G:ICORGE S C A T C I I A R D , A. C. B A T C H E L D E R , ALEXANDER BROWNA N D ~ I A RZOSA Y
3610
[ CONTRIBUTIOX FROM THE DEPARTMENT OF CHEMISTRY, MASSACHUSETTS INSTITUTE OF TECHNOLOGY, AND THE MENT OF PHYSICAL CHEMISTRY, HARVARD MEDICAL SCHOOL]
Preparation and Properties of Serum and Plasma Proteins. VII. Equilibria in Concentrated Solutions of Serum Albumin’J BY
GEORGE S C A T C H A R D , ALANe. B A T C H E L D E R , 3 ALEXANDER B R O W N 4 AND
The studies of osmotic equilibria in solutions of serum albumin described in paper 116have been extended to much higher concentrations of albumin in 0.15 molal sodium chloride a t PH 5.4 to 7.2 and 2;’. This study was again made with bovine serum albumin, which behaved osmotically the same as the more precious human albumin. The albumin was crystallized by a method slightly different from that used with the preparation previously stud:,ed and its osmotic behavior was also slightly different. :Experimental Technique The measurements of the osmotic pressure were carried out ,using the techniques that have been described in Paper 11. The pr0tei.n concentrations in all of the present experiments were determined by micro-Kjeldahl analysis for nitrogen, using a factor of 6.25 to convert grams nitrogen to grams protein. The chloride concent:rations in experiments 55-60 were determined by leaching with several portions of hot water the residuum remaining after evaporation of an aliquot of‘ the solution inside the membrane to dryness a t 105” and titrating the dissolved chloride with dilute silver nitrate solution. A differential potentiometric end-point was employed. In experiments 63-66 the residuum was digested with nitric acid on the steam-bath and the excess silver was ti-trated with sodium chloride solution, a s - i n paper 11, but using a potentiometric endpoint as above. The pH was determined on solutions diluted to 6% albumin with 0.15 M sodium chloride. The bovine serum albumin was prepared by the Xrmour Laboratories,’ Chicago, using the method of Cohn and Hughes,* and was designated as ACB-2. Fo:r experiments 53, SS, 65, and 6G the 25yoalbumin was u s t d as received. For the other experiments thc allmtniii solution was dialyzed against distilled witc‘r :it 0-5” for four clays and (1) This work has been carried out under contract, recommended hy the Committee on Medical Kesearch, between t h e Office of Scientific Research anti Development and Harvard University. (2) This paper is also given the number 111 in t h e series “Physical Chemistry c i f I’roteiri S,,Iittions.’’ 13) P r e s e n t at1drt-s. FIerrriles P o w d e r Company, IVilniingtn. Delaware. (4) Present address: Carbide and Carbon Chemicals Corporation, South Charleston. West Virginia. ( 5 ) Present ad(3ress: University of Pittsburgh, Pittsburgh, Pennsylvania. ( G ) G Scatchard A . C. BatchPlder apd A. Brown, THISJ O U R N A L , 68, 2320 i1946). (7) We ne1cor.e this opportunity to thank Dr. Jules Porsche of t h e Armour Lalioratiiries for this material and for his cooperation in many other ways. (8) E. J. Cohn and W. L. Hughes, Jr., to be published.
vel. 68 DEPART-
Osmotic
M A R Y ZOSAb
then dried from the frozen state. The solutions for the osmotic measurements were made up from this dried material and solid sodium chloride, and 0.1 .M sodium hydroxide solutions were used for PH adjustment when necessary. Results The experimental results are presented in Table 1. The first column gives the number of the experiment, the second gives the concentration of protein in the inside solution and the third the concentration in the outside solution, columns 4 and 5 give the PH, and the valence of the protein calculated from the @H and the titration curve of paper 11. Columns 6 and 7 give the mean concentration of sodium and chloride ions on the two sides of the membrane. Column 12 gives the measured osmotic pressure. Column 8 shows the values of - bz3 X lo4 calculated from the equation In m,/mi =
(1)
-328~2
There is no evidence that bz3 changes with albumin concentration or with PH. Column 11 shows the difference between the measured value of m3’ and the value calculated from equation 1 with b23 = -4.2 X lop4, with thexssumption that m3 is exact. Our earlier measurements gave an average of -3.6 X l o w 4in this $H range. In paper I1 we calculated Bz by the equation P = 0.26a~(i B ~ w ~ ) (2) and found no evidence that Bz varies with the concentration, and that i t can be represented from 22 = 9 to - 17 by the equation
+
B~ x 105 = 554 - ~ 7 . 4 2 ~
(3)
Our present results over a larger concentration range show that Bz increases with increasing albumin concentration, and can be represented by the equation H2 X IO6
=
(117 - 24.5z2)(1
+ 0 . 0 0 2 ~ ~ )(4)
Coluniii 13 gives B X 105calculated by equation 2 and column 1-1 gives the measured osmotic pressure minus that calculated from equation 2 with B determined from equation 4. At w z = 60, the approximate concentration of most of the previous experiments, our new results give Bz X lo5 = 467 - 27.422
(5)
The factor of z2, which is certainly very nearly the same as that in the previous experiments, was chosen exactly the same. The constant term is definitely smaller. Our measurements indicate that the Armour crystallized bovine serum albumin interacts more
OSMOTIC EQUILIBRIA IN CONCENTRATED SERUM ALBUMINSOLUTIONS
Dec., 1946
TABLE I
No.
