Idea Transcript
THE
OSMOTIC COEFFICIENT OF SODIUM IN SODIUM HEMOGLOBINATE AND OF SODIUM CHLORIDE IN HEMOGLOBIN SOLUTION* BY
(From
WILLIAM
the John
Herr
C. STADIE
AND
F. WILLIAM
Musser Department of Research of Pennsylvania, Philadelphia)
(Received for publication,
January
SUNDERMAN Medicine,
University
19, 1931)
We report in this paper a continuation of the studies from this laboratory of the effect of protein (hemoglobin) on the thermodynamic properties of ions in solution. We have selected for that purpose a determination of the osmotic coefficient of ions as they coexist in aqueous protein solutions in their commonest modes; viz., (1) Naf as alkali proteinate NaHb, (2) Naf and Cl- as a neutral salt (NaCl) in a Hb solution. The osmotic coefficients were calculated from the freezing point depression as determined by the method of Stadie and Sunderman (1931). Theory The osmotic coefficient, ‘p, is by definition the ratio between observed (r) and theoretical (?rO)osmotic pressure or the corresponding freezing point depressionsA and A,. That is A
A’
’ = :o = ro = 1.86 (C)
(1)
where (C) is the total concentration of all ions in mols per kilo of water and 1.86 is molal lowering of the freezing point of water. In a solution of NaHb we have sodium ions and the Hb. The total depression is A = ANa++ AHb * Presented at the Thirteenth International Physiological held in Boston, August, 1929 (Am. J. Physiol., 90, 526 (1929)). 227
Congress
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INTRODUCTION
228
Osmotic Coefficient
Hb is present in small molecular concentration and we are able to make suitable correction for Am. We make the assumption that changes in the osmotic activity coetlicient of Hb when the concentration of Na is changed, if it occurs at all, will have a negligible effect upon the total A. We then get ANE3 -~ PNa - 1.86 (Na)
Similarly for solutions of NaCl and NaHb we have ‘N&l
+
‘NaHb
ANsHsis determined separately and by keeping NaHb small and making the assumption that its effect on A~~ei (or vice versa) is negligible we get AN&l
(PNaC1 = 3.72 (NaCl)
Method of Calculation of Concentrations-It is unimportant in dilute solution whether concentrations are calculated in mols per liter or mols per kilo of water. In concentrated solutions and in protein solutions on the contrary the two methods of calculation give quite different results. The question of choice between the two is important. We have not found any adequate discussion of the problem anywhere. Rivett (1911) in his studies on the osmotic pressure of salts in the presence of sugar recognized it but gives no solution. Most observers of osmotic pressure in concentrated solutions have calculated concentrations in mols per kilo of water. Debye and McAulay (1925), on the other hand, in their study of the osmotic pressure of salts in the presence of sugar express concentrations on a liter basis because in the development of their equation they consider a spatial arrangement of ions. The thermodynamical derivation of the relation between Ni RT *H~O + *i ’ an expression in which the sum of the concentrations of the ions is expressed in mol fractions, Z Ni, and the mol fraction of water, NHzo. In molality terms this nearly approximates s = (C) RT where (C) = mols of solute per kilo of HzO. Many osmotic pressure and concentration gives ?r =
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A =
W. C. Stadie and F. W. Sunderman
229
measurements, by Rivett (1911), Morse and his associates (1915), and others, in concentrated solutions give consistent results only when calculated this way. Our own experiments are in accord with this interpretation and for these reasons we have calculated the concentrations of our experiments in mols per kilo of water. EXPERIMENTAL
Washing
10 11 12
No.
K X 10-E mhos at 25’
4.6 3.5 3.3
wash water was 0.7 mM per liter.1 To obtain a concentrated solution of isoelectric reduced hemoglobin we reduced these crystals of isoelectric oxyhemoglobin in the following way. The crystal paste was transferred to a liter sat.urator and reduced to Hb by 1 hour rotation in an atmosphere of COz and Hz. The COz was now removed by rotation for 1 to 2 hours in an atmosphere of hydrogen which was repeatedly renewed. A concentrated (11.5 mM Hb per liter) solution of reduced hemoglobin was obtained which on analysis of a 3 cc. sample showed 0.18 mM of COz per liter, a negligible quantity. The freezing point of this solution was 0.006” whichispracticallythe theoreticalvalue with 64,000asthe molecular weight of hemoglobin. The conductivity was 5.7 X low5 mhos. 1For conveniencewe retain in both papers the old convention 1 mM of oxygen capacity = 1 mM of hemoglobin.
