T H E STUDY OF COLLOIDAL DIMENSIONS, THERMODYNAMIC ACTIVITY, AND T H E MEAN MOLECULAR WEIGHT OF T H E MIXED PROTEINS I N BLOOD SERUM’ ANCEL KEYS Division of Biochemistry, The M a y o Foundation, Rochester, Minnesota Received August 1 , 1037
Estimates as to the molecular weights of blood serum albumin and globulin by the osmotic method (Adair (1, 2, 3, 4, 15)) and by the ultracentrifuge method (Svedberg) are in reasonably close agreement. Serum albumin has a molecular weight of about 70,000, as compared with about 170,000 for globulin. Other things being equal, these values would indicate that at equal concentrations (in units of mass) albumin would have 2.4 times the osmotic activity of globulin. I n biological systems the proteins occur as mixtures, and the relation between the total colloid osmotic activity and the several components in such mixtures is of importance. This is particularly true of blood serum, in which it is generally believed that the osmotic activity of the colloids (almost entirely proteins) is a primary force involved in the preservation of the fluid balance between blood and tissue. In the literature on this subject there are a number of discrepancies,-disagreements with theoretical requirements as well as in the detailed numerical results. Previous investigators have sought, empirically, to formulate an equation which will describe the relation between colloid osmotic pressure and the concentration of the proteins in blood serum (cf., e.g., 6, 8, 17). In blood serum the proteins are albumin and globulin (plus an insignificant amount of fibrinogen), and, if we may accept the application of Dalton’s law of partial pressures to this system (cf. Adair (l)), the relation must be of the form: Colloid osmotic pressure = f’A
+ f”G
(1)
i.e., the C. 0. P. will be the sum of a function of the albumin concentration and a function of the globulin concentration. The simplest form these 1 Presented a t the Fourteenth Colloid Symposium, held a t Minneapolis and Rochester, Minnesota, June 10-12, 1937. 11
12
ANCEL KEYS
functions could take would be as coefficients, Le., constants for multiplication: C. 0. P. = k’A
+ k”G
(2)
Values for k’ and k” have been obtained for human blood serum by Govaerts (8) and von Farkas (6) :
+ 19.5G (Govaerts)
(3)
+ 25.1G (von Farkas)
(4)
C. 0. P. (mm. HzO)
= 75.4A
C. 0. P. (mm. HtO)
= 68A
where the concentrations of albumin and globulin are in grams per 100 cc. and the temperature is about 20OC. Recently, Wells, Youmans, and Miller (17) have proposed the formula:
C. 0. P. = Total protein (21.4 + 5.9A)
(5)
Curiously enough, these authors stress the point that their formula omits globulin, and they argue that globulin is without any important effect. It would seem, however, that their formula (5) should be written:
C. 0. P.
=
(4+ G) (21.4 + 5.9A)
(6)
or
C. 0. P. = 5.9A2
+ 21.4A + 5.9AG + 21.4G
(7)
The data of Wells and his colleagues may be fitted to equation 2 above by the method of least squares2. When this is done we have:
C. 0. P. = 71.5A
+ 8.5G
(8)
as the best fit for these data. In this laboratory we have studied the C. 0. P., albumin and globulin, in serums from fourteen subjects, with a t least two experiments on each; eight of these subjects were normal, while six were patients with cirrhosis of the liver. Colloid osmotic pressure measurements were made in duplicate a t 0°C. by the classical equilibration method as applied by Adair. Proteins were estimated by the Kjeldahl method, using the factor 6.25 to convert nitrogen to protein concentration; separation of albumin and 2
The least squares equations for the general type equation, C . 0.P. = k‘A k”G
are :
+ 2A(C. 0. P.) =k’ZA* + k“ZAG ZG(C. 0.P.) = k‘2AG + k“ZGZ
(1)
(2)
MIXED PROTEINS IN BLOOD SERUM
13
globulin was made by the method of Howe (IO). These data were fitted to equation 2 (above) by the method of least squares with the result:
C. 0. P. (mm. HzO) = 45.2A + 18.8G
(9)
The numerical values for k’ and k” in the equations given above (3, 4 , 8 , and 9) cannot be compared directly, for reasons which will be discussed below, but the ratios of the osmotic activity in serum of albumin to globulin, Ic’llc’’,may be compared. This is done in table 1. The colloid osmotic pressure measured in all these studies, as well as the effective force in the living animal, is the sum of the simple osmotic pressure of the proteins as particles and the Gibbs-Donnan effect which arises from the fact that we have to deal with protein ions. The calculation of k’/k’’ from molecular weights would be complicated if it could be shown, first, that the Gibbs-Donnan effect is of greatly different magnitude with albumin than what it is with globulin, and, second, that the GibbsTABLE 1 Ratio of the osmotic activity of albumin as compared with globulin in human blood serum k‘/k”
AOTEORITI
3.9 2.7 8.4 2.4 2.4