pH
w2'
U'2
59 284.0 0.0 .1 64 104.5 .09 56 59.82 .0 63 156.3 66 140.4 .1 .O 58 285.5 .2 6.5 216.7 55 63.92 .32 60 184.5 1.8 57 69.16 0.0;'
-a
ms
- b21
x
ma'
10'
1.80 4.12 4.16 4.40 8.11 3.76 3.93 4.16 5.83 4.46
5.39 0 . 1 0.1564 0.1486 ,1479 5.41 .3 .1544 ,1467 ,5.42 .4 .1504 5.42 .4 ,1564 .1460 ,1482 6.30 7.2 ,1661 6.31 7 . 3 .I815 ,1603 ,1621 6.33 7 . 4 ,1765 .E131 6.39 7 . 8 ,1572 .1538 .1711 7.05 12.2 ,1506 7.23 13.5 ,1553
strongly with sodium chloride than the Harvard IMedical School preparation 456 by an amount which might indicate interaction with about one more chloride :Lon per albumin molecule. It appears to have .she same molecular weight but its osmotic pressure a t w2 = 60 is less by 0.92 mm.
Discussion The concentrations studied in this paper cover such a range, that it is desirable to extend the equations used in the previous paper. The general methods used there lead to complications, but the restriction to a special case of a three component system and the use of certain approximations makes the integration much simpler. Equation 1 of paper l 9is
md
-Baa
-&a
1.075 22.8 1.088 52.3 1.116 52.7 1.075 56.7 1.016 101.6 0.932 46.1 0.958 48.3 1.070 52.2 0.987 70.4 1.083 54.4
-
mz' calcd.
0.0098 ,0001 .0000 - .0005 - ,0084 - ,0007 .0009 .0000 - ,0047 - ,0003
B
P 219.1 42.42 20.64 77.77
78.0 282. G 165.5 23.77 138.7 30.18
X 106
662 493 483 548 765 943 854 614 984 910
2611 PP calcd.
0.5 - .6 .D - .9
+
.2 +l.(J -0.4
- .9 - 0 .7
+ '
.Y
(10)
Equation 10 differs from the combination of 21 and 2 of paper 116 by the term - In (1 - z&qi/4mi) and the higher terms in the expansion of p23. The largest value of ( z ~ m ~ / 4 m studied ~) here is 'less than 0.003, which corresponds to an error of 0.15$& in mi. Therefore, the constancy of bBR is equivalent to constancy in &, and terms higher than may be neglected. The values of - P$ calculated from equation 10 are given in column 10 of Table I, and the values of - P 3 3 used in the calculations are given in column 9. For the osmotic pressure we take equation 4 of paper Igwith some rearrangement, again for a three component system with dmK/dms equal to zero, to give
We will consider the special case in which each dmJ/dm2 is zero. Then
Substitution of the definitions of potentialsg gives
To integrate, we will assume that the first term on the right is negligibly small since we have seen in paper I that it is less than the experimental error. We will also assume that the factor in parentheses in the second term is independent of m2. For sodium chloride it varies only from 1.86 to 1.83 as rnIf varies from 0.05 to 0.2 M , so the variation due to changes in nt2 may well be ignored.'" We will also assume that j 3 2 ~may be represented by ,@K pi2Km~ P ~ 2 z K n 2 ~ / 2. . . Then
+
-
(YK
+
+
+
PsKmK)
P",m
In
nzz - 2 , u K i In (1 + -) m m K VA
mK
+ POz2~m2,/2+ 8!22~m:/6
f
=
...
(9)
For sodium chloride, with the definition of vzi of paper I9 (9) G Scatchard, ~ H I SJOURNAL, 68, 2315 (1946) (10) Each of these assumptions must be justified for each particular case The use of a more general expression is not very com-
plicated.
