J. theor. Biol. (1976) 56, 401-416
On the Energy Upconversion Mechanism of Light Utilization by Chlorophyll in Photosynthesis E. ROLAND MENZELJf
Department of Chemistry, University of Kentucky, Lexington, Kentucky 40506, U.S.A. (Received 27 December 1974, and in revised form 5 March 1975) A model for the primary mechanism of light utilization by chlorophyll in photosynthesis, involving singlet-triplet annihilation, has recently been proposed (Fong, 1974). In that model it is asserted that the photosystem II fluorescence yield doubling observed on strong illumination is predicted exactly. In this paper the model is critically examined. It is shown that a number of fundamental errors occur in the above model, such that the doubling prediction is incorrect. It is shown that such doubling can be accounted for only if a reaction center chlorophyll in its first excited singlet state interacts with an antenna chlorophyll in its lowest triplet state, and that this doubling arises independently of chemical activity. In view of this reversal of the physical situation from the Fong model, there is no longer justification for a highly symmetric reaction center dimer adduct configuration. The consequences of the corrected treatment are examined. Within the upconversion framework a model is proposed, which is consistent with the photosystem II fluorescence yield doubling on strong illumination, as well as with the absence of such doubling in photosystem I.
1. Introduction A model concerned with the basic mechanism of light utilization by chlorophyll in photosynthesis has been proposed (Fong, 1974). In this model (henceforth termed the F K F model) pairwise interaction between reaction center chlorophylls in the lowest triplet state with antenna chlorophylls in the first excited singlet state via the singlet-triplet (S-T) annihilation process is suggested. The S - T annihilation is taken to lead to upconversion to a charge transfer state, which can undergo a chemical transition to initiate enzymatic processes. A crucial theme in the F K F model is the assertion t Present address: Xerox Research Centre of Canada, 2480 Dunwin Drive, Mississauga, Ontario L5L 1Jg, Canada. 401
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that the model exactly predicts a doubling of the fluorescence yield of photosystem II (PSII), as observed experimentally. In this paper the rate equations utilized in the F K F model, leading to the PSII quantum yield doubling prediction, are examined. In section 2 the pertinent experimental findings and the F K F model are briefly reviewed. It will be shown in section 3 that a number of fundamental errors occur in the F K F rate equations, as a result of which the above doubling prediction is incorrect. It will be shown that the F K F rate equations are, in fact, not applicable to the system at hand, and that their use leads to the result that no photosynthetic action takes place. In section 4 the correct rate equations are taken up with particular emphasis on the possibility of prediction of increased PSII fluorescence yield under strong illumination. Such an increase will be shown to be possible, though a doubling cannot be predicted with certainty. This doubling does not result from quenching of the chemical transition from the charge transfer state, as in the F K F model, but is entirely independent of the chemical step, a fundamentally different situation physically. It will be shown that this doubling can be accounted for only, within the F K F upconversion framework, if the reaction center chlorophyll molecule contributes its first excited singlet state to the upconversion process! Therefore, the justification for the highly symmetric reaction center dimer configuration is no longer present. It will be shown also that triplet-triplet (T-T) annihilation cannot be ruled out, as done in the F K F model, from having a possible role in the upconversion to a chemically active state, on the basis of the above fluorescence yield increase on high illumination. In section 5 the various alternatives to the F K F model, within the framework of an underlying upconversion scheme, are discussed, with attention to the experimental information needed to discriminate between these alternatives. Finally, a model utilizing an upconversion scheme is proposed. This model is consistent with the fluorescence yield doubling in PSII, as well as with the absence of such doubling in photosystem I (PSI). The occurrence of an upconversion process is plausible in view of recent in vitro reports (Menzel, 1974).
2. Review of the FKF Model, Pertinent Experimental Findings, and the Physical Basis of the Upeonversion Process In the F K F model the reaction center of PSII is taken to be a highly symmetric dimer adduct configuration, wherein the two chlorophyll a molecules are bound together via two water molecules. An unsymmetric dimer structure, involving one water molecule only, is indicated by the work
ENERGY UPCONVERSION IN PHOTOSYNTHESIS
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of Ballschmiter & Katz (1969). In the F K F model a reaction center chlorophyll in its lowest triplet state interacts with an antenna chlorophyll in its first excited singlet state. Resulting S-T annihilation leads to upconversion of the reaction center molecule to a chemically active charge transfer state. Experimentally, it is found that the fluorescence associated with PSII incurs a doubling of quantum yield on high illumination intensity, as compared to low illumination. Such doubling is not observed in PSI. The PSII quantum yields on low and high illumination are about 0.025 and 0.05 respectively (ef. Govindjee, Papageorgiou & Rabinowitch, 1973). This fluorescence is predominantly bulk (i.e. antenna chlorophyll) fluorescence There are some 300 antenna chlorophylls to each reaction center. A central aspect of the F K F model concerns the prediction of the PSII fluorescence yield doubling. To this end, a "composite" energy level scheme, wherein no explicit distinction between antenna and reaction center chlorophylls is apparent, is taken to represent the situation. In this scheme the ground state of the system is denoted by 10). State I1) is the lowest triplet state, 12) is the first excited singlet state and 13) is the charge transfer state. The chemical transition rate from the charge transfer state is denoted by ft. The number of molecules in state [j) is denoted by N~, the relaxation rate from state li) to state [J) is denoted by a u. The upconversion process is denoted by the term o-uArt N2. The set of steady state rate equations, with Cru
11>+[2> -~ 13> + 10>, "/~1 0"21 N2 +0"31N3 -o-ioN1 - a , N1 N2 = 0 =
N2 + AIo No + o-32N3 - a21 N2 - a20 N2 - 0"~N1 N2 = 0 1~3 = o-uNi N 2 - ( f l +o-31 +o-32)N3 = 0 is taken to describe the system under steady state illumination in the F K F model. Steady state solution with the assumptions of No constant and O-31N3, O-20N2, O-ioN1 negligible are then performed in the F K F treatment. Under low illumination the rate fi is taken to exceed the rate o'32. On high illumination the rate fi is taken to be negligible. In the F K F model the ratio of fluorescence yield (state 12)) on high illumination and yield on low illumination becomes equal to 2. A fluorescence yield increase by more than a factor 2 is not obtainable in the F K F treatment. In situ experiments show an increase by more than a factor 2 (Lumry, Mayne & Spikes, 1959). In situ results, apart from some alterations in relaxation rate values, should be describable also by the above rate equations, provided that the chemical rate is set to zero. This difficulty is remedied in the F K F treatment by the (unsubstantiated) assumption that extraneous effects have been introduced in the in situ experiments. The rationale given for invoking the highly
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symmetric reaction center dimer configuration is the need for increased intersystem crossing and the need for an anomalously long triplet lifetime in the reaction center. We briefly consider the physical basis for the upconversion process, since we will have need to consider it in section 5 of this paper. The S-T annihilation process arises from the dipole-dipole interaction mechanism. This mechanism is the same one, which has been treated in detail (FSrster, 1948) in the study of radiationless intermoleeular resonant singlet energy transfer in connection with concentration depolarization of fluorescence. In terms of this singlet-singlet energy transfer, in addition to the r-6 dependence, where r denotes the distance between interacting molecules, the overlap between the absorption and fluorescence bands figures in the determination of the effectiveness of the dipole--dipole interaction. The theoretical formulation can be generalized to S-T annihilation, as well as T-T annihilation. In Fig. 1 a general dipole-dipole interaction scheme is shown. One of the
1~6. 1. Intermolecular radiationless resonant energy transfer scheme resulting from the dipole-dipole interaction mechanism.The pair of arrows denotes the energy transfer process. See text for discussion. interacting molecules looses energy in going from state 1i> to state [j> and the other molecule gains the corresponding amount of energy in going from state Ik> to state 1l>. The band overlap of importance is that corresponding to emission from state 1i> to state lJ> with the absorption from state [k> to state II>. At this juncture, a brief reason for concern with an upconversion scheme is appropriate. It is unlikely that the chlorophyll a first excited singlet state can by itself be responsible for the photosynthetic activity. The low in vivo fluorescence yields indicate that radiationless decay (intersystem crossing, internal conversion, etc.) is very rapid, very roughly at a rate of 109-101° see -1, if in vitro data are any guide at all (Parker & Joyce, 1967). Therefore, enzymatic processes, to be competitive, would have to be at least as fast,
ENERGY U P C O N V E R S I O N IN PHOTOSYNTHESIS
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substantially faster than chemical reactions generally. The lowest chlorophyll triplet state by itself does not appear to be responsible for the photosynthetic role either, since there would be little reason to expect resulting PSII fluorescence yield doubling on strong illumination.
