12086
J. Phys. Chem. 1996, 100, 12086-12099
Primary Charge Separation and Energy Transfer in the Photosystem I Reaction Center of Higher Plants Nigel T. H. White,† Godfrey S. Beddard,*,†,‡ Jonathan R. G. Thorne,† Tim M. Feehan,† Tia E. Keyes,† and Peter Heathcote§ Department of Chemistry, UniVersity of Manchester, Manchester M13 9PL, U.K., and School of Biological Sciences, Queen Mary and Westfield College, Mile End Road, London E1 4NS, U.K. ReceiVed: February 15, 1996; In Final Form: April 22, 1996X
Using low intensity femtosecond duration laser pulses at 708 nm, we have observed absorption transients associated with electron transfer through the primary electron acceptor A0 in the photosystem I (PSI) reaction center from spinach under nonreducing conditions. At this wavelength the electron donor P700 is excited directly, although some antenna chlorophylls are also excited. Using a nanosecond duration preflash of 690 nm to oxidize P700, and then measuring the absorption transients from the antenna alone, it is possible by subtraction to isolate the absorption transients arising from electron transfer. We discuss this method critically. The spectrum of A0- - A0 does not appear promptly but takes ∼3 ps to reach maximum intensity and resembles those spectra previously obtained from higher plants, with a maximum bleaching at 685 ( 2 nm and a shoulder in the region 670-675 nm. The decay time of the primary radical pair P700+A0- is calculated as 20 ps. Analysis of absorption transients indicates that the intrinsic rate constant forming the primary radical pair P700+ A0- cannot be measured directly because energy migration in the antenna is fast and quenching is approaching “trap limited” behavior. With use of a detailed model of the antenna energy migration based on the X-ray structure, the intrinsic rate constant for electron transfer is estimated as k1 ∼ 0.7 ps-1. The implications of these findings on energy and electron transfer are discussed.
1. Introduction There are two types of photosynthetic reaction center in the oxygen-evolving photosynthesis of plants and cyanobacteria, which each have bacterial counterparts.1 The high-redox potential or “quinone reducing” type II reaction centers are found in photosystem II, purple bacteria, and green filamentous bacteria. In this type of reaction center the electron transfer cofactors are bound to two core polypeptides which do not bind antenna pigments. Isolation of these reaction centers from the accessory antenna pigments has allowed the detailed study of primary charge separation by ultrafast spectroscopy.2-8 Low-redox potential or “ferredoxin reducing” type I reaction centers are found in photosystem I (PSI), heliobacteria, and green sulfur bacteria.9 These contain a relatively large number of, i.e., approximately 100, antenna pigments intimately bound to the two reaction center core polypeptides. These antenna chlorophylls (Chl) form an integral part of the reaction center and cannot be completely removed by detergent. Consequently energy migration and electron transfer are intimately connected, each process being “entangled” with the other. The antenna has been intensively studied. It is heterogeneous and contains many chlorophylls, several types of which can be distinguished spectroscopically.10-13 The longest wavelength pigments have peak absorptions at 712-724 nm which are below the energy of P70010,12,14,15 and act as pseudotraps. Several different arrangements of pigments have been proposed to describe the antenna energy transfer.10-12,14,16,17 Some experiments and calculations10,11,14,16,17 have led to the suggestion either that spectral funnels18 with the longest wavelength absorbing chlo* Author to whom correspondence should be addressed. † University of Manchester. ‡ Present address: School of Chemistry, University of Leeds, Leeds LS29JT, U.K. § Queen Mary and Westfield College. X Abstract published in AdVance ACS Abstracts, June 15, 1996.
S0022-3654(96)00470-4 CCC: $12.00
Figure 1. Schematic of the arrangements of the pigments and electron transfer components in the reaction center: data taken from Krauss et al.20 The special pair P700 is at the center of the picture, possible accessory chlorophylls are C1 and C2, the primary electron acceptor is A0, and the secondary electron acceptors and A1 and Fx, FA, and FB.