that
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Preparation of Xolution of NaHb-Considerable experience made it evident that consistent results for ANa. could not be obtained without unusual precautions in the preparation of the solution of NaHb. Washed horse red blood cells were electrodialyaed by the method of Stadie and Ross (1926). A mixture of 80 per cent O2 and 20 per cent CO2 was passed through the crystal paste which was then placed in collodion sacs and dialyzed against water saturated with O2 and COz for 24 hours. The crystals were then washed repeatedly in ice water by stirring for 1 to 2 hours and separated by centrifugation. The conductivity of the supernatant wash water was as low as we have ever been able to obtain and the hemoglobin concentration of the
230
Osmotic Coefficient
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From this point great care was taken to avoid access of COZ or oxygen. The sodium hydroxide was prepared from metallic sodium. 25.00 cc. portions of the hemoglobin solution were transferred to small flasks filled with Nz and the alkali added from a 3 cc. micro burette reading to 0.001 cc. During the addition a plentiful flow of COz-free Nz into the Erlenmeyer flask was maintained. Each solution was transferred to the freezing point apparatus under a stream of nitrogen and the apparatus during the determination was kept filled with N,. The solutions were made up as rapidly as possible and were maintained at 0” until used. The water content of the stock hemoglobin was determined by drying at 110’ and from this value and the base and water added the concentration of sodium per kilo of water calculated. The hemoglobin concentration was determined calorimetrically by the St’adie (1920) method. The freezing points were determined by the method of Stadie and Sunderman (1931), determined in duplicate, agreement within 0.001” being obtained. Preparation of NaCl-Hb Solutions-The precautions outlined above were unnecessary. Crystals of Hb from electrodialysis were washed once or twice with ice water, dissolved by addition of the requisite quantity of NaOH, and dry NaCl added by weight. The wat’er content of each sample was determined by drying at 110”. Determinations were made on oxy-, reduced, carbon monoxide, met-, and cyanohemoglobin solutions prepared from the crystals (Stadie and Hawes (1928)). The correction, ANsnb, for each solution was determined before the addition of NaCl. The freezing points of all these solutions were determined by the method of Stadie and Sunderman (1931) in duplicate, agreement to within 0.001” being obtained in all solutions except two where the difference was 0.002’. Osmotic Coefficients of NaCl in Water-In order to have values for comparison with the coefficients in hemoglobin the osmotic coefficients of NaCl in water alone were determined by our own technique. The values are given in Table I. Our values are about 1 per cent higher than those selected by Lewis and Randall (1923) from the assorted observations of Jahn, Rodebush, and Roberts and Harkins.
W. C. Stadie and F. W. Sunderman
231
Results Osmotic Coeficient of Na+ in NaHb-The observations are of two types. In the experiment reported in Table II the Hb concentration was maintained constant and the Na concentration varied from 5.8 to 117.0 mM per kilo of HZO. Reduced hemo-
Osmotic
Coeficient
of
NaCl
in
TABLE
I
Water
Calculated
from
N&l
Freezing
Points
‘NaCl
0.957 0.943 0.933 0.922 0.918 0.913 0.910
0.05 0.10 0.20 0.30 0.40 0.50 0.60
TABLE
Osmotic
Coeficient (Hb) AHb
N2.
Mean.......,.
II
Na+
= 13.5 mM per = 0.006” NE3
Hb
mdb per kg. Hz0
5.8 11.8 29.3 46.8 64.4 87.8 117.0
of
in NaHb kilo
ANa
Solutions
of Hz0
corrected
‘PNa
“C.
0.4 0.9 2.2 3.5 4.8 6.5 8.6
0.008 0.017 0.044 0.072 0.097 0.127 0.167
.. ... ... ... .. .. ... ... ... .. ... ... ... ... .
0.74 0.77 0.81 0.83 0.82 0.78 0.77 0.79
f0.027
globin was used to obtain a concentrated base-free solution to which Na could be added in varying quantities. The base-free reduced hemoglobin gave an observed Anb of 0.006’ and this value was subtracted from the observed values of A for the NaHb solutions.
