Explanation of the Colloidal State of Protein Bodies1

Jacques Loeb (†).

I.

Living matter is, at its foundation, of a colloidal nature. We cannot imagine a single organism consisting only of crystalloids. This fact compels us to recognize that the special properties of the colloidal state condition vital phenomena, or are inseparably connected with them. Therefore, the systematic study of the essence of true vital phenomena must be based on a scientific theory of the state of colloidal substances. A theory consisting of simple assumptions, or of assumptions based only on qualitative experiments, is not, in our opinion, a scientific theory. By a scientific theory we understand the derivation of consequences from rational mathematical formulas, which make it possible to determine colloidal properties with adequate accuracy.

Protein bodies appear to us as amphoteric electrolytes, which can form salts both with acids and with alkalis. With alkalis, Na-, Ca-proteinate is obtained; with acids—protein chloride, protein sulfate, etc. Whether a protein acts as an anion or as a cation depends on the concentration of hydrogen ions in the solution. However, there exists a definite concentration of hydrogen ions at which the protein body does not combine appreciably either with acid or with alkali. This concentration of hydrogen ions is called the isoelectric point of the protein. Its position is specific for each protein body. For gelatin and casein it lies at \(p_H = 4.7\)2, for crystallized egg albumin at \(p_H = 4.8\). Gelatin can combine with acid only when \(p_H\) is less than 4.7, and with alkali only when \(p_H\) is greater than 4.7. The same can be observed under the action of various salts. If one adds to a solution

gelatin with \(NiCl_2\), then nickel gelatinate is formed only when \(p_H\) is greater than 4.7, whereas on adding \(K_4Fe(CN)_6\) a compound with ferrocyanide is formed only at \(p_H\) less than 4.7. The validity of this can be shown by means of the known methods, of which I spoke in my last book1.

Proof of the ability of protein bodies to combine stoichiometrically with acids and bases can be obtained from titration curves. For this purpose (as perhaps in general for all work in the field of proteins) protein as the starting material must be taken at the \(p_H\) of its isoelectric point. We have already seen that protein bodies combine with acids only at a \(p_H\) lower than the \(p_H\) of the isoelectric point, which for gelatin and casein lies at \(p_H = 4.7\), and for crystallized egg albumin at \(p_H = 4.8\). Weak dibasic and tribasic acids dissociate at \(p_H\) below 4.7 as monobasic acids. Under these conditions \(H_3PO_4\) forms \(H^+\) and the monovalent anion \(H_2PO_4^-\). If the acid combines stoichiometrically with the isoelectric protein, then it must be assumed that, in order to bring to the same height the concentration of hydrogen ions, say \(p_H = 3.0\), one must take three times as many \(\mathrm{cm}^3\) of \(0.1\,n\) (normal solution) \(H_3PO_4\) for gelatin, casein, or egg albumin than of \(0.1\,n\) hydrochloric or nitric acid. Experiment confirms this conclusion.

Fig. 1. Titration curves of crystallized egg albumin with hydrochloric, sulfuric, oxalic, and phosphoric acid.

The situation is different with sulfuric acid. It splits off both hydrogen ions at \(p_H < 4.7\). Therefore one must take an equal number of \(\mathrm{cm}^3\) of \(0.1\,n\) sulfuric or hydrochloric acid in order to bring a 1% solution of isoelectric protein to the same \(p_H = 3.0\). Experiment confirms this proposition as well. Fig. 1 presents titration curves for crystallized egg albumin with four acids: \(HCl\), \(H_2SO_4\), \(H_3PO_4\), and oxalic acid. In the titration, 1 g of isoelectric protein was in \(100\,\mathrm{cm}^3\) of water mixed with various quantities of \(0.1\,n\) acid. The quantities in \(\mathrm{cm}^3\) of \(0.1\,n\) acid contained in \(100\,\mathrm{cm}^3\) of solution are plotted on the ordinates of the curves; on the abscissa are plotted the values of \(p_H\), which

protein solutions after the addition of acid are taken. In order to bring 1% isoelectric protein in a volume of 100 cm³ to the same degree of \(p_H\), it is necessary each time to take exactly three times as many cm³ of 0.1 \(n\) solution of \(H_3PO_4\) as compared with the amount of hydrochloric or sulfuric acid. In order to bring a 1% solution of initially isoelectric albumin to \(p_H = 3.2\), it is necessary that 100 cm³ of the solution contain 5 cm³ of 0.1 \(n\) hydrochloric acid solution and 15 cm³ of 0.1 \(n\) phosphoric acid solution. To bring the same protein to \(p_H = 3.4\), 4 cm³ of 0.1 \(n\) hydrochloric or sulfuric acid solution and 12 cm³ of 0.1 \(n\) phosphoric acid solution are required, and so on.