rophylls nearest to P700 or that pools of pigments exist. Other experiments, it is claimed,12,19 do not support these possibilities. The trapping of energy by P700 has been described as near to both diffusion limited13 and trap limited.17 Recently the geometry of the reaction center and antenna has been partially solved by X-ray crystallography20,21 and is shown schematically in Figure 1, where for clarity the protein has been removed to expose only the reaction center and antenna pigments. This structure shows how the reaction center electron transfer cofactors fit within what may loosely be described as an oval bowl of antenna chlorophylls.21 The nearest antenna molecules to the electron transfer cofactors are on the lumenal side of the structure near P700, the stromal side being the open top of the bowl. The general arrangement of the electron transfer chlorophylls is proposed to be similar to those in purple photosynthetic bacteria22,23 in that adjacent to the dimer of chlorophylls acting as electron donor (P700) are found two © 1996 American Chemical Society
Photosystem I Reaction Center of Higher Plants
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accessory chlorophylls (C1, C2) and two electron acceptors (A0, A0′) arranged about an approximate C2 symmetry axis. It is widely accepted that P700 represents a chlorophyll dimer,24 but the exciton coupling between reaction center chlorophylls and between antenna molecules in PSI has not been discussed as extensively as that for purple photosynthetic bacteria8,25,26 or PSII.27 To describe P700 strictly as a dimer is incorrect,28 but, for clarity, we use the term dimer in this paper as a shorthand and remember that while the largest coupling is between the special pair of chlorophylls, the couplings between either of these two molecules and the others are not negligible. Similarly, exciton coupling between antenna pigments may be calculated, although not as precisely since the molecular orientations are not yet finalized.20,21 However, this calculation indicates that the coupling is small enough that after ∼100 fs the molecules may be treated as if they were separate so that energy migration by hopping occurs. Following the primary electron acceptor A0 is a phylloquinone electron acceptor A1, which in turn donates electrons to Fx an iron-sulfur center bound to the two reaction center core polypeptides psaa and psbb.29-31 The sequence of electron transfer events is shown in eq 1. The rationale behind our experiments was to excite P700 directly and observe the intrinsic rate of electron transfer k1 to A0 in the absence of, or prior to, excitation diffusion from the antenna. k1
P*700 98 A0 f A1 f [Fe4S4]X
(1)
The only previous studies directly exciting P700 used relatively long pulses of 35 ps.32 A (13 ps)-1 rate constant for electron transfer to A0 was measured33 using intense 1 ps laser pulses at 610 nm, which excited P700 indirectly via the antenna pigments. However, the conclusion that P700+A0- forms around 13 ps 33 has subsequently been challenged by a number of fluorescence and transient absorption studies.12,13,17,34,35 During the course of our investigation two separate reports appeared exciting P700 via the antenna and reported time constants for charge separation between P700 and A0 of 4-6 ps.36,37 Hastings36 used membrane preparations from the cyanobacterium Synechocystis PCC 6803 psbb DI/DII/C- which lacks PSII, and contains 100 Chl per P700. Kumazaki37 used a PSI preparation extracted with ether containing a residual 12 Chl per P700. The nature of A0 is uncertain, but it has been suggested that it is a monomeric Chl-a.38,39 The A0- - A0 difference spectrum associated with the reduction of the primary acceptor was previously obtained32,40 by comparison with absorption changes in the presence of open and closed reaction centers and under conditions where A1 was reduced, so that the lifetime of A0was prolonged into the nanosecond region. Similar A0- - A0 spectra have been obtained by comparing absorption changes in PSI reaction centers in which the secondary electron acceptor A1 has been extracted or reconstituted.39,41 These A0- - A0 difference spectra resemble published (Chl-a- - Chl-a) in vitro difference spectra,42 suggesting A0 could be a Chl-a monomer absorbing near 690 nm. However, a sideband is seen around 673 nm, which is not characteristic of a Chl-a spectrum. It has been suggested that the difference spectrum includes contributions from electrochromic effects on pigments close to the primary electron donor P700 and acceptor A0.17,43 The recent studies of A0- - A0 in the cyanobacterium Synechocystis PCC 6803 psbb DI/DII/C- 36 gave a spectrum interpreted as arising from a Chl-a monomer peaking near 690 nm, but lacking the sideband around 673 nm seen in higher plant PSI reaction centers.32,39,41 Early indirect measurements,44 which suggested that A0- was reoxidized in 40 ps were supported by Shuvalov et al.,32 who
reported that A0- was reoxidized in 32 ( 5 ps. More recently this time-constant was measured as about 20 ps.36 However, each of these values is much shorter than the corresponding value in other types of reaction centers. In PSII,45,46 purple bacteria2-8,23,47 and green filamentous bacteria48 time-constants for electron transfer from the bacteriopheophytin primary electron acceptor range between 200 and 500 ps. In heliobacteria49,50 and green sulfur bacteria51 forward electron transfer from the primary electron acceptor is characterized by an approximately 600 ps time-constant. Hastings et al.36,52 studied energy and electron transfer processes in a PSI containing membrane preparation from the cyanobacterium Synechocystis PCC 6803 psbb DI/DII/C-. Energy transfer and trapping at low 52 and high 36 excitation energies was discussed. At high excitation energies (4-8 photons/reaction center) the spectrum of A0- - A0, and reoxidation kinetics of A0- of 21 ps were reported.36 Recently, however, Hecks