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dl per k~. Hz0
232
Osmotic Coefficient
In the experiments given in Table III the ratio between Hb and base remained constant but by dilution the concentration of Na and Hb was reduced 3.8- and 7.0-fold respectively. The observed freezing points were corrected for Am, with use of Adair’s (1925) equation for osmotic pressure 2.55 C * = 1 -
0.0168
C
W) %.+I per kg. Hz0
5 10 15 20
*Hb “C.
0.003 0.006 0.010 0.015
In Table II there is no consistent change of $0~~ despite a 20Within the fold change in Na concentration and Hb:Na ratio. limits of the method we believe that the results show a practically constant osmotic coefficient. In Table III the Hb:Na ratio is constant but there is a 3% It is possible to fold and 7.0-fold change of NaHb concentration. say that there is no change in qN* All three experiments give for $0~~approximately the same values whose mean is 0.75. Our conclusion (see Table IV) is that Na+ in concentration from 5 mM to 175 mM per kilo of water as NaHb when Hb varies from 3 to 20 mM per kilo of water has a constant osmotic coefficient of 0.75. This latter value is in accord with that of Adair (1925) and of Austin, Sunderman, and Camack (1926) whose values at a few isolated concentrations of Na and Hb lay between 0.75 and 0.80. It may be pointed out here that the OH- concentrations are in all cases negligible. The most alkaline solution was one containing Na = 175 and Hb = 229. The calculated OH- of this solution would be 10e5 mM, a negligible quantity in its effect on A. Osmotic CoefJicient of NaCl in Hemoglobin Solutions-The data are given in Table V and show quite conclusively that P&o1 in hemoglobin solutions is the same as in water over a considerable This is in conformity with range of Hb and NaCl concentration.
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where C = gm. of hemoglobin per 100 cc. of solution, and from which the freezing point depressions in the following tabulation were calculated.
W. C. Stadie and F. W. Sunderman
233
the conclusion of Van Slyke, Wu, and McLean (1923) based on stoichiometrical analyses of whole blood. We wish to point out TABLE
Osmotic
Coeficient
Hb
NC3
I
per kg. Hz0
n&.-q.
in Oxyhemoglobin
per kg. X20
27.7 47.3 69.3 92.7 106.5
Hb
*corrected
= constant
,
-
‘NC%+
= 6.3
“C.
“C.
0.043 0.069 0.098 0.138 0.157
0.041 0.065 0.092 0.129 0.146
0.79 0.74 0.71 0.75 0.73 .1
0.74
f
0.020
-
Na: 3.3 4.6 8.4 13.1 15.8 22.9
Hb
= constant 0.036 0.050 0.086 0.143 0.175 0.255
25 35 64 100 121 175
-
= 7.7 0.035 0.048 0.082 0.137 0.165 0.237
0.75 0.74 0.69 0.74 0.73 0.72 0.73
TABLE
*to.015
IV
Summary Experiment
No.
m&f per kg. HxO
1 2a 2b
NZ3
Hb
13.5* 4.4~16.8 3.3-22.9
Mean..................................................
m.-eg.
- Na Hb
‘Na
pet kg. Hz0
5.8-117 28 -107 25 -175
0.4-8.6 6.2* 6.2*
0.79 0.74 0.73 0.75
* Constant.
that since the calculations of q&C1 are made from freezing point depressions, the conclusion is without extrathermodynamic assumptions.
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4.4 7.5 11.0 14.7 16.8
III
as NaHb
Aobserved
Na: mu
of Naf
234
Osmotic Coefficient DISCUSSION
Activity of Na+ in NaHb-There is no quantitative theory at hand to explain the osmotic behavior of Na ions combined as NaHb. We are not concerned here with the precise mode of TABLE
Osmotic Hb
N&l
kg’
i.0
HbOz
8.0 16.8 9.0 8.0 26.3
V
in Hemoglobin
Solutions P NaCl in Hb c N&I in 1120
A~aCl
nu.f per kg. Hz0
“C.
85 203 276 296 466 485
0.298 0.703 0.814 1.022 1.599 1.738
0.95 0.93 0.80 0.93 0.92 0.96
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m”HP;
of NaCl
Coejicient
1.00 1.00 (0.86) 1.01 1.01 1.06 1.02
7.5 9.6
RHb
312 341
1.057 1.177
0.91 0.93
0.99 1.01 1.00
HbCO
21.4 25.8
274 614
0.975 2.124
0.96 0.94
1.03 1.03 1.03
HbCn
5.7 13.3
226 298
0.801 1.001
0.95 0.90
1.03 0.98 1.01
MtHb
9.8 14.8 14.3
270 356 370
0.952 0.211 1.246
0.95 0.92 0.91
1.03 1.00 0.99 1.00
Mean
of all..
.. . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . .. . .
1.012
*to.005
chemical combination but it is possible to say that it is of such a nature that the Naf can diffuse sufficiently far into the solvent so as to exert a considerable osmotic pressure. In other words NaHb is ionized and for simplicity we may regard it as completely ion-
W. C. Stadie and F. W. Sunderman
235
0.34 J+ -
log
fcl
=
1 +
0.69
J+
where J is the ionic strength and is calculated by the equation J = [HI + [Cl1 + m; C,
where nP = 24 = valence of edestin and C, = molecular concentration of protein using 17,000 as the molecular weight. He obtains plausible agreement with observed values.
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ized. We can further say that the attracting and repulsive forces and the interaction of adjacent portions of the hemoglobin molecule upon Na+ ions influence them in such a way that the osmotic coefficient is diminished to 0.75. This, of course, is in conformity with our general expectations in compounds of this character. The explanation of the fact that marked changes in the Na:Hb ratio and changes of concentration of NaHb do not influence found in a consideration of the huge discrepancy in ‘PN& + is readily the size of the combining masses. The compound NaHb can be pictured as one in which a few small sodium ions are distributed in a more or less uniform manner over a huge hemoglobin molecule. In such a case the interionic distances between the sodium ions would be so great that each ion may be considered thermodynamically isolated with respect to other sodium ions. Ionic interaction between sodium ions would be nil and therefore changes in the ratio Na+:Hb or the concentration of NaHb would be without influence on the osmotic coefficient activities so that (P&+ would be independent of these changes. We believe that our experiments show that NaHb cannot be regarded as a high valence salt of the type Na,Hb in which ionic interaction would be marked and would produce profound effects on the osmotic properties, with changes of concentration. In this respect our conclusions are in conflict with the views of Adair (1928) who has measured the activity coefficient jcl of the chlorine ion in solutions of edestin chloride by means of membrane potential measurements and found a decrease of jci from 0.86 to 0.59 with roughly a 4fold change in concentration of Cl and a 13-fold change of edestin concentration. On the basis of this experiment Adair regards edestin as a multivalent protein ion of valence 24; further he calculated jci by the Debye-Htickel equation in the form
236
Osmotic Coefficient
stant so that J = constant C,. That is to say, the molecular protein concentration is the major factor in his equation for calculating J and therefore fol and his calculated values would have an entirely different magnitude if a molecular weight other than 17,000, Adair’s value, was used for edestin. Since Cohn (1925) gives 29,000 as the minimal and 58,000 as the probable molecular weight of edestin, a simple recalculation from Adair’s data using 58,000 causes the agreement between calculated and observed values to disappear. Again the number of charges per hypothetical ion of edestin (using 17,000) as calculated from Adair’s ratios of [Cl] :C, vary from 31 to 100. Nevertheless, Adair regards the number as constant at 24. Logically a variable nP value should be used in the calculation of J but in such a case the agreement of for with observed values again disappears. Besides this internal evidence in Adair’s experiments which must be considered before his conclusions are accepted, there is some direct experimental evidence particularly designed to throw light upon this question of quantivalence. Stadie (1928) showed that a considerable change in the number of charges upon the hemoglobin molecule was without effect upon the activity coeEiGent of the bicarbonate ion and concluded that hemoglobin could not be regarded as a quantivalent ion in its effect upon the ionic strength. Again Simms (1928) has subjected the question to a careful analysis and has shown that even simple multicharged particles no longer behave as quantivalent ions in respect to ionic strength when the distance between charges exceeds a certain
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Now, in a general way edestin chloride is analogous to NaHb both being ionized into a simple ion and a complex protein ion and it would be expected on the basis of this analogy, that the thermodynamic behavior would be the same; yet the electromotive force determinations of for in edestin chloride show an effect of protein which is absent in the osmotic determination of (PNa. Several serious difficulties must be overcome before the application of the quantivalent notion of the protein ion in the calculation of J, the ionic strength, can be accepted on the basis of Adair’s experiments with edestin chloride. One has already been discussed in the preceding paragraph. Another is the fact that n2 C Adair’s ratios of -E-? J are high (0.78 to 0.95) and roughly con-
