Contribution to a Theory of Photosynthesis

978

JAMES FRANCK AND KARL F. HERZFELD

CONTRIBUTION TO A THEORY O F PHOTOSYNTHESIS JAMES FRAKCK

Department of Chemistry, T h e rniversity of Chicago (Fels F u n d ) , Chicago, Illinois AND

KARL F. HERZFELD

Department of Physics, The Catholic I’nivemity of America, Washington, D . C. Received February 16, 1941 INTRODUCTION

The number of fundamental experiments available on which a theory of photosynthesis might be based has increased considerably in the last two years. On the one hand, repetition of certain important experiments has shown that some hitherto generally accepted data have to be discarded; on the other hand, new methods of observation have been introduced, and the new results so obtained must now be taken into account. The change in the situation is indeed so far reaching that practically all theories published hitherto are now obsolete. We may illustrate this by enumerating a few of the more important facts. The quantum yield of photosynthesis was believed to be 1/4, whereas new experiments have shown it to be actually 1/10 t o 1/12 (13, 6, 18). All theoretical considerations about the chemical nature of the intermediate products of photosynthesis and all thermochemical conclusions, therefore] have to be radically changed, since the number of photochemical steps and correspondingly,the energy balance is changed by a factor of 2 to 3.’ Experiments in which rapid changes of the photosynthetic rate were studied revealed the fact that the carbon dioxide intake of a strongly synthesizing plant continues for a short time in the dark. The amount of carbon dioxide “picked up” in this way can become comparable to the number (2, 14, 15) of chlorophyll molecules present. These experiments show that theories based on the hypothesis of the so-called photosynthetic 1 For instance, the theory of Franck and Herzfeld (J. Chem. Phys., 1937) belong, to the group which has to be discarded. But a t the same time we should like to use the opportunity to say that we do not agree with Wohl’s (28) criticism of t h a t theorys in so far as he tries to prove that i t is inconsistent in itself. \Ye mention as an example that, according to our calculations, the time needed for a chain back-reaction of the type assumed by us is 10-4 see., instead of several seconds as estimated by Wohl, but even 10-4sec. is perhaps too long. Furthermore, in criticizing our assumptions regarding the amounts of energy necessary for each step, Wohl does not take into account our hypothesis that the peroxide involved is one that is much more stable than hydrogen peroxide. We agree, on the other hand, with Wohl’s statement that the assumptions introduced by us are not sufficient t o avoid a long induction period but only change its sign.

A THEORY O F PHOTOSYNTHESIS

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unit are not in accordance with the facts. For, whereas the unit hypothesis requires that the concentration of carbon dioxide and of the intermediate products simultaneously connected with the photosynthetic apparatus shall be several thousand times smaller than the concentration of the chlorophyll, the amount of carbon dioxide “picked up” in the dark reveals that the 5 photosynconcentration of carbon dioxide present in a form accessible t thesis is of the same order of magnitude as that of the chlorophyll. A still more direct contradiction to the hypothesis mentioned results from the facts observed by Ruben, Kamen, and coworkers (20),who made use of radioactive carbon dioxide to study the preparatory dark reaction which precedes photosynthesis. It was found that carbon dioxide reacts with an acceptor molecule RH in a carboxylation process by which RCOOH is formed. The concentration of this substance is again of the same order of magnitude as that of chlorophyll. Since there are also other considerations which make the photosynthetic unit seem implausible (9), we regard all theories making use of this unit as at least very improbable.’ Xew observations on the fluorescence of chlorophyll show that a much more direct connection between the strength (15, 7 ) of the fluorescence and the process of photosynthesis exists than has been hitherto generally supposed. JTe mention especially the fact that addition or removal of carbon dioxide produces characteristic changes in the fluorescence which correspond exactly with changes in the rate of photosynthesis. Such results are a strong indication that the reduction of carbon dioxide takes place by a direct energy exchange between the chlorophyll molecules which absorb the light energy and molecules of carbon dioxide and intermediates which make use of the energy for the reduction processes. Theories which assume that the photochemical part of photosynthesis results merely in a production of some reducing substance, which in turn reduces carbon dioxide in a mechanism chemically independent and spatially feparated from the chlorophyll, are not in accordance with these observations (16,21). The experimental facts will be discussed more thoroughly in the next part of this paper, but the examples already mentioned offer enough justification for the statement that no theory of photosynthesis published hitherto is in sufficient accord with the facts t o be regarded as an adequate theoretical description. (We have to except Burk and Lineweaver’s (3) general mathematical analysis which, on account of its generality, is very adaptable.) On the other hand, these theories have served the purpose for which they were developed; they have clarified the situation, they have stimulated new experiments and, moreover, most of them contained parts

* To this group of theories belong Emerson and Arnold’s ( 5 ) original picture of the unit (see, also, 1, 10, 20, 16)

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which have been used in each subsequent attempt. We hope the same will be true for the following theory; a t least we have convinced ourselves of its usefulness, since a great number of experiments on photosynthesis performed in the laboratory of one of us during the last few years have grown out of problems suggested by the point of view expressed below. These la& remarks, superfluous for most readers, are made because discussions have convinced us that not all of the workers in this field realize that one of the main purposes of a theory is to induce new experiments and that by its very nature a theory can contain only a partial truth. DISCUSSION OF THE TaEORY

Photosynthesis, the process by which carbon dioxide and water are reduced to the oxidation state of a carbohydrate while molecular oxygen is liberated, is a photochemical reaction sensitized by the dye chlorophyll, and takes place in steps. According to the most recent results, 10 to 12 quanta are necessary to reduce one carbon dioxide molecule. Even taking into account the possibility that inefficient absorption acts may occur, one can safely assume that the number of actual photochemical steps involved is not very much smaller than ten. If, for instance, this number is eight, one has to assume that seven intermediates, partially reduced derivatives of carbon dioxide, exist. If photosynthesis proceeds a t a constant rate, each of these intermediates must have the same opportunity to undergo a photochemical reaction as the carbon dioxide itself. If a certain minimum amount of carbon dioxide is present, the rate of photosynthesis does not change either temporarily or permanently when the concentration of carbon dioxide is suddenly doubled. This is understandable, as has already been pointed out by several other authors, only if a limited number of acceptor molecules exists with which the carbon dioxide molecule reacts before it undergoes photochemical changes and with which it remains firmly connected until the stepwise reduction is completed. Otherwise, one would have to expect that an increase of the carbon dioxide concentration would reduce the probability of the intermediates undergoing photochemical changes until their concentration is built up t o the same height as that of the carbon dioxide. Kamen, Ruben, and coworkers (20) have shown, in their important paper referred to previously, that the acceptor molecule is not identical with the chlorophyll but is a colorless substance of a molecular weight'around loo0 and reacts with the carbon dioxide a p parently in a carboxylation reaction.a Since that reaction is hindered by The carboxylation reaction which is assumed to take place in the plant must be different from the usual ones. Carbon dioxide is bound in the plant with an energy which corresponds at leaat to 10 kg.-cal., while the usual carboxylation compounds are much weaker. Our conclusions are independent of the chemical nature of the binding reaction.

A THEORY O F PHOTOSTNTHESIS

98 1

cyaiiide, one has to assume that it proceeds with the help of a catalyst which we may call catalyst A. The preliminary reaction between the acceptor and carbon dioxide proceeds then in two steps :

+ COz F! RH.COz RH.COs + Cat. A F! RCOOH + Cat. A RH

(1)

(2)

IC a plant is irradiated with strong light in the presence of a very low carbon dioxide concentration, the concentratioit of intermediates will become small, since the velocity of reaction 1 becomes limiting. If, on the other liaiid, the catalyst X is poisoned by cyanide, n strong irradiation will also reduce the concentration of intermediates to a very small quantit'y even in the presence of a surplus of carbon dioxide. yiiice reaction 2 will now become limiting. These considerat,ions explain somr observations of lufdemgarteii (2) and McAlister and Myers (14, 15) 011 the pickup of carbon dioxide in tlie dark after an illumiriation period. The first-mentioned author studied the pickup of carbon dioxide in algae partially poisoned by cyanide! and observed that this uptake of carbon dioxide continues in the dark for more than 2 min. As stated above, the total aniount taken up in the dark, so f a r as one can estimatt>,is comparable to the amount of chlorophyll present, but more experimental work is necessary to make quantitative comparisons possible and to make it \vorth while to compare the shape of the observed curves with the theoretical ones. The experimental curves are appareiitly made with thick layers of algae arid not with well-known quantities of cyanide. RlcAlister arid Myers observed that, a t loa- carbon dioxide concentrations, the pickup in the dark lasts for about 2 miri. It must be mentioned that the counterpart to the pickup is also observable. If a plant first denuded of intermediates-for instance, by strong irradiation in the preseiice of cyanide-has taken up much carbon dioxide during a dark period following the illumination, it contains an unequal distribution of photosensitive substances. The concentration of the intermediates remains as low as it was during the illumination, while that of RCOOH has become high during the dark pause. Resumption of irradiation produces irregularities in both the carbon dioxide uptake and the fluorescence, which are superimposed on the usual induction period phenomena occurring a t the beginning of each illumination period. Indeed some observations of Katz and Wassink and others (22, 23, 24) and of McAlister and Myers made under such conditions are easily interpretable from this point of view. (A more detailed description mill be found in a paper of Franck, French, and Puck on the fluorescence of plants.) IVe regard the substance RCOOH as the substance which undergoes the photochemical changes. Since it is no longer necessary t,o restrict the

982

JAMES

mmcK

AND K . m L F. HERZFELD

number of photochemical steps to four, several great difficulties in the formulation of a theory of photosynthesis are eliminated. The first is the well-known difficulty of the energy balance. The light energy absorbed not only has to provide energy equal to the heat of combustion of a carbohydrate to carbon dioxide and water but also the energy to be used as the heat of activation of each photochemical intermediate and of the end product. These heats of activation must play an important r61e in the energy balance, since the intermediates have a considerable lifetime, as shown by the fact that interruptions of illumination of about half an hour do not measurably alter the relative concentration of the intermediates in a plant. Moreover, some additional energy will be required, since the photosynthetic process does not produce oxygen molecules directly but rather peroxides, which split off oxygen in an exothermic reaction. Calculations which one will find in the last section of this paper show that no difficulties occur if one uses the fact that eight photochemical reactions (or more) are involved in the reduction of one carbon dioxide molecule. Furthermore, it is now possible to assume that the photochemical reduction of carbon dioxide has a much closer similarity to other reduction processes of carbon dioxide which some bacteria exhibit in the dark when supplied with hydrogen donors. Willstatter (27) originally discussed the possibility that reactions of the type:

