STUDIES IN THE PHYSICAL CHEMISTRY OF THE PROTEINS

X. THE SOLUBILITY OF HEMOGLOBIN IN SOLUTIONS OF CHLOR- IDES AND SULFATES OF VARYING CONCENTRATION*

BY ARDA ALDEN GREENt

(From the Department of Physical Chemistry in the Laboratories of Physiology, Harvard Medical School, Boston)

(Received for publication, November 21,193l)

INTRODUCTION

The solubility of proteins in aqueous solutions of neutral salts has formed one basis for their classification and characterizations. Thus solubility of one class of proteins, the globulins, is increased by the addition of small amounts of salt and decreased in more con- centrated solutions of electrolytes. Albumins, on the other hand, are relatively soluble in water, but their solubility, also, is de- creased in sufficiently concentrated solutions of certain salts. The increase in solubility of certain proteins on the addition of neutral salts was discovered in 1856 by Denis (10). This property was subsequently used in effecting separation between proteins, but it was not until 1905 that an exhaustive study of the solubility of globulins in dilute salt solutions was reported. In that year appeared the classical papers of Hardy (14) and of Mellanby (17) upon serum globulin and of Osborne and Harris (18) upon edestin. There have since been many other contributions to this descriptive chemistry of the proteins.

The theoretical explanation of the effects of electrolytes upon proteins awaited, of necessity, the development of an adequate theory of strong electrolytes. The classical theory of Arrhenius,

* 9 preliminary report of a part of this investigation was presented at The Thirteenth International Physiological Congress at Boston, August, 1929 (13).

t National Research Council Fellow in Medicine, 1927-29, during which time this investigation was in progress.

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48 Physical Chemistry of Proteins. X

which depended upon the “degree of dissociation,” and, therefore, upon the number of particles present, neglected the electrical interaction of ions. Differences in the effect of different salts, especially of those of different valence types, on protein behavior were studied by Mellanby (17) who described in the following terms the solubility of globulins in salt solutions.

“Solution of globulin by a neutral salt is due to forces exerted by its free ions. Ions with equal valencies, whether positive or negative, are equally efficient, and the efficiencies of ions of different valencies are directly pro- portional to the squares of their valencies.”

This statement of Mellanby is now recognized as a description of the principle of the ionic strength which was later formulated by Lewis (16). In studying mixtures of electrolyte solutions the latter found the following empirical relation. “In dilute solu- tions, the activity coefficient of a given strong electrolyte is the same in all solutions of the same ionic strength.”

The ionic strength does not explain differences in behavior between salts of the same valence type manifested in more con- centrated solutions. The deviations from the ideal gas laws exhibited by solutions of strong electrolytes have been described in terms of the “activity coefficients” of the salts. The theory of Debye and Hiickel(9) considered the influence of interionic forces upon activity coefficients. These equations have been found to be in close agreement with the experimental observations for many classes of strong electrolytes. The applicability of this equation to proteins has been considered by Cohn and Prentiss (8), by Stadie (22), and by Adair (1).

The two preceding papers in this series have dealt with the solubility of hemoglobin in concentrated solutions of different electrolytes under varying conditions (11) and in potassium phosphate buffers of varying concentration and pH (12). In this paper we consider the solubility of t.he same protein in solutions of chlorides and sulfates of widely varying concent,ration, especially in dilute solutions where their solvent effect can be investigated.

EXPERIMENTAL

The method of determining solubility is essentially the same as that employed in the foregoing papers. The crystallized horse

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A. A. Green 49

hemoglobin used was prepared as far as possible in the salt solution in which solubility was later determined. The crystals were placedincovered containers, the desired electrolyte solution added, the mixture saturated with carbon monoxide, and then shaken gently at 25” in a constant temperature bath until equilibrium was reached; generally 4 or 5 hours were required. The solutions were filtered at constant temperature and the filtrates analyzed. The crystals were returned to their containers and more electrolyte solution added. Most of the points on the sodium sulfate curve were obtained by repeated washing with a solution of a given concentration until constant solubility was reached. The same procedure was used in studying solubility in chlorides, but the solubility is so high in concentrated chloride solutions that it was not possible to obtain filtrates of constant salt content, but true equilibrium was reached since the points all lie on a smooth curve. In determining solubility in the rest of the electrolytes two bottles of crystals were used and the salt concentration was first increased from equilibrium to equilibrium and finally decreased in the successive equilibrations. The fact that the earlier and later points all lie on the same smooth curve and also that the points in the more concentrated solutions check those obtained in the previous series of experiments indicate that true equilibrium was reached.