3. Rate Equations We consider the rate equations in the F K F model. We add to these the rate equation for the ground state. As we shall see shortly, the rate equation for the ground state must be included, unless no assumptions are made regarding the relaxation rates to and from the ground state. Certainly the explicit consideration of the ground state rate equation is quite proper. gu Within the F K F framework we have, with I 1 ) + 12) -, 13)+ [0) 1V0 = - A I o N o +0-20N2 + a l o N l + a , N1N2 = 0
(0)
/ql = 0"21N2 + 0 - 3 1 N 3 - a t o N 1 - 0 - , N I N 2 = 0
(1)
1V2 = AIo No + a32 N3 - 0-21N2 - 0"20N2 - 0-, NI N2 = 0
(2)
Ar3 = 0-, N1 N 2 -- (• q- 0-31 q- °"32)N3 -- 0.
(3)
Here, and in the remainder of this paper, we conform to the F K F notation. Equation (0) pertains to the ground state. Under steady state conditions ~ j = 0. Adding equations (0) and (2), we obtain under steady state
0-32N3-0-21Nzq-0-1oN1 :
0.
(4)
(0-32 q- 0-31)N3 -- 0-uN1 N 2 = 0.
(5)
Adding equations (4) and (1) we obtain
Adding equations (5) and (3) we obtain/~ = 0, which means that no photosynthetic activity occurs ! The fundamental error responsible for this undesirable result is the neglect of a "regeneration" of chlorophyll to either of state 10>, II>, or 12). The neglect of this regeneration means that equations 0 to 3 cannot be steady state equations if photosynthetic activity takes place. We therefore add a regeneration term y to equation (2) in accord with the F K F model (cf. section 5, Fong, 1974). Solution of the rate equations in the same steps as above yields the expected result: PN3 = ~. We next consider the F K F assumptions, namely negligible values of 0-31N3, 0-20N2, 0-10N~, as well as constant No. We solve for steady state
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conditions, adding the term ~ to equation (2). We obtain AIo No = 0.. N 1N 2
from equation (0),
f21 N2 = f . N1 N2
from equation (1),
0-.N1 N2 = (fl+fa2)N3
from equation (3).
The first and third of these relations yield AIoNoI(fl + 0.32) ----N 3.
The second relation yields f 2 x / f . = N1, which, together with the first relation, yields AIo No/f21 = N2.
The total number of chlorophyll molecules in a given system is a constant. Therefore, since also 3' = tiara under steady state, we can write No +N1 +N2 +N3 = constant. From the above relations for Nt, N2, N3, and the F K F assumption of constant No we obtain No + 021/0.u + Alo No/f21 + AIo N0/(f32 + fl) = constant, or
loll2 t + Io/(fl + 0"32) -- constant,
since all 0.ij, as well as A are constants. Since there must be a correlation between the rate fl and the illumination intensity, I o, for a given system, the above result means that the rate equations cannot be steady state equations with the above assumptions, except for a single illumination intensity. We note in passing that the assumption of negligible 0.3t N a is a questionable one. The spin-selection rule for S-T annihilation indicates that state 13) has triplet characteristics. In molecules, such as chlorophyll, internal conversion among excited singlet states is very rapid. The same is expected among excited triplet states, unless the gap between states [3) and Jl) is large, and no triplet lies between the two. If one considers an excited singlet state 1F~ and the corresponding triplet state 3Fj, one usually finds that 3Fj lies at the same energy, or below, tF i. Noting now that the second excited singlet state of chlorophyll lies below state 13), one is led to expect that the corresponding triplet state lies between states 13) and I1). Therefore, a
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407
small value of tr31 seems unlikely. Apparently, a misprint occurs in equation (8) of the F K F model (Fong, 1974). If one takes reasonable order of magnitude values of roughly l0 s sec -1 for the rates tr32 and a2~, then, according to the F K F equation (8), fl ~ 1016, an incredibly large rate. The condition fl >> tr32, in addition to being dimensionally correct, suffices to lead to relation (9) in the F K F treatment. The difficulties with the F K F treatment go further, however; the intermolecular nature of the S-T annihilation process is not accounted for in the F K F rate equations. This is most readily seen from consideration of a fictitious intramolecular singlet-triplet annihilation process. Physically, such a process would require simultaneous excitation of two electrons to excited states within one molecule, a most improbable event. The resulting rate equations would be exactly the equations (0)-(3) (with the term 3' added, if a chemical transition occurs), i.e. the equations (0)-(3) are purely intramolecular in nature.
4. Corrected Rate Equations
In Fig. 2 we show the explicit intermolecuIar nature of the S-T annihilation process. Primed states belong to reaction center chlorophylls, double-primed states correspond to antenna chlorophylls, along the lines of the F K F model. Accounting for the intermolecular nature of S-T annihilation, and including the regeneration term 3', we have the following set of rate equations for the
F~G. 2. Schematic representation of the explicit iatermoleeular nature of the singlettriplet annihilation process, which is denoted by the pair of arrows. See text for discussion of symbols.
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12"> -~ 10"> + 13'>)
system, within the F K F scheme (with 11'> +
, t , I 0 = 19'o= - . 4 t IoNoI +0-2oN2 +0-1oNz
o=~,~
=
o = R~ =
I
!
I
!
,
(0')
t
,
,!
(1')
0-21Nz-0-1oN1+0-sl N 3 - 0 - , N 1 N 2 I
l
t
!
,
,
,
,
A loNo -l'-0-32 N3 -0"21 N2 - 0-20 N2 -I-7 !
U
,
r
,
0 = R ~ = 0-. N I N2 -- (/~ + 0"32 "1-0-31)N3 o =
~3 =
0 =/q~
=
-A"IoN'~ +d~oN'~ +0-1oN1 . . . +0-.N1 . . . . N2 ll
II
It
It
l,
l,
(o")
0")
0-21N2-0-1oNx 11
(29 (3')
It
It
It
l
11
0 = 1V'~= A I o N o - 0 - 2 o N 2 - 0 - 2 t N 2 - 0 - , N I N v
(2")
Solution of equations (0')-(3') under steady state conditions leads again to r =
pN~.