COz

+ 4H

-+

CHzO

+ HzO

occur in photosynthesis. Van X e l (21) supplemented such assumptioiis by the idea that the light energy is used only to produce hydrogen donors, while the actual reduction is a dark reaction. Making use of the fact that, according to the new measurements of the quantum yield, eight photochemical steps are possible, we arrive a t the following scheme: Molecules which we may call R’H, without specifying their nature, act as hydrogen donors. The energy necessary for the transfer of the hydrogen atoms is supplied by the light energy absorbed by the chlorophyll. Four absorption acts are necessary to reduce one carbon dioxide molecule, and four R’ radicals remain. These regain their hydrogen atoms by oxidizing water molecules. The energy required for this process is again supplied by four further absorption acts. The experiments on the chlorophyll fluorescence in relation to photosynthesis, mentioned in the introduction, make it improbable that the actual reduction process of carbon dioxide is a separate reaction not connected directly to the photochemical steps, We therefore assume, in deviating from Van Niel’s idea, that the transfer of the hydrogen atom to the carbon dioxide is directly produced by the use of the excitation energy of the chlorophyll. R’H molecules then have to be members of the molecular

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complex containing the chlorophyll molecule itself and RCOOH or its derivatives. It simplifies the picture if one identifies the R’H molecules with the chlorophyll itself. In other words, one adopts the often-discussed idea that the chlorophyll not only acts as a sensitizer but also undergoes chemical reactions during photosynthesis. Indeed, the results of some new experiments with chlorophyll in organic solution make that hypothesis very probable. We refer, among others, to experiments on the reversible bleaching of chlorophyll solutions (25) and to experiments demonstrating a relation between fluorescence and some photooxidation process. According to the interpretation of these experiments given by Weiss and Ftabinowitch (25) and by Franck and Livingston (8), excited chlorophyll acts as a hydrogen donor in vitro and may therefore also do so in living plants. The hesitation in assuming that it acts in this way in photosynthesis was based on the belief that the mqnodehydrochlorophyll would be colorless because of destruction of the syscem of conjugated double bonds. In that case, it could not regain its hydrogen atom with the help of another absorption act. But the chlorophyll contains many hydrogen atoms whosepresence or absence will not affect the conjugated bond system and, in the experiments mentioned, Franck and Livingston found strong indications that the particular monodehydrochlorophyll which is formed when an excited chlorophyll transfers one hydrogen to an acceptor remains as green as before. It seems, therefore, to be quite possible that chlorophyll enters into the course of the photochemical reactions. The picture described, in so far as it contains statements about definite chemical compounds, is not claimed to be original, nor is its correctness essential for the following theory of the chemical kinetics of photosynthesis. However, this picture does fit well into the framework of the theory presented. The main difficulty encountered in formulating a theory of chemical kinetics of photosynthesis is an apparent contradiction between the value for the velocity of a dark reaction calculated from the shape of the so-called light saturation curve and that obtained by actual measurement of this velocity. The rate of photosynthesis rises linearly with the light intensity in the region of weak illumination but becomes light saturated a t high intensities; Le., after a certain rate is reached, the rate remains constant and independent of further increase in the light intensity. This applies to observations made at room temperature in the presence of so much carbon dioxide that its concentration is not limiting. The saturation value has the temperature coefficient of a normal thermal reaction, while a t low intensities the rate is independent of temperature. One concludes that the saturation occulg because a normal, thermal, chemical reaction (i.e., a dark reaction) becomeslimiting at high light intensities, while a t low intensities this reaction is so much more rapid than the photochemical ones that the rate is determined only by the velocity of photochemical reactions which

984


have practically no temperature coefficient. One can calculate the velocity of the dark reaction from the value of the saturation rate, the number of light quanta absorbed and the low-intensity yield by making the assumption that thg absorption acts of the chlorophyll molecules are mutually independent and are indiscriminately used for photochemical reactions. This calculation, when applied to a normal leaf, for instance, results in a period of about 60 sec. as the time necessary for the dark reaction to run halfway through its course. Actual measurements of the reaction velocity made by Emerson and Arnold gave the result, in striking contradiction to expectations, that the dark reaction runs through half of its course in 1/100 sec. These measurements, which were repeated several times with the same result, are made by the study of photosynthesis in plants irradiated with sufficiently strong, short flashes of light. The dependence of the rate upon the duration of the dark pause between the flashes enables one to calculate the time necessary for the dark reaction to run to its completion. If the dark pause is greater than that critical time, each light flash finds the photosynthetic apparatus in a state which is no longer influenced by the previous illumination; the photosynthetic yield per flash then becomes independent of the duration of the dark pause. If, on the other hand, the dark pause is too short, the flash will still find some substrate produced photochemically by the previous flash and the yield per flash becomes smaller. Poisoning with cyanide prolongs the length of the dark pause necessary to obtain the full yield per flash. However, if the dark pause is made long enough, the final value of the yield per flash obtained in the presence of cyanide turns out to be identical with that obtained from an unpoisoned plant. If so much cyanide is used that the saturation value for continuous light is reduced to about one-fifth of its original value, the time necessary for completion of the dark reaction, i. e., the so-called Blackman period, becomes a few tenths of a second (4,5). As has been previously shown, the contradiction between the calculated and measured values for the Blackman period is not the only difficulty which one encounters. There is also the relation to be clarified between the Blackman period measured in this way and the period observed for the pickup phenomenon in plants partially poisoned with cyanide,-a period which is about one thousand times longer. Furthermore, one has to explain the important result found by Emerson and Arnold and extended by Arnold and Kohn that a maximum yield per flash exists, in which the amount of oxygen evolved or carbon dioxide absorbed is again several thousand times smaller than the number of chlorophyll molecules present (4,5, 12). One notes here, too, the difference between that value and the amount of carbon dioxide taken up by the plant in the dark pickup. The apparent contradiction between the velocity of the dark reaction, as given by the method of the light flashes, and its value calculated from the


985

shape of the saturation curve, as well as the phenomenon of the flash saturation, can be explained by the introduction of one very simple hypothesis: the limiting dark reaction is a process in which catalyst molecules present in a concentration several thousand times smaller than the concentration of chlorophyll operate on a photochemical product which is chemically very unstable. The catalytic reaction stabilizes the photoproduct. All the photoproducts not stabilized during their lifetime are eliminated by back reactions. The lifetime of the unstable product must be long enough so that during the time taken by the catalyst to diffuse to a substrate molecule the losses of the substrate are negligible, while on the other hand the lifetime must be short compared with the working period of the catalyst molecules. The term, “working period,” may be taken to mean the average time lapse during which a catalyst molecule which has just reacted is unable to do so again. That this hypothesis allows an adequate description of the experiments will be demonstrated first for the case of the flash experiments. If, by a sufficiently strong light flash, a large amount of unstable photoproduct is made, the molecules of the catalyst, which we call catalyst B, will stabilize only as many substrate molecules as there are catalyst molecules. Each molecule of the catalyst B stabilizes only one substrate molecule, while the excess of substrate is consumed by back reactions during the recovery period of the catalyst B. If the time interval between the light flashes is greater than the recovery time, each light flash will find all the B molecules in an active condition, while if the dark pause is too short, the number of active molecules available during each light flash will be smaller, so that the yield per flash is reduced. The shorter the time lapse between the flashes, the less efficient is the utilization of the light and the more back reactions occur, while the total rate per unit of time approaches the saturation value of the continuous illumination. This hypothesis,* as will be shown in a more rigorous manner in the mathematical part of this paper, offers a satisfactory explanation for the phenomenon of saturation in continuous and in flashing light, but needs to be supplemented in order to provide an understanding of the influence of cyanide. Why does cyanide prolong the Blackman period, and what are the relations between the prolonged Blackman period and the prolonged time needed for the dark pickup of carbon dioxide in the presence of cyanid87 If cyanide is a poison for the molecules of The explanation given above has been known to us for about three years and waa also used by us in papers read on different occasions. We delayed in publishing this new theory, however, until more experimental evidence was collected. While tpe experiments are decidedly in favor of our assumptions, the waiting period brought u8 the advantage t h a t i t is now possible to publish a much more complete theory, in which the different hypotheses have experimental foundations.

986


catalyst B, it should reduce the number of active catalyst molecules and consequently reduce the saturation yield per flash. Since this value, according to Emerson and Arnold and also according to an unpublished result of Weller and Franck (26), remains unaffected, one has to conclude that the molecules of catalyst B are not influenced by this poison. We know, on the other hand, that the molecules of catalyst A are sensitive toward cyanide. (This conclusion follows from the experiments of Ruben and Kamen that cyanide hinders the formation of RCOOH, and from the experiment of Aufdemgarten on the carbon dioxide pickup.) We therefore have to consider an explanation which involves two catalytic reactions, one of which can be partially poisoned. It was possible to explain the saturation phenomenon occurring under normal conditions (in the absence of inhibitors) by the limitation of the catalytic reaction involving only B. If, therefore, the process in which catalyst A plays a r6le has no observable influence on the normal saturation curves, it means that the formation of RCOOH from COz and R H is rapid compared to the catalytic B reaction. If, on the other hand, by addition of cyanide the number of A molecules is reduced and correspondingly the RCOOH formation is slowed down, this latter step can become the slowest one. If that occurs, the saturation rate will be reduced. How much poison one needs to slow up the A reaction sufficiently for it to become the slower of the two and therefore the limiting one, depends on the relative concentrations of the two catalysts and the ratio of their working periods. We can now understand why the amount of cyanide necessary to produce such changes will be quite different in different species of plants, since those which have a great surplus of catalyst A will be less sensitive than plants having only a small amount. In the flash experiments the influence of catalyst A is likewise unobservable as long as the velocity of its reactionis greater than that of the reaction involving B. But if, by the addition of cyanide, the order of these velocities becomes reversed, the Blackman period will be prolonged without any influence on the maximum yield per flash. After a dark period sufficiently long to reach the dark equilibrium, the ratio of the concentration of RCOOH to that of R H will depend only upon the carbon dioxide concentration and will be independent of the velocity of the reaction involving catalyst A. The yield of the first light flash will therefore be the same in the presence and in the absence of cyanide. But if the amount of RCOOH consumed by the flash is not replaced in toto by a reaction between R H and COZ during the dark pause, the next light flash will find a smaller amount of RCOOH present. The yield per flash will gradually diminish, until an equilibrium between consumption of RCOOH during the flash and replacement during the dark pause is reached. The yield per flash will therefore become small. Only if the dark pause lasts long enough so that just as much RCOOH can be


