ENERGETICS OF PROCESSES IN THE LIVING CELL¹

O. Meyerhof.

It may be considered an established fact that metabolism may with equal justification be examined from two points of view—energetic and purely chemical. In recent times the second point of view has to a considerable extent come to the fore. This is, to some degree, a reaction against the exclusive position that the adherents of a purely energetic caloric approach to questions of metabolism sought to occupy. Hardly anyone will now dispute that it makes no sense to construct purely schematic rules, even for human beings, basing them only on the need for calories and a protein minimum.

In connection with this question I would first of all like to point out that even where nutrients most directly proceed to the formation of mechanical energy, i.e. in muscle, even there one cannot speak of isodynamia, of the equivalence of these substances according to their heats of combustion. I am not even speaking of the fact that, in conversion into mechanical work, what matters is not the total energy liberated in the form of heat, but only the so-called “free energy,” which may differ substantially from the former. It may be supposed that precisely in the combustion of nutrients the difference between these two quantities is not so very great. But it seems to me extremely important that, as I have shown in the isolated frog muscle, the muscle uses exclusively carbohydrates for the production of work, and that lactic acid, which is the true working substance in the muscle, is formed only from carbohydrates. If the organism is capable of producing work even on an exclusively protein or fat diet, this is due to its ability first to convert proteins or fats into carbohydrates. Certain difficulties for such an interpretation were presented by the circumstance that the “isodynamic equivalence” of food substances, their capacity to replace one another as a source of energy during work, if not

¹ The fifth chapter of the book The Chemical Dynamics of Life Phenomena. Translated by V. A. Engelhardt. The book is being published in full in Russian by the State Publishing House.

ENERGETICS OF PROCESSES IN THE LIVING CELL

is complete, it is nevertheless expressed to a sufficient degree. Meanwhile, in the conversion, for example, of fats into carbohydrates, considerable losses of energy would have to occur. From 1.6 cal. of fat it would be possible to obtain only 1 cal. of carbohydrates, while 0.6 cal. would have to be liberated in the oxidation of fats into carbohydrates. Yet Étard found that if fats are counted instead of sugar, the productivity of human muscular work falls by only 5%; Krogh has recently found a decrease of 10%. But here we must remember that we are dealing with warm-blooded animals, and that the presumed oxidation of fats into carbohydrates makes it possible to economize other sources of heat. If the same experiments were carried out on cold-blooded animals, then it would undoubtedly be found that the value of fats as a source of muscular work is much lower than the value of carbohydrates. A number of scientists, including Graham Lusk, believe that fats are not first converted into carbohydrates, but may serve directly as a source of the energy necessary for work. The possibility is not excluded that in the living organism this may occur, but it is nevertheless very improbable. Only further experiments can resolve this question.

In the present chapter we shall consider the energetic significance of metabolism in general, independently of the particular case of the mechanical work of muscle. First we shall dwell on the significance of respiration as a whole, and then on certain individual chemical processes in cells in which chemical work is performed, in particular on the processes of assimilation of carbon dioxide and nitrates. The subject of my own investigations was the chemical assimilation of carbon dioxide by nitrifying bacteria. The assimilation of nitrates in green plants has recently been studied by O. Warburg. The same author has recently clarified the energetic aspect of the photochemical assimilation of carbon dioxide.

One can hardly doubt that the most diverse kinds of plant and animal metabolism can be explained only from the standpoint of energy exchange. Let us recall the bacteria which, in their respiration, oxidize inorganic substances such as hydrogen sulfide, ammonia, iron, and so forth, without consuming organic material in the process. Or let us try to explain from a single general point of view all kinds of anaerobic fermentation. We can do this, despite all the variety of chemical processes taking place here, if we take into account that the cell needs the energy of these chemical reactions. Therefore the energy ultimately released by the cell in the form of heat is by no means a by-product in the transformation of substances; on the contrary, chemical metabolism proceeds to a considerable degree precisely at the expense of this energy. This point of view, in a semi-quantitative respect, may be applied to the study of all kinds in general of