et al.53 have used picosecond photovoltage and fluorescence methods to study the same mutant and reported a time-constant for trapping of excitons of 22 ( 4 ps, and a timeconstant for reoxidation of A0- of 50 ( 15 ps. They attribute the results of Hastings et al.36 to the stronger annihilation present in that experiment. We here report measurements of absorbance transients associated with electron transfer through A0 in PSI reaction centers isolated from spinach (Spinacea oleracea). Excitation was at 708 nm, which maximizes excitation into P700 relative to equilibrium when other pigments are present. Under lowintensity excitation energy conditions and with P700 neutral, we observe A0 reduction and reoxidation, in contrast to earlier predictions.34,43 Our results in conjunction with a model of energy migration indicate that the primary radical pair P700+ A0- forms in 1.3 ps. We aim to show that the intrinsic rate constant cannot be measured directly but can only be obtained with an intimate knowledge of energy migration in the antenna. The kinetics of the reoxidation of A0- that we observe are broadly comparable with the results of Hastings et al.36 but not with those of Hecks et al.53 We observe a spectrum of A0- A0 that resembles those previously observed in spinach PSI reaction centers32,39,41 but differs from that observed in cyanobacteria.36 In each of the experiments so far reported in the literature antenna absorption transients had to be subtracted in order to identify and isolate transient decays and spectra associated with electron transfer. This is necessary as the reaction center cannot be isolated from antenna pigments as in purple bacteria. One approach used in the subtraction method was to alter the redox state of P700 chemically33 and so eliminate electron transfer, the other was to oxidize P700 with a 532 nm, nanosecond duration preflash32 and so measure antenna transients alone.36,37,52 We also examine critically the antenna subtraction method and point out its shortcomings. 2. Methods and Materials Two different PSI reaction center preparations from market bought spinach (Spinacea oleracea) have been studied containing about 45 chlorophyll antenna molecules per reaction center. One was prepared using high concentrations of the non-ionic detergent Triton X-100 54 and was similar to the preparation of Shuvalov et al.;32 the other was prepared by the method of Malkin55 using lauryldimethylamine oxide and low concentrations of Triton X-100 and was the preparation used by Wasielewski et al.33 Both preparations gave similar results. Samples in 50 mM Tris-Cl at pH 8.0 were prepared in a 1 mm path length cell. An absorbance of around 1.0 at the peak
12088 J. Phys. Chem., Vol. 100, No. 29, 1996
Figure 2. Ground state absorption spectrum of spinach preparations (dotted line) and calculated spectrum (solid line). See text for details.
wavelength of 674 nm was used for recording transient spectra and double this for transient decay measurements. Figure 2 shows a typical absorption spectrum. The samples also contained 1 mM sodium ascorbate and 100 µm phenazine methosulfate (PMS) to re-reduce P700+ between flashes at 10 Hz. No degradation of the material was observed during the time course of the measurement, fresh samples were used for each measurement. The method of Heathcote et al.56 was used to doubly reduce the phylloquinone electron acceptor A1 57 and so to prolong the lifetime of A0- to several nanoseconds. The sample was adjusted to pH 10.0 with 0.2 M glycine-KOH buffer, and 0.2% (w/v) sodium dithionite was added under anaerobic conditions. The sample was then illuminated for 1 h in an ice bath at 4 °C, also under anaerobic conditions, by a quartz halogen lamp filtered through a copper sulfate solution. The cuvette was sealed with the sample under argon after this period. The femtosecond pump-probe transient absorption experiments were performed as described previously58 but with the addition of a continuum amplifier. Pulses of k-a, then kq ) ka and trapping is diffusion limited, and when k-a > k1 then kq ) k1ka/k-a, which is the trap limited case. We estimate values for the rate constants for each type of trapping by fitting the data using the kinetic scheme represented in eq 4. This equation has been solved by using the eigenvalue method; further details are given in the Appendix. Each species i has a population at time t of
Pi ) ∑ci,j exp(λjt)
(6)
j
where λj are the eigenvalues, which are always negative, and ci,j is the contribution of species i to the decay. As all of the eigenvalues are different, none of the species is described by a single exponential decay. In Figure 10 we compare the calculated decay profiles for P700*, P700+, A0-, and S* compared with their experimental counterparts, except P700* which has not been unambiguously observed. The upper part of Figure 10 relates to diffusion limited quenching; the lower part, to trap limited quenching. The data were fitted simultaneously with the calculated profiles and one set of rate constants for ka, k-a, k1, and k2 by matching only the calculated amplitudes to the data as the relative extinction coefficients are unknown. An additional decay of (3.5 ps)-1 (60% amplitude) is present in the antenna decay, S*, and is attributed to energy redistribution before trapping, but for clarity was not added to the calculated decays, Figure 10. The observed antenna decay time at long times is 20 ( 3 ps (see section 3.2). The different appearance of the 685 nm transient identified with A0/A0- in Figure 10,
Figure 10. Comparison of calculated (smooth lines) and experimental data for a simultaneous fit of each transient under diffusion limited conditions (top) and trap limited conditions (bottom). Curves a correspond to P700+; curves b to A0-, at 685 nm; curves c to the P700* calculated curve only; curves d to the antenna decay; and curves e to the calculated antenna (long component only). See text for further details.
