J. Phys. Chem. B 2000, 104, 5625-5633
5625
Red Chlorophyll a Antenna States of Photosystem I of the Cyanobacterium Synechocystis sp. PCC 6803 J. M. Hayes,* S. Matsuzaki, M. Ra1 tsep, and G. J. Small* Ames LaboratorysU.S. Department of Energy and Department of Chemistry, Iowa State UniVersity, Ames, Iowa 50011 ReceiVed: February 3, 2000; In Final Form: March 24, 2000
The antenna chlorophyll a (Chl a) molecules of photosystem I of green plants and cyanobacteria that absorb further to the red than P700, the special pair of the reaction center, have long been of considerable interest. Recently, the results of nonphotochemical hole burning experiments at liquid helium temperatures, which included use of high pressure and external electric (Stark) fields, led to the conclusion that the cyanobacterium Synechocystis sp. PCC 6803 possesses two “red” antenna states whose S0 (ground state) f Qy(S1) origin absorption bands are at 714 and ≈708 nm (Ra¨tsep et al. J. Phys. Chem B 2000, 104, 836). The results indicated that the 714 nm state is due to strongly coupled Chl a molecules (C-714), a dimer or, possibly, a trimer. It was concluded that the 714 nm state is responsible for the fluorescence origin band at 720 nm. Presented here are the results of theoretical simulations of the dependence of the hole spectra on burn wavelength and burn fluence that are consistent with the conclusions of Ra¨tsep et al. They lead to a more detailed characterization of the two states, including determination of their site distribution functions (SDF) and the electron-phonon coupling parameters of the S0 f Qy transitions. The higher energy state is found to lie closer to 706 nm than 708 nm. The electron-phonon coupling of the 714 nm transition is strong with a total Huang-Rhys factor (St) of 2.0 due to low-frequency modes at 18 and ≈70 cm-1. The coupling of the 706 nm transition is weaker by a factor of 1.5. It is concluded that both C-714 and C-706 are, at a minimum, dimers that are not in close proximity to each other. The large widths, ≈300 cm-1, of the SDF suggest that the structures of C-706 and C-714 are fragile. The spectroscopic properties of P700, C-706, and C-714 are compared and discussed in terms of excitation energy transfer at low temperatures. A new model that explains why only about half of the PS I complexes undergo irreversible charge separation in the low-temperature limit following excitation of the higher energy bulk antenna states is presented.
1. Introduction Photosystem I (PS I) of green plants, algae, and cyanobacteria possess chlorophyll (Chl) Qy(S1)santenna states that lie lower in energy than P700* (* ≡ Qy state), the primary electron donor state of the reaction center (RC). This intriguing state of affairs also exists for PS II of green plants but probably not for the photosystem of the purple bacterium Rhodobacter sphaeroides.1 The existence of “red” antenna states raises two immediate questions, the first being how they affect the efficiency of excitation energy transfer (EET) from the bulk antenna Chls to P700 and, thus, that of charge separation. Trissl has argued that the deleterious effect of the red antenna “trap” states for EET from higher energy antenna states to P700 at room temperature is compensated by the enhanced absorption they provide at wavelengths longer than 700 nm.2,3 The second question, which this paper is concerned with, pertains to the electronic structure of the red antenna states that leads to their lying lower in energy than P700*. This question is interesting since P700 is a dimer of Chl molecules (the “special pair” of the RC) that are strongly coupled, as indicated by the observation that4 the optical reorganization energy of the S0 (ground state) f P700* transition due to low-frequency modes (phonons) is nearly as large as those of the analogous transitions in the RC of Rb. sphaeroides and Rhodopseudomas Viridis whose special pairs * Corresponding authors. E-mail:
[email protected] and jmhayes@ iastate.edu.
of bacteriochlorophyll molecules are denoted by P870 and P960, respectively (for a review see ref 5). In that review the positive correlation between the linear electron-phonon coupling that determines the optical reorganization energy, and the magnitude of the permanent dipole moment change of the absorption transition of the special pair, is emphasized. Theoretical and experimental results which indicate that the monomers of P960* and P870* are strongly coupled by both electrostatic and electron exchange interactions are also discussed. It is electron exchange coupling which results in charge transfer character that can result in a large permanent dipole moment for the primary electron donor state. The only PS I complex for which an X-ray structure is available is that of Synechococcus elongatus,6,7 a cyanobacterium. This complex exists in trimeric and monomeric forms.8 The X-ray structure is that of the trimer. The PsaA and PsaB proteins of the monomer form a heterodimeric core that houses the RC and binds about 70 Chl a antenna molecules. The structure clearly reveals P700, but the resolution of 4 Å is insufficient to assess whether interatomic distances between the two Chl monomers are short enough for significant electron exchange coupling. The structure, function, and molecular genetics of PS I have recently been reviewed.9 We recently reported 4.2 K absorption and hole-burned spectra for the trimeric PS I complex of the cyanobacterium Synechocystis sp. PCC 6803, its monomeric form and mutants
10.1021/jp000447u CCC: $19.00 © 2000 American Chemical Society Published on Web 05/19/2000
5626 J. Phys. Chem. B, Vol. 104, No. 23, 2000
Figure 1. Absorption and hole spectra of PS I of Synechocystis at 4.2 K. The hole spectrum was burned at 670 nm with a fluence of 900 J. Satellite holes are indicated by vertical lines and labeled with the wavelength of the hole maximum.