metabolism. When one molecule of sugar is fermented into alcohol or carbon dioxide, 26 cal. are liberated; when a molecule of sugar is oxidized—672 cal. The ratio is about 1:25. In alcoholic fermentation the increase in the weight of yeast amounts to 1 g of dry substance for every 100 g of fermented sugar, i.e., 1% of the weight of the sugar. On the other hand, when sugar is oxidized by the mold fungi penicillium glaucum or aspergillus niger, the increase in weight amounts to as much as 33–43% of the weight of the decomposed sugar. This ratio corresponds to a twenty-five-fold increase in the amount of energy liberated in the oxidative splitting of sugar. But such a comparison can be made only between the anaerobic growth of yeast and the growth of fungi that are entirely incapable of fermenting sugar. It is impossible to compare the growth of yeast under anaerobic conditions and in the presence of oxygen, because in the latter case the yeast not only respires, but at the same time also ferments sugar, although the latter process, from the energetic point of view, appears under these conditions to be entirely superfluous. Pasteur was mistaken in supposing that yeast ferments sugar only under anaerobic conditions and not in the presence of oxygen. Only the fungus mucor mucedo behaves in this way, in which the energetic significance of fermentation thus appears with particular clarity. Therefore a purely energetic approach to metabolic processes may not be applicable in all cases. Nevertheless, the examples cited show that energy metabolism is connected with definite vital functions of the cell, in particular with its growth. That this is indeed so is confirmed by J. Loeb’s experiments on sea-urchin eggs. Loeb showed that in these cells, which are obligate aerobes, the processes of division stop immediately as soon as the cell is deprived of access to oxygen, i.e., the processes underlying its energy metabolism are stopped. On this basis many older physiologists, such as Liebig, Pflüger, and also Zuntz, were inclined to the opinion that during growth an accumulation of potential energy may take place. The living proteins formed as a result of the assimilation of food would have to possess a greater store of energy than the dead proteins of the food. I subjected this hypothesis to experimental testing in the most diverse ways, but always obtained negative results. Warburg had already shown that the growth of cells and their respiration can be completely separated from one another. If, for example, fertilized sea-urchin eggs are placed in a very dilute solution of phenylurethane (0.01%), then cell division stops completely, while no difference whatever is observed in the rate of oxidation processes. If, as a result of a decrease in assimilation or of the cessation of the formation of certain structures, part of the oxidation energy remained unused, then one would expect that, when division stops,

more heat will be released during the growth bud than during cell division. This, however, is not observed. The amount of heat formed per unit of oxygen (I have called it the “caloric coefficient of oxygen”) remained in both cases one and the same1. On the other hand, if living proteins contain more potential energy than dead ones, then, by suddenly killing a large number of cells, we should observe the liberation of heat; in reality this does not occur. I, for example, placed a large quantity of energetically respiring avian erythrocytes, in the form of a thick mass, in the bomb of a calorimeter and then suddenly killed them by adding acrolein. No measurable quantity of heat was thereby liberated. The precision of these experiments is such that it permits one to assert that the difference in the heats of combustion of living and dead matter (this heat amounts to 5,800 cal. per gram) does not exceed 0.1 cal.2.

We see, therefore, that by this route we cannot find an explanation of the necessity of a constant exchange of energy for cells that perform no external work. Growth and vital activity, as such, do not yet constitute work in the thermodynamic sense. On the other hand, however, we see that cessation of metabolism entails the cessation of all manifestations of life in the cell—the movement of protoplasm, cell division, secretion, etc. The plant physiologist Pfeffer proposed a theory according to which aerobic cells, when the access of oxygen is cut off, can pass over to anaerobic metabolism, since the first stages of the breakdown of food substances take place without the participation of oxygen. In such a case anaerobic cleavage would serve as a certain energetic substitute for respiration in the absence of oxygen. But I found that this hypothesis is applicable only to muscle, and specifically to its carbohydrate metabolism. If the access of oxygen is cut off for respiring blood corpuscles or aerobic bacteria, then no metabolism accompanied by the liberation of heat is any longer observed, just as under these conditions there is also no accumulation of products of anaerobic cleavage. The latter is evident from the fact that, in contrast to muscle cells, in the present case after prolonged anaerobiosis no intensification of respiration is observed.