curves b, is due to the two limiting methods of analysis described below. In the trap limited case all of the energy initially absorbed into P700 is transferred to the antenna. In the other diffusion limited case no energy from P700* reaches the antenna. We now aim to show that experiment is closer to the trap than the diffusion limit. 4.2. Diffusion Limited Quenching. In the diffusion limited case (Figure 10 (top)) the data are fitted with ka ) (20 ps)-1, k-a ) (20 ps)-1, k2 ) (6 ps)-1, and k1 ) (0.5 ps)-1. Note that the calculated electron transfer rate constant k1 is very large in this limit, and therefore the 685 nm transient (both experimental and calculated), attributed to A0- formation, rises rapidly. The experimental 685 nm transient was obtained as in eq 2 with R ) 0 as appropriate to diffusion limited quenching. The calculated decay of A0-, top curve b, is clearly too short to properly match the experimental data at both shorter and longer times. The rapid decay rate, k2, is required to produce a maximum absorption of A0/A0- at about 3 ps. 4.3. Trap Limited Quenching. In the trap limited case (Figure 10 bottom) the calculated rate constants are ka ) (3.5 ps)-1, k-a ) (0.5 ps)-1, k2 ) (20 ps)-1, and k1 ) (2 ps)-1. The experimentally measured fraction of excitation that enters P700 directly is 0.21; we associate this fraction with R (eq 2) in calculating the A0 (685 nm) transient which assumes that all excitation into P700 enters the antenna. The exact amplitude of the A0/A0- transient will lie between that calculated with R ) 0 and 0.21, i.e., between Figure 10b (top) and Figure 10b
Photosystem I Reaction Center of Higher Plants (bottom) and will depend upon the rate constants but will be closer to the trap limit. The rate constant k2 is less than that measured directly from the A0- (685 nm) transient, which is (32 ps)-1. This is a consequence of A0 being populated from P700* which itself must decay slowly (Figure 10b bottom)) as a result of the rapid energy transfer to and from the antenna. Our 20 ps time constant is almost identical to the 21 ps time constant for A0- reoxidation observed in cyanobacteria by Hastings et al.36 but does not agree with the 50 ( 5 ps reported by Hecks et al.53 All of these lifetimes are, however, 5-10 times faster than the comparable event in the type II (bacterial) reaction centers.2-8 The model of eq 4, while simple, does explain the overall features of the kinetics as may be seen in Figure 10. For example, the calculated energy transfer rate constant k-a from P700* to the antenna is faster than that for the electron transfer step k1 by 4 times; consequently the 13 ps decay time of the antenna is caused by the relatively small value of k1 compared to k-a. A comparatively rapid transfer from P700* to the antenna is implied not only by the large spectral overlap of pigments but also by the small activation energy of fluorescence yield which has been measured as 0.08 eV (645 cm-1) in spinach and 0.036 V in Synechocystis,63 both of which are comparable to kBT at room temperature, and by the rapid appearance of transient bleaches of shorter wavelength chlorophylls than those excited. 4.4. Energy Migration and the Intrinsic Donor-Acceptor Rate Constant, k1. In the antenna we may view electron transfer as a time-dependent process. When excitation is primarily into the peripheral antenna pigments, the electron transfer rate is virtually zero for a period of a few picoseconds as energy has yet to migrate to P700; subsequently the electron transfer rate increases. For our model of energy transfer which we discuss in detail below, Figure 11(top) shows the fractional excited population of the special pair, or excitation residence probability, at time t, following excitation of the pair itself (upper two curves), or following excitation of a peripheral chromophore (lower two curves). Because we wish to study the energy migration with this calculation, there is no electron transfer from P700. We define the effective excitation cluster size as twice the reciprocal of the special pair residence probability. Figure 11 (bottom) shows the effective size of the cluster containing P700 plotted when P700 is excited directly. In a spectrally flat model this figure shows that excitation exists on the excited P700 for less than 100 fs followed by rapid transfer to a cluster of ∼610 molecules which exists between ∼0.1 and 1 ps. Between 1 and 20 ps a gradual increase of the effective cluster size occurs until all 48 molecules are involved. Introduction of funnel character to the model further emphasizes the persistence of the excitation at early times over approximately six sites only. This cluster represents the “core reaction center” of P700, accessory chlorophylls, and two acceptors. The period following 1 ps shows that the excitation spreads over an effective number of ∼21 molecules. The figure shows how the character of the funnel serves to increase the special pair residence probability (decrease the effective cluster size and localize the excitation) compared to a spectrally flat model, both for special pair and peripheral excitation (at all times longer than a picosecond). We now discuss how to calculate limits to the intrinsic electron transfer rate k1 and compare these with experiment. The observable rate of electron transfer is just the (timedependent) residence probability of the excitation on the electron transferring P700 site multiplied by the intrinsic transfer rate.
J. Phys. Chem., Vol. 100, No. 29, 1996 12093
Figure 11. (Top) Residence probability vs time of excitation on the special pair after exciting the pair (1) and a peripheral chlorophyll (2) for a funnel model (a) and a spectrally flat model (b). (Bottom) Variation of the antenna size with time for (1a) the funnel and (2a) the spectrally flat model. See text for further details.