Since it is highly implausible that antenna chlorophylls are converted to reaction center chlorophylls during photosynthetic activity, and conversely, we can also write under steady state N'o + N'~ + N ; + N'3 = K'
(6)
N~ + N't' + N~' = K"
(7)
where K" and K' are constants. We note that equations (0")-(2") can in principle also apply to reaction center chlorophylls (i.e. the dimer partner of the molecule described by the primed system of equations). In the F K F framework, however, the doubleprimed equations describe antenna chlorophylls. We consider the fluorescence yield for the double primed system. The fluorescence yield is defined as the ratio between the radiative decay rate 0-rad of state 12") and its total decay rate. The rate a'~o may contain an internal conversion contribution, as well as an intermolecular radiationless resonant energy transfer portion. We therefore write 0-,ad = f ~ 0 , where f is a constant of value less than 1. The fluorescence yield, ~b, is then = f0-~0/(e~o + 0 - h + 0-.Ni). Since Ni increases with illumination intensity, reaching perhaps a saturation value, eventually, we see immediately that the fluorescence yield for the double-primed system cannot increase with increased illumination, but stays constant, perhaps decreasing on sufficiently strong illumination. While the S-T annihilation process can involve only antenna chlorophylls which lie close to the reaction center, there is very efficient resonant energy transfer within the antenna system, so that the double-primed system does describe the antenna chlorophylls. It is conceivable to consider the situation wherein reaction center singlet energy can find its way into the antenna system. This
ENERGY U P C O N V E R S I O N IN PHOTOSYNTHESIS
409
possibility provides no remedy, which is shown as follows. In the F K F scheme the reaction center is comprised of two molecules. There are roughly 300 antenna chlorophylls to each reaction center, hence about 150 to each reaction center molecule. If the increased PSII fluorescence yield (by about 0.025) is due in reality to increased reaction center fluorescence, then the reaction center fluorescence yield would have to exceed unity. We are thus led to conclude that the F K F scheme does not predict the observed PSII fluorescence increase under strong illumination, but leads to constant fluorescence yield of PSII, except for possible decrease under very strong illumination. The lack of prediction of this fluorescence increase can perhaps be remedied, if one turns the F K F scheme around. Suppose, for the moment, that an antenna chlorophyll in the lowest triplet state interacts with a reaction center chlorophyll in the first excited single, state. Then, the state reached upon upconversion is a state of the antenna chlorophyll molecule. This situation is at first starting, since one is accustomed to consider the reaction centers the loci of the photosynthetic activity. For the moment we simply note that the upconverted antenna chlorophyll molecule must be associated very closely with the reaction center, by virtue of the r-6 dependence discussed in section 2. More detailed considerations are deferred to section 5. For the moment we pursue the consequences of the "reversed" situation. The double-primed system of equations now describes reaction center chlorophylls, whereas the primed system now describes the antenna chlorophyll system. The double-primed system contributes little to the PSII fluorescence, and the increase in PSII fluorescence on strong illumination must be extracted from the primed system of relations [(0')-(3'), and (6)]. We solve for N~ under steady state conditions. Adding equations (1') and (3') we have - (a;2 +
fl)N'3 +
a~ t N ~ - a t o N~ = 0
(8)
which, together with relation (0'), yields
{ - A 'IoNg+(a;x + 0.2D)N:~}/(fl + 0"32) = n~. From equations (8) and (9) we obtain . N2)/0.10 . . = N1. (A .I 0 N. O- . 0"20
(9) (10)
Substituting equations (9) and (10) into equation (3') we have It
l
I
l
,
,
l
t
,
O'uN2A I o No/0.1 o + (/~ + 0"31 + 0"32) A lo No/([J + 0"32) It
t
•
/
,
I
I
t
,
= {*.N2a20/alo+(fl+a3t +0"32)&2t+a20)/(fl+a32)}N2. (11) At this stage the quantity N~ remains troublesome. In order to deduce the behaviour of N~ as function of illumination intensity we digress briefly into consideration of a more simple system, as shown in Fig. 3. For
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o/l::
At,
l
t
10
1o~
F~o. 3. Three-levelenorgy transfer scheme. The straight arrow up denotes optical pumping, the straight arrow down denotes (including possible radiationless contribution) fluorescence. The waved arrows denote radiationless relaxation (with a possible radiative contribution in case of ~rlo).The symbols ~r~jdenote the decay rates.
this system the rate equations (steady state) are lqo = - A l o N o +a2oN2 + a i o N 1 = 0 1~l = c r 2 1 N 2 - a l o N 1 = 0 1~2 = A I o N o - a 2 0 N 2 - a 2 1 N 2 = 0 N o + N I + N 2 -- k
(12)
which, under steady state conditions, yield
No = k/{1 +AIo[(a2o +a21)+Aloa21/alo(a2o +a21)} N t = AIo No a21lcrlo(~2o + a21) Nx = AIo No/(a2o + a21).
(13)
Under low illumination intensity we have N o approximately constant and equal to k, and N 1 as well as N2 increasing linearly with Io. For very high illumination N o becomes proportional to 1/Io, leading to serious depletion of the ground state, a condition termed bleaching. Under this condition N1 and N2 become constants. We now return to relations (0") to (2") and note from the above digression that on low illumination the double-primed system behaves like the system described by the relations (12) and (13). We can, therefore, substitute N~ in equation (I 1) by ~1o, where g is a proportionality constant, as long as the illumination is not so strong, as to cause bleaching. Relation (11) becomes a,, uloA 70 Nr/a~ o + (B + a61 + ~r62)A 70 N~/(~ + a62)
= {o.0tlo O'2o/a't o + ( ~ + o~l + a;2)(a~l + o~0)/(/~ + o~2)}N~.
(14)
From the experimental operational standpoint, a constant fluorescence yield (corresponding to emission from state 12')) is reflected by a constant ratio N~]/o. Under low illumination, relation (14) yields f
t
l
F
N'2[Io -- A No/(0"21 +~r20).
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411
On high illumination, the terms in ~ in equation (14) dominate and we have l l t N'z/I o = A No/a2o.
Here it is assumed that the condition N~ = ~iro can stin be maintained when the limit of high illumination regarding t¢~ is reached. We have also made the reasonable assumption that 0.gl cannot be many orders of magnitude larger than 0%. The ratio, R', of high illumination fluorescence yield to low illumination fluorescence yield becomes I
t
I
R' = (0.21 +a20)/0.2o. (15) Prior to further considerations it is worthwhile to examine the assumption that N~ can be written as cd0 in the N~ high illumination limit. We assume that A " I 0 N~ is not so large as to cause bleaching. As long as A" is not vastly larger than A'. this assumption is reasonable. Under these circumstances the assumption N~ = cGo may break down if the quantity ¢! tt tt ~,N~ becomes comparable to 0.2o or 0.21, as seen from equation (2") (0.2o is expected to be smaller than 0.~1)- On the other hand, equation (1 l) indicates that 0.aN~ needs only exceed 0.~0 substantially for the high illumination situation regarding the primed system to be attained. If the assumption N~ = CCIo breaks down when this limit is reached, or before, then, as ' Very rough " is reached, we have simultaneously 0..N~ < 0.1o. o-uN '1 ,~, 0'20 order-of-magnitude estimate of the rates 0.~o and a~o ('~109 and ,~0103 respectively) yield 2,2/l,1~T"/~7'J~< 10-6. This means that for every reaction center chlorophyll excited to the first excited ringlet state some 106 antenna chlorophylls must be excited to the lowest triplet state. There are only about 300 antenna chlorophylls to. each reaction center. We therefore take the assumption N~ = ~Io to be substantiated, as long as 24"1o N~ does not cause bleaching. This condition satisfied, the ratio R' must be about 2 to be consistent with experiment. This yields 0.~1 ~ a~o. Since 0.~o is not a purely radiative rate, but contains a radiationless contribution, there is no difficulty in understanding the low/n vivo fluorescence yields. We have shown that the reaction center chlorophylls must operate in the first excited singlet in the F K F framework, if the PSII fluorescence behaviour is to be accounted for. Therefore, if one considers only the correlation with the PSII quantum yield doubling, justification of need for an anomalously long triplet lifetime of the reaction center chlorophylls, as well as the need for faster intersystem crossing, disappears, and becomes actually "counterproductive". Thus, there appears to be little justification for the F K F highly symmetric dimer reaction center configuration. The need for an anomalously long triplet lifetime is puzzling in any case. Even without such lengthening, the triplet relaxation rate can be expected to be some 5-6 orders of magnitude
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smaller than the remaining intramolecular rates, even if only rough extrapolation of in vitro results (Parker & Joyce, 1967) is made to the in vioo case. Finally, we address the alternative of T-T annihilation as an alternate path for unconversion. Once the term auN~ N~ is replaced by the term au N~ N~', the procedures outlined in this section can be followed. The result is that T-T annihilation may also cause doubling of the fluorescence yield on high illumination. Thus, merely on the basis of fluorescence yield considerations, T-T-annihilation cannot be ruled out, as done in the F K F model. 5. Discussion
We have up to now confined our attention very closely to following the details of the F K F scheme. One could alternately conceive of the situation, where the regeneration (term ?) does not proceed to state 12'), but to state 11') or 10'). It turns out (we delete the algebra here) that the essentials of section 4 are not significantly affected. Also, instead of direct up conversion to the charge transfer state, one can envisage upconversion to a triplet state and subsequent radiationless relaxation to a charge transfer state. Again, the essentials of section 4 are not affected. The pumping of state I1') or 12') need not be optical. One could have the radiationless energy migration processes 12")+10') ~ 10")+12') and IlU>+10 ') ,--10">+11'). These alternatives do not affect the essential content of the preceding sections. Rather than dwelling further on rate equations, we consider the question of experimental discrimination between various alternatives. If the upconversion to a charge transfer state is direct, then this state should have triplet character, if S-T annihilation pertains, and singlet character, if T-T annihilation prevails. Electron spin resonance studies might be useful in this respect. One can roughly estimate the energy of the lowest triplet state from consideration of the in vitro case, where the lowest triplet lies at about 10,000 cm -1 (Parker & Joyce, 1967). If T-T annihilation is of photosynthetic importance, then the charge transfer state cannot lie • above roughly 20,000 cm - t . Finally, the relaxation rates a~l and ~r~o are of importance. We return to consideration of the reaction center structure. The investigation of Katz and co-workers (Ballschmiter & Katz, 1969; Norris, Uphaus, Crespi & Katz, 1971 ; Katz & Norris, 1973) gives an indication of a rather unsymmetrie reaction center dimer (or oligomer) configuration. Suppose now that one of the reaction center dimer (or oligomer) partners behaves spectroscopically as an antenna molecule, whereas the other partner behaves
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IN P H O T O S Y N T H E S I S
spectroscopically as the "trap" molecule, P 700, in PSI (cf. Govindjee et aL, 1973). Then, the considerations of section 4 are still applicable, but now the upconversion involves two molecules of the reaction center, one of these being very strongly coupled to the antenna system. In this picture the unconversion of an "antenna" chlorophyll is no longer difficult to accept, but now the reaction center configuration cannot be highly symmetric. We propose a model within an upconversion scheme, which allows one to understand the fluorescence yield behaviour of both PSI and PSII. This model is summarized in Fig. 4. In this figure the molecule A is an antennalike chlorophyll of the reaction center and the molecule T is the trap molecule ~HOTOSYSTEM I
- - - - S
PH OTOSYSTEM II CT
CT
SO
so
I
(or TI)
SO
A
T"
A
So
T
FIG. 4. Model for the primary mechanism of light utilization by chlorophyl a in photosynthesis. A denotes an antenna-like chlorophyl molecule associated with the reaction center; T denotes the trap molecule. Here So, St, TI, and CT denote the ground state, first excited singlet, lowest triplet, and charge transfer state, respectively. See text for discussion.