In muscle, however, the product of anaerobic metabolism—lactic acid, which has accumulated during the absence of access to oxygen—then causes a greatly increased absorption of it. Although aerobic bacteria and erythrocytes, in the absence of oxygen, show no energy metabolism at all, they nevertheless do not perish immediately, but only gradually undergo destruction; and the destruction proceeds the more rapidly, the higher the temperature during the absence of oxygen.

To the question of the significance of the energy metabolism of non-working cells, i.e. of the significance of respiration at rest, it is still impossible to give a direct answer, and one must be content with hypotheses. For the respiration of resting muscle I have given a satisfactory explanation, considering it as an expression of constant readiness for work. But it is difficult to say to what extent such an explanation is applicable to cells that do not perform work in the physical sense. Developing Warburg’s idea, I recently proposed, as one hypothesis, the supposition that, owing to the liquid state of the protoplasm and the instability of the substances entering into the composition of the cell, physical and chiefly chemical processes occur spontaneously in the latter, tending to disturb the existing equilibrium of energy potentials in the cell. In order that the life of the cell may continue, it is necessary to preserve these potentials, and, consequently, in order to prevent or to direct in the reverse direction the processes that alter these potentials, a certain amount of work must be performed. In a dead system one could keep a mixture of such substances unchanged for as long as desired by creating conditions that hinder the course of reactions. In the living cell, however, this is possible only by means of continuous cyclical processes. In addition, it may be supposed that all the other functions of the cell as well, such as secretion, the concentration of one substance or another, etc., are conditioned by the same metabolism on which cellular respiration also depends.

Here we have had to move in the realm of hypotheses. We obtain much greater satisfaction, however, by studying those cases in which metabolic processes are connected in a definite way with the work produced by the cell. We shall now turn to an acquaintance with certain such processes, in which energy is used for chemical work, namely to an acquaintance with the so-called coupled reactions.

The first case concerns chemosynthesis—the assimilation of carbon dioxide by nitrifying bacteria. As is known, in 1890 the Russian bacteriologist Vinogradsky discovered a large number of different species of bacteria that can grow on a purely mineral medium. By oxidizing inorganic compounds, they prove capable of obtaining the energy necessary for the assimilation of carbon, which goes toward the construction of their cellular substance. Among the various species of these

bacteria, the nitrifying bacteria, widely distributed in soil, have been best studied and are of the greatest importance in the world economy. Vinogradskii discovered two types of these bacteria. The first type, nitrosomonas, forms nitrous-acid salts (nitrites) according to the equation:

\[ \mathrm{NH_4^+ + 3O = H^+NO_2^- + H_2O + H^+ + 70\,000\ calories.} \]

The second type, nitromonas, forms nitric-acid salts (nitrates):

\[ \mathrm{NO_2^- + O = NO_3^- + 21\,700\ calories.} \]

Since in these bacteria there is a complete separation between energy metabolism and assimilatory metabolism, I attempted to study more closely, in them, the laws of energy metabolism. This seemed to me all the more attractive because these bacteria had never yet been studied from the physiological point of view. I shall dwell here on only one point—namely, on the connection between oxidation and the assimilation of carbonic acid in these bacteria. Qualitatively this connection can be detected in the following way. In two parallel experiments we determine the amount of oxygen absorbed by nitrate bacteria in one hour; the bacteria are placed in a phosphate solution, \(P_{\mathrm{H}} = 8.4\), initially containing a certain amount of carbonates. In one experiment we leave the carbonic acid, while in the other we gradually remove it by shaking the experimental mixture in a closed space with a solution of caustic soda. The latter first absorbs carbonic acid from the air and then gradually extracts carbonic acid from the experimental solution as well. We observe that in the experiment where \(\mathrm{CO_2}\) is present, respiration, owing to the increase in the number of bacteria, gradually intensifies; in the other experiment it gradually falls. The concentration of hydrogen ions, thanks to the phosphates, remains more or less constant throughout.

In order to take into account the assimilation of carbonic acid quantitatively, the organic carbon formed during definite intervals of time was determined by Messinger’s method, and its quantity was compared with the amount of nitrite oxidized. Vinogradskii carried out similar determinations on bacteria that form nitrite. Concerning the ability of nitrate bacteria to assimilate carbonic acid, he expressed himself only hypothetically, by analogy with the nitrite bacteria. In experiments with nitrate bacteria it turned out that the ratio

\[ \frac{\text{mg of oxidized nitrogen}}{\text{mg of assimilated carbon}} \]

amounts on average to 135 (i.e., for every 135 mg of oxidized nitrogen, 1 mg of carbon is assimilated).

