Principles of General Physiology

But, while there is no doubt that the ratio given holds for hemoglobin saturated with oxygen at its pressure in the atmosphere, say 160 mm. of mercury, it is a curious fact that in the presence of salts, as in the curve on p. 45 of Bancroft's book (1914), the course of the curve has the appearance of going beyond the ordinate marked 100 per cent, saturation. Is it possible that the saturation point is assumed to be that of the asymptote of the rectangular hyperbola deduced by the application of the law of mass action? As we shall see presently, this is one of the points that remains to be proved. It is quite possible that it will be found to be the case that complete saturation is attained at 160 mm. oxygen tension, but if it should be found that, under higher tensions in the presence of salts, more oxygen can be taken up than that corresponding to one molecule of oxygen to one atom of iron, the fact that this obtains at 160 mm. tension must be due to chance, certainly an unlikely possibility. Thus we have met with the first puzzle, but a more difficult one will be found immediately.

There are one or two interesting problems with regard to the function of iron in haemoglobin which have not. so far as I know, been investigated. Hsematin, which is hsemoglobin minus its protein constituent, but containing iron in the same form of combination, loses oxygen by the action of reducing agents and becomes ha?mochromogen. This latter takes up oxygen from the air again. Now, has hjemochromogen the property which hemoglobin has, as we shall see presently, of taking up different amounts of oxygen from different pressures? It would appear that it has not, since the oxygen of hsematin cannot be removed by the airpump. In fact it behaves as a chemical compound should, according to the phase rule, as we shall see. Methsemoglobin, again, contains iron in organic combination, but does not give up its oxygen to a vacuum. It has been stated that a protein, obtained from yolk of egg by Bunge, contains iron. 4s it capable of taking up oxygen 1 The behaviour of dry haemoglobin to oxygen is another point of interest.

Douglas, Haldane, and Haldane (1912) point out that the relative affinity of haemoglobin for oxygen and carbon monoxide varies in different individuals. They regard this as due to the globin, since the hsematin part is always the same. If so, it is difficult to see how the iron, which is a constituent of the latter, is alone concerned with the taking up of these gases. Fischer and Brieger (1912) have made an interesting investigation of the behaviour of certain iron compounds to oxygen. They regard the combination of oxygen in the blood as an analogous case and that it is in the form of a peroxide, which is stable in alkaline solution, unstable in acid solution, similar to the ferrates and ferrites which they have prepared. At present, however, it is difficult to bring these results into comparison with the system of haemoglobin and oxygen, since they were obtained by the use of hydrogen peroxide as source of oxygen, and I cannot find evidence in their work that the relative proportion of ferrate and ferrite is determined by the tension of oxygen gas.

Let us now consider the fact which has already been incidentally referred to. Let us expose haemoglobin to oxygen at a pressure of only 10 mm. of mercury. We find that the amount of oxygen taken up by it is 55 per cent, of that present in saturation (Barcroft, 1914, p. 16). If exposed to a pressure of 40 mm. of mercury, it is 84 per cent, saturated and so on. We thus obtain a curve, such as is given in the plate opposite p. 16 of Barcroft's book (1914). This relationship was carefully worked out by Barcroft and Camis (1909), and is known as the "dissociation curve" of oxyhsemoglobin. We shall find presently that the form of the curve varies with temperature and with the presence of electrolytes, but, for the present, we will merely take the fact that the amount of oxygen taken up is in proportion to the pressure of oxygen, that is to the concentration of oxygen present in the solution.

Now this fact has not sufficiently aroused the astonishment of investigators. Assuming that oxyhsemoglobin is a chemical compound of oxygen and haemoglobin, we naturally look around for similar ones, but, so far as chemical compounds are concerned, our search is in vain. There is none like it known to the chemist. Certain systems have, indeed, been hastily given as analogous ; let us examine them, since they are instructive in themselves. Dissociation of Calcium Carbonate. — Calcium oxide combines with carbon dioxide at ordinary temperatures to form the carbonate and, if this is heated, as in the lime kiln, the carbon dioxide is again driven off and the oxide obtained. It has been stated, probably from a misunderstanding of the table of Le Chatelier (1883), a part of which is given below, that, at a given temperature, different pressures of carbon dioxide are in equilibrium with different relative proportions of the carbonate and oxide, just as there are of haemoglobin and oxyhaemoglobin in equilibrium with oxygen at different pressures, if we assume that oxyhsemoglobin is a chemical compound.