The amount of hemoglobin dissolved was determined, as before, by Kjeldahl nitrogen analyses on the filtrates. Horse hemoglobin is assumed to contain 17.7 per cent of nitrogen. The sulfate solutions were analyzed for salt by heat-coagulating the protein without the addition of further salt, washing the precipitate salt- free, and carefully evaporating, drying, gently igniting, and weigh- ing the filtrate. The magnesium sulfate determinations were checked by transforming a few samples to barium sulfate and weighing as such. The ammonium sulfate concentration was, however, determined by heat-coagulating the protein in the presence of a slight amount of phosphate buffer, washing the pro- tein salt-free, and distilling over the ammonia in the filtrate. The chloride determinations were made according to the Wilson modification of the Van Slyke met’hod (23).

The density of many of the saturated solutions was determined and graphical interpolation employed where necessary.

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50 Physical Chemistry of Proteins. X

TABLE I

Solubility of Carboxyhemoglobin at 25”

‘~~-l~~~~-l~~~~l~l~ii// p 1 4 1 pH 1 Hbsolubility I$$$

Solubility in potassium chloride

20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20

16 16 16 16 16 16 16 16 16 16 16 16 16 16

-

-

-

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1

-

nozs per 1

0.108 0.110 0.258 0.272 0.374 0.425 0.614 0.698 0.807 0.970 1.002 1.040 1.295 1.63 1.76 1.94 2.70 3.20

-

-

1.020

1.051

1.083 1.067

1.112

1.150 1.169

0.114 0.338 6.62 0.116 0.341 6.59 0.281 0.537 6.59 0.297 0.545 6.69 0.415 0.644 6.64 0.474 0.689 6.69 0.701 0.837 6.65 0.807 0.899 6.65 0.943 0.971 6.65 1.15 1.07 6.64 1.19 1.09 6.62 1.23 1.11 6.66 1.565 1.25 6.66 2.0 1.41 6.74 2.16 1.47 6.60 2.395 1.545 6.61 3.34 1.83 6.76 3.90 1.98 6.62

Solubility in sodium chloride

0.004 0.004 0.114 1.021 0.121 0.117 0.123 0.242 0.264 0.249 1.0340 0.272 0.525 1.0612 0.600 0.53 0.604 0.55 0.622 1.05 1.25 1.60 1.1386 1.95 2.20 2.79 2.46 1.1650 3.195 2.83 3.72 3.10 1.1895 4.23

0.06~ 0.341 0.35: 0.514 0.52: 0.77t 0.77! 0.79 1.12 1.40 1.67 1.79 1.93 2.06

6.60 6.54 6.66 6.76 6.53 6.66 6.70 6.81 6.69 6.75 6.71 6.61 6.80 6.83

-7

g$. i%g?z 2 61.2 64.4 62.8 66.3

100.0 109.0 101.0 112.0 123.0 136.5 124.0 138.6 145.0165.6 150.0173.2 163.0190.0 160.0189.6 159.0188.8 160.0190.5 170.0206.0 163.0199.5 166.0204.0 159.0196.5 140.0 173.2 110.0134.0

1.809 1.821 2.037 2.049 2.135 2.142 2.219 2.238 2.279 2.278 2.276 2.280 2.314 2.300 2.310 2.293 2.238 2.127

24.2 24.7 1.393 62.8 65.9 1.820 67.8 71.2 1.852

100.0109.0 2.039 105.0115.0 2.061 155.0177.0 2.248 157.0179.0 2.253 163.0 186.0 2.269 198.0235.0 2.37 226.0276.0 2.441 240.0304.0 2.483 248.0319.0 2.504 254.0334.0 2.526 277.0379.0 2.579

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TABLE I-COnChded

Solubility in potassium sulfate

1 ids per 1.

1 0.0268 1.0119 0.083‘ 0.283 6.73 41.4 1 0.0673 0.210 0.458 6.72 49.0 1 0.0904 0.283 0.532 6.77 53.0 1 0.1064 1.0263 0.333 0.577 6.80 48.6 1 0.1155 0.361 0.601 6.38 46.1 1 0.1760 0.551 0.743 6.60 49.0 1 0.205 0.642 0.801 6.70 43.3 1 0.322 1.0501 1.005 1.003 6.67 37.3 1 0.403 1.26 1.12 6.90 25.7 1 0.490 1.0669 1.53 1.24 6.45 20.5 1 0.520 1.0644 1.62 1.28 6.60 13.3

21 21 21 21 21 21 21 21 21 21 21

rm.per o;o$m

42.8 51.0 55.2 50.7 47.7 51.2 45.2 39.0 26.9 21.3 13.8:

1.631 1.708 1.742 1.705 1.679 1.709 1.655 1.591 1.430 1.328 1.142

Solubility in sodium sulfate

22 24 22 23 24 15 15 15 11

0.006 0.018 0.13 6.72 ~ 30.2 30.9 1.490 0.015 0.045 0.21 6.71 31.1 31.9 1.504 0.0523 1.0153 0.156 0.404 6.70 45.0 46.9 1.671 0.141 0.446 0.667 6.84 48.1 50.6 1.704 0.133 0.420 0.648 6.68 43.8 46.1 1.664 0.30 0.940 0.970 6.71 43.7 46.5 1.668 0.40 1.0576 1.265 1.125 6.66 32.1 33.8 1.529 0.55 1.0735 1.69 1.30 6.68 17.3 17.7 1.248 0.675 1.0816 2.12 1.455 6.60 9.5f 9.78 0.990

Solubility in ammonium sulfate

0.058 1.0120 0.180 0.424 6.41 0.205 1.0300 0.648 0.805 6.64 0.239 0.748 0.865 6.45 0.267 0.846 0.92 6.54 0.387 1.23 1.11 6.58 0.572 1.82 1.35 6.52 0.621 1.98 1.41 6.59 0.645 1.0507 2.05 1.43 6.60

-

41.8 43.2 54.9 57.8 49.4 52.1 54.4 57.5 45.2 47.8 38.4 40.8 26.0 27.6 25.1 26.7

21 21 21 21 21 21 21 21

-

-

1.636 1.762 1.717 1.760 1.679 1.611 1.441 1.427

Solubility in magnesium sulfate

0.52: 6.66 0.87 6.59 1.21 6.54 1.43 6.64 1.91 6.60 1.92 6.41 2.06 6.49 2.69 6.1

52.0 54.2 1.734 83.0 88.6 1.947 96.0 103.5 2.015

87.0 93.6 1.971 62.2 65.3 1.815

55.6 58.3 1.766 47.9 49.7 1.696

8.25 8.43 0.926

21 1 0.0652 1.0186 0.272 21 1 0.177 1.0411 0.756 21 1 0.339 1.0643 1.46 21 1 0.478 2.05 21 1 0.862 1.1120 3.63 21 1 0.881 1.1159 3.69 21 1 1.02 1.1251 4.23 21 1 1.77 7.25

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52 Physical Chemistry of Proteins. X

The pH of all saturated solutions was determined with the hydrogen electrode as soon as possible after filtering. The hemoglobin and the electrolyte solutions were adjusted as nearly as possible to pH 6.6 before the experiment began, and where necessary small quantities of acid or alkali were added to the electrolyte solutions during the experiment. The pH values as determined lie for the most part between 6.5 and 6.8 in the range of minimum solubility. The data are presented in Table I. The ionic strength term of Lewis, .B, is calculated per 1000 gm. of HZO.

Activity Coeficients of Hemoglobin in Solutions of Chlorides and Sulfates

In a heterogeneous equilibrium in which a solution is saturated with a solid component, at constant temperature and pressure, the activity of the substance in the solid phase must be the same as that in the liquid phase. This is independent of any other components in the solution. The addition of electrolytes to a saturated solution of hemoglobin does not change the activity of the hemoglobin although it changes the solubility, or the concen- tration. The ratio of the solubility of a substance at zero electro- lyte concentration, X0, to the solubility in a solution of given electrolyte concentration, S, is the activity coefficient, y, of the

substance in that solution. y = 5 S’

The Debye-Htickel theory of interionic forces in solutions of strong electrolytes yields a simplified equation for the evaluation of the activity coefficients in various solutions of electrolytes. The application of this theory to oxyhemoglobin in phosphate solutions at 0” has already been discussed by Cohn and Prentiss (8). The simplified form of the Debye equation including t’he “salting out” term added by Hiickel is

in which y is the activity coefficient, S is the solubility, X0 the solu- bility in the absence of electrolytes, p the ionic strength, ZIZz the valence type, K, the “salting out” constant, 0.5 a theoretical constant having this value at 25”, A a constant which depends upon the mean effective diameter, b, of all ions in a solution, and K a “reciprocal distance.”