of the reaction center. There is in principle no reason why the trap molecule must contribute its first excited singlet to the upconversion, whereas the antenna-like molecule, or for that matter a "'bona fide" antenna molecule (which happens to lie close to the reaction center), must contribute its lowest triplet. The inverse procedure should be just as feasible. The preference of one over the other is envisaged simply to be one of the energies involved, i.e. is envisaged to depend on the emission-absorption overlap discussed in section 2 in connection with the dipole-dipole interaction nature of the process. Similar considerations apply to the T-T annihilation alternatives. T.B.
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The suggestion here is that PSII utilizes the lowest triplet state of the antennalike chlorophyll of the reaction center, such that it is upconverted to the chemically active charge transfer state. PSI, on the other hand, utilizes the trap molecule, such that it is upconverted to the charge transfer state. In terms of the considerations of section 4, PSII can then display a doubling of fluorescence yield on strong illumination, but PSI cannot. While this model is an admittedly highly speculative one, it does appear to be consistent with experiment, and utilizes a plausible upconversion mechanism (Menzel, 1974). Perhaps, rather than direct upconversion to the charge transfer state, upconversion to a high-lying triplet (or singlet, in the case of T-T annihilation) is preferable. This triplet can then decay to a chemically active charge transfer state via a radiationless process akin to intersystem crossing. The charge transfer state is here envisaged as not relaxing to states So, $1 or T1. This alternative is considered here to be the more likely one because of the relaxation rates anticipated for the charge transfer state, if attained directly through upconversion. In terms of direct upconversion, the relaxation rates a~l and a~2 can be estimated very roughly to be of the order of I0 9 s e c - I , even substantially larger, perhaps, in the case of a~l, which (now considering the S-T annihilation situation) should be comparable to the rate of internal conversion among excited singlet states. Thus, to be even competitive, fl must be of that order of magnitude, a rather high value. On the other hand, in the indirect upconversion ~ can be substantially smaller. Up to this point attention to experiment has been restricted essentially to consideration of the PSII fluorescence yield doubling upon high illumination. Assessment of the possible merit of a singlet-triplet annihilation scheme in photosynthesis must entail consistency with further experimental findings. We consider the reaction center triplet lifetimes. To provide a large quantum yield of photosynthesis a substantial fraction of reaction center chlorophylls (trap-like or antenna-like in the above scheme) must be maintained in state I1), so that further photon absorption in the antenna system will find the reaction centers "primed" for photosynthesis. This requires long triplet lifetimes. In fact, it has been found that photosynthetic electron transport associated with PSII is linear in illumination down to levels so low that each photosynthetic unit receives only about one photon every 3 see (Sauer & Park, 1965). In terms of the S-T annihilation scheme the triplet lifetimes must then be substantially longer than 3 see, an extraordinarily long lifetime. The question now is whether such a long lifetime is at all plausible. In some phthalocyanines (Vincett, Voigt & Rieckhoff, 1971) and free-base porphyrins (Gouterman & Khalil, 1974), which are structurally similar to chlorophyll, radiative triplet lifetimes can be in the
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10-100 sec range. The triplet radiative, as well as radiationless, decay rates in phthatocyanines increase with increasing spin-orbit coupling, with radiationless rates increasing to a greater extent (Menzel, Rieckhoff & Voigt, 1973). This suggests that a low radiative rate occurs concomitant with a low radiationless rate. Thus, a long chlorophyll reaction center triplet lifetime could be expected, but a lifetime in the second range is nevertheless quite unprecedented. Perhaps an exciton coupling, such as suggested by Fong (1974) might come into play here. Reaction center triplets have been observed via their absorption (Moraw & Witt, 1961) and ESR (Leigh & Dutton, 1974) spectra, but only upon blocked or saturated photochemistry. This might suggest that under light-limiting conditions one would expect to observe the reaction center triplets if the S - T upconversion scheme pertains, hence one might conclude that this scheme cannot be significant in photosynthesis. On the other hand, one might interpret the reaction center triplet findings as indicating that the triplets are very efficiently used up in photosynthesis and therefore elude observation unless photochemistry is quenched or saturated. The requirement of a very long triplet lifetime certainly makes the significance of S - T annihilation in photosynthesis open to question and the scheme must be viewed with much caution until reaction center triplet lifetimes in vivo and in situ become available. I am indebted to Professor Kenneth Sauer for a number of very helpful comments and for bringing to my attention several experimental findings which need to be considered in an assessment of the merit of the S-T upconversion scheme. REFERENCES BALLSC~MtTER,K. & KATZ,J. J. (1969). J. Amer. chem. Soc. 91, 2661. FONG, F. K. (1974). J. theor. Biol. 46, 407. F6RSTER, T. (1948). Ann. Phys. 2, 55. GOUTE~r~AN,M. & KHan., G. (1974). J. molec. Spee. 53, 88. GOVm~EE, PAPAGEOROIOU,G. & RAB~OWrrCH, E. (1973). Practical Fluorescence, Theory, Methods and Techniques (G. G. Guilbault, ed.), chap. 13. New York: Marcel Dekker. KATZ, J. J. & NORMS, J. R. (1973). Current Topics in Bioenergetlcs (D. R. Sanadi & L. Parker, eds), vol. 5, p. 41. New York: Academic Press. LEXGH,JR, J. S. & Du-rrON, P. L. (1974). Bioehim. biophys. Acta 357, 67. Ltr~mY, R., MAX'NE,B. & SPIKES,J. D. (1959). Discuss. Faraday Soe. 27, 149. MENZEL,E. R. (1974). Chem. Phys. Lett. 26, 45. MmqZEL,E. R., RECKHOFF,K. E. & VOIGT,E. M. (1973). J. chem. Phys. 58, 5726. MORAW, R. & Wrrr, H. T. (1961). Z. phys. Chem. 29, 25. NORMS, J. R., UPHAUS,R. A., CRESt'I,H. L. & KATZ, J. J. (1971). Proc. hath. ,4cad. Sci. U.S.A. 68, 625. PARKER,C. A. & JOYCE,T. A. (1967). Photochem. Photobiol. 6, 395. SAtmR, K. & PARK, R. B. (1965). Biochemistry 4, 2791. V~C~Tr, P. S., VOIOT,E. M. & R~cr.no~, K. E. (1971). Jr. chem. Phys. 55, 4131.
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Note added in proof: I f reaction center bleaching occurs upon high illumination the quantity ,ru0do in equation (14) can be replaced by a constant and relation (15) remains valid provided that this constant is substantially larger than cr~o.