According to Hildebrand, oxalic acid at \(p_H \leqq 3.0\) is monobasic, but the more readily splits off the second hydrogen ion the more \(p_H\) rises above 3.0.

The titration curves show that, in order to bring our solution of isoelectric protein to the same \(p_H < 3.0\), it is necessary to take almost twice as much 0.1 \(n\) oxalic acid solution as hydrochloric acid; whereas, for establishing a reaction at \(p_H > 3.0\), it is necessary to take not double, in comparison with hydrochloric acid, the amount of 0.1 \(n\) oxalic acid solution, but less.

In a similar way it can be shown, with the aid of titration curves, that isoelectric protein combines with alkalis also according to stoichiometric laws, just as some weak acid, say acetic acid, would combine with the same alkalis. If the number of cm³ of 0.1 \(n\) solution of sodium hydroxide, potassium hydroxide, limewater, or baryta water, in the same volume of 100 cm³, necessary for bringing a 1% solution of isoelectric protein to the same \(p_H\), is plotted on the ordinate, and the corresponding \(p_H\) of the protein solution on the abscissa, then it is found that the corresponding values for all four alkalis lie on one curve. This was to be expected if the combination proceeds strictly according to stoichiometric rules.

Similar data, arguing for the existence of stoichiometric relations, can be cited, according to the author, for casein and gelatin and, according to Hitchcock, for edestin and serum globulin. It can hardly be doubted that similar relations will also be found for all protein bodies. It follows from this that protein bodies react with acids and bases exactly as amorphous crystalloids do, for example amino acids. If representatives of colloid chemistry had applied to their protein solutions methods for determining the concentration of hydrogen ions, no one would have thought that the reactions of proteins with acids and alkalis follow, instead of stoichiometric rules, the empirical adsorption isotherms of Freundlich.

The purely chemical character of the combination of protein bodies with hydrochloric acid is also manifested in the determination of the chlorine potential in solu-

...solutions of protein chlorides. In Werner’s view, when hydrochloric acid is added to a solution of \(NH_3\), the \(H\)-ions of the hydrochloric acid will bind to the ammonium ion, while the \(Cl\)-ions will remain free. The same type of reaction is also observed when hydrochloric acid is added to the isoelectric solution of gelatin. This follows from measurements of the chlorine potential in solutions of isoelectric gelatin. One-percent solutions of initially isoelectric gelatin contained, in \(100\ \mathrm{cm^3}\) of solution, different amounts of a \(0.1\,n\) solution of \(HCl\). The \(p_H\) of the solutions was determined each time with hydrogen electrodes, and \(p_{Cl}\) with silver–silver chloride electrodes. Gelatin had no effect on \(p_{Cl}\), whereas \(p_H\) naturally increased. Thus it becomes clear that part of the hydrogen combined with the \(NH_2\)- and \(NH\)-groups of the protein molecule, while chlorine, on the contrary, remained free (Table 1). Hitchcock obtained similar results with crystallized egg albumin, edestin casein, and serum globulin. These data may be regarded as valid for the majority, if not for all, protein bodies.

TABLE 1.

From the titration curves there follows yet another fact: salts of protein bodies are capable, to a considerable degree, of undergoing hydrolytic dissociation. If we add an acid, even \(HCl\), to an isoelectric protein, then one part of the acid binds to the protein, forming protein chloride, while another part remains free. Thus an equilibrium is obtained between free acid, protein chloride, and nonioniz-

with protein (isoelectric). The more acid is added to the original isoelectric sol, the more proteinhydrochloride is formed, until, finally, the entire mass of protein is converted into proteinhydrochloride. The amount of free acid can be established by measuring $p_H$, and then it is possible, by a simple calculation, to determine how much of it is bound to the protein. By saturating a protein solution with acid it is possible to find the weight of the compound of the protein with the acid. In this way Turкok found that the combining weight of gelatin is about 1090.

II.