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A. A. Green 53

When the number of ions in solution is so small that their size is negligible in comparison with the distance between them they may be considered as point charges and Equation 1 reduces to

- log y = log s - log so = 0.5 ZlZZ 4; (2)

This equation has been shown to hold for cobaltamines (3) and other difficultly soluble strong electrolytes in very dilute salt solutions. The molecular concentration of the cobaltamines is in general such that their contribution to the ionic strength is of the order of 5 X lo-*. Thus their solubility could be studied in solutions of low ionic strengt.h and it was possible to accurately determine S,, the solubility in the absence of any electrolyte, rather t.han SO, the solubility in the absence of added electrolyte. The solubility of hemoglobin in the absence of salt is relatively high, about 20 gm. per liter. The molecular concentration, how- ever, is only 0.0003 M and of the same order as that of the cobalta- mines. The contribution of the hemoglobin to the electrical environment remains unknown and in all of our calculations has been ignored. Moreover, difficulties of various kinds were en- countered in making the measurements in very dilute solutions of salt. The results were less consistent and greater difficulty was experienced in controlling and measuring the hydrogen ion activity.

When the number of ions is increased their mean effective diame- ter must be taken into account. The right-hand side of the equa-

tion is then multiplied by the factor l

1 + A 1/i’ This term

changes the equation to

- log y = log s - log so = 0.5 ZIZZ

1+L44/, (3)

the equation of a curve rather than that of a straight line. This is the equation used by Cohn and Prentiss (8) to describe the solu- bility of horse oxyhemoglobin at O”, in phosphate buffers up to an ionic strength of 1.0.

A third term must be added when more concentrated solutions of elect.rolytes are considered. Deviations of the behavior of strong electrolyt.es from the equation that Debye advanced in 1923 were subsequently ascribed by Htickel(l5) to changes in the dielec- tric constant of t’he solution and shown to be approximately

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54 Physical Chemistry of Proteins. X

proportional to the concentration. The added proportionality factor, K,, is the so called “salting out” constant in Equation 1.

The solubility of hemoglobin in concentrated solutions of multi- valent electrolytes may be adequately described, as was seen in Studies VIII (ll), by the linear equation for the solubility of non- electrolytes (20) and proteins in concentrated salt solutions (5)

log S = p - K,‘/x (4)

where X is again the solubility and P the ionic strength. p is the intercept constant and is the hypothetical solubility in the absence of salt, termed hypothetical since, of course, hemoglobin is a globulin whose solubility passes t,hrough a maximum with increas- ing salt concent,ration. p is nevertheless a convenient constant varying with the temperature and the amphoteric properties of the protein. Ii,’ is a salting out constant characteristic of the protein independent of the temperature and of the pH when a given elec- trolyte is employed, but varying with the electrolyte. The evaluat,ion of the constants K,' and /3 affords an adequate charac- terization of the precipitation of a protein in concentrated solutions of electrolytes.

In studying the solubility of carboxyhemoglobin in phosphate buffers of varying ionic strength and pH (12) it was found that at the point of minimum solubility the protein acted as though it were composed not only of the neutral molecule, but of positively and negatively charged molecules as well. It was also found that the pH of minimum solubility varied with the salt concent.ration. The magnitude of the effect of electrolytes on t,he acid and basic dissociation constants was such that the proportion of charged to uncharged molecules at pH 6.6 was approximately constant, although slightly greater in the very dilute solutions of phosphate. Thus, although the slope of the solubility curve at pH 6.6 in dilute solutions was such that the Debye-Hiickel equation did not appear to apply, if one considered the neutral molecule alone, it was found to act as though A in Equation 1 were 1.5, the value used in describ- ing the phosphate buffers themselves (4), and Z,Z, were 4, the value used describing solubility in phosphates at 0”. The variation in the dissociation constants was such that if the solubility had been determined at pH 6.7 rather than 6.6 the protein would have con- sisted of an approximately constant proportion of charged to uncharged particles.

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A. A. Green 55

The pH of the saturated solutions of hemoglobin in sulfates and chlorides was not so accurately controlled as in the phosphate buffers. The points lie for the most part on smooth curves, how- ever, and the variation in pH is not sufficient, apparently, to take the protein far from the pH of minimum solubility.

A satisfactory picture of the variation of activity coefficients can be obtained from a study of variation of solubility at approximately pH 6.6. The consideration of Equations 1 and 4 in relation to the solubility of hemoglobin in phosphate buffer solutions revealed the applicability of the first to dilute solutions and of the second to concentrated solutions. Equation 4 has been shown to be applica- ble to hemoglobin in concentrated sulfate solutions (11). The applicability of Equation 1 to solubility in both chlorides and sulfates is considered in the following.

Apparent Valence Type, .ZJ~

The “valence” type is evidently “apparent” when one is dealing with a complicated protein molecule. Hemoglobin has been found to behave as though it were a bi-bi- or a uni-quadrivalent type in the Debye sense. Consideration of the solubility of oxyhemo- globin in relation to the Debye equation led Cohn and Prentiss (8) to the following conclusions.