W. C. Stadie and F. W. Sunderman
237
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distance. These considerations lead us to doubt whether Adair has established the notion that charged protein ions behave as quantivalent ions in their effect on the ionic strength and to consider the extension of the Debye-Htickel theory to protein solutions by the application of this hypothesis as hazardous. Activity of NaCl in Hemoglobin Solutions-The experiments on the osmotic coefficient of NaCl in hemoglobin solutions over a very wide range of concentration lead unequivocally to the conclusion that hemoglobin is without effect on the osmotic properties of NaCI. Since this conclusion is arrived at completely without extrathermodynamic assumptions it must receive considerable weight. Considerations of the following character immediately lead us to a dilemma from which we can suggest no certain escape. There is a considerable amount of data derived entirely either from membrane or single electrode potentials which indicate that proteins influence the activities of ions. Thus Pauli and Schon (1924) and Northrop and Kunitz (1926) attributed the discrepancy between electrometric and stoichiometrical concentrations to the formation of an unionized protein chloride complex. Later Pauli and Wit (1926) adapted the complete ionization hypothesis and concluded that the activity coefficient of chloride ion is changed by protein. Van Slyke, Hastings, Murray, and Sendroy (1925) calculated a difference in activity coefficients of the chloride ion and the bicarbonate ion in red blood cells and plasma, the ratios Stadie and Hawes (1928) showed being 9.77 and 62 respectively. a systematic effect of hemoglobin upon the activity coeficient of the bicarbonate ion. Adair (1928) also, in membrane equilibrium experiments showed a diminution of chloride ion activity in NaCI- hemoglobin solutions. It is true that in every case the conclusions are limited by certain assumptions, the most serious and usually the only extrathermodynamic one being that which eliminates the liquid junction potential. Harned (1924), Taylor (1927), Giintelberg (1928), and others have repeatedly pointed out the uncertain validity of this assumption and though biochemists have been well aware of this, nevertheless, they have tended to ignore it in drawing their conclusions. Since the magnitudes of liquid junctions are completely unknown, especially in protein-containing solutions conclusions drawn from electrometric measurements involving them must be made with
238
Osmotic Coefficient
F,
-FL
= RTlnfyc
f: c
where F,, F’, are the free energies of the salt in the given state (with protein) and standard state, f* and fL the respective mean ion activity coefficients, and C is the molal concentration. If the first generalization of the preceding paragraph is true it is evident that sincef, = fL F,
- FL = 0
when passing from a protein solution to pure water at the same molal concentration. The fact that the mean ion activity coefficient is calculated from the freezing point depression does not alter the validity of
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some reserve. Freezing point and ele&rometric measurements of ion activities are both based on thermodynamic considerations and hence should give precisely the same results, as has been amply demonstrated in simple aqueous solution (Lewis and Randall, 1923). These considerations would make it appear that our present knowledge of the activity of ions in the presence of proteins may be summed up in a general way in two statements: (1) The mean ion activity coefficient of a salt (e.g. NaCl) dissolved in a protein solution is 1.0 with respect to its value in pure water at the same molal concentration; whereas (2) the single ion activity coefficient of one of the ions (e.g. Cl-) is systematically changed from its value at the corresponding concentration in water by increasing concentrations of protein. These two conclusions can be shown to be contradictory by a consideration of what is measured in the determination of the two types of activity coefficients. In the case of the mean ion activity of the salt it is clear that it is the free energy change from the given state to the standard state (activity = 1.0) which is measured. If for convenience we take as the standard state a solution of the salt in pure water at any given molal concentration, the equation for this free energy change is
W. C. Stadie and F. W. Sunderman
239
this argument since such a method measures the free energy of the water which is related to that of the salt by the relation F N&l
N Hz0 =