The colloidal state of protein bodies is manifested in the special action of electrolytes—acids, bases, or salts—on the swelling of protein gels, the osmotic pressure, and the viscosity of protein solutions. Electrolytes affect these properties so similarly that they can all, in all probability, be reduced to a single cause. If we explain one of these properties, for example osmotic pressure, then at the same time we shall understand all the other phenomena as well. In our experiments the osmotic pressure was determined in protein solutions (gelatin, crystallized egg albumin, casein, and edestin), which contained 1 g of dry isoelectric protein in 100 cm³ of water, to which in different cases various amounts of a 0.1 N acid solution had been added. The solutions were placed in a collodion bag, and the latter was suspended in a liquid free of protein, whose initial $p_H$ was brought to the $p_H$ corresponding to that of the sol solution. Naturally, the acid used for this purpose was the same as that added to the protein solution.

Fig. 2. Change in the osmotic pressure of protein solutions under the influence of acids. The osmotic pressure depends on the $p_H$ of the protein solution and on the valency of the acid anion.

The osmotic pressure was determined 18 hours after setup. It depended in a characteristic manner on the $p_H$ of the protein solution and on the valency of the acid anion. The curves in Fig. 2 prove this for gelatin solutions. Similar curves are obtained for other proteins, such as egg albumin, casein, and edestin. The curves show that the osmotic pressure of a protein solution has its minimum in the isoelectric ...

tric point of the protein. When small amounts of acid are added, the osmotic pressure gradually rises to a maximum, and with further addition of acid it again decreases. Further, the curves show that only the valency, but not the nature of the acid anion, has an influence on the osmotic pressure of the protein solution. As we could see above from the titration curves, the anion bound to the protein is monovalent in phosphoric acid, \(H_2PO_4^-\), and not \(PO_4^{---}\); in accordance with this, the curves in Fig. 2 show that the effect on the osmotic pressure of phosphoric and hydrochloric acids is the same, if it is referred to one and the same \(p_H\) of the protein solutions. We then see that the descending branch of the curve for the action of oxalic acid, which at \(p_H < 3\) is a monobasic acid, practically coincides with the descending branch of the action of hydrochloric acid. The curve representing the action of sulfuric acid lies almost twice as low as the curve for hydrochloric acid. From the titration curves of protamine sulfate we saw that the anion is dibasic. As a result of the experiments it became clear that all monobasic acids—hydrobromic, nitric, acetic, etc.—and all weak dibasic and tribasic acids, such as tartaric, malonic, citric, which at \(p_H < 4.7\) dissociate as monobasic acids, give the same curves as hydrochloric acid and phosphoric acid. From all this we may conclude that only the valency, and not the nature of the acid anion, affects the osmotic pressure of protein solutions; further, that on the acid side of the isoelectric point of the protein all acids which behave as monobasic affect the osmotic pressure in exactly the same way as hydrochloric acid, and that, finally, this effect is considerably greater than the effect of strong dibasic acids, such as sulfuric acid.

If alkali is added to an isoelectric protein solution, it can be shown that a small amount of alkali increases the osmotic pressure; with further addition the pressure passes through a maximum and again undergoes a decrease. All monobasic alkaline cations, such as \(Li \cdot\), \(Na \cdot\), \(K \cdot\), \(NH_4 \cdot\), act identically; for dibasic ions the same is obtained, only the curve of the action of alkali when \(Ca \cdot \cdot\) or \(Ba \cdot \cdot\) is used lies almost twice as low as under the action of monobasic alkalis.

Finally, as regards salts, the facts found by Loeb establish that salts always lower the osmotic pressure of proteins.

The curves for the action of acids and salts on the osmotic pressure of protein solutions are very similar to the curves for the influence of the same acids and salts on the swelling and viscosity of identical protein solutions. These data are highly characteristic of the colloidal state, and any theory of the colloidal state must be capable of explaining the curves obtained not only qualitatively but also quantitatively.