“The solvent action of a neutral salt upon a protein, oxyhemoglobin, has been found identical to the solvent action of a neutral salt upon a bi-bival- ent or a uni-quadrivalent compound.”

“To conclude that oxyhemoglobin is bivalent or quadrivalent might be correct, but would be unjustified at the present time. . . . Our experi- ments permit neither deduction. They render it certain, however, that oxyhemoglobin behaves in this respect as though it were bivalent or quadri- valent, and that the action of neutral salts in dissolving proteins is identical to their action in dissolving other slightly soluble substances.”

The neut’ral carboxyhemoglobin molecule in solutions of phosphate behaves as though it had the same apparent valence type (12).

In chloride solutions it is possible to estimate the value of the apparent valence type since the salting out effect of chloride is relatively small, and Equation 2 may, in dilute solutions, be solved by simultaneous equations for Z& and XO if the value of A be taken from the literature. We have employed the value given by Scatchard (19). The results are reported in Table II. 23~ is 4.

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56 Physical Chemistry of Proteins. X

It must be reiterated that on the basis of this equation hemoglobin merely acts as though it had this apparent valence type.

Evaluation of SG, Solubility of Carboxyhemoglobin in Absence of Salt

The estimation of SO is an extrapolation and its accuracy is dependent upon the applicability of the equation by which the extrapolation is made. On the basis of the calculation by Equa-

TABLE II

Apparent Valence Type and Solubility in Absence of Salt of Carboxy- hemoglobia at 25” and pH 6.6 Estimated by the Equation

0.6 ZlZZ 4; Log s = Log SO + 1 + A &

Log s I s I

0.5 z,z* I

Log so

1.393 0.004 2.10 1.282 1.820 0.121 2.11 1.288 1.852 0.123 2.07 1.300 2.039 0.264 1.97 1.304 2.061 0.272 1.95 1.318 2.248 0.600 1.85 1.280 2.253 0.604 1.89 1.283 2.269 0.622 1.92 1.290

Sodium chloride; A taken as 0.775

Potassium chloride; A taken as 0.816

1.809 0.114 2.05 1.280 1.822 0.116 2.02 1.288 2.037 0.281 1.99 1.289 2.049 0.297 1.99 1.294 2.135 0.415 1.94 1.290

Average.. . . . . . 1.99 I 1.291

tion 2, from the solubility in dilute chloride solution reported in Table II, the minimum solubility of hemoglobin in the absence of salt is 19.5 gm. per liter.

The solubility of t,he neutral form alone in the absence of salt as determined by extrapolation from the data for solubility in phos- phate solution is 11 gm. per liter. If the increase in solubility is

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A. A. Green 57

defined by Equation 9 of Studies IX and the values of pKIKz and pK3K4 given there be accepted, the total solubility at pH 6.6 is about 17 gm. per liter, but the minimum solubility at pH 6.8 is only about 15 gm. per liter. Log X0 at the pH of minimum solubility, then, is 1.29 by extrapolation from the data for solubility in chlo- ride, and 1.18 from the data for solubility in phosphates. The discrepancy may be due either to experimental error, especially in the unbuffered chloride solutions, or to estimation of the dissocia- tion constants in dilute solutions of phosphates. In any case the true value of log SO is probably 1.24 fO.06. In considering the solubility in sulfates the value 1.20 makes it possible to more accurately describe the data in terms of the other constants of Equation 1. In Fig. 1 the curves are drawn with this extrapolated value.

Calculation of the Salting Out Constant, K,

Hemoglobin is not precipitated in the most concentrated solu- tions of sodium or potassium chloride. In sodium chloride there is not even a diminution of solubility. However, the solubility curve in potassium chloride does exhibit a maximum. No such curve can be described on the basis of the original Debye equation. It is necessary to employ a salting out constant as was done by Hiickel. The calculation of this constant is carried out in Table

III. The term log S - 2\/z

- diminishes in more concen- l+A2//1

trated solutions. If this deviation from the Debye equation be divided by the ionic strength a constant value results. The deviation is given in the fourth column of Table III and is 1.30

- log s + 2x4

1 + A di- K, for carboxyhemoglobin at 25” and

pH 6.6 in sodium chloride solutions is 0.09 and in potassium chlo- ride solution is 0.15.

In concentrated solutions of elect’rolyte in which the protein is precipitated, the solubility is described by Equation 4. If, as previously pointed out (7), Equations 1 and 4 apply simultaneously,

0 replaces log So + 0.5 -mG fi and K, is K 1+/l& s S.