It is somewhat difficult to explain the meaning of the numbers in the above table without using expressions derived from the phase rule, which would tend to confuse the issue as regards our present problem. In the first place, we must confine ourselves to one temperature, as is obvious, and assume that calcium carbonate and oxyhaemoglobin are analogous ; so that, taking the first line of the table, let us suppose that a temperature of 547°, with calcium carbonate, corresponds to one of 15° in the case of oxyhaemoglobin. This is, of course, admissible. Now the table states that the dissociation pressure of calcium carbonate at 547° is 2'7 cm. of mercury. That is, calcium carbonate is in equilibrium with carbon dioxide gas at that pressure, so that no change takes place. Next suppose that, without changing the temperature, we reduce the pressure of carbon dioxide to 1 cm. of mercury, and maintain it at this level by the use of a relatively large volume of gas, as we do when dealing with haemoglobin and oxygen. What happens is that carbon dioxide comes off, and

continues to do so until the whole of the carbonate is decomposed and pure calcium oxide remains (see Findlay's book, 1904, p. 79). With oxyhnemoglobin, on the contrary, reducing the oxygen pressure does not lead to total reduction, but to a different state of equilibrium in which there is a smaller amount of oxygen " combined " with the hemoglobin. If, again, we start with calcium oxide at 547°, and expose it to carbon dioxide at a pressure of 2'7 cm. of mercury, the ichole is converted into carbonate ; if the pressure of carbon dioxide is less than this, no change takes place at all.

If the system is a closed one, so that there is only a limited amount of carbon dioxide present, and at a pressure of 3 cm. of mercury, then a certain quantity of the gas combines with a part of the calcium oxide until the pressure is reduced to 2 '7 cm. of mercury : after that, nothing further happens. But this has nothing to do with the haemoglobin system, since oxyhemoglobin may be in equilibrium with an unlimited atmosphere of oxygen at any pressure, and remain at the same percentage saturation indefinitely.

It is perhaps useful to state the case also in terms of mass action. A detailed account will be found on p. 55 of Cohen's book (1901) from which I take the following condensed statement. As in all heterogeneous systems, it is not a simple matter, at first sight, to understand what are to be regarded as the active masses of the constituents. That of carbon dioxide is no doubt given by its pressure. As to that of the solids, calcium carbonate and calcium oxide, the consideration of water and of naphthalene will assist. Water, in a closed space and at a given temperature, is in equilibrium with a certain definite pressure of its vapour. Naphthalene, although a solid, behaves similarly, but its vapour pressure is very small and difficult to measure. We may, therefore, assume that calcium carbonate and calcium oxide are also in equilibrium with a definite pressure of their vapours at a particular temperature. This pressure is sometimes called the " sublimation tension."

Now, just as the tension of water vapour is independent of the mass of the water, so are the sublimation tensions of our calcium carbonate and calcium oxide independent of their total masses. Since the chemical reaction takes place between molecules, it must be in the vapour phase surrounding the solids. At a given temperature, the concentrations of the vapours of calcium carbonate and calcium oxide are constant, being proportional to the sublimation tensions. In general, the active mass of a solid at a given temperature is therefore constant. Next, bv the law of mass action, we have, in equilibrium, at a given temperature : —

where the concentrations are taken as being equal to the vapour pressures. Now (CaCO3) and (CaO) are constant, hence also Kj(CaCO3) and K.2(CaO) are also constant; call the former K3 and the latter K4 and we have : — Thus, when calcium carbonate dissociates into calcium oxide and carbon dioxide, at a given temperature, the pressure of carbon dioxide has a constant value, which is independent of the relative proportion of the two solids. This is called the dissociation tension of calcium carbonate at the temperature in question, and we have seen above what happens when the tension of carbon dioxide is varied at a given temperature.