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produced during this period as is consumed photochemically during a light flash will the former yield per flash be observed. The way in which,. in the presence of cyanide, the yield per flash varies with the length of the dark period, has been observed by Weller and Franck in experiments wherein Chlorella algae were exposed to flashing light in the presence of cyanide. For short dark pauses the rate is the same in flashing light as in continuous light. The yield per flash rises linearly with the length of the dark period. For longer time intervals between the flashes, the yield rises more slowly than linearly until it finally reaches the constant saturation value. The mathematical equations corresponding to these observations will be found in the last part of this paper. In the discussion of the action of catalyst B, it is necessary to decide whether B stabilizes only one of the intermediate photoproducts or more than one. The saturation phenomena do not give an answer to this question, since they do not depend on the particular steps a t which a bottleneck is formed. But it is possible to draw some conclusions from the distribution of the relative concentration of the intermediates. In the range of low intensities, where photosynthesis is proportional to light intensity, one can have a constant rate only if the concentration of all intermediates is the same. At high intensities, where a large fraction of the unstable intermediates reacts again, a very unequal distribution would be produced if the back reactions did not take place with the same frequency for all the intermediates. A transition from saturation intensity to a very weak one would then produce irregularities for the rate a t weak light intensity. An experiment carried out by F. F. Rieke (19) shows that such effects are absent if the irradiation with the stronger light is not made with an excessively high light intensity. One therefore comes to the conclusion that the freshly formed photoproducts are all unstable and can be stabilized only with the help of catalyst B. This would be astonishing were the photochemical intermediate products to be quite different from one another. But since, according to our assumptions, each photochemical act is a shift of a hydrogen atom in the activated complex from one bond to another, all the photochemical processes will greatly resemble each other. I t seems quite natural to assume, therefore, that after each photochemical process the same catalyst B has to perform a stabilizing reaction on the products. Before we discuss the relation between the Blackman period and the pickup phenomena, we can write some model equations which are in agreement with our assumptions : I . Preparatory dark reactions: RH RH.COz

+ COz + RH*COz

+ Cat. A

RCOOH

+ Cat. A

988


+

I

I

H chph-RCOOH hv -+ chph intermediate il followed by: rhph intermediate il catalyst B * + chph intermediate SI catalyst B The intermediatgs not stabilized by the catalyst undergo back reactions : chph intermediate il-+ H chph COZ RH \

+

+

+

+


989

decreased if, as we assumed, the back reaction results in the splitting off of carbon dioxide from the compound to form RH and COZ. The process which occurs is as follows: In the region of light saturation the rate of photosynthesis remains constant when the irradiation is increased. Therefore the efficiency of utilization of the light declines and the number of back reactions increases with increase in the light intensity. Eventually the A molecules no longer suffice to keep up with the back reactions. The concentration of all the other intermediates is reduced. Whether this emptying of the photosynthetic apparatus starts a t intensities in the neighborhood of tHe saturation intensity or a t much higher values depends on the relative number of catalyst A molecules. In case the number of A molecules is reduced by cyanide to such an extent that this reaction is the limiting one and is responsible for light saturation, even a moderate light intensity will largely empty the photosynthetic apparatus. If, under these conditions, the light is suddenly turned off, practically all the free RH will combine slowly with carbon dioxide. This pickup will last some minutes, and the amount of carbon dioxide taken up will be about as great as that of RH present which is comparable to that of chlorophyll. The difference in the order of magnitude of the time used for the pickup and the Blackman period is then due to the fact that in the flash experiments only as much carbon dioxide combines with RH during the dark pause as is photochemically used up by a single light flash, while on the other hand, a t the end of an illumination period with continuous very strong light, practically all the RH is free and will combine with carbon dioxide.’ As was mentioned in the introduction, we conclude from fluorescence phenomena that the photochemical reduction of carbon dioxide takes place a t the chlorophyll itself. The very fact that the fluorescence in Chlorella is directly proportional to the light intensity in the region where photosynthesis already shows signs of light saturation was used by Ornstein and coworkers as evidence against the above conclusion. Omstein’s argument was the following: If saturation is produced by a catalytic limitation, one would expect that, a t saturation, the material which the catalyst cannot handle will accumulate. This material is unable to undergo a further photochemical reaction and, if the reaction takes place directly on the surface of the chlorophyll, the pigment should become covered with a neutral layer of these inert molecules. Such an unreactive layer is known to raise the fluorescence yield, as does the addition of a narcotic. The argument, however, cannot be used to disprove the theory outlined above, since, according to our considerations, there will not be an accumulation 6 There is a direct connection between the intensity at which t h e photosynthetic apparatus starts t o become denuded and t h a t a t which strong photooxidation (solarization) begins. This question will be discussed in a paper by Franck and French.

990


of photoinsensitive matter if normal light saturation is reached, since the rapid back reactions transform these substances immediately into a photosensitive state again. The conditions are different, however, if the photosynthetic apparatus becomes more or less denuded. In that case the chlorophyll will, to a great extent, be in contact with R H instead of with RCOOH or intermediates. R H is assumed t o be photostable and can therefore be expected to increase the fluorescence yield by its contact with the chlorophyll, There are three different ways in which the photosynthetic apparatus may be denuded: (1) irradiation in the absence of carbon diokide or in an atmosphere containing a very small amount of carbon dioxide (less than & per cent); (2) irradiation in the presence of enough carbon dioxide but under the influence of inhibitors of the carboxylation reaction (like cyanide); (3) irradiation under normal conditions but with an intensity exceeding the saturation value to such an extent that the apparatus is emptied by excessive back reactions. Actually, in all three cases a greater fluorescence yield is observed experimentally. The fluorescence of hydrangea leaves, for instance, is increased about 70 per cent under these conditions, when the concentration of photosensitive intermediates becomes very small. Later on there will be found a mathematical treatment of these cases. The equations presented describe the variation in the amount of chlorophyll connected with photoinsensitive substance as a function of the light intensity. Using empirical values for the fluorescence yield of the chlorophyll when connected only with photosensitive material and when connected entirely with the photoinsensitive RH, one obtains the fluorescence yield &s a function of the light intensity. Figure 1 shows that observed and calculated data are in the best agreement. A more detailed discussion of these fluorescence phenomena will be found in a paper of Franck, French, and Puck (7). Finally, we wish to discuss briefly the fact that the catalyst C, to which we attributed the function of liberating oxygen from a peroxide (page 988; equations V to VIII), also has an influence on the photosynthetic rate and correspondingly on fluorescence phenomena. As will be shown extensively in the paper of Franck, French, and Puck, the reaction involving catalyst C is the limiting reaction during the so-called short induction period, which occurs after dark pauses of about 1 min. to 1 hr. and which reduces the rate of photosynthesis during the first minute or two a t the beginning of an illumination period. In higher plants and also in many cases in algae, a close analogy exisists between the changes observed in the rate curve of photosynthesis and the J intensity curve of fluorescence as a function of time, gut they are opposite in direction during the induction period. If, after a dark period, the plant is irradiated with strong light, photosynthesis starts a t the very first,

991


moment of irradiation but falls to a very small value in about 1sec. Thereafter it rises slowly, reaching the steady rate in about 1 to 2 min. The fluorescence, on the other hand, rises in the first second three to four times its normal strength and decays then for 1 to 2 min. until the normal strength i s reached again. Each sudden transition to a higher rate of photosynthesis is preceded by an induction loss and a corresponding outburst of fluorescent light. Extensive experimental studies of our own, as well as analysis of the results available in the literature, show that the

Y

0.

A A ,lo a,:, LlG H T

INTENSITY

w I'.01

:,

a

k L A

ergs/cm'sec

FIG.1. The upper curve represents the fluorescence yield of hydrangea leavee, as a function of the light intensity. The ordinates are not absolute values, but are approximately in units of 10-6. The dots are direct measurements, while the curve is theoretical (equation 47). The lower curve gives the photosynthesis i n relative units against light intensity (same units a s for the upper curve), the points representing again the measurements, the curve the theory. In other plants, the relative positions of these two curves are different.

following hypothesis, which is an extension of an assumption made by Gaffron, is in accordance with all known facts. The catalyst C is divided into an active and an inactive portion. The concentration ratio of these portions depends upon the concentration of reducing material in the chloroplasts. During a dark period the equilibrium is shifted towards the inactive (apparently oxidized) catalyst. Illumination reactivates (reduces) the catalyst to a degree which is proportional to photosynthesis itself, since the amount of reducing substance present is proportional to photosyn-

992


thesis. (Peroxides and reduced substances are made in equal amounts by photosynthesis but the peroxides have a short lifetime in the cell, while the removal of the photochemically reduced substances by diffusion to other parts of the cell or by chemical transformation is certainly much tlower; that makes the concentration of the reducing material proportional so photosynthesis.) The reactivation of catalyst C takes time; therefore in the beginning of an illumination period the peroxides are not readily removed. Their concentration grows, since more is made per unit of time than the still inactivated catalyst C can remove. A side reaction is started by that accumulation, and the peroxides attack some metabolic product present in the chloroplasts. These oxidized products cover a part of the chlorophyll but are also adsorbed particularly strongly a t the catalyst B. Both factors, but especially the last one, reduce the further production of peroxide to such an extent that the small amount of active catalyst C can now take care of the new production of peroxides. The reactivation of catalyst C starts slowly while the adsorbed oxidation products are removed by plant respiration. Both factors cause the slow transition to the steady rate of photosynthesis. We must leave the discussion of the experimental material supporting this explanation to the other paper mentioned above. The importance of this interpretation of the short induction period lies in the fact that it shows that a third catalytic reaction is connected with the photosynthetic process. Moreover, it reveals that an interaction between metabolic processes and photosynthesis takes place. Such metabolic interactions are, according to our opinion, also responsible for the slow changes in the rate of photosynthesis occurring in higher plants irradiated for hours under constant external conditions (Harder and coworkers (11)). The short induction periods have nothing t o do with a building up or an adjustment of the concentrations of the intermediates to the proper proportions. Induction periods, or, more accurately, periods of abnormal rate during the beginning of an illumination, which are due to the latter phenomena, take a much longer time, especially a t low light intensities. Such anomalies of long duration occur after a plant is kept for many hours in darkness or after the plant is nearly freed from intermediates by one of the treatments mentioned above, applied during the last illumination preceding the observation. That a plant kept for a very long time in the dark, or even grown completely in the dark (this last only in those plants in which chlorophyll can be fully developed by growing in the dark), starts to photosynthesize immediately on being illuminated (even though with an abnormal rate) is, according to our interpretation, a proof that intermediates are also present under these conditions. Any decline in the concentration of these intermediates in the dark which might be caused by their limited stability is at least partly compensated by a slow


