Principles of General Physiology

Barcroft and Hill (see Barcroft's book, 1914, Chapter III.) made experiments to determine the heat evolution, and found a value of 1/85 calories per gram of haemoglobin. From the formula of van't Hoff, it is possible to calculate the molecular weight of haemoglobin, on the assumption that each gram combines with 1-34 c.c. of oxygen. The result came out nearly identical with the accepted molecular weight, 16,669, and it is clear that it affords considerable support to the view of true chemical combination. But here we come across another puzzle.

Ordinates — percentage saturation of haemoglobin with oxygen. Abscissae — tension of oxygen in mm. mercury. © — curve from dialysed solution. ] — curve from undialysed solution. The first curve (electrolytes absent) corresponds to HUfner's curve and is a rectangular hyperbola. It passes very nearly through the experimental values. The second curve (salts present, in low concentration) is Bohr's curve. The difference between the degree of saturation is especially marked at the lower oxygen tension.

The heat of combination of oxygen and haemoglobin has been determined by other experimenters, and results considerably lower than that mentioned have been obtained; the numbers may be found in Meyerhof's paper (1912, 1, p. 164). If we consider only that of Torup (1906), which was obtained by a method essentially the same as that of Barcroft and Hill, and there is no apparent reason to doubt the accuracy of the determination, we find only 0-678 calorie per gram. R. du Bois-Reymond (1914) found values between 1'06 and 1*77, in the mean, 1'36. •

In the consideration of the problem we must not forget that the condensation of gases on surfaces (adsorption) is also accompanied by the evolution of heat, as would indeed be expected from the compression, or perhaps liquefaction, involved. If we take, for example, the values obtained by Titoff(1910), we find that the heat evolved in the adsorption of various gases by charcoal is of the same order as the values of the "heat of combination" of haemoglobin with oxygen. Thus: at 0°, 1 g. of charcoal adsorbed 0"259 c.c. of nitrogen under a pressure of 10"2 mm. of mercury, with a development of heat of 0'373 calorie per c.c. adsorbed. The corresponding values for carbon dioxide and ammonia are about 0'33 and 0'4 calorie. One gram of haemoglobin at room temperature takes up 1'34 c.c. of oxygen, and gives off 1'85 calories, that is, 1'37 calories per c.c. If we take Torup's result, we have 0'41 calorie per c.c. oxygen taken up. I merely call attention to the fact, without drawing conclusions.

Effect of Salts and of Acid. — The dissociation curve of pure haemoglobin, as we have seen, can be expressed by the equation to a rectangular hyperbola. If, however, we compare this curve with that given by Bohr for haemoglobin as present in blood, we see that the latter has a different shape. Now, it was shown by Barcrof t and Roberts (see Bancroft's book, 1914, p. 22) that Bohr's curve is correct for normal blood, and that if the blood is dialysed, the first form, similar to that obtained by Htifner with pure solutions of haemoglobin, is obtained. Fig. 191 is a reproduction of one given by Barcroft and Roberts.

The physiological importance of this fact is similar to that referred to above in connection with temperature. In the presence of salts, haemoglobin gives off its oxygen more readily, so that if the oxygen tension in the tissues has fallen to 10 mm. of mercury, the percentage saturation of the haemoglobin of the blood may be reduced to 25 per cent., whereas, if the haemoglobin were in pure solution in water, it would only be reduced to 55 per cent, of saturation.

same as that of salts, but more marked (see Fig. 192). Investigation shows that the effect is due to the hydrogen ions. Again, its importance is obvious. All cells produce carbon dioxide in activity and muscle in particular produces lactic acid. Both facilitate the giving off of oxygen to the active cells. Christiansen, Douglas, and Haldane (1913) show that the amount of carbon dioxide taken up by blood is greater by one-tenth when the haemoglobin is reduced than when saturated with oxygen. Venous blood can, therefore, take up more carbon dioxide at the same tension than arterial blood can. As the blood takes up oxygen again in the lungs, this carbon dioxide is more easily given off. From the adsorption point of view, this fact is not difficult to explain. According to Freundlich (1909, p. 116), and the experimental results of Hempel and Vater '(1912), from a mixture of solutes each constituent is adsorbed and the relative proportion is governed by their relative powers of lowering surface energy, but even that one which lowers surface energy most is adsorbed less than from a pure solution. Hence it appears that the lower the tension of oxygen, the more carbon dioxide would be adsorbed, and the lower that of carbon dioxide, the

more oxygen. Each gas, in fact, assists to drive off the other, but we require more knowledge of the relative lowering of surface energy at the haemoglobinplasma boundary effected by the two gases before we can make any calculations on this basis. The form of the dissociation curve is very sensitive to the concentration of hydrogen ions, so that it can be used as an indicator for changes in this direction occurring in the blood, either as the result of muscular work, of want of oxygen, or in pathological states of "acidosis."