deficient in the PsaF, K, L, and M protein subunits.1 The focus in that work (hereafter referred to as paper I) was on the redmost antenna states. Before discussing the results of I and the intent of this paper, it is appropriate to first briefly review what is known about the red antenna states of Synechococcus elongatus since its PS I structure is expected to be similar to that of Synechocystis. Two red antenna states located at 708 and 719 nm (low-temperature wavelengths) have been identified; see ref 10 and references therein. The Chls responsible for these two states are designated as C-708 and C-719. It was shown in ref 10 that selective excitation with wavelengths of 719 nm and even longer at room temperature results in efficient charge separation. Thus, thermally activated EET from the red antenna states to P700 and/ or to P700 from higher energy antenna states populated from the red antenna states is facile. Such red excitation at liquid helium temperatures does not lead to significant charge separation since kT is small relative to the relevant energy gaps. The kinetics associated with the upward EET processes have not been determined. It was estimated in ref 10 that five or six Chl a contribute to C-708 and four or five to C-719 but, given the relative weakness of the “red” absorption, there is a considerable uncertainty in these numbers. Considerable progress toward understanding the PS I red antenna states of Synechocystis sp. PCC 6803 (hereafter referred to as Synechocystis) was made by Gobets et al.11 on the basis of polarized site-selected fluorescence spectra obtained at 4 K. The 4.2 K absorption spectrum shown in Figure 1 is similar to but better resolved than the 77 K spectrum reported in ref 12. The red-edge of the spectrum is very similar to that shown in ref 11. It reveals the relatively weak absorption band at 708 nm. Gobets et al. concluded that only one state at 708 nm contributes to the 708 nm band and, furthermore, that it is responsible for the fluorescence origin band observed near 720 nm at 4.2 K under nonline narrowing excitation conditions. (The fluorescence origin bands of Synechocystis mutants deficient in the L, K, M, and F/J/I proteins are also located near 720 nm.13) Thus, the assumed Stokes shift of ≈12 nm (230 cm-1) is much larger than observed for “normal” antenna states whose Stokes shift is an order of magnitude smaller, and is comparable to the ≈500 cm-1 Stokes shift for P870 of Rb. sphaeroides. The Stokes shift is given by ≈2∑iSiωi, where Si is the HuangRhys factor of the ith phonon with frequency ωi coupled to the electronic transition. (Here, and in what follows, a phonon is defined as an intermolecular mode or low-frequency intramolecular Chl vibration.) The dependence of the position of the
Hayes et al. fluorescence origin on excitation wavelength reported in ref 11 established that the inhomogeneous broadening contribution to the absorption band of the fluorescent state is large. The resolution of the spectra reported by Gobets et al.11 was insufficient for determination of the frequencies and HuangRhys factors of the active phonons. They inferred that the counterpart of C-719 of Synechococcus elongatus does not exist in Synechocystis and suggested that the 708 nm state is most likely a strongly coupled dimer. However, on the basis of 4.2 K nonphotochemical holeburned spectra, it was concluded in paper I that, in addition to a red antenna state near 708 nm, there is a second state at ≈714 nm due to Chls designated as C-714. One result from that work that supports this conclusion is the nonphotochemical holeburned (NPHB) spectrum shown in Figure 1 for the wild-type trimer of Synechocystis. The sharp zero-phonon hole (ZPH) coincident with the laser burn wavelength (λB) of 670.0 nm is accompanied by a number of low-energy satellite holes which are the result of downward EET from the state(s) excited at 670 nm to lower energy antenna states. Of interest here is the broad satellite hole at 714 nm. That it lies 6 nm (120 cm-1) below 708 nm suggests that it is not associated with the state that is mainly responsible for absorption at 708 nm, and, therefore, that it represents a second red antenna state. (The 714 nm hole was also observed for wild-type monomer and mutants deficient in the PsaF, K, L, and M proteins.) Further support for this was provided by the results of Stark and high-pressure hole burning experiments performed with λB values between ≈690 and 718 nm. The Stark experiments yielded f‚∆µ values, where ∆µ is the magnitude of the permanent dipole moment change associated with the absorption transition and f is the local field correction factor. For λB ) 714.0 and 706.5 nm, f‚∆µ ) 2.3 ( 0.2 and 0.78 ( 0.15 D, respectively. For λB values between 690 and 702 nm f‚∆µ values were in the 0.5-0.6 D range, values typical for Chl a monomer in polymers and Chl a states of proteins localized primarily on a single Chl a molecule (see paper I). The value of 2.3 D for λB ) 714 nm is the largest yet observed for a photosynthetic Chl a state, only a factor of about 2 smaller than the value of 5.2 D for P870 of the Rb. sphaeroides.14 That it is a factor of 3 larger than the value at 706.5 nm is difficult to reconcile under the assumption that the 708 nm absorption band (that tails out past 720 nm) is due to a single red antenna state. The high-pressure hole-burning experiments yielded the linear rate of shifting with pressure of the ZPH. Large shift rates close to -0.5 cm-1/MPa were observed for λB values close to 714 nm and at longer wavelengths. Such rates rival those observed for the exciton levels of the B850 ring of BChl a molecules of the LH2 complex of purple bacteria as well as the B875 ring of BChl a molecules of the LH1 complex of purple bacteria.15,16 As reviewed in paper I, the BChl a molecules of these two rings are strongly coupled. Theoretical analysis indicated that15,16 the large linear pressure shift rates for B850 and B875 stem, to a significant extent, from electron exchange coupling between nearest-neighbor BChl a molecules. A shift rate of -0.5 cm-1/ MPa is about a factor of 5 larger than those of Qy states highly localized on a single Chl molecule.15,16 The non-line-narrowed hole profile of the 714 nm state (Figure 1), together with its large permanent dipole moment change and linear shift rate with pressure, points to it being due to strongly coupled Chl a molecules. Further support for this, based on preliminary analysis of its linear electron-phonon coupling strength, was presented in paper I. The analysis was based on the λB dependence of the intensity of the ZPH relative
Red Chlorophyll a Antenna State
J. Phys. Chem. B, Vol. 104, No. 23, 2000 5627
to the phonon sideband hole structure as well as the Stokes shift associated with the 714 nm state taken to be responsible for the fluorescence origin band at ≈720 nm. It indicated that the electron-phonon coupling of the 714 nm state is strong and due to phonons centered near 16 and ≈100 cm-1 with HuangRhys factors of ≈1.4 and 0.6, respectively, corresponding to an optical reorganization energy of ≈80 cm-1. Theoretical simulations of the λB and burn fluence dependencies of the hole profiles were not presented in paper I. Such, obtained using the theory of Hayes et al.,17 are presented here. They are consistent with the 714 nm state (but not the 706 nm state) being responsible for the fluorescence at 720 nm. The simulations lead to more accurate determination of the electronphonon coupling parameters and inhomogeneous broadening of the 714 nm state’s absorption band. They also identify and characterize the second red antenna state at ≈706 nm. The Chls responsible for this state are referred to as C-706. The experimental hole profiles that are fit were obtained during the course of the experiments that led to I. The interested reader is referred to I for experimental details. The spectroscopic properties of C-706 and C-714 are compared with those of P700 and discussed in terms of EET involving their excited states. 2. Results and Discussion Hole profiles burned at wavelengths (λB) throughout the lowenergy absorption region (722-706 nm) are shown in Figures 2-6 (noisy curves). For each λB, the hole profiles are shown for four burn fluences. Also shown in each figure are fits to the experimental profiles obtained using the temperature-dependent equation for the hole profile of Hayes et al.17 defined as Aτ(Ω,T) - Aτ)0(Ω,T) with
Aτ(Ω,T) ) e
-∑kSk(2njk+1)
∞
R
∑∑ ∏ k R)0 R′)0
[Sk(njk + 1)]R-R′[Sknjk]R′ (R - R′)!R′!