Zsigmondy assumed that the influence of acids on the osmotic pressure is based on a change in the dispersity of the protein present

in solution. But since the degree of dispersion cannot be measured exactly, this assumption is only a speculation. It gives no explanation of why viscosity and swelling change similarly to osmotic pressure. We must recognize the following explanation as correct: if acids or alkalis are added to an isoelectric protein solution, an ionized protein salt is formed from a greater or lesser part of the protein, depending on the amount of acid added. This ionization determines the peculiarities of the colloidal state, owing to the inability of protein ions to diffuse through membranes through which crystalloids easily penetrate. These membranes may be made of collodion or parchment; the walls of blood capillaries may serve as them, and probably also the membranes of all cells. Further, if the diffusion of one kind of ion is impeded by a membrane, as is the case for colloidal ions, while crystalloid ions pass without hindrance, then in the end an unequal distribution of diffusible crystalloid ions is established on the two sides of the membrane. This was first shown by Donnan. The unequal distribution of diffusible ions is the basis for the peculiarities of the colloidal state of protein bodies.

III.

If a bag made of collodion is filled with a solution of gelatin chloride at \(p_H = 3.0\) and this bag is immersed in an aqueous solution of hydrochloric acid with the same \(p_H = 3.0\), the acid passes from the protein solution into the external liquid free of protein. The basis for such an unequal distribution of oppositely charged ions on the two sides of the membrane is the ability of the membrane to freely transmit \(H\)- and \(Cl\)-ions and to retain protein ions. Donnan showed, on the basis of the principles of thermodynamics, that the products of the concentrations of oppositely charged diffusible ions, \(H^{\cdot}\) and \(Cl'\) in our case, are identical on both sides of the membrane if osmotic equilibrium has been reached. If \(x\) denotes the molar concentration of \(H\)- and \(Cl\)-ions in the external liquid, \(y\) the molar concentration of free \(H\)- and \(Cl\)-ions in the protein solution, and \(z\) the concentration of chlorine ions bound to the protein, then the equilibrium will be determined by the following equation, first proposed by Procter and J. A. Wilson to explain the influence of acid on swelling:

\[ x^2 = y(y + z) \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots (1) \]

If it is required to explain the influence of the action of acids, alkalis, and salts on the osmotic pressure of protein solutions, then it is necessary first of all to investigate whether changes in osmotic pressure occur together with corresponding changes in the concentrations of diffusible ...

diffusion of ions in the internal and external liquid, and whether these differences in concentration can be calculated from Donnan’s equation (1).

The author was able to establish that such a relation does in fact exist. To prove it, however, it is necessary to determine precisely the membrane potentials that are established at osmotic equilibrium between the protein solution and the aqueous external liquid. Up to now, in colloid chemistry, no attention at all has been paid to this property.

If Donnan’s equation is written in the following form:

\[ \frac{x}{y}=\frac{y+z}{x} \]

then \(\frac{x}{y}\) is a measure of the molar excess of hydrogen ions relative to the concentration of hydrogen ions in the internal liquid, and \(\frac{y+z}{x}\) is a measure of the molar excess of chlorine ions in the internal liquid relative to the concentration of \(Cl\)-ions in the external liquid. Donnan showed that between the internal and external solutions there must be a difference of potential which, at \(24^\circ\) C., reaches \(59 \times \lg \frac{x}{y}\) millivolts, or \(59 \times \log \frac{y+z}{x}\). \(\log \frac{x}{y}\) is equal to \(p\) of the internal liquid minus \(p_H\) of the external liquid. The \(p_H\) of both liquids is easily determined by means of hydrogen electrodes. \(\log \frac{y+z}{x}\) is equal to \(P_{Cl}\) of the external liquid minus \(P_{Cl}\) of the internal liquid, and both these quantities can be determined by titration or by means of \(AgCl\)-electrodes. On the other hand, the potential difference between the protein solution and the external liquid at the collodion membrane can be determined directly with the aid of two identical indifferent calomel electrodes (and a saturated solution of potassium chloride), using a Compton electrometer (Kompton). If, by means of Donnan’s equation, the unequal distribution of crystalloid ions capable of diffusing (for example, \(H'\) and \(Cl'\) in the case of gelatin chloride) on both sides of the membrane is indeed determined, then the potential difference directly determined with identical calomel electrodes must be equal to the difference of potentials obtained in millivolts from the relation \(59\,(p_H\) inside—\(p_H\) outside) or \(59\,(p_{Cl}\) outside—\(p_{Cl}\) inside).

