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Twodimensional electronic spectroscopy of the B800–B820 lightharvesting complex

Edited by Robin M. Hochstrasser, University of Pennsylvania, Philadelphia, PA, and approved July 5, 2006 (received for review April 11, 2006)
Abstract
Emerging nonlinear optical spectroscopies enable deeper insight into the intricate world of interactions and dynamics of complex molecular systems. 2D electronic spectroscopy appears to be especially well suited for studying multichromophoric complexes such as lightharvesting complexes of photosynthetic organisms as it allows direct observation of couplings between the pigments and charts dynamics of energy flow on a 2D frequency map. Here, we demonstrate that a single 2D experiment combined with selfconsistent theoretical modeling can determine spectroscopic parameters dictating excitation energy dynamics in the bacterial B800–B820 lightharvesting complex, which contains 27 bacteriochlorophyll molecules. Ultrafast sub50fs dynamics dominated by coherent intraband processes and population transfer dynamics on a picosecond time scale were measured and modeled with one consistent set of parameters. Theoretical 2D spectra were calculated by using a Frenkel exciton model and modified Förster/Redfield theory for the calculation of dynamics. They match the main features of experimental spectra at all population times well, implying that the energy level structure and transition dipole strengths are modeled correctly in addition to the energy transfer dynamics of the system.
Twodimensional optical experiments constitute a promising addition to the field of ultrafast spectroscopy. The success of 2D IR spectroscopy in adapting techniques from multidimensional NMR is steadily expanding into the visible range, where coherent couplings between electronic transitions, frequencydependent excitation transfer processes, and chromophore–environment interactions in complex molecular systems can be investigated with femtosecond time resolution. As demonstrated first by Jonas and coworkers (1–3) for visiblerange laser excitation pulses, Fourier analysis of the signal electric field in a phasecontrolled, fourwave mixing experiment yields 2D frequency maps representing the full (within the laser pulse spectral window) thirdorder optical response of the system. 2D electronic experiments performed thus far are based on heterodyne detection of a threepulse photon echo signal, which is separated from other nonlinear signals by phase matching in a noncollinear beam geometry (1, 2, 4–6), or fluorescence detection after phase cycling using pulseshaping techniques, as performed by Tian et al. (7). Brixner et al. (4, 5) developed a particularly robust experimental setup combining inherent phase stability, phase matching, and heterodyne detection by spectral interferometry, and they later demonstrated that the method was well suited to the study of multichromophoric pigment–protein complexes (8).
Multiple thirdorder nonlinear signals interfere to give the overall threepulse photon echo signal, and thus quantitative analysis is essential for disentangling contributions to 2D spectra and identifying the source of spectral features. Simulation of 2D electronic and IR spectra has been performed within the thirdorder optical response function formalism (9, 10), using perturbative treatment of system–bath interactions and modified Redfield (11, 12) and generalized Förster theories (13–15) for calculation of quantum dynamics. A fourwave mixing experiment applied to a strongly coupled molecular system measures signals involving twoexciton states, and the number of twoexciton states scales approximately with the square of the number of chromophores. Therefore, large molecular systems pose an interpretative and computational challenge, but they also are an area where the usefulness of multidimensional optical spectroscopies may be explored.