This ratio, however, did not remain constant. At low nitrate concentrations it was smaller than at high ones, i.e.

at the beginning of the growth of the culture, through the oxidation of the same amount of nitrite, more carbon was assimilated than at the later stage. At a low nitrate concentration the coefficient is exactly 100. If we now assume that glucose is formed during assimilation, then this will require 112,000 cal. for each atom of carbon.

\[ \mathrm{CO_2 + H_2O = \frac{1}{6}(C_6H_{12}O_6) - 112{,}000\ cal.} \]

If one proceeds from the coefficient \(\frac{N}{C}=100\), it turns out that for each mole of oxidized \(\mathrm{KNO_2}\), 1,300 cal. were used in assimilation.¹) Since the molecular heat of the reaction \(\mathrm{NO'_2 + O = NO'_3}\) is equal to 21,700 cal., 1,300 cal. amounts to 6% of this quantity. By direct calorimetric measurement I found, as the average value from a series of experiments, 20,400 cal., i.e. five percent less than corresponds to the heat of the reaction. Although these heat measurements are not sufficiently exact to judge from them the amount of assimilated carbon, nevertheless they confirm the results of direct determinations.

In any case, they prove that no other processes of importance in energetic terms occur in the present case. These results are especially interesting if they are compared with those obtained in experiments with nitrite-forming bacteria. Vinogradsky published several relevant quantitative observations. From his determinations we find that in this case the ratio \(\frac{N}{C}\) is equal to 35, i.e. it is one third of that observed with nitrate bacteria (1 mg of carbon is assimilated upon the oxidation of only 35 mg of nitrogen). But this by no means indicates a more productive use of the energy of oxidation; on the contrary, it remains the same, since in the present case the heat of reaction, calculated per atom of nitrogen, proves to be three times greater than in the oxidation of ammonia, and the amount of energy used, as in the first case, amounts to only 6%.

Strictly speaking, one should compare not the quantities of heat evolved, but the quantities of free energy. The latter, however, cannot be determined under the conditions of the experiment. Nevertheless, on the basis of a number of comparisons, one may conclude that the ratio between the quantities of free energy remains the same as the ratio between the total quantities of energy, i.e. equal to 1:3.

I have cited these experiments with nitrifying bacteria by way of introduction, before turning to the exposition of the extremely inte—

¹) \(\dfrac{14 \times 112000}{12 \times 100}=1300\) cal.

…results obtained by Warburg and his collaborator Negelein in experiments with the alga chlorella. As is known, nitrogen in nature passes through a definite cycle. From the energetic point of view, the most important transformations are, first, precisely the oxidation described above of the ammonia formed in the decay of animal remains, which, under the influence of the nitrifying bacteria of the soil, is converted into nitrate; and, second, just the reverse process, taking place in plant cells—namely, the reduction of nitrates to ammonia and to the amino group of proteins. From the point of view of energetics, the most important moment in this process is the reduction of \(NO_3\) to \(NH_3\). The attachment of ammonia to the carbon chain has great biochemical significance, but takes place almost without liberation or absorption of energy. The reduction of nitrates to ammonia is simply the sum of the two equations given above, with the reactions proceeding only in the reverse direction:

\[ \mathrm{HNO}_3 + \mathrm{H}^{+} + \mathrm{H}_2\mathrm{O} = \mathrm{NH}_4 + 2\mathrm{O}_2 - 91700\ \text{cal.} \]

Indeed, in the reduction of nitrates by plants we encounter exactly the same processes as occur in nitrifying bacteria, only here they are linked in the reverse order.

