

volves aloss of a water molecule. Only one of the hydrogens released would be considered exchangeable (i.e., the one on the amino group). Thus, the percentage of exchangeable hydrogen is l/l&h of the total weight of the water lost by peptide bond formation. This fraction (0.055%) of the excess weight of the hydrolyzed protein can be consid- ered as exchangeable hydrogen.

Total 112.45 2.0912

Correction for hydrogen loss in peptide bond formation: 0.69; 2.0912 - 0.69 = 1.4012. Average exchangeable hydrogen by weight = 1.4012. * Data from Kominz et al. (8). t From Table 1, last column.

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TOTAL BODY WATER AND THE EXCHANGEABLE HYDROGEN R57

6 CH&H 6 CHzOH 6 CHZOH 6 CHzOH I I I I

5C- H ’

/ 1 H 4C

--I\ OH

3&.-

if OH

and a molecular weight of (162),, the number of ex- changeable hydrogen atoms is (3), giving a percentage of hydrogen exchangeability of 1.85 %.

In branched chained polysaccharides it is obvious that the percentage of exchangeability by weight will be less than 1.85%.

However, for the purpose of estimating a theoretically maximum amount of hydrogen exchangeability, we will use the mean value of 1.85% for calculations.

NONAQUEOUS EXCHANGEABLE HYDROGEN IN LIPIDS

There is only one noncarbon-bound hydrogen atom in the general formula of fatty acids: C&H,,-,COOH. One of the most common fatty acids found in mammals is stearic acid with a formula of C,,H,,COOH. It has a molecular weight of 284 and only one hydrogen atom is exchangeable. Therefore, the percentage of hydrogen exchangeability by weight is 0.35 %.

Triglycerides (triacylglycerols) constitute the major- ity of storage lipid in man. They result from the esterifi- cation of fatty acids with the three carbon alcohol, glyc- erol. In the process of esterification, the fatty acids lose their only exchangeable hydrogen atom and therefore their hydrogen exchangeability is 0. For our theoretical calculation we will keep the figure of 0.35%.

According to Schoenheimer and Rittenberg (13) none of the hydrogen atoms attached to pure fat should be replaceable by its isotope. Ussing (20) in short experi-

TABLE 5. Myosin (hydrolyzed protein)

Amino Acid AminP/c~~/lOO g * *

H Exchangeability/ Total Exchangeable Amino Acid, % by H x Amino Acid/l00

wtt g Protein

Cystine 1.03 1.66 0.0171 Aspartic 11.40 1.50 0.1710 Threonine 4.88 1.68 0.0820 Serine 4.31 1.90 0.0819 Glutamic 22.80 1.36 0.3101 Proline 2.53 0.76 0.0192 Glycine 2.92 2.66 0.0777 Alanine 6.94 2.24 0.1555 Valine 4.92 1.71 0.0841 Methionine 3.28 1.34 0.0440 Isoleucine 5.50 1.52 0.0836 Leucine 10.35 1.52 0.1573 Tyrosine 3.25 1.10 0.0358 Phenylalanine 4.46 1.21 0.0540 Histidine 2.32 1.93 0.0448 Lysine 12.40 2.74 0.3398 Arginine 7.13 3.44 0.2453 Tryptophan 0.80 1.47 0.0118

Total 111.22 2.0150

Correction for hydrogen loss in peptide bond formation: 0.62; 2.0150 - 0.62 = 1.395. Average exchangeable hydrogen by weight = 1.395. * Data from Kominz et al. (8). t From Table 1, last column.

Ii AH I

H CH

ments of L-12 h noted that the lipds of rats extracted with petrol ether showed no exchange. Schloerb et al. (12) stated that the rapidly exchangeable hydrogen of fat is negligible in amount.

Distribution of exchangeable hydrogen in 70-kg man. Utilizing the values of percentage of hydrogen ex- changeability by weight in the various body compart- ments, water, protein, fat and carbohydrates, and based on the body composition of a 70-kg normal man with 20% fat we calculated the values shown in Table 6.

In Table 7 several hypothetical possibilities of hydro- gen exchangeability in the different solids have been calculated, thus establishing a range of theoretical hy- drogen exchangeability.

From Tables 6 and 7, it is clear that the maximum amount of nonaqueous exchangeable hydrogen by weight in the body is 5.22% of the total exchangeable hydrogen. Stated otherwise, a maximum upward distor- tion of total body water measurements due to the maxi- mum possible exchangeability in these biochemical components would amount to an error of 5.22% of the

TABLE 6. Composition of a 70-kg healthy man (20% fat)

% % of To-

Exch H+ kg tal Exch H

Water

Fat Protein (actin) Carbohydrate Calcium, P, Fe, etc.

Total

All his protein considered actin 41.000 58.57 (11.11%) 4.555 95.17

14.000 20.00 (0.35%) 0.049 1.02 13.000 18.57 (1.33%) 0.173 3.62 4.83 0.500 0.71 (1.85%) 0.009 0.19 > ’ 1.500 2.15

70.000 100.00 4.786 100.00

Water

Fat

Protein (myosin) Carbohydrate Calcium, P, Fe, etc.

