Principles of General Physiology

The results of certain experiments which I had occasion to make with regard to emulsin (1912, 2), in which rabbits were injected with the enzyme, led me to examine carefully the evidence as to the existence of anti-enzymes] In the experiments referred to, it was found that a " precipitin " was formed for the vegetable protein present as impurity in the emulsin used, but that there was no precipitin for the enzyme itself. The serum, in point of fact, did retard the action of emulsin, but the effect was found to be merely due to diminution of the acidity of the solution ; when this was brought back to its initial value by the addition of acid phosphate, the inhibitory effect disappeared. Moreover, making an emulsin solution of the same hydrogen ion concentration as that produced by the addition of "immune-serum" caused the same degree of retardation.

It is to be noted that " anti-emulsin " was the first anti-enzyme supposed to be produced (Hildebrandt) ; it is generally regarded as a typical one and certainly has more evidence in its favour than any other one. This evidence is discussed in my paper referred to above. When the serum of an animal shows, normally, " anti-enzymic " properties, it is naturally impossible to obtain satisfactory evidence that these can be increased by the injection of the enzyme in question, since the property exhibits large natural variations. In other cases, adsorption of enzymes by colloidal substances is sufficient to account for the " an ti " properties ; Hedin (1906) showed that the adsorption of trypsin by charcoal is precisely similar to a typical retardation by anti-enzymes.

Thaysen (1915) finds that the so-called " anti-rennin " of serum is to be entirely accounted for by the two influences referred to above, the adsorption of the enzyme on the one hand, and the effect of change in hydrogen ion concentration, as found by myself in the case of emulsin. There is no true antibody formed. We shall see later that enzymes are not proteins, at least the fact has been definitely established in some cases and in none is there evidence of their being so. This, in itself, is a priori reason for doubting the production of true antibodies, until it has been shown that substances other than proteins can give rise to their formation.

Under special circumstances, substances preventing the action of enzymes are to be met with. An interesting one is that present in intestinal ivorms, protecting them from the action of trypsin. The properties of this substance were especially investigated by Hamill (1906) and it was found to be soluble in 85 per cent, alcohol, not destroyed by boiling in neutral or acid solution, but readily in alkaline solution. It is not a colloid. When added to a tryptic digest, it is found to disappear slowly, so that ultimately the enzyme recovers its full activity and is, therefore, merely temporarily paralysed. Its disappearance in the alkaline digest is natural, owing to its sensibility to alkali. As will be seen, this substance has none of the characteristics of Ehrlich's antibodies.

The behaviour of raw serum or egg-white to trypsin is peculiar. If the curves on p. 129 of my monograph (1913, 2) be referred to, it will be noticed that the action on raw egg-white starts slowly but becomes more rapid until it ultimately reaches the same point as when the substrate had been previously boiled. This may be due to the presence of some inhibitory substance similar to that of the intestinal parasites, or perhaps to the adsorption of the enzyme by the protein, which is itself a difficult one for attack ; as this protein is slowly attacked, the enzyme is set at liberty, so that it is available for the further conversion of the easily attacked proteoses resulting from the initial hydrolysis of the protein.

Concentration of Substrate. — According to the law of mass action, it is to be expected that the rate of change in an enzyme reaction would be directly proportional to the concentration of the substrate. This is so, in the main, so long as the concentration does not exceed a certain value, which differs in individual cases. In that of caseinogen, for instance, below 5 per cent, the rate is proportional to the concentration, although not in simple linear ratio ; above 5 per cent., the rate continues about the same up to 8 per cent., but in 10 per cent, solution it is rather less than in one of 8 per cent. There appear to be two factors concerned. The rate of a reaction in such colloidal heterogeneous systems, as we have seen, is determined by the amount of the adsorption compound between enzyme and substrate in existence at any given time. Remembering further what we have learned with regard to adsorption in general, we see that, at a certain

concentration of substrate, the active surface available will be "saturated," so that further increase in concentration will not result in more adsorption and therefore in no increase in the rate of the reaction. If the " concentration " of the activesurface is increased relatively to the substrate, there will be increase until tins surface is saturated. This circumstance, however, seems capable of explaining only the fact of eqwility of rate above certain relative proportions of enzyme and substrate, and is well illustrated by tinfollowing two experiments by E. F. Armstrong (1904, 1, p. 508). A very small amount »\ lactase acted on different concentrations of lactose for forty-six hours ; it was found that the amount hydrolysed was the same in all, although the reaction wa,s by no means at an end, thus : —