993

series of oxidation steps extending from the carbohydrate state to the end products, carbon dioxide and water, and taking place a t the photosynthetic apparatus. This process is not to be confused with normal tissue respiration, the course of which involves quite different intermediate products. An estimate of the order of magnitude of this reverse reaction will be found in the last section. The conclusions drawn above from chemical kinetics show that photosynthesis is by no means a simple photochemical process in which only the molecules carbon dioxide, water, and chlorophyll participate. It is, rather, a complicated interaction between light and dark reactions in which three different catalysts, the acceptor molecules for carbon dioxide, the intermediates, and very probably proteins play a decisive r6le besides chlorophyll, carbon dioxide, and water. Since photosynthesis is regarded not only under the conditions prevailing now on earth as the only source for a primary synthesis of organic matter but a jortiori a t the time when the solid c m t on the surface of the earth was first formed, one has to conclude that the original process in which organic molecules were first synthesized photochemically was a quite different and a much simpler one. Indeed, a t that time the conditions were favorable for a direct synthesis of organic molecules from carbon dioxide and water under the action of sunlight without the help of dyestuffs. Ultraviolet light, belonging to the Schuman region, was able to reach the surface of the earth, since the atmosphere contained practically no free oxygen and consequently no ozone which now shields the shorter wave length. Light in the Schuman region is known to be absorbed by carbon dioxide and water themselves and to cause reduction (and oxidation) processes by which organic molecules could be formed. DIFFERENTIAL EQUATIONS FOR THE MAIN PHOTOSYNTHETIC PROCESS

According to the theory outlined above, the photosynthetic process can be divided into three parts,-the initial process of carbon dioxide intake, the main photochemical process, and the liberation of oxygen from the peroxide. Each of these parts embodies catalytic reactions, with specific catalysts which we call A, B, and C. Let N be the total number6 of molecules of chlorophyll, Y that of catalyst A, n that of catalyst B, and n' that of catalyst C. In the main photosynthetic sequence, there are eight reactions, arranged in two groups of four, so that the reactions belonging to the two different groups alternate. We call the number of molecules of a given substance x1 or yb, depending on the group to which it belongs; e.g., 2 8 would be the complex with intermediate 3, number of molecules of H chlorophyll

+

e N is either the number of chlorophyll molecules or the number of carrier molecules adsorbed t o chlorophyll, whichever is smaller.

994


ys the number of molecules of dehydrogenated chlorophyll with intermediate 4. A typical reaction cycle is then as follows: X,(s = 2, 3, 4; s = 1, the H chlorophyll-C02 complex, has to be treated separately) absorbs a light quantum (reaction velocity kx8) and goes over into an unstable substance (tautomer of xa of higher energy content). Either one of two things can now happen to &. It may react with a molecule of free catalyst B (the number of these molecules is u ; see later) with a reaction velocity k&,u; the catalyst transfers a hydrogen atom from H chlorophyll to the intermediate El, changing the intermediate s to inter1 (or end product, if s = 4) and the H chlorophyll t o dehymediate s drogenated chlorophyll, the result being called y.. Or, any not acted upon in time by the catalyst goes back to x,, with a reaction velocity k&,. In turn, a molecule of the second group y. (s = 1, 2, 3, 4) absorbs light (velocity ky,) and forms an unstable intermediate qs. This in turn is either acted upon by the same free catalyst B, which transfers a hydrogen atom from water to dehydrogenated chlorophyll, thus changing that back 1 attached, and leaving, in effect, to H chlorophyll with intermediate s half a molecule of peroxide behind. The speed of this reaction is kSqpu. Or, q, reacts back in a monomolecular reaction k4qs to y.. The equations which describe these processes are as follows:

+

+

-de* -- kx, - k2& dt

- k3t8u

s = 1, 2, 3, 4

The behavior of the first x has to be considered in connection with the carbon dioxide intake. Furthermore, we make the assumption that a molecule of catalyst B, after it has reacted with either 6 or I), is in an inactive (reduced) state, and that the change back into a free or active (oxidized) state is a first-order reaction of speed kev, where v is the number of molecules of inactive catalyst B. Therefore

u+v=n

(5)


995

The carbon dioxide intake

As mentioned above, Ruben, Kamen, and coworkers (20) have shown that carbon dioxide can be bound to a carrier in two ways, loosely or strongly, the change from the former to the latter being due to a catalyst, which we call A. A can again exist in two forms, free (number of molecules I’) or inactive, after it has reacted (number of molecules V ) . The regeneration of free molecules is monomolecular, and the reaction velocity is KaV. Call X’ the number of molecules of the carrier which are loosely bound to carbon dioxide, and the completely free state of the carrier X”. We then assume that an equilibrium is always established. Free carrier

+ COz

Loosely bound carrier

Xl’[CO*] = K X ’

(7)

+

Then the free catalyst reacts with the loosely bound complex, COZ carrier, and changes it into the chemically bound complex, H chlorophyll carrier COz,which is the initial step in photosynthesis. The quantity of this substance is called xl. Therefore the speed of formation of x1 is

+

+

KiC’X’

(8)

Let us introduce the quantity X

x

=

X’

+ X”

Le., the total amount of the carrier either free or loosely bound. Then, from equation 7,

We now assume that light absorption in X has no chemical effect, and that light absorption in the tightly bound complex (xl) changes it to the unstable intermediate E l , as in the other z steps. & , in turn, is either changed by catalyst B into yl or reacts back. This has been embodied in equation 2. But in distinction to the back reaction of other E’s, the back reaction of El leads not to x1 but to free carrier, X , that is, the energy set free by the back reaction dissolves the chemical bond between the carrier and carbon dioxide. Therefore, the equation for x1 is dt

=

KIUX’ - kxl = K z U X - kxl

!10)

996


with

Finally we have the equation

X

+ Z X +~ + Zy. + 278 Z&

=

N

The unstable compounds .E and 7. are present only in such small quantities that they can be neglected, and therefore6

X

+ Zx,+ Zy,

=

N

(13)

That completes the equations.' The last of the three parts in the whole photosynthetic process consists, we assume, in the liberation of gaseous oxygen from peroides by catalyst C, one oxygen molecule resulting from two peroxide molecules. While we think that this process is responsible for the transient phenomena a t the beginning of illumination, we shall not consider the details now. We think that they are unimportant for the stationary phenomena, a t least for the group of plants studied so far. Steady illumination; stationary state In this case all of the time changes, equation 11 and 12 that

(3

KzC'X = K ~ ( v

, are

zero. It follows from

r-)

OS

Then, according to equation 10,

or

7 Number of unknowns: four each of z a ,y,, e., and q 8 ; plus u, u, U,V , X',and X". The total is twenty-two, S u m b e r of equations: three of form 1, four each of forma 2, 3, and 4, and equations 5, 6, 7, 10, 11, 12, and 13 make a total of twenty-two also.

.4

THEORY O F PHOTOSYNTHESIS

997

Here K3v is the maximum amount of carbon dioxide that can be made available per second. For the main photosynthetic process, we get from equations 1 to 4

kys = k4tls

+

k~t)aU

It follows from a comparison of equations 3a and 4a that k35s

=

k6%

( s = 1, 2, 3,

4)

(16)

and from a comparison of equations l a and 2a that k351

=

(S

ks78-1

= 2, 3,

4)

(17)

Equations 16 and 17 together show then that all the Sa’s are equal among themselves, say 5, and all the llals equal among themselves, say 7. Furthermore, it follows from equations 2a and 3a that all the x.’s are equal among themselves, say x, and all the ya’s equal among themselves, say y, so that the sixteen equations l a to 4a reduce to three: equations l b , 3b, arid 17.

kx

=

k2t

= k49

+

+

k3&

(1b)

k35~

(3b)

Subtracting equation 3b from equation l b and using equation 17, one finds

Furthermore

X

+ 4(x + y) = N

The equations 5 and 6 for the catalyst B take the form ksv - u4(kat

+ kst)) = ksv - (n - 1?)8ka( = 0

(sa)

or

Now multiply equation 13a by k and equation 18 by 4 and add, eliminating y. One finds

kX

+ 8 k =~ kN + 4ki (1 -

998


This is the equation for the distribution of available reaction places (carrier or chlorophyll molecules). Next comes the equation (lob) which correlates the rate of carbon dioxide supply with the rate of the photochemical process and determines the number ( X ) of places left free because the catalytic supply reaction cannot follow fast enough. Remembering that x1 = x, we rewrite equation 10b

Equation l b determines the stationary state of the unstable intermediates 6 and equation 19 the reaction balance of the catalyst B. Eliminating 6 from equations 20 and l b by equation’lg, we find &ally, as the two algebraic equations with the two unknowns x and v which have to be solved,

The number ( P ) of oxygen molecules developed per second is one-fourth of all the four processes of the second group which form a peroxide, Le., in general 1 P = - Zk6qrU (22) 4 I n the present case, that is (see sa),

If we call the maximum photosynthesis 1

ksn = P ,

equations 20” and 20‘ can be rewritten: kz=P

[1 +

1

k3n(Pm Ic2pm- P )

kz the ratio of the back reaction of f to the rate a t which the completely k3n ’ free catalyst B attacks it, is the dimensionless quantity which characterizes the saturation curve in the most useful units

plotted against

-

h THEORY OF PHOTOBYNTHESIS

999

The general solution of equations 23 and 24 is rather complicated, because of the influence of the intake of catalyst A contained in the expression { ) of equation 24. Therefore we will first discuss the case where the carbon dioxide intake has a su5ciently large maximum speed so that it does not act as a bottleneck for photosynthesis.