The observed rate of electron transfer is a weighted average of the rates of the populated chromophores at a given time following excitation. We examine some model cases below and assume trap limited transfer at times t > 3 ps and an observable antenna decay rate (at long times), kq equal to (20 ps)-1. a. Upper Limit for k1. This is the special pair transfer rate in a spectrally “flat” model, where there is an equal probability of each of the 48 chromophores of the system being excited but only two of these (the special pair) being electron transfer sites; then 1/k1 ) 2/48 × 20 ps ) 0.83 ps, which corresponds to the (long time) 0.04 residence probability on P700 in Figure 11 (top, spectrally flat model). b. Lower Limit for k1. If we consider only six chromophores comprising the inner core (analogous to those of PSII) of which two are the special pair transfer sites, we obtain a residence of 0.33 and 1/k1 ) 0.33 × 20 ) 6.7 ps. Thus, on the basis of these two simple models, we obtain the limits: 0.8 ps < 1/k1 < 7 ps. c. Traps at 712 nm. We now extend this treatment to cater for spectral inhomogeneity, instead of using a spectrally flat model. When the inner core comprises two special pair pigments at 697 nm, two accessory chromophores at 697 nm, and two trap sites at 712 nm, the latter effectively trap excitations. The residence probability on the special pair is reduced from case b to a value of 0.16 and 1/k1 ) 0.16 × 20 ) 3.2 ps. It is principally the effect of these two 712 nm chromophores at the bottom of the funnel that limits the electron transfer rate.
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d. Full Spectral Model.50 We now match the whole of the observed PSI absorption spectrum with chlorophyll spectra having different maximal wavelengths, (Figure 2), and the effective antenna size is reduced from 48 by energy partitioning and is given by
∑i gi exp(-∆Ei/kT) ) 21
(7)
where gi is the number of molecules with an absorption maxima difference of ∆Ei from P700. The residence probability on P700 is 0.09 (Figure 11 (top), long time funnel case) producing 1/k1 ) 1.8 ps. The model is now described in full below. 4.5. Simulation of Energy Migration. We have refined our estimate of k1 by using dipole-dipole energy transfer to describe each step in the energy migration, starting from every pigment in the antenna, including the P700 trap, and weighting the result in proportion to the number of pigments present and their absorption and emission spectra. At each step in the calculation the rate constants ki,j from one molecule to all other molecules are included so that all possible jumps are included. We have also calculated the exciton interaction energies between all of the antenna molecules; 9 interaction energies average ∼30 cm-1, and the remainder are 1%; but, the spread of energy around the antenna slows down, and by 4 ps only 24 molecules are excited. As time proceeds P700 decreases in population due to transfer to A0, and at 16 ps most population remains in the red most pigments with some small population in a few surrounding bluer absorbing molecules. The antenna pigments are attempting to reach equilibrium with one another but are eventually frustrated by the P700*-A0 electron transfer. The relatively slow transfer from these pigments to P700 generates the observed antenna decay time; see Figure 13. We find by examining many such images that if the excitation is not into P700, it migrates mainly on only that half of the structure in which it was initially placed, which is as much a geometric effect as a spectral one.69,81 Excitation of a peripheral antenna molecule indicates a similar partitioning between the two halves of the antenna occurs. Furthermore it is clear that A0 and A0′ can act as antenna molecules, transferring energy into P700. Figure 13 compares simulated and observed decay profiles, excited at 700 nm and probed at 690 nm with k1 ) (2 ps)-1, and all other rate constant determined by the molecule’s separation and spectra. The simulated decay was calculated by weighting the populations of each molecule in the antenna as a result of exciting each molecule in turn and weighting the molecule’s population with its absorption spectrum at the exciting and probing wavelengths. The faster decaying component (Figure 13) is due to energy equilibration; the longer decay represents trapping. The longer decay rate, kcalc, obtained
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Figure 14. Calculated antenna decay rate constant (at times >3 ps) with the logarithm of electron transfer rate constant k1, calculated for the antenna with pigment composition matching the absorption spectrum in Figure 2 (a) and for a spectrally flat model (b) and using the geometry of the antenna20 and reaction center as in Figure 1. The points are the calculated data from the simulation described in the text and the solid lines from eq 5.
