Photosynthesis Research 23: 283-289, 1990. © 1990 Kluwer Academic Publishers. Printed in the Netherlands.

Regular paper

Energy migration in purple bacteria. The criterion for discrimination between migration- and trapping-limited photosynthetic units A.Y. Borisov A.N. Belozersky Laboratory, Moscow State University, Moscow 119899, USSR Received 31 March; accepted 26 July 1989

Key words: photosynthetic unit, energy migration, excitation trapping Abstract

A criterion has been evolved for distinguishing between migration- and trapping-limited photosynthetic units (PSUs). Its application to purple bacteria has proved their PSUs to be of trapping-limited type. It means that any improvements of the molecular structure of their PSUs cannot noticeably increase the overall rate constant of excitation delivery from antenna BChls to reaction centers (RCs).

Abbreviations; PSUs- photosynthetic units, RCs- reaction centers, Chl- chlorophyll, BChl- bacteriochlorophyll, R-intermolecular distance, q~e, tk~-quantum yields of the primary excitation trapping and wasteful losses respectively, zn- excitation and fluorescence lifetimes respectively

Introduction

Energy migration plays a very important role in photosynthesis: this phenomenon is responsible for an efficient 'harvest' of incident light and its channeling to energy-converting RCs. The appearance of extended 'molecular antenae' was an outstanding event in the evolution of photosynthesis because the light energy absorbed by RCs is not sufficient for sustaining life even in the simplest living cells. Most photosynthetic organisms have more than a hundred antenna molecules per RC. It means that, on average, hundreds ofintermolecular jumps of an excitation must precede its trapping in RC. And here the important questions arise [which were extensively discussed in the literature, e.g. in the reviews by Pearlstein (1982), Zuber (1987) and others]. 1. What is the space organization of such molecular antennae like? 2. Is it really important for efficient energy migration? In a series of works by Fetisova and coworkers

[see Fetisova et al. (1985a-d) for example] the case of RCs as irreversible traps was extensively studied. The authors of these works have stated that the involvement of rectangular regularity in the mutual positions plus specially introduced similar orientations for antennae chlorophylls may increase the overall rate constant of excitation delivery from them to RCs by tens, and even hundreds of times. In quantitive terms it is the most radical standpoint among the group of authors who believe photosynthesis efficiency to be governed by the energy migration rate (migration-limited models of PSUs). The alternative PSU models were analysed in the works of Robinson (1967), Paillotin (1972), Knox (1977), Borisov (1978), Pearlstein (1982), Borisov (1986), and Borisov (1987). In this paper an attempt is, at least, made to distinguish between these models with reference to purple bacteria.

Method

The method applied was first used in the work of Borisov (1987). In earlier works PSU models

284

00b

0b

0

0

0

0

O@

@0

@ 0

O0

0 A

B

Fig. 1. The scheme of two photosynthetic units with 18 (A) and 12 (B) pairs of BChl antenna molecules surrounding one reaction center. All circles denote pairs of the long-wavelength BChl molecules: P870 (black circles) is in the center, its six neighbours (grey circles) are denoted as 'a' and the outer BChl molecules as 'b'.

analysed had rectangular regularity. Even for a square of 25 molecules (24 antennae molecules and RC in the center) one needs to solve a system of six differential equations representing five types of antenna Chls and RC. It is difficult to solve such a system analytically, and that is why most theoreticians preferred to deal with different statistical methods (like Monte-Carlo, the probability matrix, etc.). Starting with the work by Kudzmauskas et al. (1983) we have introduced a hexameric antennae structure which has greatly simplified the strict analytical solution of a corresponding set of differential equations at least for the class of simplest photosynthetic organisms, the purple bacteria, having no more than 30-40 antenna molecules per RC. This approach appears to be more reasonable, because (a) the hexameric type of antenna structure was reliably established in the works of Miller (1979) and Stark et al. (1984), (b) the quantity of antenna BChls per RC is now widely accepted to range from 24 (Zuber 1987, Zuber et al. 1987) to 36 (Clayton 1980, Parson 1987, Zuber et al. 1987) for purple bacteria like Rps. viridis and Rh. rubrum with homogenous long-wavelength antenna molecules. A model with 12 pairs of BChl molecules lying in the same membrane plane (Zuber et al. 1987) and surrounding on RC (Fig. 1B) will be analysed below for simplicity. (a) Each circle in Fig. 1 represents a pair of antenna molecules. Six ones designated as 'a' are in the inner, and those designated as 'b' (six in Fig. 1B and 12 in Fig. 1A) are in the outer circles surrounding