∫
dν ×
N0(ν - νm)e-σPφτL(ωB-ν)lR,R′(Ω - ν - (R - 2R′)ωk) (1) the absorption at Ω following burning at ωB with photon flux P for time τ. N0(ν-νm) is the Gaussian distribution of zerophonon line frequencies (site distribution function, SDF) centered at νm; Sk, ωk, and njk are the Huang-Rhys factor, frequency, and thermal occupation number of the kth coupled phonon; and σ and φ are the absorption cross section and holeburning quantum yield. L(ωB-ν) is the single-site absorption profile at the burn frequency, ωB. It is further defined below. The absorption is described as the sum of the zero-phonon line, l0,0, and multiphonon terms, lR,R′, vide infra. As discussed in refs 5, 18, and 19, it is often the case for photosynthetic complexes that the one-phonon absorption profile can be characterized by two contributions from phonons centered at ω j 1, and ω j 2 with ω j2 > ω j 1. Their one-phonon profiles are given by g(ω) D(ωk) (k ) 1, 2) with g(ω) the phonon density of states and D(ωk) the frequency-dependent electron-phonon coupling constant. Thus, in eq 1 ∑k reduces to just two terms, k ) 1, 2. Since the hole profiles reported here were obtained at 4.2 K (the low-temperature limit where kT , ω j k), eq 1 reduces to the result of ref 17 generalized to the two-mode case (k ) 1,2):
Aτ(Ω) ) e
-St
∞
∏∑
k)1,2 R)0
( )∫ SkR R!
dν ×
N0(ν - νm)e-σPφτL(ωB-ν)lR,k(Ω - ν - Rω j k) (2)
Here, St is the total Huang-Rhys factor equal to S1 + S2 and the lR are line-shape functions with R ) 0,1, 2, ... corresponding to the zero-, one-, two-, ... phonon transitions. We define γ as the full width at half-maximum (fwhm) of the Lorentzian zerophonon line. As reviewed in refs 5 and 19 the overall one-phonon profile of antenna Qy states is typically dominated by phonons centered at ∼20-30 cm-1 with a one-profile width of ≈30 cm-1 (see ref 20 on the LHC II antenna complex of PS II for a recent example). In what follows, such phonons will be referred to as ω1 phonons. The higher frequency phonons which, until I, had only been observed for P870 and P960 of the bacterial RC,21,22 are referred to as ω2 phonons. For P870 and P960, ω j 2 ) 120 and 145 cm-1, respectively. In order to use eq 2, expressions for the one-phonon profiles l1,k (k ) 1, 2) are required. The l1,1 profile can be quite well described by a Gaussian on the low-energy side with fwhm ΓG and a Lorentzian on the high-energy side with fwhm ΓL so that the fwhm of the one-phonon profile is (ΓG + ΓL)/2.17 The lR,1 profiles (R g 2) are obtained by folding l1,1 R times, which is appropriate for coupling to a distribution of phonons or a localized phonon whose damping due to anharmonicity is governed by terms linear in its coordinate. It is also appropriate for a localized phonon whose frequency varies because of structural heterogeneity. In that case the one-phonon profile would be best described by a Gaussian. As in ref 22, we use a Lorentzian for the one-phonon profile of the ω2 phonon. Use of a Gaussian profile would not significantly affect the results. Finally, the expression for L(ωB-ν) given in ref 23 reduces to ∞
L(ωB - ν) ) exp - [
∑k Sk(2njk + 1)] k)1,2 ∑ ∏ R)0
() SkR
× R! j k) (3) lR,k(ωB - ν - Rω
in the low-temperature limit. With ωB replaced by Ω, eq 3 is the expression for the absorption spectrum of a single site whose zero-phonon line is at frequency ν. Equation 2, as written, is restricted to hole-burning processes in which the burning quantum yield, φ, is not distributed. Thus, it is not strictly applicable to NPHB where the kinetics are dispersive.24-26 Such kinetics were recently determined for the Fenna-Matthews-Olson BChl a antenna complex of Chlorobium tepidum.27 Nevertheless, the use of eq 2 for the NPHB spectra of Synechocystis should not significantly affect the analysis of the hole profiles. As will be shown, the hole spectra can be fit by adjusting the relative values of the experimental burn fluences (Pτ in eq 3) in a manner consistent with dispersive kinetics. That is, for example, the ratio of the highest to lowest burn fluence used in the experiments needs to be significantly reduced for fitting. Also, eq 2 does not account for the blueshifted anti-hole associated with NPHB of ππ* excited states.28 This anti-hole, which is very apparent in Figures 2-6 (see asterisk), interferes with the real-phonon sideband hole (PSBH) located to higher energy of the ZPH at λB. Thus, the quality of the fits to the hole profiles will be mainly judged on the basis of the ZPH and pseudo-PSBH which lies to lower energy of the ZPH. Simulated and Experimental Hole Profiles. Experimental hole spectra (noisy dotted curves) obtained with four burn fluences are shown in Figures 2-6 for λB ) 722, 718, 714, 710, and 706 nm, respectively. In each figure the ZPH coincident with λB is indicated by a downward arrow. The pseudo- and real-phonon sideband holes (PSBH) appear to the immediate left and right of the ZPH at ≈-18 and ≈+18 cm-1, respectively. Thus, the spectra directly provide a good estimate for ω j 1. The
5628 J. Phys. Chem. B, Vol. 104, No. 23, 2000
Hayes et al.
TABLE 1: Linear Electron-Phonon Coupling and Other Parameters for the 714 nm Antenna State of Synechocystisa S1
ω j1
ΓG
ΓL
S2
ω j2
Γ
ΓI
γ
1.6 ( 0.2
18 ( 2
15 ( 5
15 ( 5
0.4 ( 0.1
70 ( 10
65 ( 10
300 ( 20
0.5 ( 0.1
a The unit of ω j 1, ΓG, ΓL, ω j 2, Γ, ΓI, and γ is cm-1. ω j 1 and ω j 2 are the peak energies of the phonons that couple to the 714 nm transition and S1 and S2 are their Huang-Rhys factors; ΓG and ΓL define the one-phonon profile of the ω j 1 phonons and Γ the fwhm of the one-phonon profile of the ω j 2 phonons (see text for further details). ΓI is the inhomogeneous broadening contribution to the fwhm of the 714 nm absorption band, i.e., the width of the site distribution function (SDF) which, on the basis of the fits to the hole spectra in Figures 2 and 3, is centered at 717.20 nm (13 947 cm-1). γ is the fwhm of the zero-phonon line as determined by the resolution used to record the hole spectra (see text). The error limits given are values for which the fits to hole spectra burned at 722 and 718 nm are clearly worse than those shown in Figures 2 and 3.