The first application of 2D electronic spectroscopy to a photosynthetic system was to the sevenchromophore FennaMatthewsOlson protein from green sulfur bacteria (8, 16). Here, we explore application of the method and extension of analysis to the larger (27 chromophore) and more complex lightharvesting complex III (LH3) from purple bacteria Rhodopseudomonas acidophila strain 7050, which contains both a set of weakly interacting and a set of strongly interacting chromophores, and features energy transfer and relaxation within and between the two sets. LH3, the structure of which has been solved to 3.0 Å (17), is a spectroscopic variant of the well studied peripheral antenna lightharvesting complex II (LH2), which carries out the initial steps of sunlight absorption and excitation energy transfer in purple photosynthetic bacteria. LH3 is a ring of nine identical subunits, each a heterodimer of transmembrane polypeptides ligating three bacteriochlorophyll (BChl) pigments (17), which together form two concentric BChl rings labeled B800 and B820 corresponding to the approximate wavelengths of their characteristic nearIR Q_{Y} absorption bands. B800 consists of nine widely spaced, weakly interacting BChls, whereas the B820 ring is characterized by strong electronic couplings among 18 more closely associated BChl pigments. A detailed pumpprobe study by Ma et al. (18) showed that LH3 exhibits dynamics similar to LH2. They determined that averaged B800toB820 energy transfer occurs in ≈0.75 ps at room temperature and ≈0.9 ps at 77 K, as compared with LH2, where the B800toB850 rates are ≈0.8 and ≈1.30 ps, respectively. A number of ultrafast nonlinear spectroscopies have been applied to the study of dynamics in LH2. For recent reviews, see refs. 19–22. Intraband dynamics were observed with time constants as fast as sub100 fs for the strongly coupled (J ≈ 300 cm^{−1}) B850 BChls and 300 fs among the more weakly coupled (J ≈ 30 cm^{−1}) BChls of B800. Based on the structural and spectroscopic data, we consider LH3 to be in many ways similar to LH2, and therefore we use the wealth of information on the LH2 complex as a starting point for the analysis of 2D spectroscopy of LH3.
In this study, from the 2D spectra and model analysis, we were able to extract parameters defining the fast BChl interactions with the environment and distributions of instantaneous environments described by static disorder. Understanding these factors in a quantitative way together with the coupling information allows unraveling of intricate intraband and interband energy transfer dynamics within the LH3 complex.
Experimental Results
Linear Absorption.
The measured and calculated absorption spectra of the LH3 complex at 77 K in the nearIR region are depicted in Fig. 1. The spectrum at 77 K shows the B800 and B820 bands located at 804.5 and 823.5 nm, respectively. The B800 band is clearly narrower than the B820 band, indicating a larger inhomogeneous distribution of the BChl molecules in the B820 ring compared with the B800 ring. Furthermore, both bands overlap substantially. At 860 nm an additional shoulder appears in the linear absorption, which is most likely caused by small B800–B850 LH2 contamination. By comparing the LH3 spectrum of our sample with that of strain 7750, which almost completely lacks the LH2 complex (17), we estimate that the amount of contamination does not exceed 7%. The laser spectrum used in the measurements (dasheddotted line in Fig. 1) covers most of the BChl Q_{Y} transitions, except for the red tail above 840 nm. Further broadening or shift of the laser spectrum to the red side could not be achieved in the current setup. This constraint limits our ability to observe the lowest frequencies in the 2D spectrum.
Experimental 2D Spectra.