Govaerts (8) yon Farkas (6) Wells, Youmans, and Miller (17) Present results Simple theory
Donnan effect is a large part of the total gross colloid osmotic pressure as measured in all these studies. It is easy to show that these factors are not of sufficient magnitude to affect the simple calculation of k’/k‘‘ appreciably. Van Slyke, Hastings, Hiller, and Sendroy (16) have shown that a t p H = 7.35 the base-combining power of albumin is about 1.4 times a s great as that of globulin; in other words, the Gibbs-Donnan effect will be greater with albumin than with globulin. In blood serum in the physiological range of pH the Gibbs-Donnan effect is of the order of 20 per cent of the total colloid osmotic pressure when the A/G ratio is about 1.8. Under the same conditions of salt concentration and pH, the GibbsDonnsn effect would be of the order of 16.5 per cent of the total C. 0. P. in a pure globulin solution and slightly less than 22 per cent in a pure albumin solution. Accordingly, the maximum error from the neglect of the difference in Gibbs-Donnan effect in albumin and in globulin solutions would be less than 5.5 per cent. In the living organism, even under pathological conditions, the variation in A/G is restricted, so that
14
ANCEL KEYS
the greatest error that, could arise from this source would still be less than 5 per cent of the total colloid osmotic pressure. The effect of pH must also be considered. The pH of different samples of serum will vary slightly and the conditions of measurement of the C. 0. P. may accentuate this variation. Since the isoelectric points of albumin and globulin are nearly the same (cf. Van Slyke and others (16)), there can be no significant differential effect on albumin as opposed to globulin and again it must be concluded that the constancy of the ratio k’/k” will be almost entirely unaffected.
0
1
Z
J
-
4
S
1
7
8
9
Protein Conc. qm per IO0 cc. FIG.1. The effect of protein concentration on the relative gross colloid osmotic pressure. Temperatures in separate series from 0” t o 22°C.
Marrack and Hewitt (14) found that variations in pH have a definite effect on the C. 0. P., but this is so small that, over the range pH 6.7 to 7.7, even the absolute magnitudes of k’ and k” will change no more than 4 to 8 per cent. It has long been known that when the concentration of a protein solution is increased the colloid osmotic pressure increases more than in simple linear proportion. In other words, the values of k’ and k ” in equation 2 are not independent of the total protein concentration. This in itself is sufficient to account for some of the apparent discrepancies in the osmotic coefficients reported in the literature. The correction for this effect in
15
MIXED PROTEINS IN BLOOD SERUM
blood serum would be relatively simple if it could be shown that the effect of protein concentration on the C. 0. P. is not dissimilar in different mixtures of albumin and globulin. Figure 1 shows that this is indeed the fact a t protein concentrations below 6 per cent. Even a t 8 per cent concentration i t is probable that differences in the effect of concentration on the osmotic activity of albumin as compared with globulin are relatively insignificant. It is clear that equation 2 may now be extended to cover more than a fixed level of total protein concentration:
C. 0. P. = fc(k’A
+ k”G)
(10)
For measurements at O O C . , we may use the data of the experiments reported in this paper: Gross C. 0. P. (mm. HzO)
= fc
(45.2A + 18.8G)
Values forf, for various concentrations of total protein are listed in table 2. TABLE 2 Values off. i n the equation: C. 0 . P. = f,(k‘A k”G) General relation betweenf, and protein taken from averages of data given in figure 1. Absolute numerical values calculated from results with twenty-eight samples of blood serum with average protein concentrations, including experiments with dilutions, of 3.49 g. per 100 cc.
+
PROTEIN
1
fa
gramsll00 cc.
1.o 1.5 2.0 2.5 3 .O
/I
PROTBIN
I
jc
grantsll00 cc.
0.98
5.5
PROTEIN
1
fc
g r a m ~ i 1 0 0cc.
1.oo
0.90
/I
1.03 1.06 1.09 1.12
6.0 6.5 7.0 7.5 8.0
1.17 1.22 1.28 1.35 1.45
So far we have attempted to provide a relation between serum albumin and globulin concentration and C. 0. P. and have extended this to cover variations in total protein concentration from 1 to 8 g. per 100 cc. The numerical values of the coefficients, however, are based on constant temperature (OOC.), constant pH (7.2 to 7.4), and constant salt concentration. Variations in these factors must now be considered. The effect on the C. 0. P. of variation in the salt concentration is illustrated in figure 2. The pathological extremes in salt concentration are less than f 10 per cent of the normal salt concentration of the serum; this range corresponds to less than f 1 per cent of the gross C. 0. P. It must be concluded that variations in the salt concentration in all natural serums are too slight to have any appreciable effect.