Figure 2. Experimental (dashed line) and calculated (solid line) holeburned spectra of PS I at 4.2 K for λB ) 722 nm. For the experimental spectra in Figures 2-6, the burn laser line width was 0.07 cm-1 and the read resolution 1 cm-1. For the calculated spectra, the zero-phonon line width was 0.5 cm-1, which gives a resolution comparable to that used experimentally. The calculated spectra in Figures 2-4 are displaced 5 cm-1 along the ordinate, and all spectra are displaced arbitrary amounts along the abscissa to aid in distinguishing the individual spectra. The burn fluences for spectra a-d were 6, 30, 150, and 450 J, respectively. The same fluences also are applicable to Figures 3-6. The asterisk marks the peak of the anti-hole. A satellite hole at 699 nm is also indicated.
smooth solid curves are the fits obtained using the parameter values given in Table 1. In Figures 2-4 they are displaced by 5 cm-1 from the experimental hole profiles for ease of comparison while in Figures 5 and 6 they are not. The parameter values given in Table 1 were determined by fitting the λB ) 722 and 718 nm hole profiles, vide infra. The broad and positive absorption at wavelengths shorter than λB in the experimental spectra is the anti-hole absorption referred to above. It is quite remarkable that the photoinduced NPHB process results in configurational changes large enough to blue-shift the absorption of the precursor state(s) to such an extent. In Figure 2 (λB ) 722 nm) the maximum of the anti-hole is shifted by ≈300 cm-1 relative to the center of the hole profile while in Figure 6 (λB ) 706 nm) the shift is reduced to ≈80 cm-1. In addition, the width of the anti-hole profile is significantly reduced. This reduction as λB is tuned to higher energies is paralleled by a reduction in the width of the overall experimental hole profile. The λB dependence of the overall hole and anti-hole profiles is inconsistent with the 708 nm absorption band seen in Figure 1 being due to a single state. Analysis of the hole profiles is aided by the determination that ω j 1 ≈ 18 cm-1. To proceed further, it is useful to have a reasonable estimate for St, the total Huang-Rhys factor. In I it
Figure 3. Experimental (dashed line) and calculated (solid line) hole burned spectra of PS I at 4.2 K for λB ) 718 nm. The asterisk marks the peak of the anti-hole. A satellite hole at 699 nm is also indicated.
Figure 4. Experimental (dashed line) and calculated (solid line) holeburned spectra of PS I at 4.2 K for λB ) 714 nm. The asterisk marks the peak of the anti-hole. A satellite hole at 699 nm is also indicated.
was estimated that St ) 2.0 for λB J 714 nm. Another approach to estimating St for such wavelengths is to measure the saturated fractional hole depth of the ZPH which, to a good approximation, is given by exp(-St).29 Values for the fractional hole depth of 0.1 were determined, which leads to St ) 2.3, within experimental uncertainty the same as the value of 2.0 reported in paper I.
Red Chlorophyll a Antenna State
Figure 5. Experimental (dashed line) and calculated (solid line) holeburned spectra of PS I at 4.2 K for λB ) 710 nm. The spectra are displaced arbitrary amounts along the abscissa to distinguish between them. The calculated spectra are scaled so that the zero-phonon hole depths match the experimental zero-phonon hole depths. A satellite hole at 699 nm is also indicated.
Figure 6. Experimental (dashed line) and calculated (solid line) holeburned spectra of PS I at 4.2 K for λB ) 706 nm. The spectra are displaced arbitrary amounts along the abscissa to distinguish between them. The calculated spectra are scaled so that the zero-phonon hole depths match the experimental zero-phonon hole depths. The position of the 714 nm hole is indicated, as is a satellite hole at 699 nm.
The parameter values obtained by fitting the ZPH and pseudoPSBH for λB ) 722 and 718 nm (Figures 2 and 3) are given in Table 1. The reason for using the hole spectra in these two figures is that at 722 and 718 nm one should be exciting the red-most antenna state with little interference from higher energy antenna states. One then proceeds to assess how well the parameter values account for the hole spectra obtained with shorter λB values. As will be seen, this approach provides information on the higher energy state that contributes to the 708 nm band. The values of 1.6 and 0.4 for S1 and S2, respectively, fall in the range of anticipated values, vide supra. The values of 15 cm-1 for both ΓG and ΓL, which define the
J. Phys. Chem. B, Vol. 104, No. 23, 2000 5629 one-phonon profile of the ω1 phonons, were obtained by varying them independently. For the determination of ΓG, particular attention was paid to fitting in the region between the peak of the pseudo-PSBH and the ZPH at λB. With ΓG fixed at 15 cm-1, ΓL ) 25 cm-1 gave poorer fits than those obtained with ΓL ) j 2 gave better fits than the 15 cm-1. The value of 70 cm-1 for ω value 100 cm-1 estimated in paper I. The uncertainty in ω j 2 is ( 10 cm-1. The fwhm (Lorentzian) of 65 cm-1 for the ω2phonon (Γ in Table 1) suggests that it may be critically damped. The fwhm (ΓI in Table 1) of 300 cm-1 for the Gaussian distribution of ZPL frequencies or SDF is considerably larger than typically observed for photosynthetic complexes. However, a large value was anticipated on the basis of the ≈400 cm-1 width of the nonline narrowed fluorescence origin band (see paper I and ref 11) since this width is approximately given by j 1 + S2ω j 2. A width of γ ) 0.5 cm-1 was used for the ΓI + S1ω ZPL which is consistent with the instrumental resolution of 1 cm-1 used to record the hole spectra (a ZPL width of γ gives a hole width of 2γ). Fitting of the hole profiles led to a center frequency (νm) for the SDF of 13 947 cm-1 (717.20 nm) for the fluorescent state. Finally, the σPφτ term in eq 2 was treated as an adjustable parameter because, for example, the value of the peak absorption cross section σ is unknown. Fitting of hole profile c in Figure 3 led to a value of 22 for σPφτ. Its value was then varied to fit hole profiles a, b, and d of Figure 3. The resulting relative values of σPφτ are 1:2.5:6.25:9.38, where 6.25 corresponds to hole profile c. The same relative values were used in fitting the hole spectra shown in Figures 2, 4, 5, and 6. These relative values can be compared with the values 1:5:25:75 based on the four experimental burn fluences values given in the Figure 2 caption. The differences between the two are, qualitatively, those expected for dispersive hole growth kinetics. That is, with increasing burn time the “effective” value of φ decreases, a consequence of the glasslike structural heterogeneity of proteins. We consider first the fits in Figures 2-4 (λB ) 722, 718, and 714 cm-1, respectively). On the basis of the ZPH and pseudo-PSBH they can be considered to be good for all four burn fluences. The fits to the real-PSBH are satisfactory up to energies where interference by the broad anti-hole becomes significant. The fits shown in Figure 5 (λB ) 710 nm) are less than satisfactory. In that figure the fits are not shifted by 5 cm-1 and are adjusted so that the maxima of the experimental and calculated ZPH are coincident. That the calculated ∆-absorbances of the ZPH are considerably smaller than those observed, and that the experimental real- and pseudo-PSBH are better resolved than the calculated PSBH indicates that a second and higher energy antenna state is contributing to the hole spectra in Figure 5. This is more apparent in Figure 6 (λB ) 706 nm) where the fits are poor. At 706 nm, excitation is at the highenergy side of the lowest energy state’s absorption band, vide infra. Therefore, relatively more phonon sideband transitions than zero-phonon line transitions of the 714 nm band are excited than with excitation at 714, 718, and 722 nm. Absorption and Fluorescence Spectra and State Assignments. Figure 7 shows the low-energy region of the experimental absorption spectrum (curve a), the calculated absorption spectrum of the lowest energy antenna state near 714 nm (curve b) and the a-b difference spectrum (curve c). Spectrum b was calculated using the parameter values in Table 1 and SDF centered at νm ) 13 947 cm-1 (λm ) 717.20 nm). The location of νm is indicated in the figure. The maximum of the calculated absorption spectrum is at 714.2 nm and its fwhm ) 330 cm-1, which is 30 cm-1 smaller than the value estimated using ΓI +