As a first approxi-

mation let us assume the applicability of the K,’ value for sulfates given in Studies VIII.

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58 Physical Chemistry of Proteins. X

TABLE III

Salting Out Constant for Carboxyhemoglobin in Solutions of Sodium and Potassium Chloride Estimated by the Equation

1.30 - Logs+ WT

K, = l+Ad; il

Log s P

2.370 1.25 1.170 0.130 2.441 1.95 1.100 0.200 2.483 2.79 1.029 0.271 2.504 3.20 1.007 0.293 2.526 3.72 0.981 0.319 2.579 4.29 0.991 0.309

Average...............................................

Sodium chloride; A taken as 0.775

2.278 1.15 1.136 0.164 2.276 1.19 1.124 0.176 2.280 1.23 1.117 0.183 2.314 1.57 1.077 0.223 2.300 2.00 0.988 0.312 2.310 2.16 0.974 0.326 2.293 2.40 0.926 0.374 2.239 3.34 0.769 0.531 2.127 3.90 0.612 0.688

Potassium chloride; A taken as 0.816 -

0.104 0.103 0.097 0.092 0.086 0.075

0.093

0.143 0.148 0.149 0.144 0.156 0.151 0.156 0.159 0.176

Average................................................, 0.154

TABLE IV

Values of A and K, for Carboxyhemoglobin at $5” When Log SO Is 1.20 and -m-h Is 4

Electrolyte.. . . . NaCl KC1 MgSOa (NH&SOI Na&04 KzSOa NarCeHsO, --

K, . . . . . . . 0.12 0.27 0.31 0.56 0.72 0.72 0.65 A . . . . . . . . . . . . . . 0.6 0.5 0.7 0.8 0.9 0.9 0.9

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A. A. Green 59

Estimation of A

The values of A used are purely empirical. If the values of K,’ calculated in Studies VIII are employed and if log X0 be taken as 1.20 and Z&J be assumed to be 4, the values of A which best describe the experimental points can be calculated and are given in Table IV. In order to obtain uniformity, the curves describing solubility in chlorides are calculated assuming log SO to be 1.20 rather than 1.29 as calculated in Table II. This necessitates the

SOUARE ROOT OF IONIC STRENGTH--

FIG. 1. The solubility of carboxyhemoglobin in various electrolytes at 25”. The curves are drawn according to Equation 1, the constants in Table IV being used.

use of a smaller purely empirical value of A. The agreement of the data with the equation can be seen in Fig. 1 where we have plotted log X against &.

There are ranges in which there is a divergence from the calcu- lated curves, notably in the dilute concentrations of ammonium and magnesium sulfates and in sodium sulfate at about & = 1.3. The studies upon phosphates considered in the previous communi- cation are also not satisfactorily described by EquaGon 1. Al- though this equation describes a decrease in activity coefficient

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60 Physical Chemistry of Proteins. X

followed by an increase in activity coefficient, the rates of decrease and increase, especially in the neighborhood of maximum solu- bility, are different for carboxyhemoglobin than for MgSO, or for a cobaltamine.

Empirical Equations for Description of Solubility

The solubility of hemoglobin in solutions of chlorides and sulfates may be satisfactorily described in terms of an empirical equation which is similar in form to the Debye-Htickel equation if the size term be omitted, which may then be written:

- log y = log S - log So = 0.5 ZZ, d; - K,p (5)

This equation is the same as that used by Bjerrum and Unmack (2) in characterizing the activity coefficients of various electro- lytes. We have changed the symbols for convenience, and written:

- log y = log s - log so = 7% d; - k,/.t (6)

in which ki and k, are empirical constants, ki being t,he “salting in” constant and k, the “salting out” constant. ki may be assumed to be the “apparent valence type” replacing 0.5 Z~ZZ in

the Debye equation. The term 1

1+ A 4; is omitted and k,

is substituted for K,, for although both are salting out constants they have not the same numerical value. The values of both constants vary with the electrolyte. If one were to attempt a comparison of this equation with that of Debye and Hiickel, this variation of k;, the “apparent valence type,” (0.5 Z,Z,) might seem improbable but Simms (21) has reported a similar phenome- non in describing the activity coefficients of amino acids and other weak electrolytes and ampholytes. However, we used this equa- tion merely as an empirical interpolation formula and its justifica- tion is the greater accuracy with which the activity coefficients are described.