Now, what are the equations to the curves obtained in the presence of acid or of salts 1 Since haemoglobin is in colloidal solution and, as we have seen (page 91), electrolytes have a powerful effect in causing aggregation of colloidal particles, this phenomenon would naturally be looked for as the explanation. A. V. Hill (1910, 2), on the hypothesis of the aggregation of molecules of haemoglobin causing the reaction to become of a higher order than unimolecular, arrived at an expression of the form : —

where y is the percentage saturation of haemoglobin with oxygen, x the oxygen pressure. This formula, by proper choice of the constants, K and n, was found to apply to the experimental data of several cases taken. In attempting to understand the meaning of this equation, it is well to point out that Hill himself (p. vi) did not profess to attach any direct physical meaning to the constants, although Barcroft (1913, p. 481) regards K as the equilibrium constant and n as the average number of molecules of haemoglobin in each aggregate. Hill subsequently adopts this view to a large extent (1913, 5).

It must be confessed that it is a very difficult matter to grasp the conditions under which the various states of equilibrium in a colloidal system are attained, and any criticism that I may make as to the above-given interpretation must not be misunderstood. It is, undoubtedly, an extremely valuable contribution to the theory, but careful consideration has made it clear to me that some doubtful assumptions are made, and that a satisfactory solutioa of the problem will only be reached by taking account of the conditions prevailing at the boundary surfaces of the phases of a heterogeneous system, micro-heterogeneous, it is true, and that the law of mass action alone is insufficient. If the phase rule requires special proof in its application to colloidal systems, so also does the simple law of mass action.

It is clear that Hill's formula applies to the curves obtained by experiment. Looking at those of Figs. 191 and 192, we see at once that, under the influence of electrolytes, the dissociation curve is no longer the rectangular hyperbola of a unimolecular reaction. But why should mere aggregation of haemoglobin change the order of the reaction ? As I understand the theory of velocity of reaction, as based on mass action, the order would be changed only if molecules of a different chemical kind came in to take part in the reaction. There seems no reason to suppose that the various degrees of aggregation of haemoglobin result in change of its chemical nature. With regard to oxygen, of course, no suggestion of this kind is possible. On the face of it, then, there seems no clear reason why the reaction ceases to obey the formula of a unimolecular reaction, since it ought still to be capable of expression as a change in concentration of one kind of molecules, namely those of haemoglobin, as they combine with oxygen to form oxyhaemoglobin.

There are two forms of equation already known to us in which we have an exponent, which we have called n in both cases. The first is that expressing the velocity of reaction, where it has the significance of the number of different kinds of molecules taking part in the reaction, whose concentration may vary independently, so that it is necessary to take account of the change in concentration of each. In this case it must, naturally, be a whole number. The second equation is that expressing the amount of a substance adsorbed by a surface as a function of the concentration of the substance. In this case, n

may be, and usually is, fractional. The curve in both cases belongs to the parabolic family, but, if we glance at those of Figs. 191 and 192, we see that, in the presence of salts or acid, the experimental curve is S-shaped, that is, more complex than either of these two possibilities alone. In the data given by A. V. Hill (1910, 2), we note at once that the values of n are mostly fractional. The explanation given is that there are present a number of aggregates of haemoglobin containing different numbers of molecules, so that the net result is a combination of different orders of reaction above the unimolecular one. But, as already pointed out, it is not clear that it is legitimate to assume that the n of Hill's formula corresponds to that of the expression for the velocity of reaction, where it refers to the number of kinds of molecules taking part. If aggregation takes place, it would seem more likely to produce a change in the effective concentration, rather than in the exponent ; that is, in C in the formula : —

and therefore in the equilibrium constant, K, of Hill's formula. Put in another way, it is not obvious why the order of the reaction, unless Hbt, is a different chemical individual from Hb, and that it dissociates differently. although the association of water and of alcohol differs at different temperatures, there is no evidence of a change in the order of the reaction, so far as I am aware. can be obtained thermodynamically by consideration of osmotic pressures, without reference to aggregation. But the applicability of mass action to the system is assumed, and the difficulty lies here rather than in the hypothesis of aggregation, which is not improbable. It is further suggested that the lowering of osmotic pressure required in this form of treatment might be due to the unequal distribution of electrolytes, described above in relation to Congored (page 160), but the electrolytic nature of oxyhsemoglobin is not yet demonstrated. The situation of the membrane is not clear when none is provided by the experimenter, although the boundary between the gas phase and the liquid phase may act as such.