We see then that this system does not help us. It is sometimes said that it is not analogous because there are changes of phase in it ; but there are also in the case of oxyhsemoglobin solutions. This substance is in the colloidal state ; its particles are sufficiently large not to pass through parchment paper ; it therefore possesses surface, and is a separate phase. This fact is pointed out by Mines (see Barcroft's book, 1914, p. 51). The Phase Rule. — As reference has been made to the application of this rule to oxyhaemoglobin, a few words are advisable to explain its general meaning. We have already seen (page 48) that, in a heterogeneous system, each component which does not mix with the others fs called a phase, and that there is a boundary surface

of separation between the phases. What are to be regarded as the components taking part in the equilibrium is not always easy to see. They may all be of the same chemical compound, such as ice, water, and steam. In a gas phase, there may be a number of different gases, but it remains one homogeneous phase. A mixture of different solids, on the contrary, consists of as many phases as there are substances present, as in the case of calcium carbonate and calcium oxide, dealt with above. The components of the system are to be regarded as those which are not mutually dependent on one another. Thus, in the calcium carbonate case, if two of the phases are taken, the composition of the third is denned by the equation : —

Suppose that we have a given mass of a gas, that is, one phase, we cannot define its state by fixing one only of its independent variables, temperature, pressure, and volume. The same volume, for example, may be obtained by 'changing pressure and temperature inversely. But if two are fixed, then the third must have a definite value; at any given values of temperature and pressure, a given mass of gas can only occupy one particular volume. Next, suppose that we have two phases, say, water in contact with its vapour. Here the condition is defined by giving one only of the variables a definite value. If we fix the temperature, the pressure under which liquid and vapour can both •exist is determined also.

Finally, suppose that we have ice also, that is, three phases. We find now that it is impossible to change any one of the three variables without causing disappearance of one of the phases. In other words, there is only one temperature and one pressure at which ice, water, and steam can coexist together, the so-called "triple-point." We see, then, that according to the number of phases present, a different number of the variable factors requires fixing in order to define perfectly the state of the system. This number is spoken of as that of the degrees of freedom, and a system is said to be invariant, univariant, bivariant, or multivariant according as the number of degrees of freedom is zero, one, two, or more than two.

A point of importance is that, in the heterogeneous systems dealt with by the phase rule, the state of equilibrium is independent of the amounts of the phases present. Willard Gibbs formulated the phase rule, which may be most concisely put thus : If P is the number of the phases, F that of the degrees of freedom, and C the number of components, then, The greater the number of phases, the fewer the degrees of freedom. In the case of water in contact with its vapour, we have two phases and one component, so that the number of degrees of freedom is,

In the calcium carbonate system there are two components, CaO and CaCO3 (since carbon dioxide is defined by CaCO3 = CaO + CO2), but three phases, gas (there can only be one gas phase) and two solid phases. Thus, Both systems are univariant, possessing one degree of freedom only. To each temperature, therefore, in both cases, there is one only definite pressure of vapour or gas with which equilibrium is possible. In applying the phase rule to the case of haemoglobin and oxygen, we have two solid phases, oxyhsemoglobin and haemoglobin, if we assume that oxyhaemoglobin is a definite chemical compound. We have one gas phase, oxygen. The number of components must be two, and therefore again :

F=2 + 2-3 = l. So that it seems that the system should behave like the calcium carbonate system, with one degree of freedom only. But this is not in agreement with experimental results, which show that the system is bivariant ; we can vary both temperature and oxygen pressure, and yet obtain equilibrium. We must either assume that, instead of three phases we have only two, or that there are three components, and it is not easy to see how this happens. Another alternative is that the phase rule does not apply to the case of micro-heterogeneous systems. There is reason to believe that curvature of surface plays a large part in the properties of the colloidal state (see page 51 above). This fact may perhaps bring reactions in which ultra-microscopic particles are concerned more into approximation to those between molecules. There may thus be a region in which transitional states between simple surface adsorption and true chemical combination are to be met with. The question requires further investigation.