When the proportion of enzyme to substrate was large, a different result was obtained : — The amount of hydrolysis is in direct ratio to the concentration of the substrate and tinvelocity constant is practically identical in all. Another factor which comes into play in such cases as proteins or glycerol is viscosity, which, as we have seen, retards the access of substrate to enzyme. The fact that gelatine shows actual retardation above a certain concentration and in a more marked degree than does caseinogen, supports this view, since gelatine forms solutions of a higher degree of viscosity than those of caseinogen. The following numbers show the change of electrical conductivity in twenty-five minutes in solutions of gelatine of different concentrations : —

We see that there is a progressive increase in the rate as the solution is more dilute. Similar facts apply to the synthesis of glycerol-glucoside by emulsin ; the rate, is diminished when the glycerol present exceeds about 65 per cent. It is important to note, however, that in this case, where it is possible to test the effect on the total amount of products when the reaction has attained equilibrium, this final amount is found to be in direct ratio to the concentration of the substrate, although the higher the viscosity, the longer the time taken to reach equilibrium.

Effect of Temperature. — Like all processes, the action of enzymes is increased in rate by rise of temperature, in some cases very considerably, more than trebled by a rise of 10°. The fact indicates that the controlling factor of this particular kind of heterogeneous reaction is the chemical reaction proper, since both diffusion and adsorption, as physical processes, have a low temperature coefficient. As the temperature is raised, it is found that, above a particular temperature, the rate begins to fall off, and at a further rise of temperature all effect is abolished. The temperature at which the maximum rate is shown has been called the optimum temperature.

It is merely due to the fact that enzymes are injured more or less rapidly by rise of temperature, and the optimum temperature is that at which the acceleration due to rise of temperature is in greatest excess over the simultaneous destruction of the enzyme. The process has been worked out by Frost Blackman (1905) and a complete explanation given. Attention should also be directed to the time factor in this connection. The lethal effect of raised temperature is not a sudden thing, so that the slowing of the reaction will be more and more apparent the longer the time that has elapsed since the commencement of the exposure to a

particular temperature. Neither the optimum nor the lethal temperature is a fixed point ; a short exposure to a high temperature may not kill an organism, while a longer exposure to a rather lower one may be fatal. Some of the earlier workers with enzymes seem to have regarded the optimum temperature of enzyme action as something mysterious, even indicating " vital action." We see that it is merely the expression of the sensitiveness of the colloidal arrangements of the enzyme system to rise of temperature, and is not confined to enzymes, but may be shown by inorganic colloids.

FIG. 85. INTERIOR OF VAN'T HOFF'S PRIVATE ROOM IN THE OLD LABORATORY AT AMSTERDAM (1877-1891).— On the left of the photograph is a window, in front of which stands a table. This table was van't Hoff s chief work- (Reproduced by the kindness of Prof. Ernst Cohen of the van't Hoff Laboratory, Utrecht. ) There is one practical point in connection with the great acceleration of enzyme action by rise of temperature. It is often necessary to stop a reaction at a particular stage ; this must not be done, if any accuracy is required, by raising the sample to the boiling point. However quickly this can be done in practice, the enzyme is not immediately destroyed, and during its short life, it acts with great energy, owing to the considerable rise in temperature. If dilution i permissible, the sample may be allowed to fall, drop by drop, into boiling water. Better, if the addition of chemical substances is immaterial, as is usually the case, mercuric nitrate may be added, which immediately precipitates and destroys the enzyme.

Although the great majority of the reactions catalysed by enzymes are known to be reversible, it is a matter of, at any rate, great theoretical interest to consider how far it is justifiable to regard all reactions as reversible. According to J. J. Thomson (1888, p. 281), if we take the view that the properties of matter in motion are sufficient to account for all physical phenomena, irreversible processes, such as those apparently made so lay frictional resistance, must be capable of explanation as the combined effect of changes, all of which are themselves reversible. "It follows that, if we 'could only control the phenomenon in all its details, it would be reversible ; so that, as was pointed out by Maxwell, the irreversibility of any system is due to the limitation of our powers of manipulation. The reason why we cannot reverse every process is because we only possess the power of dealing with the molecules en masse and not individually,

Fie. 86. EXTERIOR OF VA\'T HOFF'S OLD LABORATORY AT AMSTEKI>\M. (Reproduced by the kindness of Prof. Ernst Cohen of the van't FToflf Laboratory, Utrecht. ) while the reversal of some processes would require the reversal of the motion of each individual molecule." Nernst, also (1911, p. 442), states that reactions cannot be divided into reversible and non-reversible. " There can be no doubt that by suitable adjustment of the conditions of the experiment, it would be possible to make a reaction take place, now in one direction, now in the opposite, that is, in principle every reaction is reversible." One of the most obvious of these conditions referred to is that of temperature, as in the well-known case of the dissociation of ammonium chloride.