One may use a still simpler expression involving the equivalent concentrat.ion, C, of electro1yt.e rather t,han the ionic strength, P. In this case the equation becomes

log s = log so + k; 43 - k,C (7)

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A. A. Green 61

Here, fortunately, ki has the same value, 1.6, for all electrolytes and log X0 is 1.30. The equation may be rearranged and these values substituted whence

log S - 1.6 d?? = 1.30 - k,C (8)

If log S - 1.62/c be plotted against the equivalent concentration of electrolyte, C, a straight line results, describing the solubility in

Ll

NaCi o KCI V

N&trtA

FIG. 2. The solubility of carboxyhemoglobin at 25”. The lines are drawn according to Equation 8.

any given electrolyte. The slope of the line is k, and varies with the electrolyte used having the following values for carboxyhemo- globin of the horse at 25”: NaCl, 0.57; KCl, 0.67; MgSOd, 0.98; (NH&S04, 1.40; NazSOI, 1.64; KzS04, 1.68; and Na&$H507, 1.87. These values have been determined graphically from Fig. 2 where the agreement with the experimental points may be seen to be satisfactory. The solubility in potassium phosphates at pH 6.6

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62 Physical Chemistry of Proteins. X

q aoob D lJ

-K! -K!

#

I I I I I I

3 9 ln

CUAJOSSiO NlXO&d lNXl&!d ifi WHllklV307 U3AJOSSiO NlXO&d lNXl&!d ifi WHllklV307 Ix

-

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A. A. Green 63

may be described by the same curve as in Na2S04, where the equivalent concentration of phosphate is greater than 0.5.

It is thus possible to describe the variation in solubility of hemoglobin with one constant characteristic of the protein in all electrolytes and one constant varying with the electrolyte.

The data may be accurately described, also, if one uses another theoretically unjustified expression, in which the equivalent concentration is substituted for the ionic strength in Equation 1. The values for K, and A are of course different and log XO is 1.30 and Z,& is again 4. The relation is, of course, again purely empirical, but is worth noting as a satisfactory means of describing the solubility of hemoglobin in electrolyte solutions. We refrain from giving constants and curves since the preceding equation is a simpler form and easier to use.

Solubility of Serum Globulin in Solutions of Various Electrolytes

Mellanby in 1905 (17) described the solubility of serum globulin in solutions of various electrolytes of different valence type. Some of his results are shown in Fig. 3, I. Since the total amount of globulin present affected the amount in solution he expressed his results in terms of per cent dissolved. This was done since the ratio of dissolved protein to total protein was found to be constant for any one concentration of salt. We have plotted the logarithm of the per cent dissolved which is analogous to the logarithm of the solubility used in the hemoglobin calculations. The electro- lyte has been expressed as square root of ionic strength. It is evident that the curves for solubility are superimposable and that Mellanby was justified in deriving the “square of the valence” rule quoted above, since, of course, the ionic strength is a function of the square of the valence.

Mellanby also was not unaware of the divergence from this rule of ions of the same valence type. In Fig. 3, II we give his data for the solubility of serum globulin in various potassium salts. The decreasing order of the effectiveness as a solvent is KI, KBr, KCl, I(aS04, and KC2H302.

The range of electrolyte concentration investigated and also the range of solubility investigated makes it impossible to calculate

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64 Physical Chemistry of Proteins. X

accurately the “apparent valence type” of the protein in terms of Equation 1. However, serum globulin “salts in” as though Z& were about 12.

Xolubility of Edestin in Solutions of Various Electrolytes

Osborne and Harris studied the effect of many electrolytes on the solubility of the crystalline vegetable globulin, edestin. Some

2.0 -

NaCl 0 I KU a

N&O4 l

0 I I I 0.5 1.0 1.5

SQUARE ROOT OF I ONIC STRENGTH

FIG. 4. The solubility of edestin in various salts taken from the data of Osborne and Harris (18).

of their data have been recalculated and are given in Fig. 4 in Which we have plotted the logarithm of the solubility against the square

root of the ionic strength, i. By comparing the solubility curves

with those of hemoglobin in the same salts, it is evident that they differ in their steepness; that is, edestin has a much higher “appar- ent valence type,” Z1.Z2, Equation 1. It is impossible to calculate the exact value, but ZIZz is approximately 25 (6), whereas in

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A. A. Green 65

hemoglobin it is 4. In spite of this difference the variation in effect of the different salts at the same ionic strength is the same as in hemoglobin. Inspection of the curves shows that sodium chloride has a greater solvent power than potassium chloride. The chlorides have a greater solvent action than the sulfates. Magnesium sulfate has a lower soIvent power in lower concentra- tions than sodium sulfate, but the protein is not readily salted out in magnesium sulfate and the sodium sulfate, on the other hand, is a very effective precipitating agent. All these effects of electro- lytes on edestin are qualitatively the same as those of the same electrolytes upon hemoglobin.