In order to accelerate the usually very slow reduction of nitrates by algae, Warburg resorted to an artificial device. The rate of reduction depends on the concentration of undissociated \(HNO_3\) molecules, since only they can penetrate into the cell. Since algae do not tolerate any considerable acidity of the medium, Warburg placed them in a mixture of \(1/10\) normal sodium nitrate and nitric acid; under these conditions the dissociation of nitric acid is greatly decreased. If the course of nitrate reduction is observed in the dark, it turns out that the respiratory coefficient, which before the addition of nitrates had been equal to unity, rises sharply. As ammonia is formed, a certain amount of carbon dioxide is evolved, not arising from the absorbed oxygen. At first the ratio between the amount of this carbon dioxide and the amount of ammonia formed does not remain constant, probably because part of the ammonia immediately goes to the formation of amino acids. Later, when the cells’ need for nitrogen has been satisfied, a constant ratio is observed—2 moles of \(CO_2\) are evolved per 1 mole of \(NH_3\). In this case the reaction proceeds as follows:

\[ \mathrm{HNO}_3 + \mathrm{H}_2\mathrm{O} + 2\mathrm{C} = \mathrm{NH}_3 + 2\mathrm{CO}_2 \]

where \(C\) denotes some carbonaceous compound formed in the reduction of carbon. We may suppose that this compound is sugar.

Thus we have before us two coupled processes—endothermic reduction of nitric acid and exothermic oxidation of carbon or of one of its compounds. For the chemical work thereby produced, what is of greater significance is the free energy, and not the total amount of energy liberated in the form of heat of reaction. For the conditions of the experiment with an acid reaction, we calculated that the free energy of nitrate reduction is minus 68,000 cal., according to the equation:

\[ \mathrm{NO}_3^-+\mathrm{H}_2\mathrm{O}+2\mathrm{H}^+=\mathrm{NH}_4^+ +2\mathrm{O}_2-68000\ \text{cal.} \]

On the other hand, we have oxidation:

\[ 2\mathrm{O}_2+2\mathrm{C}=2\mathrm{CO}_2+2\times115.000=230000\ \text{cal.} \]

Adding these two equations, we obtain:

\[ \mathrm{NO}_3^-+\mathrm{H}_2\mathrm{O}+2\mathrm{H}^+ +2\mathrm{C} =\mathrm{NH}_4^+ +2\mathrm{CO}_2+162000\ \text{cal.} \]

Of the 230,000 cal. liberated in the oxidation of carbon, only 68,000 cal. are used, i.e. the energy yield amounts to 30%. From the standpoint of energetics, this reaction corresponds exactly to the reaction in the explosion of gunpowder. In the latter case carbon likewise burns to carbon dioxide at the expense of the oxygen of the nitrate (saltpeter). It is not difficult to see that in cells the oxygen causing the oxidation of carbon is taken not from the air, but from nitrate and water. Accordingly, the entire mechanism of oxidation proves to be substantially altered. Thus, for example, the absorption of free oxygen by algae is hardly delayed by the addition of cyanide salts, whereas the reduction of nitrates is stopped already by a \(^{n}/_{1.000.000}\) solution of potassium cyanide.

This process, this, so to speak, gunpowder-explosion reaction, is completely changed in the light. In this case much more ammonia is formed, but, in addition, now instead of an excess of carbon dioxide an excess of oxygen is liberated. In the light, as is known, carbon dioxide is reduced according to the equation:

\[ 2\mathrm{CO}_2=2\mathrm{C}+2\mathrm{O}_2-230000\ \text{cal. (of free energy).} \]

This need only be subtracted from the balance of the reaction just described, and then only the process remains:

\[ 2\mathrm{H}^+ +\mathrm{NO}_3^-+\mathrm{H}_2\mathrm{O} =\mathrm{NH}_4+2\mathrm{O}_2-68000\ \text{cal.} \]

Here, therefore, an influx of energy from outside becomes necessary. In the light the only source of this energy is radiant energy. Nevertheless, as it was possible to show by means of an interesting experiment, here too the reduction of nitrates is accompanied by the formation

carbon dioxide. Narcotics greatly retard the assimilation of carbon dioxide, but have almost no effect on the reduction of nitrates. If narcotized cells are exposed to light, they release the same quantity of gas as non-narcotized cells. But this gas proves to be not oxygen, but carbon dioxide—the very carbon dioxide which, in the absence of narcotics, would have been assimilated as an intermediate product. In the present case carbon dioxide plays the role of an intermediate substance, by means of which radiant energy is used for the reduction of nitrates.