The measured and calculated 2D spectra of LH3 at 77 K, corresponding to the real part of the electric field corrected for the radiative line shape, are shown in Fig. 2. All spectra are normalized to the absolute maximum, positive or negative (whichever is larger). The spectra are grouped in two ranges of the population time to accentuate dynamics on two different time scales; Fig. 2 Left displays coherent sub50fs dynamics, and Fig. 2 Right shows energy transfer from the B800 to the B820 ring on a 5ps time scale. Several features of the system are apparent in the T = 0 2D correlation spectrum. Because of the static disorder, the inhomogeneous (diagonal) linewidth is larger than the homogeneous (antidiagonal) linewidth for both the B800 and B820 diagonal peaks. Both bands peak below the diagonal line (ω_{t} = ω_{τ}, ω_{t} and ω_{τ} are the detection and coherence frequencies, respectively). Because the spectra are signed, the shift below the diagonal mostly results from cancellation between positive (bleaching and stimulated emission) and negative [excitedstate absorption (ESA)] peaks, but an ultrafast Stokes shift may also contribute. The B820 peak is shifted much further below the diagonal, indicating stronger couplings causing spectral asymmetry and significant relaxation occurring during the coherence time in the B820 ring as compared with the B800 ring. No crosspeaks are observed in the T = 0 correlation spectra between the two bands, implying that coherent interaction and/or the dipole strength crosscorrelation function between excitons in the two different rings is too small to produce a detectable crosspeak (16). Dynamics occurring on two time scales are seen. Evolution is observed in B820 within 50 fs, as seen in the series of 2D spectra at T = 0, 20 and 50 fs in Fig. 2 Left; the relative intensity of the B820 peak rapidly decays and the doublepeak feature of the B820 band merges into one peak, whereas the shape of the B800 peak remains unchanged. Energy transfer from B800 to B820 occurs with a time constant of ≈1 ps and is marked by the appearance of a crosspeak at ω_{τ} = 12,420 cm^{−1}, ω _{t} = 12,080 cm^{−1} (positively signed) and a corresponding ESA feature at ω_{τ} = 12,430 cm^{−1}, ω _{t} = 12,285 cm^{−1} (negatively signed), as seen in the 2D spectra at T = 1, 2, and 5 ps (Fig. 2 Right). Whereas the B800 peak does not change shape before it decays via population transfer, the B820 peak becomes increasingly symmetric with increasing population time as electronic transitions lose memory of their initial frequencies. The loss of memory arises from rapid relaxation within the B820 excitonic manifold and likely from the fast protein environment reorganization. The absence of peak shape dynamics for B800 indicates that there is no significant intraband energy transfer on the time scale preceding interband energy transfer, as suggested by Novoderezhkin et al. (23). In the 2D spectra, unlike in 1D measurements, the excitedstate contributions from different bands can be separated, e.g., the ESA of B820 appearing at population times T ≥ 1 ps is clearly observed in the 2D spectra, but would overlap with B800 bleaching/stimulated emission in transient absorption measurements.
Theoretical Modeling and Discussion
Model and Numerical Simulations.
To simulate 2D electronic photon echo spectra we use the excitonic model that provided the theoretical basis for the simulations of the FennaMatthewsOlson complex in refs. 8 and 16. Our minimal model is constructed by using structural information about all 27 BChls of LH3 (17) and data from previous experiments and simulations on the LH2 complex (14, 24–28). Each BChl (a site in the model complex) is represented by a twolevel system describing its S _{0} → S _{1} transition (the Q_{y} transition of the BChl) to which we assign a site energy, E_{n} , and an electronic transition dipole moment, d _{n} . The interaction between different sites is described by coupling energies J_{mn} , specified for each pair of the BChls (m, n = 1 … N; N = 27). From the parameters assigned to the sites, we construct a Frenkel exciton Hamiltonian that includes one and twoexciton states (the collective delocalized eigenstates of the complex). The lifetimes of the electronic eigenstates are controlled by their interaction with the protein environment, which is modeled by a stochastic thermodynamic bath causing rapid variations of the BChl transition energy, the S _{0} → S _{1} energy gap, and a very slowly varying protein background that introduces static energetic disorder into the system. An energy gap correlation function C_{n} (t) is assigned to each site to describe fluctuations of its transition frequency. The finite temperature energy relaxation rates between excitonic states, fulfilling the detailed balance condition, are calculated from the coupling energies and the correlation functions by using modified Förster/Redfield theory (11, 12, 14, 15). In this minimal approach we limit the description of the fluctuation of individual site energy gaps to a single mode of an overdamped Brownian oscillator model characterized by a reorganization energy, λ _{n} , and a correlation time, τ _{n} .