5630 J. Phys. Chem. B, Vol. 104, No. 23, 2000
Figure 7. (a) Experimental red edge absorption of PS I at 4.2 K. (b) Calculated absorption of the 714 nm absorption band. The center of the site distribution function (SDF) of the band is indicated by the arrow. Burn wavelength for the spectra shown in Figures 2-6 are labeled and indicated by dashed vertical lines. The 699 nm shoulder is also indicated. (c) The difference between spectra a and b.
S1ω j 1 + S2ω j 2 (see Table 1). The fwhm of 330 cm-1 is larger than the apparent width of 230 cm-1 for the 714 nm hole seen in Figure 1. However, the true width of this hole is probably considerably larger than 230 cm-1 because the blue-shifted antihole associated with the low-energy part of the 714 nm hole interferes with its high-energy side. This explains why the highenergy side of the hole is narrower than the low-energy side. We conclude, in agreement with I, that the lowest energy antenna state of PS I of Synechocystis has an absorption maximum near 714 nm in the low-temperature limit and that it is characterized by strong electron-phonon coupling and an unusually large contribution from inhomogeneous broadening to its absorption bandwidth. The calculated fluorescence origin band of the 714 nm state is obtained by reflecting spectrum b of Figure 7 at the position of its SDF. The result is a maximum at 720.0 nm. This is within (2 nm of the experimental values reported in paper I and ref 11. We consider the agreement quite reasonable given that the fluorescence occurs on a ns time scale and, therefore, that protein-Chl configurational changes, which result in mirror symmetry breakdown between absorption and fluorescence, may be occurring. Such changes may also explain why the width of the calculated fluorescence origin band is 70 cm-1 narrower than the observed width of ≈400 cm-1.1,11 The LHC II and CP29 antenna complexes of PS II also exhibit fluorescence origin bands that are somewhat broader than those predicted on the basis of the SDF and linear electron-phonon coupling analysis.20,30 In I it was argued that a state at ≈708 nm is not responsible for the fluorescence origin band at ≈720 nm. For example, if it were, the Stokes shift is 240 cm-1, which, to a good approximation, is equal to 2(S1ω j 1 + S2ω j 2). Since our results lead to ω j 1 ) 18 cm-1 and an S1 value no larger than 1.6, the value of S2 is, at a minimum, 1.3 with ω j 2 ) 70 cm-1. The Franck-Condon factor for the ZPH is exp(-2St)29 which, with St ) 1.6 + 1.3 ) 2.9, equals 0.003. This is a factor of 6 smaller than the value obtained with St ) 2.0 which was used to simulate the spectra shown in Figures 2 and 3. With St ) 2.9, the ZPH would be unobservable in Figures 2 and 3 given the level of noise in the experimental hole spectra. Furthermore, it is not possible to fit the hole spectra in Figure 6.
Hayes et al. Considered next is the a-b difference spectrum (curve c) in Figure 7. The difference spectrum indicates that the C-708 Chl a molecules absorb closer to 706 nm than 708 nm. In what follows we refer to these Chls as C-706. The low-energy tailing of spectrum c leads to the conclusion that the inhomogeneous broadening contribution to the 706 nm absorption bandwidth is large and comparable to that of the 714 nm band, ≈300 cm-1. The hole spectra in Figure 6 establish that the electron-phonon coupling is not nearly strong enough to account for the tailing (results not shown). According to I, this coupling is a factor of 1.5 weaker than that of the 714 nm state. Thus, the optical reorganization of the 706 nm state is less than 60 cm-1 (vide infra), which means that its fluorescence origin band cannot be at a wavelength longer than 712 nm. The 4.2 K fluorescence spectra of Gobets et al.11 show no indication of fluorescence other than the band at 720 nm. This suggests that the fluorescence of the 706 nm state is quenched, at least in part, by energy transfer to the 714 nm state. The fluorescence anisotropy data of Gobets et al. indicate that the transition dipoles of the 706 and 714 nm states would have to be close to parallel (or antiparallel). The burn wavelengths used to obtain the hole spectra in Figures 2-6 are indicated in Figure 7. With λB ) 722 and 718 nm one is exciting mainly the 714 nm state with little interference from the 706 nm state. This supports our earlier assertion that the parameter values in Table 1, obtained using the spectra of Figures 2 and 3, characterize the 714 nm state. At λB ) 710 and 706 nm it is the 706 nm state that is preferentially excited. Again, this explains why the fits in Figures 5 and 6 are poor. Nature of the C-706 and C-714 Chlorophyll a Molecules. As discussed in the Introduction, it was concluded in paper I that the 714 nm state is due to a dimer (or possibly a trimer) of strongly coupled Chl a molecules. The number of Chl a molecules that contribute to the entire 708 nm absorption band was estimated at 4. Our determination that the electron-phonon coupling of the 714 nm state is strong, St ) 2.0 with S1 ) 1.6 and S2 ) 0.4, provides further support for strong coupling since St is typically about 0.5 for photosynthetic Qy states associated with mainly a monomer Chl or weakly coupled Chl molecules.18-20 The large permanent dipole change of 2.3 D indicates that the 714 nm state possesses significant charge transfer character. The f‚∆µ values reported in paper I for λB ) 706.5 and 708.0 nm are 0.78 ( 0.15 and 1.0 ( 0.4 D, which are not much larger than the typical values of 0.5-0.6 D for monomer Chl a (see paper I). Thus, the Stark results are consistent with C-706 being a monomer. We think it more likely, however, that C-706 consists of more than one Chl a molecule. First, there is no precedent for a Qy state associated with a single Chl a molecule lying as far to the red as 706 nm. For example, the lowest energy state of the LHC II,20 CP29,30 and CP4331 antenna complexes and the reaction center complex32 of PS II is highly localized on a single Chl a molecule. The wavelengths of these states are respectively 678, 680, 683, and 684 nm. Second, the large inhomogeneous broadening (ΓI), ≈ 300 cm-1, of the 706 nm absorption band is difficult to understand for a Qy state localized on a single Chl a molecule. For example, the inhomogeneous broadenings of the absorption bands of the above four states are close to 100 cm-1. Third, the results of I show that the entire 708 nm absorption band (Figure 1) shifts uniformly to the red with increasing pressure at a rate of ≈-0.4 cm-1/MPa. Such a large rate is inconsistent with C-706 (and C-714) being due to a single Chl a molecule, cf. Introduction.