The reduction of nitrates occurring in the light has led us to the question of the assimilation of carbon dioxide and compels us to turn to the very latest work of Warburg (carried out in collaboration with Negelein), in which energy exchange was studied on the basis of the assimilation of carbon dioxide itself. It turns out that under favorable conditions we can here obtain a yield of useful work that surpasses everything known to us in the field of chemical exchange. If, as Warburg did, one measures with extraordinary precision the total quantity of radiant energy absorbed by a suspension of algae and at the same time determines the quantity of carbon dioxide assimilated, it turns out that the degree of utilization of radiant energy thus found is by no means constant.

First of all, the photochemical coefficient depends on the intensity of illumination. It is the higher, the weaker the illumination, so that the maximum utilization can only be determined as a limiting value lying at the very weakest light intensity. Secondly, the algae themselves exhibit differing capacities for using light energy. When kept for a long time in weak light, dark-colored cells are formed, containing much chlorophyll and possessing an especially high assimilatory capacity. In these cases the photochemical utilization of energy in yellow light reached 60% (the average of numerous experiments). This is higher than all hitherto known cases of photochemical utilization of energy. Warburg believes that the decrease in the utilization of energy in bright light depends on an excessively abundant formation of sugar in the cells. The reduction of carbon dioxide to sugar undoubtedly takes place on structural surfaces covered with chlorophyll molecules. This may be inferred from the high sensitivity of the assimilation process to narcotics. The influence of the latter can be explained only by displacement of the substrate from the solid surfaces in the cell. If, as a result of abundant formation of sugar in the cell, part of the structural surfaces becomes occupied by it, then carbon dioxide will no longer find a place for the reaction. If a ray falls on a chlorophyll molecule which at that moment is not in contact with a carbon dioxide molecule, then the light energy of the ray is lost. This depends

depends on the fact that the existence, the “lifetime” of a molecule that has absorbed radiation and can convert it into chemical work is only \(10^{-8}\) seconds. Hence it is clear how densely the chlorophyll layer must be covered with carbon dioxide in order that a large part of the radiant energy may be converted into chemical energy.

We arrive at another important conclusion on the basis of Planck’s quantum theory, or, more directly, on the basis of Einstein’s “law of equivalence” that follows from it. As is known, according to the quantum theory, radiant energy is absorbed or used discontinuously, in quanta, whose magnitude is proportional to the frequency of the oscillations of light. An individual quantum is equal to \(h\nu\), where \(h\) is Planck’s constant and \(\nu\) is the number of oscillations. According to Einstein’s “law of equivalence,” one molecule at any given moment can accept only one quantum and can be decomposed by light only in the case where \(h\nu\) is greater than or equal to the energy necessary for the decomposition of the molecule

\[ N_0 h\nu \geqq U, \]

Here \(U\) denotes the work necessary for the decomposition of 1 gram-molecule, and \(N_0\) is Avogadro’s constant. For the conversion of one molecule of \(CO_2\) into \(1/6\) of a molecule of glucose, \(U\) is equal to 115000 cal.

On the other hand, for yellow light we have \(N_0 h\nu = 49000\) cal. \((N_0 = 6.18 \times 10^{23};\ h = 1.56 \times 10^{-34}\ \text{cal}.)\). Thus the requirements of Einstein’s theorem are not directly satisfied here. \(U\) is more than twice as large as \(N_0 h\nu\), and from this we must conclude that, for the reduction of one molecule of carbon dioxide, at least three light-absorbing molecules are necessary. Such molecules are chlorophyll molecules; consequently, at least 3 molecules of chlorophyll must each accept a quantum of energy and undergo chemical change in order that one molecule of carbon dioxide may be assimilated.

In conclusion, one further important inference follows from this: if the number of quanta (\(n\)) necessary for the reduction of one molecule of carbon dioxide is constant, then the utilization of radiant energy (“the yield of the photochemical reaction”) must increase toward the red end of the spectrum in inverse proportion to \(\nu\), i.e. directly proportional to the wavelength, because \(N_0 h\nu\) increases proportionally to \(\nu\), while \(U\) remains constant. This consequence of Einstein’s law was precisely confirmed in Warburg’s experiments on carbon dioxide assimilation. Contrary to all previous assertions that assimilation takes place considerably or predominantly in the portions of the spectrum corresponding to the absorption lines,^1 Warburg

^1 It goes without saying that assimilation can take place only when light is absorbed (Draper’s law).

showed that the degree of utilization of energy depends not on the region of the spectrum, but follows the ratio of quanta, gradually falling from the red to the blue end of the spectrum.