Photosynthesis i f the carbon dioxide intake is not limiting The assumption that the carbon dioxide intake is not limiting means that Ksv is large compared to k / 8 and Ksr is large compared to k N / 8 . Experimentally this is a case where the yield in fluorescence is independent of light intensity beyond photosynthetic saturation. According to equation 21, X is then negligible, the carbon intake mechanism always supplying the carbon dioxide complex almost immediately as soon as it is used up by light. We then have 42

+ 4y = N

(13b)

We now shall discuss equation 18, the right-hand side of which appears as a second term on the left of equation 24. At low light intensities, when photosynthesis is proportional to the intensity, all the € produced is removed by the catalyst, which is almost completely free. Therefore, equation l b takes the form

kx = ka€n and equation 18 becomes

or

According to the saturation curves (see later)

At high light intensity, near and above saturation, most of back, and the balance is given by

kx = kat or

reacts

.

lo00


or (18”)

As was mentioned before and will be discussed later, there is no appreciable induction period if one goes over to weak light, after having had strong light on for some time. That means that the distribution of the different steps must be about the same for strong and weak light, Le., the left-hand sides of equations 18‘ and 18‘‘ must be approximately equal. If the ratio y/z is not to vary more than 10 per cent from weak to strong light, the absolute value of the difference between equation 18” and equation 18’ cannot be larger than 0.1. Therefore

As the first factor is about 0.9, it follows that 0.9

k4 ka < -< k2 ks

1.1

or kr k i

-

k2

kGl

That is understandable if the difference in heat of activation between the back reaction and catalytic reaction is about the same for 7 and 6. We shall abbreviate from now on

At low light intensity, therefore, all steps are practically equally distributed.

At high light intensities, a slight shift is possible.

Our equations finally take the form (23’)

1001


One sees clearly from this equation that for low photosynthesis P , the denominator P , - P can be replaced by P , and

P = l+--(l--y) k8N ( t n which represents an oxygen yield proportional to the light intensity (k), giving one COZ for 8 1 - (1 - y) quanta. t n For very large k, the second term in the bracket of equation 27 becomes dominant and has a large value, because P , - P in the denominator is very small; P approaches P,, according to the law

{

+

1 J

B

2 8

P , - P = - (1 - y ) P , ka n kX Equation 27 can be exactly solved. Abbreviate

Then

The negative sign before the root is determined by the fact that P = 0 for k = 0 (no light). For comparison with experiment, the equation can be brchght into a more convenient form by dividing by P,.

Here P / P , is the photosynthesis with the saturation value P , as unity,

kN

while - = 1 is that light intensity where there are eight times as many 8Pm quanta per second absorbed' as oxygen molecules developed in saturation. For this intensity

Tf

cy

2P -=2 P, is small

+

- 2 / ( 2 + a)'~~

cy

4 =2

+

a

-

d4a+

If only part of the chlorophyll is covered by the carrier, a correction has to be made.

1002


P Half-saturation 2- = 1 is reached for P,

or

(kN)* = 4(1

+ 2a)P,

(29”)

Table 1 gives the values of PIP, as a function of light intensity in the above-mentioned units for a = 0.02, 0.1, and 0.3. The brackets indicate the number of quanta used to liberate one molecule of oxygen. The difficulty which arises when table 1 is to be applied to an evaluation of an experimental curve is the uncertainty whether all the measured TABLE 1 Values of PIP,,, as a funetion of light intensity

0.01 0.1 0.3 0.5

0.0098 (8.16 quanta) 0.098 0.292

0.7 1

0.781 0.868 (9.22 quanta) 0.964 0.981 (16.3 quanta)

1.5 2 3 5

0.0076 (10.5 quanta)

j

0.482

0.090 0.264 0.426 0.568 0.730 (13.7 quanta) 0.864 0.915 (17.4 quanta) 0.953 0.976

0.0755 0.247 0.343 0.452 0.582 (17.2 quanta) 0.718 0.800 (25 quanta) 0.876 0.932

chlorophyll is participating in photosynthesis (for example, if the amount of carrier is less than that of chlorophyll, N is the amount of carrier). It is therefore better to measure the light intensity with respect to that intensity a t which half-saturation is reached

k

k7

ICN

2

= 8 3-1

according to equation 29”. One gets the corresponding table by multia),i.e., by 2/1.02, 2/1.1,and plying the first column of table 1 by 2/(1 2/1.3. Instead, it is simpler to plot log P against log IC and shift the experimental curve parallel to the axis until fit is achieved with one of the corresponding theoretical curves. That determines a. Then the absolute intensity a t half-saturation or the apparent quantum yield a t low intensity determines N .

+


1003

n/8N found in this way is equal to the reciprocal of the number of chlorophyll molecules supposed to exist in the "photosynthetical unit". It varies, according to the plant, between 1/500 and 1/5000. Flash illumination This section gives the theory of the experiments of Emerson and Arnold (4), in which flashes (duration 7) are succeeded by periods of darkness. Ih these particular experiment the flashes are of short duration to sec.). It is important for the simplification of the mathematical treatment that this time 7 is short compared to kT1. On the other hand, the dark interval T might be anything between IO-' and I sec. We use the fact that T is very large compared to kz', ky', (k3n)-', and (k5n)-'. As the state is stationary for successive flashes, the amount of every compound must return to its original value in a period 7 T ,Le., be the same a t the beginning of a flash as a t the end of the following dark period (beginning of next flash). That means

+

d

T+T

d

dt-=O dt

(30)

According to Kohn (12), the number of quanta absorbed during one flash is not more than 0.01 of the chlorophyll molecules. That nieans that any of the stable products z and y do not vary by more than 0.01 during one period. Therefore this amount can be replaced by the average amount (designated by a horizontal bar). Furthermore r+T

kxdt = k72 as k is zero during the dark period. In analogy to equations l a , Za, 3a, T on the following 4a, we find (omitting to write the limits 0 and 7 integrals)

+

k75* =

lez

j .$ dt + 1 k5

q.-lu dt

(IC)

and, analogously, equations 2c, 3c and 4c. One concludes k3

& u d t = k6

i.e.,

kl independent of s.

1

q,udt = kg

Eudt = k5

j uqdt

qa-l~dt

(31)

(31')

1004

'


It follows, then, that all 3 among themselves and all # among themselves are equal and kr(2

- 8)

=

/ (k& - k47) dt

(32)

Without further restriction, we can only treat the cases of very weak and very strong light. For very weak light, the amount of C; produced during a flash, k72, is small compared to i n ; all the 5 and produced is taken up by the catalyst B, and nothing reacts back; the right side of equation 32 is negligible, f = 8. Therefore the amount of oxygen produced per flash, p , is

krN

P= 8

(33)

and the amount produced per second

kN r p = S T f r

(33')

If the distance between flashes is not large compared to the recovery time k;' of the catalyst, we have the following equations: Call vo the amount of inactive catalyst still present a t the beginning of the new flash; this is augmented by krN on account of the 5 and 7 production during the flash, the regeneration of free catalyst being negligible durk r N , regenerates ing the short duration of the flash. This amount, vo free catalyst according to a monomolecular reaction, and the amount of inactive catalyst must again have fallen to vo a t the beginning of the next flash; ie.,

+

(vo

+ k7N)e-k6T = uo

or v,, = krNe-h'T(l

-

We then have as free catalyst available a t the flash n - vo = n -

(34)

The photosynthesis per flash is proportional to the light intensity k and independent of the dark period T, until kz (the back reaction) is no longer negligible compared to kr(n - u0) and krN is not negligible compared to n. From then on we have deviation from linearity in respect to k and possible dependence on the dark period. For very strong light, there is more 5 and 7 produced during a flash than corresponds t o the amount of catalyst, n. In a time which is short compared t o k;', the catalyst is completely inactivated, Le., a total amount 4([ v ) = n is transformed into the next higher stable compound, z and

+


1005

y. -411 the rest reacts back before the next flash and before an appreciable amount of catalyst can be reactivated. 4 must therefore be large compared to ka, which is about 80. On the other hand, 4 is, according to the shape of the saturation curves, about one-tenth of k3n. The latter, however, can not be greater than about 50,000. Therefore we select 4 about 1000. Again call vo the amount of catalyst still inactive a t the beginning of the flash. k r z of each [ and k r y of each r) is produced. Of these a total of n - vo is promoted, but as the reaction rates are k3& = k 3 ( k d ) u and k6r)u = kS(krg)u, each E loses n-~ - vo k32 4 k33 ksg

+

and each 7 loses n 2 -0 4

-

k32

ks g ksg

+

to the catalyst. Therefore, we have

of each $. and a corresponding amount of each r) left. This [ then reacts back monomolecularly, so that after the time t

is left. This and the corresponding quantity for r) is introduced into the right-hand side of equation 32. In the calculation, the integral over r and over the time the catalytic reaction takes is neglected, as is e-k2T (which means that everything has reacted back by the time the next flash comes). One then finds

or = k68 This need not mean’ 5 = 8. The peroxide produced by the flash is coming from the 1’s

kgg k33

+ k6g

(35)

n-vo-n-v~ 4 8

Going over, after a long series of strong flashes, to a series of weak flashes and observing whether a n induction period due t o a shift in t h e value of y exiata could decide this question. For flashillumination this experiment has not been carried out.

1006


and therefore does not permit a conclusion to be drawn as to the ratio of ka and ks. For vo we tind, through an argument similar to that for weak light, ne-kST

= vo

or p,

n-(l 8

I

>

Here we have light saturation, and if kJ' regenerated in the dark period) n p, = -

1 (all the catalyst can be

(36')

8

independent of T. Otherwise, p is diminished by the factor 1 - e--k6T, Le., k;' is the Blackman period. The number n calculated from flash saturation agrees sufficiently well with the one calculated from continuous illumination. The details of photosynthesis in the region of intermedide light are -cult to evaluate in the general case. The calculation will be limited here to the case in which two restrictions are fulfilled. First, the flash duration is so short that no appreciable amount of t and 7 disappears during the flash, Le., 7

>

8

kN K 2 v N >> - (see equation 24) 8

In this case, the carbon dioxide intake process is not limiting, and all the chlorophyll" is covered by intermediates (including the carbon dioxide complex). The E's and 7's are present in amounts too small to matter. All the intermediates can be attacked by light in the same manner. There10 Or, if there is less carbon dioxide carrier than chlorophyll, a constant part of the latter.