I', is the volume, under the pressure p ' , of that amount of a solution of component K a t concentration m K which contains one kilogram of component 1. To eliminate the solvent from the factor in parentheses, we subtract Zpnj(dpj/bmk), which is zero by the Gibbs-Duhem relation, to give
With the definitions of potentials used above
+
To integrate, we will assume that and ( V K / 3 ~ ~ m are k ) constant,'O and that PZ2 may be expressed as & j3t22m2 &22mi/2 . . . . The11
+
+
+
0 . L. HARLEAND M. CALVIN
2612
P974/2
+ PaZ2ml/3+ P%zznz:/8 + . . .
(15)
If the second and third terms are large, we should limit the expansion to the following terms. For albumin solutions with sodium chloride, however, these terms are so small that it is convenient to expand the logarithms, to give
+
13;~rrt:1'2 8!,zm2/3
+ P ~ 2 2 2 n z ~4-/ 8
.
(16)
P Z Z(1
+ BZWZ+ E&W.J;)
Therefore piz2 is determined to a good approximation from Bi2alone. Recalling that p23 is nearly inversely proportional to m3,we may write PI
=
In YZ = In r i
+ P",mo In ma + P P m + i3PZ2mj/2 (23)
in which In yt is a constant depending upon the choice of standard state. With the values of the parameters given above, we obtain for this sample of crystallized bovine serum albumin (ACB-2) in aqueous sodium chloride solutions a t 25' In y~ = In 78 - 8.0 In nat f (805 - 3422 -
+
3 . 3 3 ~ i ) n ~ z (61,700
I f we compare this with the equation PI',,/KT =
Vol. 68
(17)
and a similar expansion of equation 1 to give
- 35002z)m;
(241
This equation should be valid over the ranges of m2 from 0 to 250, m3 from 0.1 to 0.2 and z2 from 0 to -13.
Summary we find that
Combining these equations with equation 4, we obtain, for "ri;'3 = 0.15 =
$azl
576
- 3422 - 3 332; f
230 = 805
-
3472 - 3.332; = 119,000
-
(21)
7,00022 4- 3400 = 122,400 - 700022 (22)
The term itrising from bz3 is almost a third of the total a t zz -= 0 for &, but only a thirtieth for &?, and the Doniian term contributes nothing to
[COUTRIUVTED
The osmotic pressure and the distribution of salt across a semipermeable membrane have been measured for crystallized bovine serum albumin up to concentrations of 25% in 0.15 M aqueous sodium chloride a t pH 5.4 to 7.2 and 25'. Although the molecular weight appears to be the same, the protein-electrolyte and proteinprotein interactions were slightly different from those of the sample previously studied. The equations for osmotic equilibria have been extended to higher approximations. Analytical expressions have been derived for the measured quantities, for the interactions and for the activity coefficient as a function of the concentration of albumin and of salt. CAMBRIDGE, MASSACHUSETTSRECEIVED JUNE 27, 1946
BY THE DEPARTMENT O F CHEMISTRY, UNIVERSITY O F CALIFORNIA]
The Oxygen-Carrying Synthetic Chelate Compounds. VI.
Equilibrium in Solution
BY 0. L. HARLE'AND M. CALVIN 111 the previous paper of this series' the equilibriuni between oxygen anti the solid chelates was described. These were primarily on compounds of Type I ,3 that is, chelate compounds derived from the Schiff base formed by salicylaldehyde or its derivatives with ethylenediamine. The present paper contains the results of equilibrium measurements on chelate compounds in solution. The chelatcs used i r i this study were primarily of Type 1 x 3 ; that is, compounds derived from the Schiff base formed by salicylaldehyde or its derivatives with y,y '-diasninodipropylamine. ( I ) Ab.;trat,ted from t h e thesis submitted in 1944 by 0. L. Harle t o the Graduate School of t h e University of California a t Berkeley in partial fulfillment elf the requirements for t h e Ph.D. degree. ( 2 ) E. W. Hughes, n7. K. Wilmarth a n d hl. Calvin, THISJOURNAL, 68, 2273 (1946). ( 3 ) Calvin, Bailes and Wilmarth, ;bid., 68, 2254 (1946).
Type 11.
The reason for the lack of overlap between the measurements on the solids and those on solutions is primarily the fact that: (1) the pressures over solutions of Type I are very low, a few millimeters or less, so that the vapor pressure of the solvent interferes, making such measurement somewhat more difficult than those on solutions of Type I1 where the pressure range is relatively high; and (2) the pressures over the solids of Type XI are in general above one atmosphere and the