Red Chlorophyll a Antenna State
J. Phys. Chem. B, Vol. 104, No. 23, 2000 5631
TABLE 2: Properties of Red Antenna States and P700a chlorophyll C-714 C-706 P700c
absorption SDF ΓI ∑iSiωi fluorescence max (nm) max (nm) (cm-1) (cm-1) max (nm) 714.2 ≈706 702
717.2 ≈708 710
300 ≈300 100
57 ≈40 200
720 710b ≈718b
a SDF ≡ site distribution function, Γ is the fwhm of the SDF I (inhomogeneous broadening), and ∑iSiωi is the optical reorganization energy. b Predicted value. c Results from ref 4.
The possibility that C-706 and C-714 are associated with a single Chl a aggregate deserves consideration. If this were the case, the 706 and 714 nm states would be exciton levels of the aggregate. Thus, burning of the 714 nm level should produce a satellite hole at 706 nm since the two levels would be excitonically correlated. The underlying physics here is discussed in ref 21 in the context of the hole-burned spectra of the special pair, P960, of Rps. Viridis. Figures 2-4 show that burning of the 714 nm state does not produce a hole at 706 nm, but only a satellite hole at 699 nm which will be discussed later. A second reason for rejecting the above possibility is that the width of the ZPH in spectrum a of Figure 6 is resolution limited at 1 cm-1. Thus, the lifetime of the 706 nm state is g10 ps. If the 706 and 714 nm states were exciton levels of the same aggregate, the lifetime of the 706 nm level should be much shorter due to downward EET to the 714 nm level. Such EET occurs on a time scale of ≈100 fs for exciton levels of the B850 ring of BChl a molecules of the LH2 antenna complex of purple bacteria, as recently reviewed in ref 33. A third, but less convincing, argument is that the permanent dipole moment change for the 706 nm state is over a factor of 2 smaller than that of the 714 nm state.1 We conclude that C-706 and C-714 are not associated with a single aggregate and that they are not in close proximity to each other. We further conclude that if the number of Chl a molecules contributing to the entire 706 nm band is 4, as estimated in paper I, both C-706 and C-714 are dimers. However, there is considerable uncertainty in the estimate of 4, meaning that if it is an underestimate, either C-706 or C-714 could be due to a trimer. To conclude this subsection, we discuss the ΓI value of ≈300 cm-1 for the C-706 and C-714 absorption bands (Table 2). As discussed above, such a value is unusually large for an antenna Qy absorption band. Furthermore, it is about a factor of 3 larger than the values for the P700 band4 and the P870 and P960 special pair bands of Rb. sphaeroides22 and Rps. Viridis,21 respectively. We propose that the large value of 300 cm-1 is a consequence of the structures of C-708 and C-714 being fragile, i.e., easily disrupted. This is consistent with results presented in paper I for wild-type trimer, wild-type monomer, and mutants deficient in the PsaL and PsaM protein subunits. PsaM does not bind Chl a molecules but, like PsaL, is located at the connecting domain that is responsible for the formation of trimers from three monomers. Importantly, the integrated intensity of the 708 nm band of WT trimer was reduced (but not eliminated!) by ≈30% for WT monomer and the two mutants. (The 708 nm band intensity was not affected by deletion of the PsaF or K subunits that are located at the opposite side of the above connecting domain; see Figure 1 of I.) It was concluded in paper I that the Chls responsible for the 708 nm absorption band (now C-706 and C-714) are not bound to PsaL or PsaM but rather to PsaA and or PsaB, and near the interfacial regions with PsaL and PsaM. Thus, formation of the monomer or deletion of PsaM or PsaL could affect the structures of C-706 and C-714 and, thereby, the position and/or intensity of their absorptions.