1009


fore, all the z’s and w’s should give (at least approximately) the same yield of fluorescence. There are, in fact, according to Katz, Wassink, and Vermeulen (22, 23, 24) Chlorella algae which have a constant efficiency 9 0 of fluorescence yield for the range of light intensity from very weak light up beyond saturation photosynthesis. 9 0 is about 0.001. It is the fluorescence efficiency of chlorophyll with the intermediates. If there is less carbon dioxide carrier than chlorophyll, N is the amount of carrier. Call N‘ the amount of chlorophyll, 9: the fluorescence efficiency of chlorophyll loaded with x or y, and 9: that of bare chlorophyll. Then 90

=

tN N

9 0 -7

+

iN’-N91

r

7 - 91

N

i N - (91r - 90) -7 N

If, now, the light intensity is increased further for these algae, the fluorescence yield goes up and finally reaches another constant value 91. This is explained by the assumption that now the carbon dioxide intake mechanism cannot follow and therefore z and y are being replaced by the bare chlorophyll (or chlorophyll covered with loosely bound carbon dioxide). This has a higher efficiency of fluorescence, namely 9:, so that 9: = 91. From equation 26 one has, after replacing N by N - X , 2

=

1 - (N 8

X

=

- X)(1 - y)-l

(43)

or

N - 8 ~ (-l 7 )

(43’)

and equation 21 takes the form

Multiply by

k

- (1 - y)-l 8K3~

kN (1 8Ka v We now call

2* - 2 1

{

- y)-l

-1

kx = k ( 1 - ?)-I --

kx

K ~ v K ~ v

(44’)

kx = 2 and multiply by (1 - 2)

Ks v

kN ( 1 - y)-l + kN (1 + 8K3v Kz VN

?)-IJ

1

- --kN (1 - y)-l 8Ks v

(44”)

1010


With

One can write (equation 44”)

- Z(l + B ) = -BO

2’

(44”’)

Tneref ore

2 2 = (1

+ B ) f d(1+ B)2 - 4BB

(45)

The negative sign must be chosen, because, for k = 0, both Z and B are zero.

P

+

Equation 45 is of the same form as equation 29’ with 2 instead of - (1 P, kN a)-’,B instead of -(1 a)-’,p instead of -. Therefore 2 plotted 8Pm l+ff against light intensity k gives a curve of the same general shape as photosynthesis plotted against light intensity, rising first linearly and then leveling off to a constant value. But Z is proportional to k z ; therefore

+

z

m

L is first constant and then goes down to zero

k

m

k-’.

Correspond-

ingly, X is first zero and then rises t o N . In more detail, one finds from equation 45 for small intensities

Z = Bj3[1 - B(l or 2 =

N - (1 8

- p)]

4

- y)-’ [1 - K kN (1 x-

TLat gives

X At high intensities

or

=

N

kN T - 4(2 + y) = N K (1 N - y)-’

(459

1011


and (45")

One can ask when is X = + N , Le., when is half of the chlorophyll bare, and half covered with intermediates? In our interpretation, that occurs a t a light intensity where the rise in the efficiency of fluorescence has reached half its final value. From equation 43 it follows that then 2 =

1 --(I 16

- y)-l

If we call k' the value k then has,

Equation 44, after division by N , takes the form

or

If, as seems reasonable, the maximum speed of the catalytic reaction, K2vN, is large compared to the speed K ~ ofv regeneration of catalyst A and y is small, then equation 46 says that X / N is 3, when there are absorbed in every chlorophyll molecule sixteen times as many quanta per second as molecules of catalyst A can be regenerated in the same time. For the form of the curve, the ratio K3/K2N is decisive, just as k,/kan is for photosynthesis. The shape of the fluorescence curve, which first rises very slowly, demands, according to equation 45', that K v N be large. The rise gets steeper and more sudden the closer /3 is to 1, Le., the smaller the ratio ___ sKsv If this ratio is small, the calculation can be made more KzuN ' directly; equation 45 is divided by PB. We have, on the right-hand side,

2 2 - 16ks

Bj-m ( 1 - 7)

=

162

(1 - 7 ) = 2(N

-X)

1012


Therefore

Table 3 gives X / N as a function’’ of B for four values of p - 1. It follows from the results and from a general discussion of equation 47 that, a t least for 1 - @ 5 0.1, X / N is about 0.5 for B = 2. For B > 2, X / t is represented well by

The curve starts out flatter and flatter, the smaller 1 - 6 is, and then rises more steeply toward B = 2. TABLE 3 fraction of denuded chlorophyll)

a8

a function of 0 and B

x B

-

I

8Kav FN 0.0s

0.01 0.1 0.2 0.5 0.8 1 1.25 1.5 2 3 5

0.001 0.01

0.079 0.24

0,001 0.005 0.012 0.038 0.11 0.183 0.288

0.539

0.522

0.82

0.81

-1-

!

I

I -

;% K

-

0.01

-

8Kav K TN o.ooO1

0.0001 0,001

0.00001

0.01 0.032 0.09

0.01

0.346 0.52 0.67 0.802

0.33 0.5 0.63 0.80

To evaluate an experimental curve for the fluorescence efficiency plotted against light intensity, one should first determine the midpoint in the increase of efficiency. Selecting a point a t which the increase is a fraction different from 1/2, the ratio of the corresponding light intensities will determine B ; e.g., both B = 0.95 and p = 0.99 have X / N = 0.52 a t B = 2. But for the former value of p, X / N = 0.19 a t B = 1; for the latter, X / N = 0.09 at the same value. fl being determined, one gets K3vfrom equation 46 if one measures the absolute amount of light absorbed, k’N, at the midpoint (there might be a correction necessary if carbon dioxide carrier is present in a smaller amount than chlorophyll). 11 Although x and y go down, kx and ky always increase and finally approach B constant value for high intensity. The decrease in photosynthesis occasionally OCcurring for very strong Iight must be due to other causes (photooxidation?).


1013

TFR carbon dioxide intake i s limiting; catalyst A is poisoned Under certain conditions, e.g.. if a cyanide in appreciable quantities is sdded, the increase in fluorescence efficiency starts a t much lower light intensity, but the final d u e of this efficiency is the same as without poison. Under these circumstances, the saturation value of photosynthesis is also diminished; the light intensity, a t which fluorescence efficiency is appreciably increased, is then lower than that a t which saturation of p otosynthesis is approached. We interpret this by the assumption that the catalyst A is poisoned; in other words, there is an equilibrium established. Poison

+ (free + inactivated catalyst A) e (A, poison)

That means that the number v is heavily diminished, say to v l . s o w 8K3v -is independent of v ; that means that the shape of the curve KavN X / N against B is independent of the poison. What is changed is the connection between k and B , Le., the scale, if absolute light intensities are plotted. The intensity k, a t which a certain X , Le., a certain efficiency of fluorescence is reached, is proportional to v . There is a second change. Photosynthesis is now limited not by the catalyst B in the main reaction, but by the carbon dioxide intake, i.e., catalyst A. That is the case if the limiting value of kx according to equation 45"

is small compared to $ken. This implies 'that the catalyst B is not affected by the poison, or a t least much less than catalyst A. In this case photosynthesis is given by

In B , y must be left out. Photosynthesis is then directly proportional to the difference between the value the fluorescence (not the fluorescence efficiency) would have if the chlorophyll were always bare, and the true value. That the final efficiency of fluorescence is the same with and without poison means, of course, that in both cases the chlorophyll is practically completely denuded. A phenomenon similar to that in the presence of poison is observed if the temperature is lowered. This means, of course, that the temperature coefficient of K 3is larger than that of ke. As K S vis larger a t room temperature than ksn and the saturation of photosyntheBis is then determined by catalyst B, the temperature coefficient of saturation will first be that of ka. If the temperature is lowered further, K S Vbecomes the limiting factor

1014


and the temperature coefficientis determined by that of Ks, i.e., it is higher a t low temperatures, as discussed by Wohl (28). In flash illumination, the intake mechanism alone does not provide a fixed saturation for each single flash. Experimentally, the amount of oxygen developed by a single flash for very strong light is the same whether poison is present or not, but the Blackman period is much greater in the presencc of poison (see page 084). That can be explained if the oxygen development of the single flash is still determined by the catalyst B, provided the catalyst A has time to replace, in the dark period between flashes, the 2 transformed by the flash into either y or back to X. If, however. the dark period is too short for that (but still long as compared with k;', so that all of catalyst B is free by the beginning of the next flash), there is established, after many flashes, a stationary state wherein the amount 8 of z l , produced during the dark period by catalyst A, is equal to the amount removed by the flash. kT21

= (kT5

-

kTQ)

= 8

(49)

We are still assuming that the flash is very short and that k7 < I, so that only a fraction of all chlorophyll molecules absorb a quantum during a flash. The saturation C L I ~ T T of the single flash as a function of the light intensity is dependent only on the product k4(z y ) r , independent of what the individual factors of that product are, if the conditions concerning T and T are as we have assumed. Call the form of the flash saturation curve when A is not limiting

+

Then, from equation 49,

P

=

Pd(4

(509

This equation is significant only for strong light, although true even for weak light (or in the absence of poison). For weak light, z is about N / 8 and therefore k ~ inz equation 49 is determined; 8 adjusts itself to this value by keeping X so small that

N K ~ v X= k r 8

N That is true as long as X < < -, Le., 8 8Kzv

> > k7

In the absence of poison, this condition is violated only beyond photo-

1015


synthesis saturation. For a poisoned plant V I < < v. Equation 51 gives the range of the light intensity for which the catalyst A is not limiting. For strong light, on the other hand, while the plant is poisoned or a t low temperature, z1adjusts itself according to equation 49 to (9, which is now determined by catalyst A. Unfortunately, the integration of the differential equation 11 would involve more work than is justified. We will therefore discuss the process during the dark period only approximately. J A X o be the amount of X still present a t the end of the dark period. During the flash, this is augmented by k r s . We assume that this is large compared to the total amount of available catalyst A. As K 2 N is large compared to K 3 , the amount v1 of X will he changed within a very short time (possibly even during the flash) into $1, making all of the poison-free catalyst A inactive. Then the change of X into 21 occurs a t the rate a t which inactive catalyst A is regenerated, i.e., a t the rate of about K3v1. This process lasts 2’ seconds. Finally X becomes so small that K2vlX become6 comparable to K3v1 and more and morc of the poison-free catalyst goes into the active form. The exact time-dependence of this process is complicated, but we assume that it can be neglected both as to the s1 produred and the time consumed. Therefore 6 =

v1

+ K3vlt’

We should write 5“ for t’, provided T is smaller than the time needed to destroy all X . But as the saturation curve docs not vary very much if the argument of j in 50 is large, we will write’* 6 =

VI

+ K s v ~ T= (1 + K ~ T ) v ~

(52)

Therefore for strong light, equation 52, together with eq&tion 50’, describes the dependence of oxygen production per flash on the time between flashes. Under certain conditions,-namely, flash duration short against (k3n)-’, < ks, and dark period long against ksl,--we can consider equation 41’ as 50, solvcd for k m ; we get then for p , the production of oxygen per flash,

p , being n / 8 , the value of p for a long dark period.