With reference to the constancy of n (about 2-5) in the presence of different concentrations of carbon dioxide (see Barcroft's book, 1914, pp. 65 and 66), it is scarcely necessary to add that, in itself, no proof is hereby given that it is explicable as the order of a reaction. As Barcroft remarks, " since n remains so constant, it is probably the expression of some definite physical fact," and it seems to me that this is as far as we can go at present.

The constancy of n with a particular acid leads Barcroft to make the statement (1913, p. 490) that the action of acid does not lead to change in the number of molecules in the aggregates, but to a change of the equilibrium constant. But, as we have seen, it is not satisfactorily shown that n refers to the number of molecules in the aggregates, and I might venture to point out that constancy of the exponent is also a characteristic of adsorption. From the similarity of the curves in the cases of the action of acids and of salts, one would infer that. whatever the action may be, it differs only in degree in the two cases. It might be thought that, as a part of the hsemoglobin molecule is of protein nature, this would enter into combination with acid ; but, as we have seen (p. 103), there is no evidence that proteins or ammo-acids, except the strongly basic ones, combine with weak acids at all. Perhaps measurements of the electrical conductivity of haemoglobin solutions, as changed by the action of acids, might throw light on the question. Barcroft also suggests (1914, p. 316) that the H' ion causes the globin molecule to aggregate, and itself enters into combination with

the haematin constituent. Htematin itself appears to have acid properties, so that it seems difficult to accept this suggestion. On the whole, it is clear that much more work is necessary before we can regard the nature of the association between oxygen and haemoglobin as decided. I have felt it necessary to point out where existing hypotheses fail, though it would have been pleasanter to be able to take them as satisfactory. There seems some risk that the question may be considered, prematurely, to be settled. At the same time, I have no alternative hypothesis to suggest, although I cannot help thinking that the subject would repay more investigation from the adsorption point of view than it has yet received. Not having worked at it myself, I hold r.o brief for one side or the other, and cannot claim any particular value for my remarks, which are merely based on the aspects presented to an onlooker.

The Action of Carbon Monoxide. — This gas has, as it is expressed, a much greater " affinity " for haemoglobin than oxygen has, so that, in a mixture of the two gases, there is a much larger amount of carbon monoxide combined with haemoglobin than corresponds to the relative tension of the two gases. At the same time, there is a definite law regulating the proportion, which has been made the basis of a method of determining the oxygen tension of arterial blood by Douglas and Haldane (1912). According to Nicloux (1913, 1914), the relative proportions of carboxyhaamoglobin and oxyhaemoglobin is regulated by mass action.

The considerations with regard to adsorption from mixtures, referred to above (page 622) in the case of the driving off of oxygen by carbon dioxide, apply also to carbon monoxide. This gas is more strongly adsorbed than oxygen is. Optical Properties. — Haemoglobin and its derivatives give very definite absorption spectra. In Fig. 193 a series of photographs is given. The fact is of practical value in the colorimetric and spectro-photometric methods of estimation of haemoglobin in general use. One cannot, at present, assign any significance to the absorption of light from the photo-chemical point of view, except that, as we saw above (page 571), the absorption of ultra-violet light has probably a protective function.