It appears justifiable, then, to regard all reactions from this point of view although, under ordinary conditions, the position of equilibrium may be so near the state of complete change in one direction that the reaction seems to have gone entirely in one direction. When a reaction is known to be reversible, it is customary to use the sign suggested by van't Hoff(1884, p. 5), namely, two arrows pointing in opposite directions : — acid + alcohol ~\ ester + water, or more conveniently, by the modification of this suggested by H. Marshall (1902) : v **•

We owe to van't Hoff (1884) the systematic investigation of the laws of the velocity of reaction and of equilibrium. It may be of interest to the reader to see a photograph of the laboratory in which he worked from 1877 to 1887, a period of time in which so much of fundamental importance was produced The photograph of van't Hoff's workroom, reproduced in Fig. 85, and that of the exterior of the laboratory in Fig. 86 are taken from the book by Jorrisen and Reicher (1912). Fig. 87 is an interesting picture of Ostwald and van't Hoff.

We have already had occasion to refer to some facts concerning the reversibility of enzyme action. We saw that the equilibrium point may be in very various positions according to the relative rate, as determined by the chemical difficulty, of the two opposing reactions. We have seen how, at this equilibrium point, the two opposing reactions are to be regarded as still pro- FIG. 87. VAN'T HOFF AND OSTWALD IN OSTWALD'S LABORATORY AT LEIPZIG. (Reproduced by the kindness of Prof. Ernst Cohen of the van't Hoff Laboratory, Utrecht.)

ceeding, but at equal rates. The reaction with the slower natural rate is compensated for by the greater active mass at the state of equilibrium. It is to be remembered that the actual position of equilibrium is decided by the relative values of the two velocity constants. The ratio of these constants is obviously also a constant and is known as the equilibrium constant. We note further that the equilibrium position can be defined in two ways, either from the dynamical point of view, as above, by the ratio of the two velocity constants, or, from the statical point of view, as the ratio of the relative masses of the components. It is interesting to find that the equilibrium constant in the lipase reaction of Dietz, given at the commencement of this chapter, is found experimentally to be the same when calculated in both ways.

Although the equilibrium position can be defined by the relative masses of the components, it is not to be supposed that it is a statical one. The two reactions are still proceeding, the various molecules are continually changing their partners, but, during the same time, the number of changes in the one direction is equal to that in the opposite one. This conception of a dynamical equilibrium is of great importance, not only in chemistry, but also in the physiology of the cell. The idea seems to have been first clearly expressed by A. W. Williamson (1850).

Before proceeding further, some additional remarks on the law of mas* action, especially on its history, are required. Before the time of Berthollet (1799), it was generally held that the course of chemical action had nothing to do with the quantity of reacting matter. This chemist, however, pointed out how the reaction — was reversed, on the shores of certain Egyptian lakes, by the presence of great excess of calcium carbonate, so that the deposits of sodium carbonate were thus to be accounted for. As he says, " an excess of quantity can compensate for a weakness of affinity," and "the result of a chemical reaction depends not simply on the strength of the affinities, but also on the amount of the active reagents " (p. 5 of the reprint in Ostwald's " Klassiker "). This point of view was not accepted for more than half a century. In 1850 Wilhelmy applied mass action in a quantitative manner to the hydrolysis of cane-sugar by acid, and established the fact that the rate of action at any moment is proportional to the amount of substance undergoing change. Harcourt and Esson in 1856 obtained similar results, but it is the great service of Guldbergand Waage (1864) to have formulated and applied the idea in its full significance, and in a clear and systematic manner. Nevertheless, their work remained for a long time unknown, so that the law of mass action was developed independently by Jellet in 1873, and by van't Hoff in 1877.

To avoid possible confusion, it should be clearly understood that the masses spoken of are concentrations, that is, mass in unit volume. Taking again the kinetic point of view, we can see at once that it would not double the number of effective collisions if we doubled the mass and the volume at the same time ; there would still be only the same possibility of collision. We must ensure the possibility of doubling the number of collisions by doubling the number of molecules in the same space.