by varying k1 in several calculations is plotted in Figure 14 Vs k1. This figure also shows the calculated antenna decay rate when all of the pigments are of the same type (Figure 14b), so that no funnel exists. In this situation, to achieve a similar antenna decay rate, k1 must be increased by about 3 times compared to the funnel arrangement, or if k1 were unchanged, the antenna decay time would increase from 20 to 35 ps in the same sized antenna. The solid lines are obtained using eq 5. That this equation describes these data is not unexpected if trap limited quenching occurs for, as explained above, energy migration replaces molecular spatial diffusion. Equation 5 is fitted with k-a ) 1.097 ps-1 and ka ) 0.116 ps-1 for the funnel model and 2.05 and 0.091 ps-1, respectively, without the funnel. These values indicate that the equilibrium lies on the side of the antenna in both cases and more so without a funnel, hence the less effective quenching. Only at values of k1 > 20 × 1012 s-1, which is not physically realistic, does kcalc become constant and the diffusion limit reached, kcalc ) ka. Several groups have reported antenna sizes and decay times, which are summarized in Table 1. If our supposition that the antenna quenching is largely trap limited is true, these decay times contain information about the value of the intrinsic rate k1. An approximate linear relationship between antenna size and decay time has previously been observed from such data,13 and k1 ) (3.4 ps)-1 was obtained by extrapolating to zero antenna size. The “effective antenna size” has been used before to estimate k1 from the antenna decay times,37,50,52 but there is no one rational method of determining what this effective size is. This is illustrated above in our estimation of rather wide limits to k1 (Section 4.2a,c). We will take a different approach, however, and use Hemenger’s70 and Pearlstein’s68 formula describing energy migration and trapping on a lattice (eq 10). We calibrate the parameters in this formula with our simulation71 and then fit the other published data from PSI antennas with various numbers of chlorophylls. This is an attempt to overcome the difficulty of being unable to simulate energy migration on antennae with different numbers of molecules whose positions are unknown. However, we do restrict our choice to antenna surrounding PSI type reaction centers so that
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TABLE 1: no. of antenna chlorophylls, n
lifetime (ps)
calcd rate k1′ (ps-1)
ref
index, Figure 15
10 12 12 16 24 30 33 35 35 40 41 43 45 55 65 70 98 100 122
9 5.3 6.5 11 16 8 20 14 28 20 26 26 17 29 40 40 28 35 38
0.43 1.3 0.88 0.56 0.55 4.8 0.61 1.3 0.41 0.83 0.56 0.60 1.4 0.73 0.57 0.63 3.1 1.6 2.3
59 37 37 37 12, 13 37 12, 13 33 50 this work 12 12, 13 74 12, 13 74 32 52 17, 35 12, 13
2 13 12 5 3 19 8 14 1 11 4 7 15 10 6 9 18 16 17
the antennas all have similar characteristics. Pearlstein68 gives the mean antenna lifetime τm in terms of the antenna size n by
τm )
(
)(
)
2 1 βn k-a′(n -1) 1 (n -1) 1 + + + (10) ka′ kJ′ nq kJ′ ka′ k1′ k1′
where ka′, k-a′, and k1′ are the Fo¨rster rate constants for trapping from the antenna, detrapping, and charge separation, respectively; kJ′ is the rate constant for near neighbor interpigment jumps in the antenna. The superscripts refer to rate constants equivalent to those in eq 4, and the constants, β and q for a cubic lattice are68 β ) 0.262 and q ) 6. The value of n in Table 1 and eq 10 is the total number of antenna chlorophylls as opposed to the estimated effective number. Rewriting equation 8 in the form of eq 5 then, if km ) 1/τm,
km )
k1′/An BnAn + k1′
(11)
where
An )
(
)(
)
2 1 βn 1 (n -1) + ka′ kJ′ nq kJ′
and Bn )
k-a′ (n - 1) + 1 (12) ka′
The values of the constants k′a, k′J, and k′-a can be obtained from fitting eq 11 to our simulation in which n ) 48. Comparing eqs 5 and 9, A ) 1/ka and B/A ) k-a/ka, and fitting to the data in Figure 14 produces k′J ) 1.01, k′a ) 1.426 with an estimated ratio k′-a/k′a ) 0.21. The calculated68 interpigment jump time of 1/qka ) 0.17 ps is comparable to that suggested by Owens et al.13 and measured by Savikhin et al.72 and with the average time per jump taken in our simulation. The ratio k-a/ka < 1 is realistic as excitation leaves P700 at a greater rate than electron transfer k′1 as described above. The intrinsic electron transfer rate constant can be calculated from the different antenna decay measurements73 by using the data in Table 1 to obtain 1/km and n and solving eq 10 for k′1. The data for PSI are shown in Figure 15, where the literature set of antenna sizes has been normalized to our data so that all points appear on the same curve. The sequential numbers on this figure are indexes to the data in Table 1. Data sets 16-18 are from cells where the number of antenna molecules is >90,
Figure 15. Comparison of the calculated (solid line, see Figure 14)) and observed antenna decay rate constants (circles), with data taken from the references indicated (see also Table 1) vs the calculated electron transfer rate constant k1′ on a linear scale.