Hartridge and Hill (1914) have made interesting observations on the infra-red absorption of haemoglobin, comparing it with that of reduced haemoglobin and the compound with carbon monoxide. They find that it is considerable in this region, which has great radiationenergy, and that the absorption of carboxyhsemoglobin is only about half that of oxyhaemoglobin. It is clear that determinations of the absorption in this region of the spectrum would enable estimations to be made of the relative amounts of the three substances present in a solution, a point of practical importance, as we shall see later in connection with the oxygen tension in blood. The measurements would be made by a thermopile, as described in the catalogue of Messrs Adam Hilger. This infra-red absorption is of interest in another way. Light produces a change in the equilibrium between oxygen, carbon monoxide, and haemoglobin, as shown by Haldane and Lorrain Smith. We have seen that, by Nernst's formula (1913, p. 679), we can calculate the free energy of a reaction, if we know the equilibrium constant. Therefore, we have here a photo-chemical reaction, in which light energy can be stored. Hartridge and Hill calculate, from the known change of the equilibrium constant, in the above reaction, what this amount of energy is, and find that it is very considerable, in fact, much greater than that of any similar photo-chemical reaction, with the exception of that of the chlorophyll system.

Chemical Constitution. — This question was discussed briefly in Chapter XIX. (pages 560-561) in relation to chlorophyll, and the meaning of the iron content was referred to in an earlier part of the present chapter (page 614). Methods of Investigation. — A useful account of the methods used in the determination of the degree of oxygen saturation of haemoglobin is given in detail in the appendix to Barcroft's book (1914). The apparatus of Winterstein (1912, 1), especially with the later improvements (1913, 2), is, in many respects, very convenient in use, both for blood gas analysis and for respiratory exchange of small organs. It is more fragile than that of Barcroft (see Fig. 189 above).

We have seen how oxygen is conveyed to the tissues, by the agency of haemoglobin, in greater quantity than could be done if it were merely dissolved FIG. 193. ABSORPTION SPECTRA OF HEMOGLOBIN. — Photographed with grating spectrograph. 2-11, Series of dilutions of rabbit's blood, oxygenated. Dilutions range from 1 : 70 to 1 : 2,000. The ultra-violet band is seen in the more dilute specimens. Thickness of layer, 14 mm. 3, The same reduced with ammonium sulphide. The delicate band in the orange is due to sulph-

3, Blood exposed to carbon monoxide and then acted upon by ammonium sulphide. No change in the bands. The bright line spectra are those of a helium tube. in the blood-plasma, and how oxyhaemoglobin gives up oxygen to places where the tension of the gas is lower than that where the oxygen was taken up by the haemoglobin. It remains to consider the mechanism by which haemoglobin, after being robbed of the greater part of its oxygen by the tissues, replenishes its supply from the external air. Incidentally, the carbon dioxide which has been given off to the blood by the cells escapes to the atmosphere at the same time. Here we may say that, owing to its greater solubility, and to the fact of its being taken up as bicarbonate in the blood-plasma, any special provision for its carriage is not so necessary as for oxygen.

It is generally known that, in air-breathing animals, there are arrangements by which a large surface of blood is brought into contact with air, which is itself repeatedly changed. A thin membrane is all that intervenes, so that the distance through which the gases have to diffuse is extremely short. The organs in which this interchange takes place are known as lungs. I quoted above the experiment of Hooke, in which he showed that a renewed supply of air is necessary to preserve an animal from death by asphyxia It does not belong to the subject matter of this book to describe the details of the muscular mechanisms by which the air is sucked in and expelled from the lungs. Suffice it to say that their capacity is periodically increased and diminished by the action of muscles on the walls of the cavity in which they are contained.

It will be obvious that the whole of the air cannot be expelled in expiration unless the lungs are squeezed flat, a mechanical impossibility in the construction of an animal. The air in the final terminations of the branching air tubes, the alveolar air sacs, must possess, therefore, a tension in oxygen lower than that of the atmosphere, and one of carbon dioxide higher than that of the atmosphere. It is with this air that the gases in the blood enter into exchange. The problem before us is, then, how do the oxygen and carbon dioxide tensions of the arterial blood leaving the lungs compare with those of the alveolar air?