one RC special pair. The quantity of 24 BChl molecules per RC corresponds to Zuber's model for BChl b containing bacteria. (b) All antenna and RC BChls have the same overall rate constants (Ks) for the trivial intramolecular deactivations of singlet excitations (fluorescence, singlet-triplet conversion, conversion into heat, etc.). Note that hardly any noticeable effect appear if these Kz deviate within 30%. (c) All BChl molecules have similar absorption and fluorescence spectra. (d) Only excitation transfer to the closest neighbours would be considered. For example, each pair of molecules of the 'b' types have two 'a' neighbours in Fig. 1B and one in Fig. 1A. The contribution of the more remote molecules is well below 6-8%. (e) The rate constants for intermolecular excitation transfers are of the same value ( K . ) for each neighbouring BChl pairs.* (f) P870 of RC (black circle in the center of PSU) in addition to the trivial excitation deactivation (Kz) and excitation migration 'channels' to six amolecules have the excitation trapping ability, Ke being the corresponding rate constant. This excitation trapping is assume to be irreversible. As in real experiments, we shall consider a practically infinite ensemble of such PSUs. At the initial moment t = 0, they are assumed to be illuminated by an ultrashort light pulse of such energy that only * This model works even more precisely if the intermolecular spacing between 'a' and 'b' molecules is smaller like in Fig. 1A [see formula (3a), (3b)].

285 a small PSU portion (< 1%) would absorb a photon, so that hardly any nonlinear processes arise. The concentrations of photoexcited BChls in 'b', 'a' and P870 pairs will be henceforth designated as b*, a* and p* respectively. Evidently at t = 0 we have uO i , , ."t*O , , . "PO , , , = 6:6:1. The dynamics of their subsequent behavior would be governed by the differential equations: db*

dt da* dt

Kzb* - 2Kmb* + 2Kma*

(la)

kza* - 3Kma* + 2Kmb* + 6Kmp* (lb)

dp*

dt

kzp* - 6Kmp* + Kma* - Kep*.

(lc) Analysis of solutions for equations (la-c). It is well known that the solutions for sets of 'n' linear differential equations are represented by a sum of 'n' exponentials (three in our case). For example, a*(t) will be obtained in the form a*(t) = al e x p ( - 2 i t ) + a2 exp ( - 2 2 t) + a3 exp ( - 2 3 t). The amplitudes a~, b~ and Pl depend on the initial conditions and rate constants of separate processes. The exponential parameters 2~, 22,23 depend on the particular constants. Solution obtaining procedures will be omitted below (one can consult some mathematical manual); we shall analyse these solutions in application to our model. The following general conclusions are of importance. (a) If the term - K e p * in Eq. (lc) was absent all concentrations b*(t), a*(t), p*(t) would decay at the same rate constant equal to K~ and the ratio

b*(t):a*(t):p*(t) = 6:6:1 would survive for every moment. Excitation migration between 'b' and 'a' and 'a' and 'p' molecules would produce no effect because the direct and reversed excitation flows would be equal. (b) The term -K~p* changes the whole picture. Now 'p' molecules have more deactivation channels (K~ + Ke) than those of 'b' and 'a' types (K~). Therefore their excitation concentration would decay more rapidly and for every moment t > 0 we should have

p*(t) p*(t)


1011s -1.