Regardless of the form of equation used to describe the globulin- like behavior of hemoglobin in chlorides and sulfates the increase in solubility in dilute solutions of electrolytes as well as the pre- cipitation in more concentrated solutions is thus qualitatively the same as that of other proteins in the same salts. Solubility is dependent upon temperature, upon pH, and upon the nature and concentration of the electrolyte employed. The magnitude of these various solubility phenomena is dependent upon the nature of the protein. The behavior of a protein in an electrolyte solution is dependent not only upon the electrolyte used, but also upon the character of the protein itself. Composition, available charge, hydration, molecular weight and “size,” and probably many other factors must be taken into account before it will be possible to predict the behavior of any given protein in a given electrolyte solution.

I wish to thank Professor Edwin J. Cohn for his continued inter- est in these studies on the solubility of hemoglobin.

SUMMARY

1. The solubility of carboxyhemoglobin of the horse at approxi- mately pH 6.6, has been measured, in solutions of sodium and potassium chloride and of sodium, potassium, magnesium, and ammonium sulfate. Hemoglobin is a globulin whose solubility in sulfates exhibits a maximum with increasing salt concentrations.

2. The solvent power of dilute solutions of sulfates is much less than that of the chlorides.

3. The activity coefficients of the hemoglobin in these sohrtions

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Physical Chemistry of Proteins. X

can be approximately described, but only approximately in terms of the simplified Debye-Hiickel equation

- log y = log s - log So = 0.5 z,zz 4;

1 + A v’i - K8p

where log So is 1.20, ZIZz is 4, A is an empirical constant having approximately the same value as in other systems containing the same electrolytes, and K, is also an empirical constant whose value is the same as that determined in concentrated solutions of electro- lytes where the simple salting out expression holds.

4. The solubility of carboxyhemoglobin in chlorides and sulfates at 25” and pH 6.6 may be satisfactorily described in terms of the empirical equation

log S = 1.30 + 1.6 @ - k,C

where k, is an empirical constant varying with the electrolyte.

BIBLIOGRAPHY

1. Adair, G. S., Tr. Faraday Sot., 23, 536 (1927). 2. Bjerrum, N., and Unmack, A., Kgl. Danske videnskab. Selskab, Math.-

fys. Me&Z., 9,l (1929). 3. Briinsted, J. N., and La Mer, V. K., J. Am. Chem. Sot., 46,555 (1924). 4. Cohn, E. J., J. Am. Chem. Sot., 49, 173 (1927). 5. Cohn, E. J., Physiol. Rev., 6, 349 (1925). 6. Cohn, E. J., Skand. Arch. Physiol., 49, 107 (1926). 7. Cohn, E. J., and Green, A. A., J. Biol. Chem., 78, p. xxxii (1928). 8. Cohn, E. J., and Prentiss, A. M., J. Gen. Physiol., 8, 619 (1927). 9. Debye, P., and Hiickel, E., Physik. Z., 24,185 (1923).

10. Denis, P. S., Memoire sur le sang, Paris (1859). 11. Green, A. A., J. Biol. Chem., 93,495 (1931). 12. Green, A. A., J. Biol. Chem., 93, 517 (1931). 13. Green, A. A., and Cohn, E. J., Am. J. Physiol., 90,366 (1929). 14. Hardy, W. B., J. Physiol., 33, 251 (1905-06). 15. Hiickel, E., Physik. Z., 26, 93 (1925). 16. Lewis, G. N., and Randall, M., Thermodynamics and the free energy of

chemical substances, New York and London (1923). 17. Mellanby, J., J. Physiol., 33, 338 (1905-06). 18. Osborne, T. B., and Harris, I. F., Am. J. Physiol., 14,151 (1905). 19. Scatchard, G., Tr. Faraday SOL, 23, 454 (1927). 20. Setschenow, Ann. chim. et physiq., 26, series 6, 226 (1892). 21. Simms, H., J. Physic. Chem., 32, 1121 (1928). 22. Stadie, W. C., J. Biol. Chem., 77,303 (1928). 23. Wilson, D. W., and Ball, E. G., J. Biol. Chem., 79, 221 (1928).

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Arda Alden GreenCONCENTRATION

SULFATES OF VARYINGIN SOLUTIONS OF CHLORIDES AND THE SOLUBILITY OF HEMOGLOBINCHEMISTRY OF THE PROTEINS: X.

STUDIES IN THE PHYSICAL

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