-
N
FHsO NdX
where Nnzo and NNaoi are the respective molar fractions. Nor does the fact that we have a third constituent (protein) in the solution hamper our ability to determine FNaci if in the equation +
NNaCIFNaCl
+
NHbFHb
=
’
for the free energy of the system we can be reasonably sure that changes in NHbFHb are zero or negligibly small. In the case of single ion activity coeflicients the situation is not quite so clear. The presumption is that what is measured is the change of free energy of the ion in passing from the given state to the standard state. With a notation analogous to the previous case, this free energy change of this operation is ex,pressed by the equation F--
F’_ = RTIn’y J-
F- and f- are the free energy and activity coefficient of the ion in the protein solution while FI. and fL are the corresponding quantities in pure water at the same molal concentrations, It is a moot point whether such an operation has any meaning since it is questionable whether it is possible to transfer an ion from a given state to a standard state so that the measurement may be one of a process which has no reality. Indeed, Taylor (1927) has published a mathematical proof that such a process is expressible in terms of molecular free energies only and hence cannot be made to yield any information concerning individual ion activities. This difficulty need be no deterrant to handling the quantity, at least as a mathematical device and indeed much valuable information particularly in biological fields has been obtained by its free use. The significance, then, of the second statement above would be that since f- is not equal to fl F- - FL is not zero but finite. Since, how-
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NHzOFH~O
240
Osmotic Coefficient
ever, the partial free energy of the salt is equal to the sum of the free energies of the ion in both given and standard state we have P, = F+ + FF: = F; + Fi_ from which F, - F: = (F+ - F;)
+ (F- - FI_)
F,
F-i- - F;
-
FL = -
is zero (F-
-
FL)
which can only be true if both are zero or the increase of the free energy of one ion by protein is always equal to the decreaseof the free energy of the other. This would presuppose the existence of some new and unique balancing thermodynamic mechanism which is extremely unlikely. In brief we believe that the osmotic determinations of qNeCI in protein solutions and the electrometric and membrane potential determinations of the activity coefficient of Cl- by Pauli, Adair, and others are sharply contradictory. We have no solution of the problem nor do we state without reserve that the difficulty is a real one. It is quite possible that with a greater knowledge of the effect of proteins upon the thermodynamic properties of single electrodes and on the liquid junction potential, the situation will be clarified. We can only emphasize again the statement that osmotic and electrometric determinations of activity coefficients must agree. BIBLIOGRAPHY
Adair, G. S., J. Biol. C&m., 63, 529 (1925). Adair, G. S., Proc. Roy. Sot. London, Series A, 120, 573 (1928). Austin, J. H., Sunderman, F. W., and Camack, J. G., J. Biol. Chem., 70, 427 (1926). Cohn, E. J., Physiol. Rev., 6, 360 (1925). Debye, P., and McAulay, J., Physik. Z., 26, 22 (1925). Giintelberg, E., and SchiBdt, E., 2. physik. Chem., 136, 393 (1923). Harned, H. S., in Taylor, A treatise on physical chemistry, New York, 2, chapter 12 (1924).
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Since
W. C. Stadie and F. W. Sunderman
241
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Lewis, G. N., and Randall, M., Thermodynamics and the free energy of chemical substances, New York and London (1923). Morse, H. N., and associates, in Washburn, An introduction to the principles of physioal chemistry, New York, 152 (1915). Northrop, J. H., and Kunitz, M., J. Gen. Physiol., 9, 351 (1926). Pauli, W., and Schiin, M., Biochem. Z., 153, 253 (1924). Z., 174, 308 (1926). Pauli, W., and Wit, H., Biochem. Rivett, A. C. D., Medd. VetensJcapsaJcad. Nobelinst., 2, No. 9 (1911). Simms, H. S., J. Gen. Physiol., 11, 613 (1928). Stadie, W. C., J. Biol. Chem., 41, 237 (1920). Stadie, W. C., J. Biol. Chem., 77, 303 (1928). Stadie, W. C., and Hawes, E. R., J. BioZ. Chem., 77, 265 (1928). Stadie, W. C., and Ross, E. C., J. BioZ. Chem., 68, 229 (1926). Stadie, W. C., and Sunderman, F. W., J. BioZ. Chem., 91, 217 (1931). Taylor, P. B., J. Physic. Chem., 31, 1478 (1927). Van Slyke, D. D., Hastings, A. B., Murray, C. D., and Sendroy, J., Jr., J. BioZ. Chem., 66, 701 (1925). Van Slyke, D. D., Wu, H., and McLean, F. C., J. BioZ. Chem., 66,765 (1923).
THE OSMOTIC COEFFICIENT OF SODIUM IN SODIUM HEMOGLOBINATE AND OF SODIUM CHLORIDE IN HEMOGLOBIN SOLUTION William C. Stadie and F. William Sunderman J. Biol. Chem. 1931, 91:227-241.
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