Our criterion does not depends on the particular PSU structure either. It depends only on the precision of the experimental data used, mostly on the N/Np, Zfl = z * and K¢ values. N and Np. It appears likely that No = 2 is now ultimately established at least for the great majority of purple bacteria. As to the N value, N = 24 is currently the minimal quantity of antenna molecules per RC. Some authors claim N to be rather within 30-40 (Clayton 1980, Parson 1987), but this factor can only increase the value of calculated 3~. For N = 36 formulae (3a) gives 3~ = 3" = 6080 ps, just the same as the experimental values cited above. Evidently this argues in favour of our reasonings. Excitation lifetimes. The values of fluorescence and excitation lifetimes were measured for some purple bacteria by many authors. The first picosecond experiments (Borisov and Godik 1970, Bor-

288 isov and Godik 1972) were performed with limited precision. A number o f subsequent ones [for example, Campillo et al. (1977), Razjivin et al. (1982), Nuijn et al. (1986) and Sundstrem et al. (1987)], both of absorption and fluorescence types, suffered to various degrees from the nonlinear processes caused by too powerful laser pulses. Only in the recent fluorescence experiments (Freiberg et al. 1984, Borisov et al. 1985), conducted under high repetitive laser pulses of negligible energy ( ~ 106 photons per pulse), can the results be regarded as reliable, without any involvement of biexcitonic interactions. The recent absorption laser studies (Nuijn et al. 1986, Sundstrem et al. 1987, A b d o u r a k h m a n o v et al. 1989) were performed with light pulses ~ 1012photons, at which level they may be considered as rather satisfactory with only a minor quantity of excitations subjected to mutual nonlinear interactions. Trapping rate constant KRec = (rt, ) -t. This is the most crucial parameter. It was measured independently in five laboratories for Rhodospirillum rubrum, Rhodobacter sphaeroides and Rhodopseudomonas viridis reaction centers. z~ =

5-7ps

z* =

4.2 ___ 0.2 ps (Woodbury et al. 1986)

r*

2.8 + 0.3 ps (Martin et al. 1986)

=

z* =

(Paschenko et al. 1985, Freiberg et al. 1985)

3.5 + 0.6 ps (Kirmaier et al. 1988)

Thus, it seems reasonable to take this parameter within 3-5 ps. The only doubt is whether it is really the primary trapping t i m e - - m a y it not be some secondary trapping process? The hypothetical primary trapping process was suggested in the work of Fok and Borisov (1981). It was proposed to be a charge transfer state within two BChls of RC special pair: (P870)* ~ (P + P - ). It was proved in this work, that such a state may stabilize in a small fraction of a picosecond due to polarization of the nearest charged groups of proteins or proteinbound water molecules. Purple bacteria with heterogeneous antenna BChls. Most of the purple bacteria are known to have their antenna spectrally heterogeneous; usually three spectral forms dominate. For example, Chromatiurn cells have in vivo B800+ B850 BChl forms in addition to the long-wavelength B890 one.

But it appears likely that all these bacteria have similar long-wavelength antenna core around RCs (Clayton 1980, Zuber et al. 1987). Only the quantity of shorter wavelength BChls may vary physiologically up to hundreds of molecules per RC. It was demonstrated in the work of Borisov (1986) that only a small fraction of excitations is usually present in the B800+B850 forms which is equivalent to a small (10-15%) increase of the B890 form. This small increase of what we call the equivalent number of B890 molecules per RC brings about a correspondingly small increase in the excitation (fluorescence) lifetimes within the same 10-15% (Borisov 1986). Bearing in mind that the optimal N value for such a homogeneous antennae approximates to some 40-80 long-wavelength BChl molecules per RC (Borisov, unpublished), the two main conclusions of this work are believed to be likewise applicable to the purple bacteria with an extended heterogeneous antenna.

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