and these values give very large values for k′1. Our calibration of Pearlstein’s equations seems to be valid for core chlorophylls74 up to ∼65 molecules. Beyond this size the points do still fit onto the curve, but we consider that a different calibration in terms of k′a , k′-a would be needed to produce k1′ values consistent with those from smaller particles. This is presumably because our energy migration model is only accurate on a small antenna structure. One data point, (index 14, Table 1) does not fall with the rest but produces the large k′1 value of 4.8 × 1012 s-1. A reason for this could be that this decay time was obtained at high excitation intensities where annihilation is occurring. The range of values of k′1 (except index 14, 1618) fall between 0.4 × 1012 and 1.6 × 1012 s-1 with a mean value of 0.76 × 1012 s-1 which is a lifetime of 1.3 ps. While the spread of k′1 values is still large, this can be attributed to the approximations inherent in our method and particularly to the spread in the number of chlorophyll molecules present in a sample as this is less precise than the fluorescence or absorption lifetime measurement. Our calculated k′1 value for the intrinsic P700-A0 electron transfer is smaller than the (3 ps)-1 estimated by Kumazaki et al.,37 who used a simple spectral model similar to that used in our approximate calculation described in section 4.4c, but is closer to the (1.6 ps)-1 estimated by Hastings et al.,36,52 who estimated an effective antenna size of 17 so as to calculate the rate constant. Finally we note the requirements for the determination of the intrinsic rate constant k1 are to find the number, disposition, and spectral types of antenna molecules functioning to deliver energy to P700. Information at this level of detail is unlikely to be forthcoming soon, for although the position of the pigments is already known to a few angstroms, which absorbing species they belong to is unknown. However, an accurate estimate of the number of pigments combined with our model will allow k1 to be found. We note that the method of eqn 9-12 is not specific to PSI but will apply to any antenna where trap limited quenching occurs. 4.6. Magnitude of the Electron Transfer Rates P700 f A0 and A0 f A1. In this section we suggest reasons why the rates of the electron transfer processes are considerably larger than their equivalents in purple photosynthetic bacteria.2-8 In the PSI reaction center the antenna pigments are intimately associated with the core polypeptides and the electron transfer components (Figure 1). The antenna and a functioning reaction center cannot be easily and possibly never completely separated
Photosystem I Reaction Center of Higher Plants as in bacteria. As a consequence of this we suggest that in PSI a faster sequence of primary events is required than in photosynthetic bacteria so that energy is not wasted. To ensure energy is not lost from around P700* to the bulk antenna, low-energy states (such as at 712 nm) may be adjacent to P700 and partially localize the excitation energy. We observed in our simulation that this helps energy to remain near P700, either when transferred from other antenna molecules or after energy transfer from P700* when P700 is directly excited; see Figure 12. At room temperature the 712 nm states provide a sufficiently deep trap that here excitation remains longest. The advantage of the funnel in kinetic terms is a factor of about 3 in decreasing the antenna lifetime (Figure 14). However, a major factor is the antenna geometry which acts to localize the excitation close to P700 (Figure 12). A further advantage of a funnel is to increase spectral coverage.75 Examination of the low resolution structure for PSI20 indicates that P700 has two chlorophylls close to it, Chl, Chl′, which we will call C1 and C2, Figure 1. These would be analogous to BL and BM of bacterial reaction centers. The molecules comprising P700, A0, A1, and iron sulfur clusters are positioned along the proposed direction of electron transfer from the lumenal to stromal surface. They appear to be located in a cup shaped volume formed by surrounding antenna molecules but separated from them by rods of protein R-helix that are not shown in Figure 1. The chlorophylls C1 and C2, are found close to, and a little to the side of, P700 in the direction of A0 and A1. The largest energy transfer rate constants from the antenna molecules are from those below C1 and C2 on the lumenal face. However, complete functional separation of electron and energy transfer based on geometry alone would appear to be difficult to achieve because of the large spectral overlap for energy transfer between chlorophylls, and thus energy transfer can compete with electron transfer at a far larger separation. The interaction matrix element for electron transfer decreases as exp(-βr), where β, obtained empirically,76,77 is ∼1.4 Å-1 and r is the edge to edge separation. The same parameter for energy transfer decreases as r-6. Thus, with an increase in the separation from 18 Å, similar to that from P700 to A0, by the average distance to another chlorophyll molecule at about 12 Å, the electron transfer rate decreases by 1.6 × 105 times but that for energy transfer by only 21 times. Calculations of the relative rates of electron transfer based on the positions of the molecules shown in the X-ray structure20 show that, excluding accessory chlorophylls (C1, C2), electron transfer from P700 to A0 (or A1 which is at a similar distance) is larger by more than 40 times than that for any other molecule. This is entirely consistent with the rapid decrease of electron transfer rate with distance and means that geometry alone would ensure that A0 preferentially receives the electron; moreover, this discrimination would be further increased by a favorable redox potential. With similar reasoning the transfer from A0 to A1 and A1 to Fx is the most favored route (Figure 1). An additional way to increase electron transfer rate constant from P700* to A0 would be to utilize a different redox potential for A0 compared to that of the antenna chlorophylls. This is problematic, however, because if A0 is a monomeric chlorophyll, as we suggest, its redox should be similar to that of any antenna molecule. A requirement for a different redox may seem to be a minor effect, but as the excitation spends a considerable fraction of its lifetime close to the trap, the possibility of transferring an electron to an antenna molecule must be reduced. As the chlorophylls C1 and C2 are so close to P700, the rate of energy transfer to them based on distance alone is far larger than to any other molecule. The energy transfer rate to C1 or C2 from other antenna molecules is also large, and this could