On the Energy Upconversion Mechanism of Light Utilization by Chlorophyll in Photosynthesis E. ROLAND MENZELJf
Department of Chemistry, University of Kentucky, Lexington, Kentucky 40506, U.S.A. (Received 27 December 1974, and in revised form 5 March 1975) A model for the primary mechanism of light utilization by chlorophyll in photosynthesis, involving singlet-triplet annihilation, has recently been proposed (Fong, 1974). In that model it is asserted that the photosystem II fluorescence yield doubling observed on strong illumination is predicted exactly. In this paper the model is critically examined. It is shown that a number of fundamental errors occur in the above model, such that the doubling prediction is incorrect. It is shown that such doubling can be accounted for only if a reaction center chlorophyll in its first excited singlet state interacts with an antenna chlorophyll in its lowest triplet state, and that this doubling arises independently of chemical activity. In view of this reversal of the physical situation from the Fong model, there is no longer justification for a highly symmetric reaction center dimer adduct configuration. The consequences of the corrected treatment are examined. Within the upconversion framework a model is proposed, which is consistent with the photosystem II fluorescence yield doubling on strong illumination, as well as with the absence of such doubling in photosystem I.
1. Introduction A model concerned with the basic mechanism of light utilization by chlorophyll in photosynthesis has been proposed (Fong, 1974). In this model (henceforth termed the F K F model) pairwise interaction between reaction center chlorophylls in the lowest triplet state with antenna chlorophylls in the first excited singlet state via the singlet-triplet (S-T) annihilation process is suggested. The S - T annihilation is taken to lead to upconversion to a charge transfer state, which can undergo a chemical transition to initiate enzymatic processes. A crucial theme in the F K F model is the assertion t Present address: Xerox Research Centre of Canada, 2480 Dunwin Drive, Mississauga, Ontario L5L 1Jg, Canada. 401
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that the model exactly predicts a doubling of the fluorescence yield of photosystem II (PSII), as observed experimentally. In this paper the rate equations utilized in the F K F model, leading to the PSII quantum yield doubling prediction, are examined. In section 2 the pertinent experimental findings and the F K F model are briefly reviewed. It will be shown in section 3 that a number of fundamental errors occur in the F K F rate equations, as a result of which the above doubling prediction is incorrect. It will be shown that the F K F rate equations are, in fact, not applicable to the system at hand, and that their use leads to the result that no photosynthetic action takes place. In section 4 the correct rate equations are taken up with particular emphasis on the possibility of prediction of increased PSII fluorescence yield under strong illumination. Such an increase will be shown to be possible, though a doubling cannot be predicted with certainty. This doubling does not result from quenching of the chemical transition from the charge transfer state, as in the F K F model, but is entirely independent of the chemical step, a fundamentally different situation physically. It will be shown that this doubling can be accounted for only, within the F K F upconversion framework, if the reaction center chlorophyll molecule contributes its first excited singlet state to the upconversion process! Therefore, the justification for the highly symmetric reaction center dimer configuration is no longer present. It will be shown also that triplet-triplet (T-T) annihilation cannot be ruled out, as done in the F K F model, from having a possible role in the upconversion to a chemically active state, on the basis of the above fluorescence yield increase on high illumination. In section 5 the various alternatives to the F K F model, within the framework of an underlying upconversion scheme, are discussed, with attention to the experimental information needed to discriminate between these alternatives. Finally, a model utilizing an upconversion scheme is proposed. This model is consistent with the fluorescence yield doubling in PSII, as well as with the absence of such doubling in photosystem I (PSI). The occurrence of an upconversion process is plausible in view of recent in vitro reports (Menzel, 1974).
2. Review of the FKF Model, Pertinent Experimental Findings, and the Physical Basis of the Upeonversion Process In the F K F model the reaction center of PSII is taken to be a highly symmetric dimer adduct configuration, wherein the two chlorophyll a molecules are bound together via two water molecules. An unsymmetric dimer structure, involving one water molecule only, is indicated by the work
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of Ballschmiter & Katz (1969). In the F K F model a reaction center chlorophyll in its lowest triplet state interacts with an antenna chlorophyll in its first excited singlet state. Resulting S-T annihilation leads to upconversion of the reaction center molecule to a chemically active charge transfer state. Experimentally, it is found that the fluorescence associated with PSII incurs a doubling of quantum yield on high illumination intensity, as compared to low illumination. Such doubling is not observed in PSI. The PSII quantum yields on low and high illumination are about 0.025 and 0.05 respectively (ef. Govindjee, Papageorgiou & Rabinowitch, 1973). This fluorescence is predominantly bulk (i.e. antenna chlorophyll) fluorescence There are some 300 antenna chlorophylls to each reaction center. A central aspect of the F K F model concerns the prediction of the PSII fluorescence yield doubling. To this end, a "composite" energy level scheme, wherein no explicit distinction between antenna and reaction center chlorophylls is apparent, is taken to represent the situation. In this scheme the ground state of the system is denoted by 10). State I1) is the lowest triplet state, 12) is the first excited singlet state and 13) is the charge transfer state. The chemical transition rate from the charge transfer state is denoted by ft. The number of molecules in state [j) is denoted by N~, the relaxation rate from state li) to state [J) is denoted by a u. The upconversion process is denoted by the term o-uArt N2. The set of steady state rate equations, with Cru
11>+[2> -~ 13> + 10>, "/~1 0"21 N2 +0"31N3 -o-ioN1 - a , N1 N2 = 0 =
N2 + AIo No + o-32N3 - a21 N2 - a20 N2 - 0"~N1 N2 = 0 1~3 = o-uNi N 2 - ( f l +o-31 +o-32)N3 = 0 is taken to describe the system under steady state illumination in the F K F model. Steady state solution with the assumptions of No constant and O-31N3, O-20N2, O-ioN1 negligible are then performed in the F K F treatment. Under low illumination the rate fi is taken to exceed the rate o'32. On high illumination the rate fi is taken to be negligible. In the F K F model the ratio of fluorescence yield (state 12)) on high illumination and yield on low illumination becomes equal to 2. A fluorescence yield increase by more than a factor 2 is not obtainable in the F K F treatment. In situ experiments show an increase by more than a factor 2 (Lumry, Mayne & Spikes, 1959). In situ results, apart from some alterations in relaxation rate values, should be describable also by the above rate equations, provided that the chemical rate is set to zero. This difficulty is remedied in the F K F treatment by the (unsubstantiated) assumption that extraneous effects have been introduced in the in situ experiments. The rationale given for invoking the highly
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symmetric reaction center dimer configuration is the need for increased intersystem crossing and the need for an anomalously long triplet lifetime in the reaction center. We briefly consider the physical basis for the upconversion process, since we will have need to consider it in section 5 of this paper. The S-T annihilation process arises from the dipole-dipole interaction mechanism. This mechanism is the same one, which has been treated in detail (FSrster, 1948) in the study of radiationless intermoleeular resonant singlet energy transfer in connection with concentration depolarization of fluorescence. In terms of this singlet-singlet energy transfer, in addition to the r-6 dependence, where r denotes the distance between interacting molecules, the overlap between the absorption and fluorescence bands figures in the determination of the effectiveness of the dipole--dipole interaction. The theoretical formulation can be generalized to S-T annihilation, as well as T-T annihilation. In Fig. 1 a general dipole-dipole interaction scheme is shown. One of the
1~6. 1. Intermolecular radiationless resonant energy transfer scheme resulting from the dipole-dipole interaction mechanism.The pair of arrows denotes the energy transfer process. See text for discussion. interacting molecules looses energy in going from state 1i> to state [j> and the other molecule gains the corresponding amount of energy in going from state Ik> to state 1l>. The band overlap of importance is that corresponding to emission from state 1i> to state lJ> with the absorption from state [k> to state II>. At this juncture, a brief reason for concern with an upconversion scheme is appropriate. It is unlikely that the chlorophyll a first excited singlet state can by itself be responsible for the photosynthetic activity. The low in vivo fluorescence yields indicate that radiationless decay (intersystem crossing, internal conversion, etc.) is very rapid, very roughly at a rate of 109-101° see -1, if in vitro data are any guide at all (Parker & Joyce, 1967). Therefore, enzymatic processes, to be competitive, would have to be at least as fast,
ENERGY U P C O N V E R S I O N IN PHOTOSYNTHESIS
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substantially faster than chemical reactions generally. The lowest chlorophyll triplet state by itself does not appear to be responsible for the photosynthetic role either, since there would be little reason to expect resulting PSII fluorescence yield doubling on strong illumination.