If one plots P as a Pm

function of the time interval T , one gets exactly the same curve (equation N

In other words, equatioii 52 is either 9 or k - r , whichever is smaller. 8

1016


41’) as if one plots in normal flash saturation

P,

as a function of the light

energy per flash k7. v l K J ’ takes the place of k7N. The curves given by Weller and Franck (26) for the production of oxygen per flash, p, as a function of the flash period, T , have indeed the shape of saturation curves.13 Because of the approximations made, one should not values of T. expect equations 52 and 53 to be exact for the largest k 7N It is seen from table 2 that is about 0.75 for - 0.9. Therefore Pm

8Pm

-

one would expect that in the experiment plotted above, where is reached after about 0.1 sec., vlKs

-

= 0.75 Pm

9n see.-’

Persistence of carbon dioxide intake after the e n d of illumination Under those conditions of light intensity under which the efficiency of fluorescence is increased beyond its normal value (and under these conditions only), there is a delay in the intake of carbon dioxide a t the beginning of an illumination. This is distinct from the “induction period,” because there exists a compensatory intake of carbon dioxide after the illumination has stopped. The connection with fluorescence efficiency makes it clear that the effect is bound up with a delay in the establishment of the stationary value of X . For light strong enough so that almost all chloroN ) , the delay in intake is due phyll is bare in the stationary state ( X to the fact that there is a supply of x1 present a t the beginning on which the photoreaction can feed. At the end of the illumination, carbon dioxide is still taken in to provide a partial covering of the chlorophyll with xl. One would expect the following time dkpendence of the continuation of carbon dioxide intake after the illumination has been stopped. In the case of strong poisoning, one would expect vl, the amount of available catalyst A, to be small compared t o the amount X of bare chlorophyll to be covered (for very strong light X is almost N ) . The supply of carbon dioxide is now determined by the speed of reactivation of the unpoiaoned part v1of catalyst A. One has then

-

13

For small T one gets, neglecting 1 with respect to KIT:

%K*T

k,

P _ P L - - 1 _ Pm

1

+-k: n kr

k:n

+

k12

This deviates less from a straight line than an exponential function by the factor k:/(k:n kd.

+

h THEORY

OF PHOTOSYNTHESIS

1017

a constant intake equal to Kavl per second which lasts for a time t', which time is almost equal to

This is followed by a small intake of short duration which follows a different law (when almost all the chlorophyll is covered, X becomes so small that KzvlX is comparable with or smaller than K3~1;then more and more catalyst A, up to vl, is present in the activated form). The behavior would be different if v1 were comparable with X. That might first be the case in the absence of poison, but there the intake after illumination is too small or too fast to be investigated experimentally. In the presence of poison, when the phenomena now under discussion are noticeable, it is very improbable that V I is comparable to N ; that would imply that the limitation in carbon dioxide intake is due to the smallness of K s and that in the absence of poison v would be much larger than N , which is highly improbable. Because of this, the lengthy calculations for this case will not be given. We state only that here, too, the initial speed of carbon dioxide intake after the end of illumination is K3v1, and has

XO seconds. dropped to 0.637 of this value after Kay1 The experiments of Aufdemgarten (2) have shown that the carbon dioxide pickup after illumination lasts for about 2 min. so that, according to equation 54, in this case

On the other hand (see page 1016) under similar conditions the dark period needed to give nearly full saturation in flash illumination is only 0.1 sec., leading to

K3v1 = 9n Therefore

N

-

(55')

1080n

in good agreement with other estimates. Physically (as mentioned on page 990), this is due to the fact that after strong continuous illumination with the catalyst A poisoned, practically all of the chlorophyll is denuded and has to be covered after the end of the illumination, while for flash illumination the saturation curve is rather = 0.90 only 1.15n,

= 0.75 only 0.9n, and for

flat on top and so for Pm

has to be replaced between flashes.

Pm

1018


V e r y low concentration of carbon dioxide Instead of poisoning the catalyst A, one can use a very low concentration of carbon dioxide to make the carbon dioxide intake limiting. We had assumed that the establishment of the equilibrium (7) is extremely rapid. But if very little X" is present, the supply of bound carbon dioxide (XI) can become limiting even if practically all catalyst A is free. Equation 10' shows that

This formula shows that the processes considered in this paper are independentx4of the carbon dioxide concentration, if this is sufficiently high (page 981); namely, if (COZ)is large compared to K , when the last fraction in equation 57 can be set equal to 1. In this case we have assumed, in conformity with experiment, that KaN is large compared with Ks. But it follows from equation 57 that this can be reversed if (CO2)is taken very small. If it is taken small enough so that

KaN

< K3

K z N , < ks -n 8

(58)

the carbon dioxide intake mechanism will be limiting, but not as in the preceding paragraphs because catalyst A is reactivated too slowly, but because it has too little loose compound RHCOZ to work on. Experimentally (14, 15) that is the case if (COa) = 0.006 per cent or less. For the sake of simplicity we shall limit ourselves to the case where the preceding inequality signs (expression 58) are fulfilled by a wide margin. Then the catalyst A can be considered as being present almost wholly in activated form. For continuous illumination equation 21 takes the form

kX

- now being negligibly small. Ksv We have then, as in equation 48,

If we now introduce the abbreviation

14

At least if no secondary effects occur.

A TEEORY OF PHOTOSYNTEHSIS

1019

one finds from equations 59, 60, and 61,

P, is therefore the saturation value. In flash illumination we limit ourselves, as above, to flashes very short compared to k;’, (&vN)-’, with a light intensity sufficiently large that k

M T

> > n,

so that each flash is saturated, provided the flashes are

sufficiently widely separated. The equation for the change of X in the dark period after the flash is therefore, according to equation 10, dX -= -K~vX dt Using an argument similar to the one that led to equation 34, one finds

+

( k 3 ~ XJe-g2’T = Xo

(64)

where X Ois the amount of X still present a t the end of a dark period, Le., a t the beginning of the next flash. This, together with Xo = N - 85 leads to

k~ is, with the highest intensities used, not more than 0.01 (12). Therefore the bracket in equation 65 is appreciably different from 8 only if the denominator of the second term is very small. This denominator can therefore be replaced by K p T .

e = N

KzvT 8KzvT kr

+

(65’)

One then gets, as in the discussion leading to equation 53,

as the equation connecting the photosynthesis per flash, p , with the dark period T . Here we h d , for the first time, that even when we use a light intensity

1020


sufficient nearly to saturate an isolated flash, the time interval necessary to permit a certain value of P depends on the light energy k r per flash.

-

Vm

- -

1 ’krN That is, assume k r - - 2, KZv - We find from table 2 100’ 8 p , 100’ the results given in table 4. The carbon dioxide uptake after the end of a continuous illumination which has partly denuded the chlorophyll ( X = X O )is governed by equation 63 or X = Xoe-Kz’T

and the speed of the uptake is

-d X

11

__ = K2vXOe-K2’T

(67)

dt

TABLE 4 Photosynthesis per flash with very low carbon dioxide content

T. . . . . . . . . . . . . . . . .

0.05 0.56

0.1 0.75

j

0.2 0.92

0.38

0.52

1

0.63

P ............... p,,,

I

~

1

1

i.9992

0.78

-

~

1

~

aec.

0.9999 kr = 1 100 0.83

kr =

1 200

This is in agreement with the measurements of McAlister and his collaborators. The time needed for this uptake (-2 min. if (COS) 0.006 per cent) has led to the above estimate, KZV 0.01, under these conditions.

-

-

A discussion of the assumptions A starting point of the discussion is the possibility of the saturation of an individual flash, occurring when only a fraction of all chlorophyll molecules have absorbed a quantum and giving per flash a number of oxygen molecules

(a>

of between N/500 and N/5000, much smaller than even

the number of absorbed quanta. If one rejects the photosynthetic unit, this leads almost inevitably to the assumption that there is present in this small amount a substance which is necessary as carrier of the process. The speed of reaction of that substance, which we call catalyst B, is then determined experimentally by the Blackman period ( k i l ) (see page 984). What happens to the material transformed by light, which is not carried further by the catalyst? There are three possibilities: It simply accumulates on the chlorophyll, it is deposited elsewhere, or it reacts back. If it accumulated on the chlorophyll, it would cover the chlorophyll more


1021

and more, that is, whenever there is a deviation from linearity between photosynthesis and intensity, there should be a progressive diminution of photosynthesis, contrary to fact. Secondly, the “waste products’’ could leave the chlorophyll and go into the rest of the cell. Then there would exist saturation for oxygen development, but not for carbon dioxide intake. However, the saturation curve is the same for both. Therefore, we must accept the third possibility that the “waste products” react back. The next question is, in what stage of photosynthesis does the catalyst react? The distribution of the steps is not appreciqbly dependent on light intensity. That is possible only if the same bottleneck exists after every step. Now for the intake mechanism. The increase in fluorescence efficiency must mean that the chlorophyll is covered in a different manner. I t is known, experimentally and theoretically, that substitution of a photoinsensitive for a photosensitive substance increases this efficiency, no energy being used for a photochemical reaction. The (absolute) increase in efficiency is of the order 0.001. We know of some photoinsensitive substances being present, like the catalyst itself, the f“s, and 7’s. But in photostable solution chlorophyll never has an efficiency of fluorescence nearing 1, which would be necessary if substances present in such small amounts should be responsible for the observed increase. Therefore it is reasonable to assume that the chlorophyll as a whole is deprived of substances able to undergo photochemical reaction. What step is responsible for this denudation? There are several reasons which speak against the main reaction being responsible. Firstly, for different plants the light intensity a t which the increase in fluorescence efficiency takes place is situated differently in respect to the intensity where photosynthesis saturation sets in (see figure 1). Secondly, if the main catalyst B were responsible, one would expect that poison (cyanide), which induces high efficiency a t low light intensity, should affect flash saturation so that the amount of oxygen developed by each flash would be diminished (because n would be diminished) but the Blackman period k;’ would be unaffected. The opposite takes place; the dark period necessary for recuperation is lengthened, but the oxygen developed per flash remains the same“ (see page 984). Therefore, one must assume a different mechanism to be responsible for l6 T h a t might also be explained by having two catalysts acting in succession, so t h a t catalyst B would not be directly affected by the poison but through a catalyst D, which would be responsible for the regeneration kr of catalyst B. But this assumption does not explain the other points.