16
ANCEL KEYS
The extreme range, compatible with life, for the pH of the serum in man is perhaps 6.6 to 7.8, but the range which may be endured for more than an hour or so is probably no greater than from p H 6.9 to 7.6. Differences in p H of this amount will affect the C. 0. P. by less than 6 per cent of the total pressure (Marrack and Hewitt (14); cf. above). Obviously the effect of variations in p H may be neglected as a first approximation, unless the pH of the serum is altered experimentally in vitro. The effect of temperature on the colloid osmotic pressure of serum or serum proteins has been little studied. From the simple van't Hoff equation, p:= cRT, it might be expected that the C. 0. P. would vary in Blood Serum A.K. (0.9% NaC1) 0.155 N
400 0
$360
8
320
I
g
280
3 240 0,
5 200 3
Yo
3 120
8
0
80
2 B
40
e
o
0
1
2
3
Protein Conc.
-4 p'rn. 5per 6100 7
8
C.C,
FIG.2. Relations between gross colloid osmotic pressure, protein concentration, and salt concentration in various dilutions of normal human serum. All values a t pH = 7.4 and T = 0°C.
direct proportion t o the absolute temperature. Some comparisons of the C. 0. P. measured in human blood serum by the method of Krogh and Nakaaawa (12) at 22OC. and by the method of Keys and Taylor (11) a t OOC. indicate that this is approximately the case for a limited range of temperature, and we may write, tentatively: C. 0 . P.
= f C (45.2.4
+ 18.8G) X T('Absolute) 273
(12)
So far in this paper the main concern has been to provide a reasonable basis for mathematical description and comparison of measurements of
17
MIXED PROTEINS IN BLOOD SERUM
the gross colloid osmotic pressure in mixtures of albumin and globulin such as blood serum. It must be recognized a t the outset that the sharp division of plasma proteins into discrete entities labelled “albumin” and “globulin” is largely a matter of convenience. There is no reason to doubt that there are distinct species of proteins in blood plasma which correspond, a t least roughly, to what we refer to as albumin and globulin, but it is much less certain that these protein types are quantitatively separable, with unvarying precision, by any present-day methods. This does not, however, invalidate the use of these terms in a mathematical formulation of the relations between the amounts of these types and the osmotic effects of mixtures of them. Such a formulation is a preliminary step toward the practical application of the classical laws of thermodynamics to a complex system such as blood plasma. Some outlines of the further analysis of the system, in terms amenable to experimental attack, may be given here. Consider the equilibrium of a system when blood plasma or serum is separated from a protein-free transudate by a crystalloid-permeable, colloid-impermeable membrane (such as the capillary membrane in man). The essential variables may be represented, for the physiological range pH 6.5 to 8.0:
I SUBSTAN01
I1 SWWTANCI
P = Protein P- = Proteinate BP+ = Base bound by protein B+ = Free base
H+
Total base = B+ H+
c1A- = All other anions
c1All other anions = A-
We shall denote the Gibbs chemical potential by [ 1, where [ 1 = 1, where a! is an osmotic coefficient and the square brackets denote equivalent concentrations. Subscripts 1 and 2 will De used to distinguish the serum and the transudate phases respectively. As a first approximation we may assume that all ions except proteinate are univalent; this can create no very great error in natural biological systems where, in fact, less than 5 per cent of the free ions are multivalent. Applying Dalton’s law of partial pressures we have (13):
a[
* Note that H + is omitted; the number of hydrogen ions present is so small as to be negligible in summing up all ions or molecules.