3. Rate Equations We consider the rate equations in the F K F model. We add to these the rate equation for the ground state. As we shall see shortly, the rate equation for the ground state must be included, unless no assumptions are made regarding the relaxation rates to and from the ground state. Certainly the explicit consideration of the ground state rate equation is quite proper. gu Within the F K F framework we have, with I 1 ) + 12) -, 13)+ [0) 1V0 = - A I o N o +0-20N2 + a l o N l + a , N1N2 = 0
(0)
/ql = 0"21N2 + 0 - 3 1 N 3 - a t o N 1 - 0 - , N I N 2 = 0
(1)
1V2 = AIo No + a32 N3 - 0-21N2 - 0"20N2 - 0-, NI N2 = 0
(2)
Ar3 = 0-, N1 N 2 -- (• q- 0-31 q- °"32)N3 -- 0.
(3)
Here, and in the remainder of this paper, we conform to the F K F notation. Equation (0) pertains to the ground state. Under steady state conditions ~ j = 0. Adding equations (0) and (2), we obtain under steady state
0-32N3-0-21Nzq-0-1oN1 :
0.
(4)
(0-32 q- 0-31)N3 -- 0-uN1 N 2 = 0.
(5)
Adding equations (4) and (1) we obtain
Adding equations (5) and (3) we obtain/~ = 0, which means that no photosynthetic activity occurs ! The fundamental error responsible for this undesirable result is the neglect of a "regeneration" of chlorophyll to either of state 10>, II>, or 12). The neglect of this regeneration means that equations 0 to 3 cannot be steady state equations if photosynthetic activity takes place. We therefore add a regeneration term y to equation (2) in accord with the F K F model (cf. section 5, Fong, 1974). Solution of the rate equations in the same steps as above yields the expected result: PN3 = ~. We next consider the F K F assumptions, namely negligible values of 0-31N3, 0-20N2, 0-10N~, as well as constant No. We solve for steady state
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conditions, adding the term ~ to equation (2). We obtain AIo No = 0.. N 1N 2
from equation (0),
f21 N2 = f . N1 N2
from equation (1),
0-.N1 N2 = (fl+fa2)N3
from equation (3).
The first and third of these relations yield AIoNoI(fl + 0.32) ----N 3.
The second relation yields f 2 x / f . = N1, which, together with the first relation, yields AIo No/f21 = N2.
The total number of chlorophyll molecules in a given system is a constant. Therefore, since also 3' = tiara under steady state, we can write No +N1 +N2 +N3 = constant. From the above relations for Nt, N2, N3, and the F K F assumption of constant No we obtain No + 021/0.u + Alo No/f21 + AIo N0/(f32 + fl) = constant, or
loll2 t + Io/(fl + 0"32) -- constant,
since all 0.ij, as well as A are constants. Since there must be a correlation between the rate fl and the illumination intensity, I o, for a given system, the above result means that the rate equations cannot be steady state equations with the above assumptions, except for a single illumination intensity. We note in passing that the assumption of negligible 0.3t N a is a questionable one. The spin-selection rule for S-T annihilation indicates that state 13) has triplet characteristics. In molecules, such as chlorophyll, internal conversion among excited singlet states is very rapid. The same is expected among excited triplet states, unless the gap between states [3) and Jl) is large, and no triplet lies between the two. If one considers an excited singlet state 1F~ and the corresponding triplet state 3Fj, one usually finds that 3Fj lies at the same energy, or below, tF i. Noting now that the second excited singlet state of chlorophyll lies below state 13), one is led to expect that the corresponding triplet state lies between states 13) and I1). Therefore, a
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small value of tr31 seems unlikely. Apparently, a misprint occurs in equation (8) of the F K F model (Fong, 1974). If one takes reasonable order of magnitude values of roughly l0 s sec -1 for the rates tr32 and a2~, then, according to the F K F equation (8), fl ~ 1016, an incredibly large rate. The condition fl >> tr32, in addition to being dimensionally correct, suffices to lead to relation (9) in the F K F treatment. The difficulties with the F K F treatment go further, however; the intermolecular nature of the S-T annihilation process is not accounted for in the F K F rate equations. This is most readily seen from consideration of a fictitious intramolecular singlet-triplet annihilation process. Physically, such a process would require simultaneous excitation of two electrons to excited states within one molecule, a most improbable event. The resulting rate equations would be exactly the equations (0)-(3) (with the term 3' added, if a chemical transition occurs), i.e. the equations (0)-(3) are purely intramolecular in nature.
4. Corrected Rate Equations
In Fig. 2 we show the explicit intermolecuIar nature of the S-T annihilation process. Primed states belong to reaction center chlorophylls, double-primed states correspond to antenna chlorophylls, along the lines of the F K F model. Accounting for the intermolecular nature of S-T annihilation, and including the regeneration term 3', we have the following set of rate equations for the
F~G. 2. Schematic representation of the explicit iatermoleeular nature of the singlettriplet annihilation process, which is denoted by the pair of arrows. See text for discussion of symbols.
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12"> -~ 10"> + 13'>)
system, within the F K F scheme (with 11'> +
, t , I 0 = 19'o= - . 4 t IoNoI +0-2oN2 +0-1oNz
o=~,~
=
o = R~ =
I
!
I
!
,
(0')
t
,
,!
(1')
0-21Nz-0-1oN1+0-sl N 3 - 0 - , N 1 N 2 I
l
t
!
,
,
,
,
A loNo -l'-0-32 N3 -0"21 N2 - 0-20 N2 -I-7 !
U
,
r
,
0 = R ~ = 0-. N I N2 -- (/~ + 0"32 "1-0-31)N3 o =
~3 =
0 =/q~
=
-A"IoN'~ +d~oN'~ +0-1oN1 . . . +0-.N1 . . . . N2 ll
II
It
It
l,
l,
(o")
0")
0-21N2-0-1oNx 11
(29 (3')
It
It
It
l
11
0 = 1V'~= A I o N o - 0 - 2 o N 2 - 0 - 2 t N 2 - 0 - , N I N v
(2")
Solution of equations (0')-(3') under steady state conditions leads again to r =
pN~.