There are two important principles to be remembered in connection with the phase rule. The one, van't HoflTs " principle of mobile equilibrium," has been discussed previously (pages 44-45). The other, that of Le Chatelier, is related to it and may be stated thus : If a system in equilibrium is subjected to a constraint by which the equilibrium is shifted, a reaction takes place which opposes the constraint, that is, one by which its effect tends to be annulled. Take water, ice, and steam at 0°, addition of heat causes melting of ice by which the heat becomes "latent," and there is no rise of temperature until the whole of the solid phase is melted.

Sodium Bicarbonate. — A solution of sodium bicarbonate in water in contact with various pressures of carbon dioxide appears at first sight to come nearer to the kind of system we want, since, even after allowing for the increased solubility of carbon dioxide with pressure, we find that more is taken up as the pressure increases and in certain proportion to the pressure, although the amount is not great and the range is a short one. A little closer examination, however, shows that the system is in no way analogous to that of haemoglobin. In sodium bicarbonate we have a salt which is electrolytically dissociated in water, so that there is an equilibrium between the several ions and the undissociated salt. When the pressure of carbon dioxide outside is raised, more HCO3' ions are formed in the solution. The result of this is that the dissociation is put back and more sodium exists in the state of combination as bicarbonate, as is seen by the dissociation equation :

In the system, therefore, there is more additional CO2 than is to be accounted for merely by the increase of dissolved gas, but the increase is due to the fact that the salt is electrolytically dissociated. Oxyhaemoglobin does not dissociate in this way into oxygen ions, and haemoglobin ions, and, in fact, like other proteins and amino-acids, it is an amphoteric substance, and to all intents and purposes a nonconductor. We find on p. 22 of Barcroft's book (1914) that a solution of haemoglobin, which had only been dialysed for three days, had an electrical conductivity equal to that of 0'004 molar sodium chloride only ; further dialysis would have reduced it still more.

Reducible Dyestuffs. — There are a number of dyestuffs which are capable of existing in two forms, an oxidised and a reduced form. In the presence of oxygen, in many cases, the reduced form (leuco-base) is oxidised. Prof. W. A. Osborne informs me that he hoped to find amongst these a case like haemoglobin, but was unable. All of them behaved like calcium carbonate ; that is, under a given oxygen pressure, the dye was either completely oxidised or completely reduced, according to the pressure. Again a case of all or nothing.

According to the work of Alsberg and Clark (1914), haemocyanin is similar to these dyes. It is blue in the arteries and colourless in the veins, that is, the reduced form takes up oxygen and becomes blue. But this oxygen is not given off to a vacuum ; the blood merely gives up the gas dissolved in the water. It is suggested that the copper contained in the pigment may act as a catalyst, as we have seen above (page 585), the oxygen being thus more readily given off to an acceptor, such as may be present in the tissues. If so, h;?mocyanin would be analogous to a peroxide-peroxidase system.

Adsorption. — It may occur to the reader that there is one class of cases of which no mention has yet been made, namely, the taking up of gases by surfaces such as that of charcoal, adsorption, in which we certainly get a relation between the amount taken up and the pressure. This was, in fact, suggested by Wolfgang Ostwald (1908) as applying to the haemoglobin-oxygen system. But it is obvious that it is very difficult to reconcile the fact that one molecule of haemoglobin, when saturated, combines with one molecule of oxygen and no more, with anything but a chemical compound as the final result. The key to the puzzle will probably be found in a combination of the two processes. The amount of oxyhaemoglobin would be determined by the amount of oxygen adsorbed on the surface of the haemoglobin under a given pressure. At the same time, there are difficulties in the treatment of the problem from this point of view, but it has, as yet, received little attention. It seems clear that it is not permissible to use either the law of mass action or the phase rule as applying to the case, until it has been proved that they do or do not hold in the case of colloidal solutions, where there must be surface phenomena intervening, although these phenomena may not be as simple as when larger and flatter surfaces aie concerned.

Taking pure haemoglobin in solution, and regarding the oxygen dissolved under various pressures as its concentration, which is, by Henry's law, a function of the pressures, Barcroft finds (1914, pp. 17-23) that the relative amounts of haemoglobin and of oxyhaemoglobin which are present under a given oxygen pressure are in accordance with the law of mass action. The curve is a rectangular hyperbola. Under the hypothesis of adsorption, we should expect a parabolic curve. Under certain conditions, as we shall see presently, results are obtained which correspond more closely with such a curve. The greatest difficulty in the simple adsorption hypothesis is, however, that already mentioned, namely, the ratio of oxygen to iron or haemoglobin in complete saturation.