Remembering that the composition of a system in equilibrium is determined by the relative rates of two opposing reactions, we see how the law of mass action is the basis, not only of chemical dynamics but also of chemical statics. Passing on to consider its application to the action of enzymes, let us see first what is the effect of changing the concentration of one component of a reversible reaction in equilibrium. Taking the familiar ester system, the rate of hydrolysis is in proportion to the product of the concentrations of the ester and the water, that is : —

using brackets as usual to express concentrations, and k{ and k., are the two velocity constants. Then, in equilibrium : — Put in this form, we see that if we increase one component, the result must be to decrease its fellow, since the value of the fraction must remain unaltered. Suppose we increase water, the value of the fraction can only be kept constant either by increasing (alcohol) (acid) or by decreasing (ester). In point of fact, of course, the two are identical, since one cannot take place without the other! The result of excess of water should be, therefore, to increase the hydrolytic reaction of the system, as found by experiment.

The conclusion to be drawn from this fact is that, in order to obtain much indication of the synthetic aspect of enzyme action, the concentration of water must be diminished as far as possible (Fig. 80, page 300). In the living cells, where synthetic processes readily take place, it seems that there must be some very effective means of doing this, perhaps by surface condensation or imbibition on the part of colloids. But we have as yet no very clear idea of the mechanism.

As has been pointed out above, certain synthetic reactions proceed but very slowly, even in maximum concentration of the reagents, on account of their chemical nature itself. But, in the dynamic and heterogeneous systems of the cell, this small amount of synthesis must not be undervalued. Suppose that, as soon as equilibrium is established, the synthetic products are removed in some way. More will be formed in order to re-establish the stable condition and, in this manner, the process may be continuous, so that a quite appreciable degree of synthesis may take place in a short time, depending on the extent to which the reaction is accelerated by an enzyme. The removal may be effected in several ways. The product may be washed away by the blood current to some other part of the organism, it may be deposited in the form of a separate phase, such as starch, glycogen, or fat, or it may be immediately used up in an independent chemical reaction.

A particular enzyme in a cell, for example amylase in the liver, will, under low concentrations of glucose in the blood, hydrolyse the glycogen stored in the cell ; while, in higher concentrations of glucose, glycogen will be synthesised and, as it is stored in an insoluble form, the process can go on to a considerable extent. This possibility has been pointed out by Croft Hill (1898). The hydrolysis and loss of starch from germinating seeds is regulated by the growing plant. If the embryo is removed, the starch cea,ses to be hydrolysed. This is obviously a case of equilibrium of the kind just referred to, since Pfeffer and Hansteen (1893) have shown that, if the embryo of maize or barley be replaced by a little column of plaster of Paris, the disappearance of starch can be stopped or set going again according as the end of the plaster column is immersed in a tiny drop of water or in a large quantity. In the former case, the products of hydrolysis are not removed, so that the reaction soon comes to its equilibrium position. In the latter case, they are removed by diffusion as fast as they are formed, so that their concentration is maintained permanently low and no equilibrium is reached.

The reader is referred to the chapter on the reversibility of enzyme action in my monograph (1913, 2) for the numerous cases in which direct evidence of synthesis by enzymes has been observed. The fact must be again emphasised that there is no necessity for the assumption of special synthesising enzymes and that all evidence that has been brought forward to show their existence has been shown to be capable of other explanations (Bayliss, 1913, 1). If enzymes are catalysts and if the reactions are reversible ones, enzymes must accelerate both the hydrolytic and the synthetic aspects, unless they carry the reaction to completion in one direction, whatever the conditions present.

It was mentioned incidentally at the beginning of the present chapter that the actual position of equilibrium is frequently found to be somewhat different under the action of enzymes from that under acids. This fact seems to have caused some difficulty. But there are one or two considerations, of interest in themselves, which should, I think, lessen or remove the difficulty. The difficulty itself would be much more serious if these enzyme changes were associated with any considerable heat change, since, in that case, energy would have to be supplied by the enzyme or from some other source. But since the active enzyme is always present in minute amount compared with that of the substrate it does not seem possible that it could supply any appreciable amount of energy,

either by chemical or physical change. Hydrolytic actions, and it is in these that the question arises, are practically thermo-neutral, as pointed out by van't Hull' (1909, p. 1075); the heat change is very small; in the conversion of one grammolecule of methyl acetate to one of alcohol and one of acid, only — 0'9 large calories, thus : — In other words, only 0'38 per cent, of the heat of combustion of the ester. The small amount of energy required to change the equilibrium position, in the case of ethyl butyrate, in the experiments of Dietz from 85-5 per cent, of ester, when acid was the catalyst, to that of 75 per cent, when lipase was used, might quite conceivably, as Herzog (1910, p. 196) points out, be obtained from surface or volume energy of some kind. In fact, the difference between catalysis by acid and that by enzyme consists essentially in the circumstance that the former results in an equilibrium in a homogeneous system, the latter in one in a heterogeneous system.