Since it is highly implausible that antenna chlorophylls are converted to reaction center chlorophylls during photosynthetic activity, and conversely, we can also write under steady state N'o + N'~ + N ; + N'3 = K'
(6)
N~ + N't' + N~' = K"
(7)
where K" and K' are constants. We note that equations (0")-(2") can in principle also apply to reaction center chlorophylls (i.e. the dimer partner of the molecule described by the primed system of equations). In the F K F framework, however, the doubleprimed equations describe antenna chlorophylls. We consider the fluorescence yield for the double primed system. The fluorescence yield is defined as the ratio between the radiative decay rate 0-rad of state 12") and its total decay rate. The rate a'~o may contain an internal conversion contribution, as well as an intermolecular radiationless resonant energy transfer portion. We therefore write 0-,ad = f ~ 0 , where f is a constant of value less than 1. The fluorescence yield, ~b, is then = f0-~0/(e~o + 0 - h + 0-.Ni). Since Ni increases with illumination intensity, reaching perhaps a saturation value, eventually, we see immediately that the fluorescence yield for the double-primed system cannot increase with increased illumination, but stays constant, perhaps decreasing on sufficiently strong illumination. While the S-T annihilation process can involve only antenna chlorophylls which lie close to the reaction center, there is very efficient resonant energy transfer within the antenna system, so that the double-primed system does describe the antenna chlorophylls. It is conceivable to consider the situation wherein reaction center singlet energy can find its way into the antenna system. This
ENERGY U P C O N V E R S I O N IN PHOTOSYNTHESIS
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possibility provides no remedy, which is shown as follows. In the F K F scheme the reaction center is comprised of two molecules. There are roughly 300 antenna chlorophylls to each reaction center, hence about 150 to each reaction center molecule. If the increased PSII fluorescence yield (by about 0.025) is due in reality to increased reaction center fluorescence, then the reaction center fluorescence yield would have to exceed unity. We are thus led to conclude that the F K F scheme does not predict the observed PSII fluorescence increase under strong illumination, but leads to constant fluorescence yield of PSII, except for possible decrease under very strong illumination. The lack of prediction of this fluorescence increase can perhaps be remedied, if one turns the F K F scheme around. Suppose, for the moment, that an antenna chlorophyll in the lowest triplet state interacts with a reaction center chlorophyll in the first excited single, state. Then, the state reached upon upconversion is a state of the antenna chlorophyll molecule. This situation is at first starting, since one is accustomed to consider the reaction centers the loci of the photosynthetic activity. For the moment we simply note that the upconverted antenna chlorophyll molecule must be associated very closely with the reaction center, by virtue of the r-6 dependence discussed in section 2. More detailed considerations are deferred to section 5. For the moment we pursue the consequences of the "reversed" situation. The double-primed system of equations now describes reaction center chlorophylls, whereas the primed system now describes the antenna chlorophyll system. The double-primed system contributes little to the PSII fluorescence, and the increase in PSII fluorescence on strong illumination must be extracted from the primed system of relations [(0')-(3'), and (6)]. We solve for N~ under steady state conditions. Adding equations (1') and (3') we have - (a;2 +
fl)N'3 +
a~ t N ~ - a t o N~ = 0
(8)
which, together with relation (0'), yields
{ - A 'IoNg+(a;x + 0.2D)N:~}/(fl + 0"32) = n~. From equations (8) and (9) we obtain . N2)/0.10 . . = N1. (A .I 0 N. O- . 0"20
(9) (10)
Substituting equations (9) and (10) into equation (3') we have It
l
I
l
,
,
l
t
,
O'uN2A I o No/0.1 o + (/~ + 0"31 + 0"32) A lo No/([J + 0"32) It
t
•
/
,
I
I
t
,
= {*.N2a20/alo+(fl+a3t +0"32)&2t+a20)/(fl+a32)}N2. (11) At this stage the quantity N~ remains troublesome. In order to deduce the behaviour of N~ as function of illumination intensity we digress briefly into consideration of a more simple system, as shown in Fig. 3. For
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o/l::
At,
l
t
10
1o~
F~o. 3. Three-levelenorgy transfer scheme. The straight arrow up denotes optical pumping, the straight arrow down denotes (including possible radiationless contribution) fluorescence. The waved arrows denote radiationless relaxation (with a possible radiative contribution in case of ~rlo).The symbols ~r~jdenote the decay rates.
this system the rate equations (steady state) are lqo = - A l o N o +a2oN2 + a i o N 1 = 0 1~l = c r 2 1 N 2 - a l o N 1 = 0 1~2 = A I o N o - a 2 0 N 2 - a 2 1 N 2 = 0 N o + N I + N 2 -- k
(12)
which, under steady state conditions, yield
No = k/{1 +AIo[(a2o +a21)+Aloa21/alo(a2o +a21)} N t = AIo No a21lcrlo(~2o + a21) Nx = AIo No/(a2o + a21).
(13)
Under low illumination intensity we have N o approximately constant and equal to k, and N 1 as well as N2 increasing linearly with Io. For very high illumination N o becomes proportional to 1/Io, leading to serious depletion of the ground state, a condition termed bleaching. Under this condition N1 and N2 become constants. We now return to relations (0") to (2") and note from the above digression that on low illumination the double-primed system behaves like the system described by the relations (12) and (13). We can, therefore, substitute N~ in equation (I 1) by ~1o, where g is a proportionality constant, as long as the illumination is not so strong, as to cause bleaching. Relation (11) becomes a,, uloA 70 Nr/a~ o + (B + a61 + ~r62)A 70 N~/(~ + a62)
= {o.0tlo O'2o/a't o + ( ~ + o~l + a;2)(a~l + o~0)/(/~ + o~2)}N~.
(14)
From the experimental operational standpoint, a constant fluorescence yield (corresponding to emission from state 12')) is reflected by a constant ratio N~]/o. Under low illumination, relation (14) yields f
t
l
F
N'2[Io -- A No/(0"21 +~r20).
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UPCONVERSION
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On high illumination, the terms in ~ in equation (14) dominate and we have l l t N'z/I o = A No/a2o.
Here it is assumed that the condition N~ = ~iro can stin be maintained when the limit of high illumination regarding t¢~ is reached. We have also made the reasonable assumption that 0.gl cannot be many orders of magnitude larger than 0%. The ratio, R', of high illumination fluorescence yield to low illumination fluorescence yield becomes I
t
I
R' = (0.21 +a20)/0.2o. (15) Prior to further considerations it is worthwhile to examine the assumption that N~ can be written as cd0 in the N~ high illumination limit. We assume that A " I 0 N~ is not so large as to cause bleaching. As long as A" is not vastly larger than A'. this assumption is reasonable. Under these circumstances the assumption N~ = cGo may break down if the quantity ¢! tt tt ~,N~ becomes comparable to 0.2o or 0.21, as seen from equation (2") (0.2o is expected to be smaller than 0.~1)- On the other hand, equation (1 l) indicates that 0.aN~ needs only exceed 0.~0 substantially for the high illumination situation regarding the primed system to be attained. If the assumption N~ = CCIo breaks down when this limit is reached, or before, then, as ' Very rough " is reached, we have simultaneously 0..N~ < 0.1o. o-uN '1 ,~, 0'20 order-of-magnitude estimate of the rates 0.~o and a~o ('~109 and ,~0103 respectively) yield 2,2/l,1~T"/~7'J~< 10-6. This means that for every reaction center chlorophyll excited to the first excited ringlet state some 106 antenna chlorophylls must be excited to the lowest triplet state. There are only about 300 antenna chlorophylls to. each reaction center. We therefore take the assumption N~ = ~Io to be substantiated, as long as 24"1o N~ does not cause bleaching. This condition satisfied, the ratio R' must be about 2 to be consistent with experiment. This yields 0.~1 ~ a~o. Since 0.~o is not a purely radiative rate, but contains a radiationless contribution, there is no difficulty in understanding the low/n vivo fluorescence yields. We have shown that the reaction center chlorophylls must operate in the first excited singlet in the F K F framework, if the PSII fluorescence behaviour is to be accounted for. Therefore, if one considers only the correlation with the PSII quantum yield doubling, justification of need for an anomalously long triplet lifetime of the reaction center chlorophylls, as well as the need for faster intersystem crossing, disappears, and becomes actually "counterproductive". Thus, there appears to be little justification for the F K F highly symmetric dimer reaction center configuration. The need for an anomalously long triplet lifetime is puzzling in any case. Even without such lengthening, the triplet relaxation rate can be expected to be some 5-6 orders of magnitude
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smaller than the remaining intramolecular rates, even if only rough extrapolation of in vitro results (Parker & Joyce, 1967) is made to the in vioo case. Finally, we address the alternative of T-T annihilation as an alternate path for unconversion. Once the term auN~ N~ is replaced by the term au N~ N~', the procedures outlined in this section can be followed. The result is that T-T annihilation may also cause doubling of the fluorescence yield on high illumination. Thus, merely on the basis of fluorescence yield considerations, T-T-annihilation cannot be ruled out, as done in the F K F model. 5. Discussion
We have up to now confined our attention very closely to following the details of the F K F scheme. One could alternately conceive of the situation, where the regeneration (term ?) does not proceed to state 12'), but to state 11') or 10'). It turns out (we delete the algebra here) that the essentials of section 4 are not significantly affected. Also, instead of direct up conversion to the charge transfer state, one can envisage upconversion to a triplet state and subsequent radiationless relaxation to a charge transfer state. Again, the essentials of section 4 are not affected. The pumping of state I1') or 12') need not be optical. One could have the radiationless energy migration processes 12")+10') ~ 10")+12') and IlU>+10 ') ,--10">+11'). These alternatives do not affect the essential content of the preceding sections. Rather than dwelling further on rate equations, we consider the question of experimental discrimination between various alternatives. If the upconversion to a charge transfer state is direct, then this state should have triplet character, if S-T annihilation pertains, and singlet character, if T-T annihilation prevails. Electron spin resonance studies might be useful in this respect. One can roughly estimate the energy of the lowest triplet state from consideration of the in vitro case, where the lowest triplet lies at about 10,000 cm -1 (Parker & Joyce, 1967). If T-T annihilation is of photosynthetic importance, then the charge transfer state cannot lie • above roughly 20,000 cm - t . Finally, the relaxation rates a~l and ~r~o are of importance. We return to consideration of the reaction center structure. The investigation of Katz and co-workers (Ballschmiter & Katz, 1969; Norris, Uphaus, Crespi & Katz, 1971 ; Katz & Norris, 1973) gives an indication of a rather unsymmetrie reaction center dimer (or oligomer) configuration. Suppose now that one of the reaction center dimer (or oligomer) partners behaves spectroscopically as an antenna molecule, whereas the other partner behaves
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IN P H O T O S Y N T H E S I S
spectroscopically as the "trap" molecule, P 700, in PSI (cf. Govindjee et aL, 1973). Then, the considerations of section 4 are still applicable, but now the upconversion involves two molecules of the reaction center, one of these being very strongly coupled to the antenna system. In this picture the unconversion of an "antenna" chlorophyll is no longer difficult to accept, but now the reaction center configuration cannot be highly symmetric. We propose a model within an upconversion scheme, which allows one to understand the fluorescence yield behaviour of both PSI and PSII. This model is summarized in Fig. 4. In this figure the molecule A is an antennalike chlorophyll of the reaction center and the molecule T is the trap molecule ~HOTOSYSTEM I
- - - - S
PH OTOSYSTEM II CT
CT
SO
so
I
(or TI)
SO
A
T"
A
So
T
FIG. 4. Model for the primary mechanism of light utilization by chlorophyl a in photosynthesis. A denotes an antenna-like chlorophyl molecule associated with the reaction center; T denotes the trap molecule. Here So, St, TI, and CT denote the ground state, first excited singlet, lowest triplet, and charge transfer state, respectively. See text for discussion.