However this may be, in respect to the function of haemoglobin in the organism, the precise way in which oxygen is attached to it is of less importance than the investigation of the ease and rapidity with which oxygen is taken up from the air and passed on to the cells. It is especially here that the work of Barcroft and his coadjutors on the dissociation curve, as modified by various agencies, is of inestimable value. Before passing on to these important practical questions, it may be pointed out that it has been shown that some colloidal solutions take up gases in greater proportion than is to be accounted for by the increase of solubility with pressure. The experiments of Findlay (1908) may be mentioned. Those of Geft'cken (1904) are also to the point. It may be asked why, if the taking up of oxygen by haemoglobin is conditioned by a surface adsorption, other colloidal constituents of the blood do not show a similar behaviour? Now, Geffcken's experiments indicate a case which appears to be a typical one of adsorption, namely, that of carbon dioxide by colloidal ferric hydroxide, but which is more or less "specific," in the sense that oxygen is not taken up by the solution in any larger amount than by pure water. This system of carbon dioxide and ferric hydroxide would repay further investigation, especially from the point of view of reversibility. Granting that it is one of adsorption, we must remember that this process is due to a diminution of surface energy of any kind, so that, as already pointed out, chemical combination on the surface, if associated with diminution of surface energy, would take place. But this does not really help us in the haemoglobin problem, because we are still faced with the same difficulty of equilibrium with different oxygen tensions ; the hypothetical chemical compound is merely changed in position, so to speak. Moreover, it is not easy to see how a permanent equilibrium could be established, since the compound on the surface must interchange sooner or later with the molecules inside the aggregate.

Is it possible that, after all, there may be some state of combination, neither mere surface adsorption nor chemical in the true sense, but intermediate between them, as appears to have been held by van Bemmelen and by Ostwald? It might perhaps be related to surfaces of very great curvature, as met with in colloidal systems, where reactions do not obey the simple laws of mass action, nor, according to some, the phase rule. Relation to Temperature. — Under a given oxygen pressure, it is found that less oxygen is taken up by haemoglobin the higher the temperature. A series of curves will be found in Fig. 190, from Barcroft's book (1914, p. 36). This is clearly of importance with regard to the giving up of oxygen to the tissues. Suppose that blood at 38° has come into equilibrium with an oxygen tension of 100 mm. of mercury in the alveolar air of the lungs. It will be 93 per cent, saturated. From the experiments of Verzar (1912, 3), we find that the oxygen

tension in tissues varies from zero to some 10 to 20 mm. of mercury, dependent, of course, on the rate at which it is consumed in relation to that at which it is supplied. Take the case of 10 mm. From curve IV of the figure we see that at this tension haemoglobin is only 56 per cent, saturated, so that the difference between 56 per cent, and 93 per cent., namely 37 per cent., represents that available for the tissue. On the contrary, take curve II, at 25° ; at 100 mm., we have about 98 per cent, saturation ; at 10 mm. 88 per cent., a difference of 1 0 per cent. only. The advantage of the warm-blooded animal is plain.

The different position of the equilibrium at different temperatures must FIG. 190. DISSOCIATION CURVES OF OXYH^EMOGLOBIN AT DIFFERENT TEMPERATURES. Note that the higher the temperature, the less oxygen is held by haemoglobin at a given tension of the jjas. obviously be due to the greater acceleration by temperature of the dissociation of oxyhsemoglobin than that of the taking up of oxygen. Experiments on this question will be found in Barcroft's book (1914, Chapter XL), together with curves.

It may be noted that the effect of temperature is the same as that on cases of typical adsorption, where it is due to the negative temperature coefficient of surface energy. Now, since raising the temperature causes dissociation of oxyhsemoglobin, van't HofPs principle of mobile equilibrium tells us that the " combination " must be associated with evolution of heat. Further, van't Hoff has worked out a formula relating the position* of equilibrium to the heat evolved on combination.