Upper Exciton Levels of C-706 and C-714. As discussed, we conclude that both C-706 and C-714 are, at a minimum, dimers. In what follows we refer to them as dimers. The discussion that follows would, for all intent and purposes, not be affected if C-706 or C-714 were a trimer. On the basis of our results one can safely assume that the 706 and 714 nm antenna states correspond to the lowest levels of their respective dimers and are strongly allowed in absorption. Hole burning of these levels should elicit a response from the upper dimer levels as observed for the special pair, P960, of Rps. Viridis.21 With reference to Figures 2-6, the 699 nm satellite hole might appear to be a candidate for such a level. Not shown are the satellite holes at 692 and 695 nm, but see Figure 4 of I. We think it very unlikely that any of these holes correspond to the upper dimer levels, the reason being that their widths, ≈100 cm-1, are much narrower than the ≈300 cm-1 ΓI values of the 706 and 714 nm absorption bands (Table 2). That is, the absorption bandwidths of the upper levels are not expected to be narrower than the inhomogeneous broadening contribution to the bandwidths of the lower levels. A search for the upper dimer levels amidst a sea of ≈90 Chl a molecules may be futile, especially since they are probably weakly absorbing. The same problem exists for identification of the upper dimer level of P700. It is interesting, however, that satellite holes at 692 and 695 are observed for burn wavelengths in the region of the 706 and 714 nm states since the results of I indicate that the Chl a molecules responsible for the 692 and 695 nm bands are bound to the PsaF and/or J subunits which are located at the nontrimer forming side of the monomer. Apparently, the structural changes that occur as a result of NPHB of C-706 and C-714 which are located at the trimer forming side would have to extend over tens of angstroms. Comparison of the Spectroscopic Properties of P700, C-706 and C-714: Implications for Excitation Energy Transfer (EET). The spectroscopic properties of P700, C-706 and C-714 are compared in Table 2 that includes the wavelengths of the absorption and observed or predicted fluorescence origin bands, the optical reorganization energies ∑iSiωi, of their absorption transitions, the wavelengths of the maxima of their SDF and the static inhomogeneous broadening contribution (ΓI) to the absorption bandwidths. The results in Table 2 should prove useful for interpreting low-temperature (j100 K) kinetic data related to EET processes involving P700* and the 706 and 714 nm red antenna states once they have been determined. At present, all that is known about these processes is our result that the lifetime of the 706 nm state is g10 ps at 4 K. Such a long lifetime suggests that its EET dynamics could be described by weak coupling, nonadiabatic transfer theories. From Table 2 one observes that the spectral overlap between the fluorescence origin band of the 706 nm state and C-714 absorption band is favorable for transfer from the former state to the 714 nm state. Given that the transition dipoles of the two states are close to parallel (or antiparallel),11 the above long lifetime suggests that C-706 and C-714 are not in close proximty to each other. Theoretical analysis of the EET kinetics would require knowing whether or not the SDF of the three states are perfectly (positively) correlated. This seems particularly important for EET involving C-706 and P700 since their SDF are close in energy (Table 2). Our NPHB results (see also paper I) indicate that the Qy states of PSI, like those of other photosystems (see, for example, refs 20, 30, 32, 34-36) exhibit little, if any, such correlation. They show that burning a relatively sharp ZPH (selecting a narrow isochromat) into a higher energy absorption
5632 J. Phys. Chem. B, Vol. 104, No. 23, 2000 band results in broad low-energy satellite holes in the absorption bands of lower energy states. (Sharp, fwhm e5 cm-1, ZPH can be burned across the entire Qy absorption spectrum, see paper I.) For perfect correlation, one should observe satellite holes with widths that are much narrower than their associated absorption bands. The hole spectrum in Figure 1 is consistent with an absence of correlation as is spectrum a of Figure 6. In the latter spectrum one sees that burning a sharp ZPH in the C-706 absorption band does not produce a sharp ZPH in the C-714 band, only the very broad hole near 714 nm. This hole is more evident in Figure 1. The reader interested in how an absence of correlation can lead to dispersive kinetics for EET and charge separation is referred to refs 37 and 38. The results in Table 2 have important implications for EET involving C-706 and P700 in the low-temperature limit. In this regard, the relevant results are that the maxima of their SDF at ≈708 and 710 nm are, for all intents and purposes, isoenergetic and that the width of the SDF (ΓI) of C-706, ≈300 cm-1, is about a factor of 3 larger than that of P700. What this means, even when an absence of correlation between their SDF is taken into account, is that, in the low-temperature limit, a significant fraction of complexes in an ensemble are energetically poised to carry out EET from the 706 nm state to P700. This finding offers a possible explanation for why only about 50% of the complexes, following excitation of higher energy bulk antenna states, undergo irreversible charge separation in the lowtemperature limit (see Brettel39 for a review). In that review no explanation for the 50% effect based on energetics and heterogeneity is given. Later, Pålsson et al.,10 in their study of PS I of Synechococcus elongatus, proposed that it is the result of incomplete equilibration between the bulk and red antenna states. That is, the bulk antenna states of a fraction of the complexes transfer energy to P700 rather than to the red antenna states. In their model the red antenna states in each and every complex are trap states that are incapable of transferring energy to P700 at low temperatures. We suggest, instead, that equilibration could be complete, but that EET from the 706 nm state to P700 is energetically favorable in only about half of the complexes. In the other half, the 706 nm state would serve as a trap state that transfers energy to C-714. The model assumes that C-706 is the primary acceptor for EET from the bulk antenna states and that P700, rather than C-714, is the primary acceptor for EET from the 706 nm state in those complexes in which transfer to P700 is energetically favorable. 