The quantities \(p_{Cl}\) or \(p_H\) can be determined by titration and by a suitable electrometric method. The author made such measurements and found that, when various amounts of acid were added to an isoelectric solution of proteins, for example, crystallized

of egg albumin, gelatin, or casein, the membrane potential found always agrees, to within 1–2 millivolts, with the value calculated from the Donnan equation, i.e. within the limits of error. From the measurement of the membrane potential it follows, first, that the protein solution in the bag of collodion, which is in osmotic equilibrium with the external liquid and allows the ions of crystalloids to pass but not the protein ions, contains crystalloid ions in a concentration different from that in the external liquid, and, second, that this difference in concentration can be calculated from the Donnan equation.

IV.

We are now in a position to explain the curves of change in osmotic pressure in Fig. 2. Colloid chemists suppose that these curves are due to the influence of acids on the degree of dispersion or on some other actual or imaginary property of protein substances. Before agreeing with such an explanation, we must recall that the curves which represent the observed osmotic pressure are not an expression solely of the osmotic pressure of protein particles or molecules and protein ions, but, in addition, may be caused by the readily demonstrable inequality of the concentrations of crystalloid ions on the two sides of the membrane, in accordance with the Donnan equation. In other words: before constructing hypotheses about the cause of the influence of acid, we must make a correction in the measured osmotic pressure on the basis of the Donnan equation. For this purpose we wish to determine the magnitude of this correction. We shall begin with the curve that represents the influence of hydrochloric acid on the osmotic pressure of a one-percent solution of initially isoelectric gelatin. We wish to examine how the ions are distributed at osmotic equilibrium in the protein solution and in the external liquid, assuming that the electrolytes, both gelatin chloride and hydrochloric acid, are completely dissociated. Let \(a\) be the molar concentration of protein molecules and ions, \(z\) the concentration of \(Cl\)-ions bound to ionized protein, \(y\) the molar concentration of hydrogen ions of the free acid in the internal liquid, and likewise \(y\) the concentration of \(Cl\)-ions of the free hydrochloric acid. Thus the osmotic pressure of the protein solution is determined by the following formula:

\[ a + 2y + z. \]

From this we must subtract the osmotic pressure of the hydrochloric acid in the external liquid. If \(x\) is the molar concentration of \(H\cdot\) in the external liquid, then the concentration of \(Cl'\) will be the same. Hence the following expression for the osmotic pressure of the protein solution follows:

\[ a + 2y + z - 2x. \]

Fig. 3 shows how this quantity changes as a function of the \(p_H\) of the protein solution (i.e., \(y\)). If we now wish to approach the theory of the influence of hydrochloric acid on the osmotic pressure of a protein solution, then we must first of all calculate the value of the expression \(2y+z-2x\) and subtract it from the observed osmotic pressure of the protein solution; we propose to call this quantity the Donnan correction. \(y\) and \(x\) can be determined from the measurement of \(p_H\), since the \(p_H\) of the inner liquid is \(\log y\), and the \(p_H\) of the outer liquid is \(-\log x\). \(z\) can be calculated from Donnan’s equation (1)

\[ z=\frac{(x+y)(x-zy)}{y}, \]

since we know that \(x\) and \(y\) are determined by Donnan equilibrium. Let us now calculate the quantity \(2y+z-2x\) for various \(p\) of gelatin-chloride solutions (the concentration of the initially isoelectric gelatin must always be the same; in our case the gelatin is taken as \(1\%\)) and hence the osmotic pressure which results from the excess of crystalloid ions in the inner liquid as compared with the outer liquid. We always find that the calculated pressures agree almost completely with the observed ones, i.e., that the increase in the osmotic pressure of a one-percent solution of initially isoelectric gelatin upon the successive addition of small quantities of acid up to a maximum, and the subsequent decrease of the osmotic pressure upon further addition of acid, is based not on any change in the actual or hypothetical colloidal properties of the protein, but exclusively on the fact that protein ions cannot pass through membranes that are readily permeable to crystalloid ions from the colloid. As a result, the concentration of crystalloid ions must always be greater in the inner liquid than in the outer. In connection with the change in \(p_H\) of the gelatin solution, the numerical expression of the difference \(2y+z-2x\) also changes. This follows from Donnan’s equation (1), according to which:

\[ x=\sqrt{y^2+yz} \]

or

\[ 2x=\sqrt{4y^2+4yz}, \]

but

\[ 2y+z=\sqrt{4y^2+4yz+z^2} \]

and thus it is clear that

\[ \sqrt{4y^2+4yz+z^2}>\sqrt{4y^2+4yz}, \]