of the reaction center. There is in principle no reason why the trap molecule must contribute its first excited singlet to the upconversion, whereas the antenna-like molecule, or for that matter a "'bona fide" antenna molecule (which happens to lie close to the reaction center), must contribute its lowest triplet. The inverse procedure should be just as feasible. The preference of one over the other is envisaged simply to be one of the energies involved, i.e. is envisaged to depend on the emission-absorption overlap discussed in section 2 in connection with the dipole-dipole interaction nature of the process. Similar considerations apply to the T-T annihilation alternatives. T.B.
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The suggestion here is that PSII utilizes the lowest triplet state of the antennalike chlorophyll of the reaction center, such that it is upconverted to the chemically active charge transfer state. PSI, on the other hand, utilizes the trap molecule, such that it is upconverted to the charge transfer state. In terms of the considerations of section 4, PSII can then display a doubling of fluorescence yield on strong illumination, but PSI cannot. While this model is an admittedly highly speculative one, it does appear to be consistent with experiment, and utilizes a plausible upconversion mechanism (Menzel, 1974). Perhaps, rather than direct upconversion to the charge transfer state, upconversion to a high-lying triplet (or singlet, in the case of T-T annihilation) is preferable. This triplet can then decay to a chemically active charge transfer state via a radiationless process akin to intersystem crossing. The charge transfer state is here envisaged as not relaxing to states So, $1 or T1. This alternative is considered here to be the more likely one because of the relaxation rates anticipated for the charge transfer state, if attained directly through upconversion. In terms of direct upconversion, the relaxation rates a~l and a~2 can be estimated very roughly to be of the order of I0 9 s e c - I , even substantially larger, perhaps, in the case of a~l, which (now considering the S-T annihilation situation) should be comparable to the rate of internal conversion among excited singlet states. Thus, to be even competitive, fl must be of that order of magnitude, a rather high value. On the other hand, in the indirect upconversion ~ can be substantially smaller. Up to this point attention to experiment has been restricted essentially to consideration of the PSII fluorescence yield doubling upon high illumination. Assessment of the possible merit of a singlet-triplet annihilation scheme in photosynthesis must entail consistency with further experimental findings. We consider the reaction center triplet lifetimes. To provide a large quantum yield of photosynthesis a substantial fraction of reaction center chlorophylls (trap-like or antenna-like in the above scheme) must be maintained in state I1), so that further photon absorption in the antenna system will find the reaction centers "primed" for photosynthesis. This requires long triplet lifetimes. In fact, it has been found that photosynthetic electron transport associated with PSII is linear in illumination down to levels so low that each photosynthetic unit receives only about one photon every 3 see (Sauer & Park, 1965). In terms of the S-T annihilation scheme the triplet lifetimes must then be substantially longer than 3 see, an extraordinarily long lifetime. The question now is whether such a long lifetime is at all plausible. In some phthalocyanines (Vincett, Voigt & Rieckhoff, 1971) and free-base porphyrins (Gouterman & Khalil, 1974), which are structurally similar to chlorophyll, radiative triplet lifetimes can be in the
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415
10-100 sec range. The triplet radiative, as well as radiationless, decay rates in phthatocyanines increase with increasing spin-orbit coupling, with radiationless rates increasing to a greater extent (Menzel, Rieckhoff & Voigt, 1973). This suggests that a low radiative rate occurs concomitant with a low radiationless rate. Thus, a long chlorophyll reaction center triplet lifetime could be expected, but a lifetime in the second range is nevertheless quite unprecedented. Perhaps an exciton coupling, such as suggested by Fong (1974) might come into play here. Reaction center triplets have been observed via their absorption (Moraw & Witt, 1961) and ESR (Leigh & Dutton, 1974) spectra, but only upon blocked or saturated photochemistry. This might suggest that under light-limiting conditions one would expect to observe the reaction center triplets if the S - T upconversion scheme pertains, hence one might conclude that this scheme cannot be significant in photosynthesis. On the other hand, one might interpret the reaction center triplet findings as indicating that the triplets are very efficiently used up in photosynthesis and therefore elude observation unless photochemistry is quenched or saturated. The requirement of a very long triplet lifetime certainly makes the significance of S - T annihilation in photosynthesis open to question and the scheme must be viewed with much caution until reaction center triplet lifetimes in vivo and in situ become available. I am indebted to Professor Kenneth Sauer for a number of very helpful comments and for bringing to my attention several experimental findings which need to be considered in an assessment of the merit of the S-T upconversion scheme. REFERENCES BALLSC~MtTER,K. & KATZ,J. J. (1969). J. Amer. chem. Soc. 91, 2661. FONG, F. K. (1974). J. theor. Biol. 46, 407. F6RSTER, T. (1948). Ann. Phys. 2, 55. GOUTE~r~AN,M. & KHan., G. (1974). J. molec. Spee. 53, 88. GOVm~EE, PAPAGEOROIOU,G. & RAB~OWrrCH, E. (1973). Practical Fluorescence, Theory, Methods and Techniques (G. G. Guilbault, ed.), chap. 13. New York: Marcel Dekker. KATZ, J. J. & NORMS, J. R. (1973). Current Topics in Bioenergetlcs (D. R. Sanadi & L. Parker, eds), vol. 5, p. 41. New York: Academic Press. LEXGH,JR, J. S. & Du-rrON, P. L. (1974). Bioehim. biophys. Acta 357, 67. Ltr~mY, R., MAX'NE,B. & SPIKES,J. D. (1959). Discuss. Faraday Soe. 27, 149. MENZEL,E. R. (1974). Chem. Phys. Lett. 26, 45. MmqZEL,E. R., RECKHOFF,K. E. & VOIGT,E. M. (1973). J. chem. Phys. 58, 5726. MORAW, R. & Wrrr, H. T. (1961). Z. phys. Chem. 29, 25. NORMS, J. R., UPHAUS,R. A., CRESt'I,H. L. & KATZ, J. J. (1971). Proc. hath. ,4cad. Sci. U.S.A. 68, 625. PARKER,C. A. & JOYCE,T. A. (1967). Photochem. Photobiol. 6, 395. SAtmR, K. & PARK, R. B. (1965). Biochemistry 4, 2791. V~C~Tr, P. S., VOIOT,E. M. & R~cr.no~, K. E. (1971). Jr. chem. Phys. 55, 4131.
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Note added in proof: I f reaction center bleaching occurs upon high illumination the quantity ,ru0do in equation (14) can be replaced by a constant and relation (15) remains valid provided that this constant is substantially larger than cr~o.