3. Conclusions The simulations of the dependence of the hole spectra on burn wavelength (λB) support the conclusion reached in paper I (ref 1) that PS I of Synechocystis possesses two red antenna states whose absorption maxima at 4.2 K lie lower in energy than that of P700. Our analysis indicates that the 714 nm antenna state is responsible for the fluorescence origin band near 720 nm. The electron-phonon coupling of the 714 nm state is unusually strong for an antenna state (Table 1). The coupling is somewhat weaker for the 706 nm state. For the 714 nm state this strong coupling correlates well with its large permanent dipole moment change (f‚∆µ ≈ 2.3 D) and pressure shift rate (-0.5 cm-1/MPa). This is consistent with the 714 nm state being due to a dimer or, possibly a trimer, whose monomers are strongly interacting with a significant contribution from electron exchange coupling. The 706 nm state is also assigned to a dimer of Chl a molecules whose coupling is weaker. The 706 and 714 nm states are also unusual in that the inhomogeneous broadening (ΓI) contribution to their absorption
Hayes et al. bandwidths is very large, ≈300 cm-1, suggesting that the structures of C-706 and C-714 are fragile. As discussed, this is supported by the results in paper I for wild-type trimer, wildtype monomer, and mutants deficient in the PsaL and M protein units. At present, the only information available on the locations of C-706 and C-714 is that they appear to be bound to PsaA and/or PsaB and located at the trimer forming side of the monomer. Finally, Table 2, in which the spectroscopic properties of P700, C-706, and C-714 are compared, should prove useful for analysis of low-temperature (j100 K) kinetic data on EET processes involving their excited states. The results in Table 2 lead to a new model that explains why only about half of the PS I complexes of cyanobacteria undergo irreversible charge separation in the low-temperature limit following excitation of bulk antenna states. The model allows for complete equilibration between these states and the 706 nm state which is taken to be the primary acceptor state for downward EET from the bulk antenna states. The key idea is that in about half of the complexes, the 706 nm state can transfer energy to P700. In the other half, transfer to P700 is energetically unfavorable and, thus, the 706 nm state serves as a true trap state that transfers energy to C-714. In this model, the kinetics for transfer to P700 would have to be considerably faster than the kinetics for transfer to C-714. Acknowledgment. Research at the Ames Laboratory was supported by the Division of Chemical Sciences, Office of Basic Energy Sciences, U.S. Department of Energy. Ames Laboratory is operated for USDOE by Iowa State University under Contract W-7405-Eng82. References and Notes (1) Ra¨tsep, M.; Johnson, T. W.; Chitnis, P. R.; Small, G. J. J. Phys. Chem. B 2000, 104, 836. (2) Trissl, H.-W. Photosynth. Res. 1993, 35, 247. (3) Trissl, H.-W.; Wilhelm, C. Trends Biochem. Sci. 1993, 18, 415. (4) Gillie, J. K.; Lyle, P. A.; Small, G. J.; Golbeck, J. H. Photosynth. Res. 1989, 22, 233. (5) Small, G. J. Chem. Phys. 1995, 197, 239. (6) Krauss, N.; Schubert, W.-D.; Klukas, O.; Fromme, P.; Witt, H. T.; Saenger, N. Nature 1996, 3, 965. (7) Schubert, W.-D.; Klukas, O.; Krauss, N.; Saenger, W.; Fromme, P.; Witt, H. T. J. Mol. Biol. 1997, 272, 741. (8) Kruip, J.; Bald, D.; Boekema, E.; Rogner, M. Photosynth. Res. 1994, 40, 279. (9) Manna, P.; Chitnis, P. R. In Concepts in Photobiology: Photosynthesis and Photomorphogenesis; Singhal, G. S., Renger, G., Sapory, S. K., Irrgang, K.-D., Govindjee, Eds.; Kluwer Academic: Dordrecht, 1999; p 212. (10) Pålsson, L.-O.; Flemming, C.; Gobets, B.; van Grondelle, R.; Dekker, J. P.; Schlodder, E. Biophys. J. 1998, 74, 2611. (11) Gobets, B.; van Amerongen, H.; Monshouwer, R.; Kruip, J.; Rogner, M.; van Grondelle, R.; Dekker: J. P. Biochim. Biophys. Acta 1994, 1188, 75. (12) van der Lee, J.; Bald, D.; Kwa, S. L. S.; van Grondelle, R.; Rogner, M.; Dekker: J. P. Photosynth. Res. 1993, 35, 311. (13) Soukalis, V.; Savikhin, S.; Xu, W.; Chitnis, P. R.; Struve, W. S. Biophys. J. 1999, 76, 2711. (14) Middendorf, T. R.; Mazzola, L. T.; Lao, K.; Steffen, M. A.; Boxer, S. G. Biochim. Biophys. Acta 1993, 1143, 223. (15) Wu, H.-M.; Ra¨tsep, M.; Jankowiak, R.; Cogdell, R. J.; Small, G. J. J. Phys. Chem. B 1997, 101, 7641. (16) Wu, H.-M.; Ra¨tsep, M.; Jankowiak, R.; Cogdell, R. J.; Small, G. J. J. Phys. Chem. B 1998, 102, 4023. (17) Hayes, J. M.; Lyle, P. A.; Small, G. J. J. Phys. Chem. 1994, 98, 7337. (18) Jankowiak, R.; Small, G. J. In Photosynthetic Reaction Centers; Deisenhofer, J., Norris, J., Eds.; Academic Press: New York, 1993; Vol. 2, p 133. (19) Jankowiak, R.; Hayes, J. M.; Small, G. J. Chem. ReV. 1993, 93, 1471.
Red Chlorophyll a Antenna State (20) Pieper, J.; Ra¨tsep, M.; Jankowiak, R.; Irrgang, K.-D.; Voigt, J.; Renger, G.; Small, G. J. J. Phys. Chem. A 1999, 103, 2412. (21) Reddy, N. R. S.; Kolaczkowski, S. V.; Small, G. J. J. Phys. Chem. 1993, 97, 6934. (22) Lyle, P. A.; Kolaczkowski, S. V.; Small, G. J. J. Phys. Chem. 1993, 97, 6926. (23) Lee, I.-J.; Hayes, J. M.; Small; G. J. J. Chem. Phys. 1989, 91, 3413. (24) Kenney, M.; Jankowiak, R.; Small, G. J. Chem. Phys. 1990, 146, 47. (25) Shu, L.; Small, G. J. J. Opt. Soc. Am. B 1992, 9, 733. (26) Kim, W.-H.; Reinot, T.; Hayes, J. M.; Small, G. J. J. Phys. Chem. 1995, 99, 7300. (27) Ra¨tsep, M.; Blankenship, R. E.; Small, G. J. J. Phys. Chem. B 1999, 103, 5736. (28) Shu, L.; Small, G. J. J. Opt. Soc. Am. B 1992, 9, 724. (29) Hayes, J. M.; Gillie, J. K.; Tang, D.; Small, G. J. Biochim. Biophys. Acta 1988, 932, 287. (30) Pieper, J.; Irrgang, K.-D.; Ra¨tsep, M.; Voigt, J.; Renger, G.; Small, G. J. Photochem. Photobiol., in press.
J. Phys. Chem. B, Vol. 104, No. 23, 2000 5633 (31) Groot, M.-L.; Frese, R. N.; de Weerd, F. L.; Bromek, K.; Petterson, Å.; Peterman, E. J. G.; van Stokkum, I. H. M.; van Grondelle, R.; Dekker, J. P. Biophys. J. 1999, 77, 3328. (32) Jankowiak, R.; Ra¨tsep, M.; Picorel, R.; Seibert, M.; Small, G. J. J. Phys. Chem. B 1999, 103, 9759. (33) Sundstro¨m, V.; Pullerits, T.; van Grondelle, R. J. Phys. Chem. B 1999, 103, 2327. (34) Ko¨hler, W.; Friedrich, J.; Fischer, R.; Scheer, H. Chem. Phys. Lett. 1988, 143, 169. (35) Ko¨hler, W.; Friedrich, J.; Fischer, R.; Scheer, H. J. Chem. Phys. 1988, 89, 871. (36) Reddy, N. R. S.; Small, G. J.; Seibert, M.; Picorel, R. Chem. Phys. Lett. 1991, 181, 1391. (37) Small, G. J.; Hayes, J. M.; Silbey, R. J. J. Phys. Chem. 1992, 96, 7499. (38) Kolaczkowski, S. V.; Hayes, J. M.; Small, G. J. J. Phys. Chem. 1994, 98, 13418. (39) Brettel, K. Biochim. Biophys. Acta 1997, 1318, 322.