i.e., the concentration of crystalloid ions in the inner liquid—\(2y+z\)—is always greater than the concentration of the corresponding ions in the

external liquid. If we replace the expression \(2y+z-2x\) of Donnan’s correction by the identical expression

\[ \sqrt{4y^{2}+4yz+z^{2}}-\sqrt{4y^{2}+yz}, \]

then it will be clear why the osmotic pressure has a minimum at the isoelectric point of the protein, why a small amount of acid raises it to a maximum, and why further addition again leads to a decrease. At the isoelectric point the protein is not ionized, and since \(z=0\), the whole expression

\[ \sqrt{4y^{2}+4yz+z^{2}}-\sqrt{4y^{2}+4yz}=0, \]

therefore the osmotic pressure found at the isoelectric point is caused only by the protein; it is very small in view of the high molecular weight of gelatin.

With a slight addition of acid, even hydrochloric acid, gelatin chloride is formed, and a little free acid remains as a result of hydrolytic dissociation; therefore both \(z\) (the concentration of \(Cl'\) bound with the protein) and \(y\) (\(Cl'\) of the free acid as a result of hydrolysis) increase, but \(z\) at first grows faster than \(y\), and therefore an excess of ion concentration is obtained inside in comparison with the concentration outside. This continues until the greater part of the protein has passed into protein chloride, and then the excess of ions in the internal liquid will be maximal. With further addition of acid, \(z\) increases relatively little, while \(y\) grows considerably; therefore \(z\), in comparison with \(y\), may be neglected. This explains why, with further addition of acid, Donnan’s correction is again equal to zero and why the observed osmotic pressure is as low as at the isoelectric point of the protein.

In exactly the same way one may explain the action of salts. Suppose that in the bag of colloid there is a solution of gelatin chloride at \(p=-3.0\), to which we add sodium chloride. Then \(z\) (the concentration of \(Cl\)-ions bound with gelatin) will not increase from the addition of salt, while \(y\) (the concentration of chlorines not bound with gelatin) will become larger. The value of the expression

\[ \sqrt{4y^{2}+4yz+z^{2}}-\sqrt{4y^{2}+4yz} \]

will keep decreasing with increasing salt concentration and, finally, will approach the limiting value equal to zero.

If we added \(NaNO^{3}\), and not chloride, to a solution of gelatin chloride, then we may suppose that in the gelatin solution there is gelatin nitrate, for which the very same considerations hold.

Fig. 3 shows simultaneously the curves of osmotic pressure and the curves of Donnan’s correction. Both curves rise in parallel from the isoelectric point of the protein to a maximum, which for the observed pressure lies at 450 mm of water, and for Donnan’s correction curve somewhat lower. The observed osmotic pressure also ought to be higher than that calculated from Donnan’s correction, owing to the osmotic pressure of the proteins themselves. Between \(p_H = 4.6\) and \(p_H = 3.2\) there is a constant difference between the two curves, which disappears at larger amounts of acid. The disappearance of the difference at \(p_H < 3.2\), in all probability, comes down to the fact that, if \(p_H\) is too small, then the inaccuracy in calculating the second decimal of \(p_H\) causes a considerable error in calculating \(z\). Further, Fig. 3 shows that the influence of \(p_H\) on the osmotic pressure is exclusively or practically exclusively due to the excess of crystalloid ions in the internal liquid. This excess is established according to Donnan’s equation. The osmotic pressure of the protein solution itself either does not change at all with the addition of acid, or in any case not so much that it could be accessible to observation. Thus the “theory of dispersity,” as well as other speculations about the colloidal state, has absolutely nothing here to explain. The same results were obtained by the author for crystallized egg albumin and casein, and by Hitchcock for edestin. We now understand why only the valence, and not other properties, of the ion is significant for the osmotic pressure of protein solutions. The equilibrium equation for a protein solution with a monovalent ion is of the second degree, and with a divalent ion—of the third degree. Only the valence of the ion, and not its other properties, enters into Donnan’s correction.

Fig. 3. Influence of hydrochloric acid on the osmotic pressure of a protein solution and Donnan’s correction.