J. Phys. Chem., Vol. 100, No. 29, 1996 12097 be one route by which to excite P700, but correspondingly energy could transfer from P700* to C1 or C2 and then back into the antenna in preference to undergoing electron transfer. In the trap limited model this is not critical provided that the P700 is the only trap available to the antenna and that trapping is fast compared to fluorescence. 4.7. Calculated Electron Transfer Rate Constants. The rate of electron transfer may in principle be calculated from theory,78,79 but this is difficult for such a complex molecular arrangement as a reaction center, or estimated with an empirical equation based on the experimentally measured decrease of rate with separation in a number of proteins.76,77 In either case the calculated intrinsic rate constant k1 is too large for the known separation of P700 and A0 of ∼20 Å.20 For the primary step ∆G was measured as -0.25 eV 80 and estimated as -0.33 eV 38 (Em(P700) ) 0.43 eV; Em(A0) ) -1.01 eV; E(S1) ) 1.77 eV). Using a range of edge to edge separations estimated20 as 1014 Å, the empirical equation76,77 produces maximum rates at least 100 times smaller than any experimentally estimated rate constant. Clearly as the measured reaction is so fast (∼1 ps), it must be close to being activationless, in which case -∆G and λ, the reorganization energy, are expected to have similar values. In view of this and the large separation of P700 and A0, the involvement of the nearby chlorophylls C1 or C2 acting via superexchange or as intermediate acceptors is likely. There also exists the possibility that either of the pigments C1 and C2 could be A0, but the work of Hecks et al.53 suggests that, from electrogenicity measurements, a separation of ∼19 Å from A0 to P700 is correct. Using the estimated values38 Em(A0) ) -1.01 eV and Em(A1) ) -0.8 eV, the second step A0- to A1 has an energy ∆G ) -0.21 eV and a separation of 10 Å, center to center20 from which a 6-7 Å edge to edge distance is estimated from the size of the molecules. As the reorganization energy varies rapidly with separation, using the empirical equation of Moser et al.76 only allows an approximate estimation of λ ) 0.3-0.5 eV to be made with our experimental rate constant of (20 ps)-1. The A0- to A1 reaction is thus nearly activationless with values of λ that are a little smaller than those measured79 in model donor-acceptor porphyrin-quinone molecules (0.7 eV). 5. Concluding Remarks We have excited PSI reaction centers with weak femtosecond pulses of 708 nm in an attempt to observe the decay of P700* and formation of P700+ directly but are forced to conclude that energy transfer to the antenna is faster than electron transfer to A0. Measurement of the intrinsic rate constant k1 in the absence of antenna involvement may not be possible. Using simple models of energy migration, we have estimated the intrinsic electron transfer rate constant to be between 0.14 and 1.25 × 1012 s-1 and find that the antenna quenching is trap limited. Using data from other published work and a simulation of energy migration based on the X-ray structure, the primary electron transfer rate constant was estimated as ∼0.7 × 1012 s-1. We confirm that the spectrum of A0- bleaches at 685 nm and is probably a monomeric chlorophyll and find that its formation occurs within 3 ps. The decay of the transient bleach associated with A0- is 32 ps which produces a decay time 20 ( 3 ps for the A0- to A1 step. To obtain these transients, we have used the antenna subtraction method, as have others,32,36,37 but its legitimacy must be questioned when the rate constants governing quenching of the antenna by P700+ are unknown. The conditions leading to rapid electron transfer in a protein in which the antenna is closely coupled to the reaction center were
12098 J. Phys. Chem., Vol. 100, No. 29, 1996
White et al.
discussed. It is suggested (a) that the geometry of the antenna acts to localize the excitation close to the reaction center pigments and that this effect is increased by a funnel of pigment energies and (b) that the geometry of the reaction center relative to the antenna is as important as redox in determining the path of electron transfer because the nearest electron acceptor to P700 is A0 and not an antenna molecule. Acknowledgment. We acknowledge the support of the Royal Society and SERC and an SERC studentship to N.T.H.W. We thank Professor M. C. W. Evans (University College, London) for helpful discussions, Dr. Gavin Reid for critical reading of the manuscript, Dr. B. Frankland (Queen Mary and Westfield College) for the loan of filters, and Mrs. M. Yeo and Mrs. P. Ratnesar for technical assistance. Appendix The rate equations in eq 4 can be analyzed either by direct integration or by using an eigenvalue method. As we are not particularly interested in the algebraic form of the equations, the scheme presented giving sufficient information about the interrelationships between the various species, we used the latter method to calculate the time profiles of the antenna S*, P700*, P700+, A0-, and A1-. The rate constants are defined in eq 4, and kf, kt, and k-1 (P700+ f P700*) are very small compared to the other values and were 1/20, 1/200, and 1/20 ns-1, respectively. Their exact values do not appreciably affect the calculated populations, other rate constant values are given in the text. The matrix of rate equations for the first four species is
[] [
(S*)′ (P*)′ ) (A0-)′ (P+)′
-ka - kf ka 0 0
k-a -(kf + k1 + k-a) k1 k1
0 k-1 -k2 - k-1 0
] []
0 k-1 × 0 -kt - k-1 S* P* A0-
(A1)
P+
where the prime indicates a time derivative. The solution for population P of species i of has the general form
Pi,t ) ∑xi,j exp(λjt)
(A2)
j
where x is the eigenvector matrix and λ the eigenvalues. If the initial populations of species i are defined by a column matrix P0, the population at time t is found by computing the matrix equation
P ) XetΛX-1P0
(A3)
where is a diagonal matrix of the eigenvalues, {eλ1t, eλ2t, ...}. In the simulation of energy migration (section 4.5) a similar method to that outlined here was used to solve the simultaneous differential equations. etΛ
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