Since a gas always diffuses from a place of higher tension to one of lower tension, it is clear that if the pulmonary exchange is regulated by the laws of diffusion alone, the oxygen tension of the arterial blood can never exceed that of the alveolar air, and that its carbon dioxide tension can never fall below it. In the first place, it is important to grasp the meaning of the tension of a gas in a fluid, as opposed to its actual concentration. In a mixture of gases at atmospheric pressure the matter is simple, the tension of any one is proportional directly to its relative concentration. Thus, oxygen makes up 21 per cent, of the air, and therefore its tension at the ordinary atmospheric pressure is 21 per cent, of 760 mm., that is, 159-6 mm. of mercury; and, in fact, it is 21 per cent, of any pressure under which air may be placed. Now suppose that we have a volume of gas at 760 mm. pressure containing 10 per cent, of carbon dioxide, its tension is 76 mm. Place the gas next in contact with a layer of water, and allow equilibrium to be attained, keeping the tension of the carbon dioxide in the gas phase constant by adding more as required. The water •dissolves a certain quantity of the carbon dioxide, and, at its contact surface with the gas phase, a certain number of molecules of carbon dioxide are continually entering the water and a certain number leaving it, so that equilibrium means that the same number enter and leave in the same time. It follows that the tension of the carbon dioxide is the same in both phases, although if we determine its total concentration in the water and in the gas, we shall not find it to be the same. Further, let us add some alkali to the water, still keeping the carbon dioxide tension in the gas phase constant; as is well known, carbon dioxide combines with alkali to form carbonate and bicarbonate, so that the liquid phase will contain much more carbon dioxide than the gas phase per unit volume, but again the tension at the surface, and therefore throughout the liquid, must be identical with that in the gas mixture when equilibrium is reached.

We may deal with oxygen in the same way, supposing haemoglobin to be present in the liquid instead of the bicarbonate. What we have to do is to determine the oxygen and carbon dioxide tensions in arterial blood, and compare them with the alveolar tensions of the two gases. The methods used to do this are the carbon monoxide method of Haldane and Douglas, already referred to, and the aerotonometer methods. The latter consist in exposing the blood to a limited volume of gas, of a composition as nearly as possible the same as regards the tensions of its components as that of the blood. After equilibrium has been attained, the composition of the gas phase is estimated by the usual methods of gas analysis. It is doubtful whether the earlier experiments were trustworthy, since the volume of the gas was too large. Those of Krogh (1910) are free from this objection. He 'devised a method by which a small bubble of gas can be analysed with the greatest accuracy. This bubble of gas was exposed to the current of arterial blood, being kept in constant motion by the current. After a time it was transferred to the measuring tube, and the carbon dioxide and oxygen contained in it determined. The result was that the tension of oxygen in arterial blood, under the conditions of the experiments, was. always lower than that of the alveolar air. Hence, so far, there is no difficulty in the diffusion theory. The tension of carbon dioxide was found practically identical with that of the alveolar air, but never less. The actual value of the carbon dioxide tension will be referred to again later.

At this point we must consider the view taken by Bohr, who believed that his experiments showed that the alveolar epithelium has the power of actively secreting oxygen in the direction of the blood, so that the tension of oxygen in the arterial blood may be higher than in the alveolar air. Certain physiologists, Haldane, Douglas, and Barcroft, to mention three only, still hold this view in a modified way. While admitting that the evidence is against the secretion of oxygen under ordinary conditions of rest and even of temporary want of oxygen, as in muscular exercise, they hold (see especially Douglas, Haldane, Henderson, and Schneider, 1913, pp. 204 and 205) that, during the process of acclimatisation to a high altitude, with its low oxygen tension, the lung epithelium develops the power of secreting oxygen. The table given on p. 197 of the paper named gives a number of data, and it will be seen that the oxygen pressures in arterial blood, as determined by the carbon monoxide method, are considerably higher than in the alveolar air in all the cases which had become acclimatised.

It is a difficult matter to understand how such a function should have been formed in the course of evolution to meet a need very rarely arising. We must remember that it is only supposed to show itself after exposure to want of oxygen for a considerable time. We may also consider briefly some further objections brought by Krogh against the view. In the first place, Krogh points out that, owing to the form of the dissociation curve of oxyh^moglobin, the haemoglobin is nearly saturated at the ordinary alveolar tension of oxygen, so that, in order to increase the oxygen percentage by 0'4 per cent, only, an increase of tension of 30 per cent, would be necessary. Of course, this is not so serious an objection when the alveolar oxygen tension is as low as that on the top of Pike's Peak, namely, about 60 mm. ; but, even at this pressure, the haemoglobin is 86 per cent, saturated. In any case, it seems a poor result for a new and special mechanism to be formed. As far as concerns the actual work required, A. V. Hill (1913, 3) shows that what is actually necessary to raise the oxygen tension from that of the alveoli to that of the arterial blood in Douglas, Haldane, Henderson, and Schneider's experiments is a very small fraction of that done by the organism as a whole. The value is given by the expression we have frequently made use of : —