If now we combine all these data into one whole, we shall be able to establish the following proposition: the so-called colloidal state of protein solutions, insofar as osmotic pressure is taken into account, is only a consequence of equilibria as understood by classical

chemistry. These equilibria are due to the fact that the concentration of crystalloid ions is higher in the protein solution than in the external aqueous liquid, owing to the presence of a membrane that allows only crystalloid ions, but not protein ions, to pass. Therefore the colloidal state of protein bodies depends exclusively on the relative inability of protein ions to diffuse through a membrane through which crystalloid ions readily pass. Such membranes include a large part of plant and animal membranes, and it is easy to imagine what an enormous role proteins must play in regulating the osmotic pressure in the organism.

V.

We must now briefly show that the swelling and viscosity of protein solutions change under the influence of electrolytes in a manner similar to osmotic pressure. In order to be able to predict the results of experiments, we shall be dealing with the very same basic property, namely osmotic pressure. In 1910 Procter arrived at the brilliant discovery that the swelling of gelatin may be an osmotic process. In later work, together with Wilson, he confirmed this theory by quantitative experiments, deriving the phenomena under consideration from Donnan’s correction. They showed that the swelling of a solid gelatin gel in hydrochloric acid can be quantitatively explained by Donnan’s equation, if it is assumed that the concentration of crystalloid ions (in our case \(H'\) and \(Cl'\)) is lower outside than inside. The action of acid on swelling is explained by an increase of the osmotic pressure inside the gel, in accordance with the requirements of the Donnan effect. The agreement of the theoretically calculated values with those observed is astonishing.

The author considers Procter’s theory of swelling and its experimental confirmation by Procter and Wilson to be the best material for understanding the colloidal state. In its significance it follows directly after Donnan’s theory of membrane equilibrium. The authors mentioned investigated only one thing, namely, the potential of the membrane between the gel and the liquid in equilibrium with it. The author of the present article was able to fill this gap and showed that the observed difference of potentials between the gel and the external liquid can be calculated with sufficient accuracy from the value \(p_H\) of the gel minus \(p_H\) of the external medium by means of Nernst’s logarithmic formula.

VI.

It seems strange that the influence of electrolytes on the viscosity of certain protein solutions is explained in exactly the same way, but apparently this is true. According to Einstein’s formula, the viscosity of aqueous

solutions of protein is in linear dependence on the relative volume occupied by the dissolved substance in the solution. This formula is as follows:

\[ \eta=\eta_0(1+2.5\varphi) \]

where \(\eta\) is the viscosity of the solution, \(\eta_0\) the viscosity of pure water, and \(\varphi\) the ratio of the volumes of the dissolved body and the solvent. If a small amount of acid is added to a one-percent isoelectric solution of gelatin, the viscosity of the solution increases. With an increase of the acid in the solution it reaches a maximum and then decreases again upon further addition. It follows from this that a change in the amount of acid changes the volume occupied by gelatin in water. This is possible only in the case when water is absorbed by the protein, and now the whole question consists in how to explain the absorption of water by protein under the action of acid. In the view of Pauli, ionized protein is surrounded by an aqueous sheath, which is absent in non-ionized protein. If this assumption is correct, then such an action of acids would be observed for all solutions of proteins and amino acids. The author found that this is not observed for amino acids and, at least, for one protein, namely crystallized egg albumin. If Pauli’s view corresponded to reality, then the latter should have behaved exactly the same way as gelatin. The difference between egg protein and gelatin consists in the fact that gelatin is capable of forming a solid gel at a comparatively low temperature, whereas egg protein is not. In gelatin solutions, the formation of a coherent gel is preceded by the appearance of submicroscopic aggregates, which enclose water and are capable of swelling. The submicroscopic particles forming the preliminary stage of the gel increase over time in number and size. The author proved his supposition by studying aqueous suspensions of dispersed gelatin. The suspensions have a considerably greater viscosity than a fresh solution of gelatin. Such a result was to be expected if the supposition is correct that the action of acid on the viscosity of protein solutions is due to the swelling of submicroscopic particles. This agrees well with the very small magnitude of the viscosity of egg-protein solutions. The latter phenomenon is explained by the absence or extremely small content of micelles in solutions of crystallized egg protein. Finally, we can find an increase in the viscosity of suspensions of dispersed gelatin from acid or alkali in exactly the same way as we found an increase in the swelling of a gel or in the osmotic pressure of protein solutions. The viscosities were determined at \(20^\circ\). If a suspension of dispersed gelatin is melted and then rapidly cooled to \(20^\circ\), the viscosity is considerably reduced and it is no longer possible to observe the influence of acid. These experiments and an entire

a series of analogous experiments reveal a similarity between the action of electrolytes on the viscosity of gelatin solutions and the action of electrolytes on the osmotic pressure of protein solutions. Such a similarity is obtained because viscosity can be reduced to a change in the state of swelling of submicroscopic protein particles. Complete proof of such a view can be obtained from establishing the Donnan equilibrium between the particles of dispersed gelatin and the surrounding weak gelatin solution.