18
ANCEL KEYS
From the application of Gibbs-Donnan equilibria, we have :
fCl--]i
-
UC1-12
[A-]i
[H+]2
i[A--]z
[H+]I
and also:
where E is the membrane potential and X is the ion ratio (in activities) for the distribution of any diffusible ion between the two phases. In another form we may write the equation for the Gibbs-Donnan equilibrium :
+ (iA-1~) = { [Cl--]i + [A-h}
[B"]z { iC1-i)~
{ {A+]i
+ [B+]I} (16)
From the principle of electrical neutrality, we have: iA-12 =
[J3+32
(17)
- [Cl-ln
and [BP-Ii
=
[P-li
+ [A-Ii + [C1-11 - [B+Il
(18)
Finally, we have, for the true colloid osmotic pressure of the protein alone :
(C. 0. P.)o = C. 0. P.' - R T ( [BP+]li
+
@+]I
+ [Cl-]i +
[-4-]1- [B+]z - [Cl-]z - [A-]z]
(19)
and, following van't Hoff:
(e.0. P.)o =
(Tot. prot.) (Mol. wt.) RT
V
(20)
where (Tot, prot.) represents the mass of the proteins, and V the solvent volume. The equations given here are presented as a guide to the further study of natural solutions of proteins. It should be obvious that, in the last equation (20), the separation of total protein into albumin and globulin may be done by the utilization of the arguments and equations (2 through 9) presented in the first part of this paper, and that this need not involve, necessarily, a precise laboratory method for the quantitative separation of the two chief varieties of protein. For a preliminary application of the arguments given here, the necessary
MIXED PROTEINS IN BLOOD SERUM
19
measurements, in a membrane system separating serum from a proteinfree transudate a t equilibrium, are: ( 1 ) (Tot. prot.); (2) [Cl-li and [Cl-lz; (3) {H+B1and {H+lz;(4)[Tot. basell and [Tot. base]^; (6) E (the membrane potential); (6) C. 0. P. (the gross colloid osmotic pressure); (7) temperature ( T ) ;and (8) V (the solvent volume). Simultaneous measurement of all these variables is technically feasible, and from them, by use of the foregoing equations, i t should be possible to arrive at satisfactory values in this complex system for: acl-, aprot.,{BP+], and the mean molecular weight of the mixed proteins, In addition, there are sufficient cross checks so that any gross deviation from theory should be readily apparent. Preliminary experiments indicate that, in fact, there do not appear t o be any important factors not yet considered in the foregoing tentative analysis. Detailed results will be presented a t another time. SUMMARY
Discrepancies in the literature between the molecular weights of serum albumin and serum globulin and their reported osmotic effects in the mixtures occurring in blood serum are principally the result of the limitations of methods for the quantitative estimation of these proteins in the presence of each other. By the use of a variety of precautions an agreement is reached between analytical results and simple theory. Serum albumin has about 2.4 times the osmotic activity, per gram, exhibited by globulin. It is shown that this relation is not seriously disturbed by variations in pH over the range 6.7 to 7.7, nor by variations in the total protein concentration up to 6 per cent and, with less certainty, up to 8 per cent of the total concentration. The effect of total protein concentration on the relative colloid osmotic pressure per gram of protein concentration was studied, from which it was concluded that albumin and globulin, and various mixtures of these proteins, exhibit nearly the same effect, quantitatively, up to around 8 per cent concentration. A table of conversion factors is given, as well as numerical constants for the osmotic activities of the two proteins. Equations are presented which describe the relations of the activity coefficients of the proteins and of chloride in the presence of the proteins, the protein concentration, the molecular weight of the proteins, the membrane potential, and the gross colloid osmotic pressure. The analysis provides a reasonable preliminary guide to the further thermodynamic study of the complex system of blood serum and a transudate. REFERESCES
s.:
(1) A D a I R , G . Proc. Roy. SOC.(London) Ai20, 573 (1928). (2) ADAIR, G. S.: Trans. Faraday SOC. In press. (3) A D ~ I IG~. , S.,AND CALLOW, E. H.: J . Gen. Physiol. 13, 819 (1930). (4) ADAIR,G. E., A N D ROBINSOX, hf. E . : Biochern. J. 24, 1864 (1930).
20
ANCEL KEYS
( 5 ) BURKE,N. F.: J. Biol. Chem. 98,353 (1932). VON FARKAS, G.: Z. ges. exptl. Med. 63, 666 (1927). (7) FISHBERG, E. H.: J. Biol. Chem. 81, 205 (1929). (8) GOVAERTS, M. P.: Bull. acad. roy. m6d. Belg. 13, 356 (1927). A.: Biochem. Z. 276, 223 (1935). (9) GRONWALL, (IO) HOWE,P. E.: J. Biol. Chem. 49, 109 (1921). (11) KEYS,A., AND TAYLOR, H.: J. Biol. Chem. 109, 47 (1935). (12) KROGH,A., AND NAKAZAWA, F.: Biochem. Z. 188, 241 (1927). (13) KYLIN,E.: Z. ges. exptl. Med. 93, 480 (1934). (14) MARRACK, J., AND HEWITT,L. F.: Biochem. J . 21, 1129 (1927). (15) ROCHE,J., ROCHE,A., ADAIR, G. S., AND ADAIR,M. E.: Biochem. J. 26, 1811 (1932). (16) VAN SLYKE,D. D., HASTINGS, A. B., HILLER,ALMA, AND SENDROY, J., JR.: J. Biol. Chem. 79, 769 (1928). (17) WELLS, H. S., YOUMANS, J . B., AND MILLER,D. G., JR.: J. Clin. Investigation 12, 1103 (1933).
(6)