At 660 μμ (red color) up to 63.5% of the energy is utilized; at 578 μμ (the yellow mercury line)—53.5%; finally, at 436 μμ (the blue mercury line), a maximum of 34.8% can be utilized.

An even more correct conception is obtained if one compares the coefficient of utilization of light energy for the same cells at different wavelengths. The ratio of the effects at $\frac{660\ \mu\mu}{578\ \mu\mu}$ is 1.13, whereas the ratio of the wavelengths is 1.14; the agreement is complete. For $\frac{578\ \mu\mu}{478\ \mu\mu}$ the effects are in the ratio $1:1.55$, and the wavelengths as $1:1.32$. Warburg believes that in the latter case the discrepancy is due to the fact that in blue light the yellow pigment—xanthophyll—also absorbs light, whereas its assimilating capacity is lower than that of chlorophyll. Correspondingly, the utilization of energy proves to be somewhat lower than would be expected according to Einstein’s law. If we now assume that the maximum coefficient of utilization of radiant energy observed in the experiments represents the truly highest possible limit of utilization of the latter, then we can calculate how many quanta are necessary for the assimilation of 1 mole of carbon dioxide.

For example: in red light 115,000 cal. are utilized. For this there must have been available

$$ \frac{115000 \times 100}{63.5} = 181000\ \text{cal.} $$

On the other hand, at $\lambda = 660\ \mu\mu$ ($\nu = 454 \times 10^{-12}$) one quantum per mole corresponds to 43,700 cal. Consequently, the number of quanta needed for the reduction of one mole of $\mathrm{CO_2}$ is

$$ \frac{181000}{43700} = 4.1. $$

In exactly the same way, for yellow light we obtain the value 3.8, and for blue—4.7; all these data are mean values obtained from a large number of experiments. Thus it turns out that four quanta of energy are necessary for the assimilation of one mole of carbon dioxide. Therefore the best utilization of light is achieved when $4N_0h\nu = U$; this condition is satisfied at the red end of the spectrum, whereas in its other regions we have $4N_0h\nu > U$. At the same time, in the indicated dependence we have an exact explanation of the circumstance that precisely in red light lies the limit of assimilation.

We began this chapter with a difficult question, to which as yet no exhaustive answer can be given—what purpose is served by the chemical exchange of energy? Consideration of several precisely studied processes of energy exchange has led us, finally, to the fundamental problem of cellular energetics—to the accumulation of solar energy in green plants.

Here we have become acquainted with very valuable results achieved in this direction. We have seen that, under favorable conditions, a large part of radiant energy can be converted into chemical work. Warburg’s discovery that, in assimilation, quantum theory is fully applicable, and that four quanta of energy are required for the reduction of one molecule of carbon dioxide, gives us certain indications also regarding the chemical mechanism of the assimilation of carbon dioxide. This allows us to hope that, in time, it will be possible to obtain an answer to the question of the use of oxidation energy in the chemical metabolism of the cell.

1. According to my slightly corrected calculations, this value averages 2.85 cal. In doing so it was assumed that \(O_2\) is in solution. For comparison with heats of combustion, in the determination of which oxygen is introduced in the gaseous state, the heat of solution of oxygen should also be added; we then obtain 2.95 cal. Repeating my experiments, Scherer, using Gill’s thermoelectric method, found, probably, the more correct value 3.05–3.2 cal. These figures closely agree with the caloric coefficients of proteins and fats, which are equal to 3.2–3.3. ↩

2. 40 \(\mathrm{cm}^3\) of erythrocytes, containing 2 g of nitrogen (which corresponds to 12 g of protein), raise the temperature of 250 \(\mathrm{cm}^3\) of water by less than \(0.004^\circ\), i.e., give less than 1 calorie; per 1 g of protein this amounts to less than 0.1 cal. ↩