Total

Same man considering his protein is myosin 41.000 58.57 (11.11%) 4.555 95.01

14.000 20.00 (0.35%) 0.049 1.02

13.000 18.57 (1.395%) 0.181 3.78 4.99 0.500 0.71 (1.85%) 0.009 0.19 1 1.500 2.15

70.000 100.00 4.794 100.00

Same man considering his protein is collagen Water 41.000 58.57 (11.11%) 4.555 93.90

Fat 14.000 20.00 (0.35%) 0.049 1.01

Protein (collagen) 13.000 18.57 (1.83%) 0.238 4.91 6.10 Carbohydrate 0.500 0.71 (1.85%) 0.009 0.18 1 Calcium, P, Fe, etc. 1.500 2.15

Total 70.000 100.00 4.851 100.00

Same man considering his protein is tropomyosin Water 41.000 58.57 (11.11%) 4.555 94.99 Fat 14.000 20.00 (0.35%) 0.049 1.02 Protein (tropomyosin) 13.000 18.57 (1.40%) 0.182 3.80 5.01 Carbohydrate 0.500 0.71 (1.85%) 0.009 0.19

1

Calcium, P. Fe, etc. 1.500 2.15 Total 70.000 100.00 4.795 100.00

Water Fat Protein Carbohydrate Calcium, P. Fe, etc.

Total

Average of all previous samples 41.000 58.57 (11.11%) 4.555 94.78 14.000 20.00 (0.35%) 0.048 13.000 18.57 (1.49%) 0.194 0.500 0.71 (1.85%) 0.009 1.500 2.15

70.000 1oo:oo 4.806 100.00

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R58 J. M. CULEBRAS AND F. D. MOORE

TABLE 7. Distribution of exchangeable hydrogen assuming minimum and maximum exchange in fat and carbohydrate compartments

All nonaqueous H potentially exchangeable does exchange

Exchangeable H Aqueous Nonaqueous

g % exch H % exch H %

All potentially exchangeable H in protein and carbohydrate exchanges. Fat H exchangeability

assumed 0

Exchangeable H Aqueous N;;c;quHey

g % exch H % 0

All potentially exchangeable H in protein ex- changes. Fat and carbohydrate H exchangeability

assumed 0

Exchangeable H Aqueous Nonaqueous g % exch H % exch H %

Water 4.555 94.78 94.78 4.555 95.73 95.73 4.555 95.91 95.91 Fat 0.048 0.99 Protein 0.194 4.04 5.22 0.194 4.08 0.194 4.09 4.09 Carbohydrate 0.009 0.19 0.009 0.19 I 4.27

Total 4.806 100 94.78 5.22 4.758 100 95.73 4.27 4.749 100 95.91 4.09

total body water measurement. The same calculations, Were this phenomenon to occur in man, the total made for the four different proteins (actin, myosin, amount of nonaqueous exchangeable hydrogen in pro- collagen, and tropomysin), only differed in an amount tein would be lo-60% smaller than that calculated in less than 1.2%. Table 7.

Of the total maximum nonaqueous exchangeable hy- drogen in the body, most of it (77.25%) is in protein; there is a small fraction in fat (19.12 %) and an almost neglibible one in carbohydrates (3.63 %).

This figure is clearly a maximum that is not achieved as demonstrated by data on comparative measurements (3). Evidently, the nonaqueous exchangeable hydrogen in the three heterogenous solids (protein, fat, and carbo- hydrate) do not demonstrate their theoretical maximum exchange rates in vivo. All carbohydrate will exchange freely, due to the fact that carbohydrates are stored in the aqueous phase and are readily water soluble. On the other hand, lipids are essentially insoluble in water, and hydrogen exchange is probably very slow as well as being tiny in amount.

There is evidence that protein hydrogen exchangea- bility can be modified by exercise. Krogh and Ussing (9) in studies with frogs observed that during a 12-h period the uptake weight of deuterium increased by muscular activity. The authors postulated that a particular atom taken up in a certain position by contraction may be removed to some other place and leave the active group ready for repetition of the exchange.

We have been unable to find any in vivo study in the literature where the dynamics of nonaqueous exchange- able hydrogen following changes in pH were investi- gated. Changes in pH would alter dissociation rates and this might affect the amount of nonaqueous hydrogen availability.

The question arises as to the steric or configurational aspects of hydrogen exchange in protein. Investigating deuterium exchange in water-soluble proteins, Blout et al. (1) found that at the end of 24 h many proteins demonstrate a percentage of amide hydrogens that had not yet exchanges with deuterium. Heating the solution in all cases induced complete deuterium-hydrogen ex- change. These authors concluded that there are highly hydrophobic regions in some portions of the protein molecule which inhibit an exchange between hydrogen and its isotope. These areas, termed by Blout as hard-to- exchange amide hydrogens (HEAH) would be associ- ated with helical portions of the polypeptide chains so surrounded by hydrophobic bonds that the hydrogen exchange reaction would be very slow. The percentage of HEAH for some 10 proteins showed a variation from less than 10% for gamma globulin to 60% for insulin.

Although these possibilities are of great theoretical interest, they have proven to be of little importance in the actual estimation of total body water by tritium dilution. Comparing body desiccation versus tritium dilution for measuring TBW in the rat, we obtained a nonrandom difference of 1.2% of body weight between the two methods (3), the higher value being for the tritium dilution. The results showed a highly signifi- cant correlation with body weight. It seems that the actual interference of nonaqueous exchangeable hydro- gen in TBW measurement by tritium dilution is smaller than the maximum possibility calculated in this paper.

The authors are grateful to Professor Elkan R. Blout for his valuable comments.

Present address of Jesus M. Culebras is Departamento de Cirugia de Aparato Digestivo, Centro National de Especialidades Quirurgi- cas “Ramon y Cajal,” Madrid, Spain.

Received for publication 24 March 1976.

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