VII.

It would be a pity to miss the opportunity to show, by an example, how neglecting the determination of the concentration of hydrogen ions leads to errors. In 1921 Kuhn1 published an article in which he tried to prove that different acids of one and the same degree of valency affect the swelling of gelatin differently. To prove this, it is necessary to start from an isoelectric solution of gelatin and compare the action of different acids on the swelling of gelatin at one and the same concentration of hydrogen ions in the gel, since only then does the gel have the same concentration of gelatin ions. Kuhn, in general, did not measure the \(p_H\) of his gelatin. However, it is by no means immaterial whether acid is added to isoelectric gelatin or to gelatin of another \(p_H\). Kuhn did not measure the \(p_H\) of the gel with hydrogen electrodes, but took the concentration of hydrogen ions from Kohlrausch’s tables, as if the question were the dilution of acid in pure water and the presence of protein would not change the \(p_H\). From our titration curves we know that, after adding acid to isoelectric gelatin, the \(p_H\) is higher than after adding an equal amount of acid to an equal volume of pure water. According to the Donnan equilibrium it also follows that the \(p_H\) inside the gel is different in comparison with the external liquid, but in Kuhn’s work there is not a single word about the Donnan equilibrium. As a result of all these errors, the concentrations of hydrogen ions in the protein solutions, which Kuhn considered equal, were very different, and from this it is perfectly clear why he came to the conclusion that different monobasic acids affect the swelling of gelatin in different ways. It would be a wonder if Kuhn, with his erroneous methods, could even once compare the action of two different acids at one and the same \(p_H\). The same objection must be raised against similar earlier experiments on the action of electrolytes on swelling. Such experiments forced the attribution to different anions of the same degree of valency of a different influence on swelling (Hofmeister series). In all these experiments the investigators did not measure the \(p_H\) of their gel and erroneously reduced actions caused by differences in \(p_H\) to differences of acid anions.

VIII.

Thus we arrive at the conclusion that the chemistry of protein bodies does not differ from the chemistry of crystalloids. Proteins combine with acids and bases according to stoichiometric rules and form electrolytically dissociated protein salts. The extraordinarily large protein ions and molecules cannot diffuse through a gel or other partitions that are readily permeable to small crystalloid ions. Therefore, under certain circumstances, an uneven distribution of diffusible ions occurs between the protein solution and the external aqueous liquid, or between the protein gel and the aqueous solution. In this case the total concentration of crystalloid ions in the protein solution, or inside the gel, is always greater than in the external aqueous liquid. This fact explains the colloidal state of protein solutions and gels. Measurements of the membrane potential have shown that Donnan’s theory of membrane equilibrium correctly conveys the presence of a certain excess of crystalloid ions in the internal liquid. All effects of electrolytes on swelling, viscosity, and osmotic pressure are derived with satisfactory accuracy from Donnan’s equation, which is not an empirical but a theoretical formula. At the same time, we establish that the colloidal state of protein bodies can be explained quantitatively on the basis of theoretical mathematical deductions. The so-called colloid chemistry, which originally gave the impression of being a new chemistry, is apparently maintained only by neglecting the equilibrium conditions of classical chemistry, at least insofar as proteins can be taken into account. This neglect had two bases. First, the omission of pH measurements by representatives of colloid chemistry, which created complete uncertainty in a factor that is the most important variable in all these questions. Second, inattention to the membrane potential of protein solutions and gels. It follows from this that, in order to explain the colloidal state of protein bodies, the theory of membrane equilibrium must be brought in.

Translated by V. Bashmakov.

1. Kuhn, A., Kolloidchemische Beihefte, 1921, 14, 147. ↩↩↩

2. \(p_H\)—the logarithm of the concentration of hydrogen ions, taken with the opposite sign. Thus, at Sørensen’s suggestion, the concentration of hydrogen ions is characterized. ↩