1022


denudation (increase in fluorescence efficiency),-a mechanism that can be poisoned by cyanide, while catalyst B cannot. What is this mechanism? First the poisoning is of a character that often occurs with catalysts. Secondly, there is a one-to-one correspondence between increase in fluorescence efficiencyand delayed carbon dioxide intake. Thirdly, Ruben and Kamen (20) have shown that the carbon dioxide exchange is affected by a catalyst that brings the carbon dioxide from a weakly bound to a strongly bound form (see page 979). The assumption that we h a w made follows then as the simplest. We still have to discuss the reason why it has been assumed that reacts back to X and not to r1 , as one might think in analogy to the other t's (see pages 988, 989). If t1reacted back to zl,the only loss z1would undergo at strong illuniination per second would be the amount "forwarded" by the catalyst, Le., about k6n/8. On the other hand, under our present assumption, the loss in z1 per second is kzl , because every z1 that a,bsorbs a quantum is either influenced by the catalyst or reacts back to X. The intake mechanism would therefore have to supply, in the first case, the amount k 6 n / 8 (or less, if the intake mechanism were limiting), and in the second, present case, kzl . Balance between the carbon dioxide supply and the z1 loss determines the amount, X, of denuded chlorophyll. Under the first assumption, the loss is independent of light intensity a t saturation and therefore X should have a finite value smaller than N if photosynthesis saturation is reached. If,now, poison is added, the rate of carbon dioxide intake is diminished, and even if the rate of photosynthesis is also changed, the highest valuc of X should be different from that without poison. Experimentally, however, the efficiency of fluorescence is the same with and without poison, after the rise is completed. That means that X is the same in both cases, which seems difficult of attainment if X is not about N in both cases, Le., if, finally, practically all the chlorophyll is not denuded. On the basis of our assumptions, when the carbon dioxide intake mechanism has to make good the loss k z l , it is clear that, a t sufficiently large k , this implies a N ) whatever the finite speed of the mechanism of vanishing z1 (X carbon dioxide supply, so that for sufficiently strong light the result is the same with and without poison.

-

Available energy and reaction velocities The energy difference between C02 HzO and one-sixth of C&H12OE 0 2 is 132 kg.-cal. We take one quantum per mole to correspond to 43 kg.-cal., of which 8 are needed, Le., 344 kg.-cal. Of the reaction velocities, wc estimate

+

+

1023


where +lo-" is taken to be the collision factor in the liquid (17). That leads to a heat of activation &8 = 1 kg.-cal. Further (page 1005), OS

N

108 = 1011e-=

10" would be a rather small factor for a simple molecule, but seems reasonable for such a large molecule. That makes Qz = 11.2 kg.-cal. We now have to see whether sufficient activation energy is available to make back reactions so small that they do not disturb our calculations. First consider catalyst B. We assume that a t low light intensities practically everything is active. Therefore the equilibrium u Ft. 0 must be almost entirely on the side u. If we permit 0.01 of 0, that means that u is 2.5 kg.-cal. above u. Furthermore, in flash saturation, t or 7 reacts back very quickly after the flash, while 0 persists for 1/50th of a second before going back to u. During this time we want no appreciable back reaction yr

+

0

-+

t

+u

The speed of this reaction would be k:Nn

and we want for a catalyst molecule ks > kjN or 80

0'8

> f 10-11 1 0 1 9 e - ~

If we allow k:N = 5, that means Qj = 9, or, as the forward reaction has an activation energy Qa of 1, an energy difference between $. u and y v equal to 8 kg.-cal. That gives for one of the processes r -+ -+ y, the following diagram :

+

* I I

I I

I I

:

9

43

t

Y+U

I I

I

I

i

Y+

+

1024

JAMES FRANCIC AND KARL F. HERZFELD

+

It follows that the energy level of y8is 43 - 11 1 - 9 - 2.5 = 21 kg.-cal. above that of z 8 . The step from y. over to .re+l is subject to quite similar arguments, cxcept that this leaves, in addition, a quarter of a peroxide molecule. We call X1the amount of energy by which such a peroxide molecule is above free 02. Furthermore, w~ call TZthe binding energy of the carbon dioxide complex zl. Then M'C get the following balance. COZ-+ COZcomplex z1 + y1-

- 22 or

zz

+21 +21 -

-+

1 -21 4

1 . . . = 6-Sugar

. .. =

+ O2

134

+ 8 X 21 - Zl = 134 kg.-cal. 168 - 134 = 34 kg.-cal. = Z1 + ZZ -22

-

One might suggest that the binding energy of the carbon dioxide complex, 22, 10 to 20 kg.-cal., and Z1, the energy of the peroxide above free oxygen, 24 t o 14 kg.-cal. The speed of the formation of 5 in the back reaction is, under these assumptions,

k:

x

1

10-'nN = 2

x

lo-"

x

x

lo-'

x

10l6 x N

1 2

= -

x

104N

As kz is about &k3n, about one-tenth of the produced reacts to z I , while nine-tenths decomposes again to y.. That is, it would take about two days to bring back a half-and-half distribution if all the chlorophyll were originally covered with y. REFEREXCES (1) ARNOLD, W . : J. Gen. Physiol. 17, 145 (1933). (2) AUFDEMGARTES, H.: Planta 29, 643 (1939); 30, 343 (1939). H. : Cold Spring Harbor Symposia Quant. Biol. (3) BURK,D., AND LINEWEAVER, 3, 165 (1935). (4) EMERSON, R . , AND ARNOLD, W.: J. Gen. Physiol. 16, 391 (1931); 16, 191 (1932). W . : J. Gen. Physiol. 16, 397 (1931); 16, 191 (1932). (5) EMERSON, R . , AND ARNOLD, (6) EMERSON, R., . ~ K DLEWIS,C. M.: Am. J. Botany 26, 808 (1939). J., FRESCH,E . , AND PUCK,T.: Unpublished work. (7) FRANCK, J., AND LIVINGSTON, R . : J. Chem. Phys., in press (1941). (8) FRANCK, (9) FRANCK, J., AXD TELLER, E . : J. Chem. Phys. 6, 861 (1938). (10) GAFFRON, H., AND WOHL, K . : Naturwissenschaften 24, 87, 103 (1936). AND COWORKERS: Planta 20, 699 (1933). (11) HARDER (12) KOHN,H. J.: Kature 137, 706 (1936). W . M., STAUFFER, J. J . , DUGGAR, B. M., AND DANIELS,F . : J. Am. (13) MANNING, Chem. SOC.60, 266 (1938). (14) MCALISTER, E . D . : J. Gen. Physiol. 22, 673 (1939)

MEASUREMENT OF ANGLES OF LIQUID LENSES

1025

(15) MCALISTER, E. D . , AND MYERS,J.: Smithsonian Inst. Pub., Misc. Collections 99,6 (1940). (16) ORNSTEIN, L. S., WASSINK,E . C., REMAW, G. H., AND VERMEULEN, D.: Enzymologia 6, 110 (1938). (17) RABINOWITCH, E.: Trans. Faraday SOC.33, 1225 (1937). (18) RIEKE,F. F . : Unpublished work. (19) RIEKE,F. F.: Oral communication. (20) RUBEN,S., KAMEN,M. D., HASSID,R. Z., AND DEVAULT, D. C.: Science SO, 570 (1939). (21) VAN XIEL, C. B.: Arch. Mikrobiol. 3, 1 (1931). (22) VERMEULEN, D., WASSINK, E . C., A K D REMAK, G. H.: Enzymologia4,2M (1937). (23) WASSINK, E. C., AWD KATZ,E.: Enzymologia 6, 163 (1939). (24) WASSINK, E . C., VERMEULEW, D., REMAW, G . H., A N D KATZ,E . : Enzymologia 6, 100 (1938). (25) WEISS, J., hWD RABINOWITCH, E . : Proc. Roy. S O C . (London) A162, 251 (1937). J. : Unpublished work. (26) WELLER,S., AND FRAWCK, (27) WILLSTATTER,R. : R’aturwissenschaften 21, 252 (1933). (28) WOHL, K . : Z. physik. Chem. B37, 105, 122, 169, 106, 209 (1937).

IXVESTIGATIOK OF THE TENSIOK MECHAIL’ISMS RESPOSSIBLE FOR LEKS FORMATION AXD A NEW METHOD FOR MEASURING T H E ANGLES OF LIQUID LEYSES’ SEJ’ILLE F. MILLER

Research Dzvzszon, The New Jersey Zinc Company (of Pennsyluanza), Palmerton, Pennsylvania Received Aprzl 8, 1941 I. INTRODUCTION

In this paper a n attempt is made to coordinate several existing theories relating to the behavior of water-insoluble organic liquids on water or dilute acid substrates so as to bring these theories into agreement with the demonstrable fact that both spreading and lens formation are spontaneous processes and therefore must involve decreases in the free energy of the system. The lens formation of those liquids which form films on water surfaces is ascribed to a decrease in free energy (-Afo) which occurs through the orientation of the molecules in the film. Several important consequences of this concept are pointed out, and it is shown that thP behavior of real systems conforms to these conclusions. Presented before the Division of Colloid Chemistry a t the One Hundredth Meeting of the American Chemical Society, held in Detroit, Michigan, September 9-13, 1940.

Contribution to a Theory of Photosynthesis

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