The photon echo signal constituting our 2D spectrum is calculated in the impulsive limit (infinitely short excitation pulses) and therefore it includes only the rephasing Liouville pathways of the total thirdorder nonlinear response (those pathways are given in ref. 5). To calculate the 2D spectrum on a short time scale (T ≤ 100 fs), we do not use the Taylor expansion method successfully applied to long population times in refs. 8 and 16. Instead, the rephasing response functions are expressed in terms of reduced density matrix propagation operators, and a factorization of the delay times between laser pulse interactions with the complex is introduced, leading to a simplified doorway–window picture (9). Thus, each response function is written as a product of three contributions dependent on a single delay time between the pulses only. This approximation greatly accelerates the numerical calculations and enables explicit averaging of the 2D spectra over individual energetically disordered realizations of the LH3 complex and orientational averaging with respect to the polarization of the laser electric field. Both coherence dephasing caused by population relaxation and pure dephasing caused by excitonic energy gap fluctuation are taken into account. The spectra are thus calculated in a selfconsistent manner with both line shape and relaxation/energy transfer dynamics being calculated from the same correlation functions. Moreover, the temperature dependencies of both the line shape and the relaxation rates are consistently accounted for by the thermodynamic properties of the energy gap correlation function. The effect of the finite frequency width of the laser pulse is taken into account by weighting the calculated 2D spectrum with the estimated Gaussian laser pulse spectrum. This correction compensates only for the limited frequency bandwidth of the laser pulse; the effect of pulse overlap within the photon echo excitation sequence is not accounted for.
The crystal structure and coupling energies estimated by Krueger et al. (27) for the LH2 complex suggest that the complex can be split into a strongly interacting block of BChls forming the ring responsible for the B850 and B820 bands in LH2 and LH3, respectively, and more weakly coupled ring of BChls responsible for the B800 band. We split the complete Hamiltonian into two blocks between which weak coupling (no mutual mixing of states) is assumed and inside of each block we assume strong interaction leading to delocalization. Because the number of twoexciton states in the Frenkel Hamiltonian grows with the square of the number of sites, this division reduces significantly the size of the problem. The potential penalties and the approximation thus introduced are discussed below. Previous studies on LH2 suggested the existence of two distinct site energies in the B850 ring (14, 19). Therefore we introduce two site energies, E _{B820} ^{α} and E _{B820} ^{β} for the BChls in the B820 ring and a single site energy E _{B800} for the B800 BChls. In our model, we assume the energy gap correlation function of all sites in B820 to be identical and characterized by reorganization energy, λ_{B820}, and correlation time, τ_{B820}. The corresponding quantities for the B800 ring are denoted by λ_{B800} and τ_{B800}. A Gaussian distribution of site energies within the rings with standard deviations σ_{B800} and σ_{B820} is assumed. Because we explicitly average over the disorder, our description also includes a certain distribution of mean values of individual realizations as discussed in ref. 26. Additional external disorder parameters Σ_{B800} and Σ_{B820} that might play a significant role for the complexes embedded in membranes (24, 26) are assumed to be zero for the complexes in solution. For the sake of simplicity we neglect effects of the coupling disorder in current treatment, although to achieve a higher level of agreement with the experimental data this effect has to be included (29). The orientation of the transition dipole moments is assumed to be along the A, C ring axis of the BChl (30) and is calculated from the crystal structure (see ref. 17). The absolute value of the transition dipole moments is assumed to be the same for all BChls in the complex. We use the coupling values calculated for LH2 by the transition density cube method in ref. 27. Assuming the coupling and the orientation of dipole moments are fixed, our minimal model is fully characterized by nine free parameters.
Modeling of 2D Spectra of LH3.
We fit simultaneously the linear absorption spectrum of LH3 and its 2D electronic correlation spectrum at population time T = 0 fs. We do not explicitly fit later population times; however, the agreement with the experimental spectra for T > 0 is good, suggesting that our minimal model captures most of the characteristic features of the LH3 complex.
For our initial calculations, we took the LH2 parameters from refs. 24–26, with the B850 site energies adjusted to reproduce the absorption maximum of the B820 band of the LH3 complex, i.e., E _{B800} = 12,500 cm^{−1}, E _{B820} ^{α} = 13,130 cm^{−1}, and E _{B820} ^{β} = 12,600 cm^{−1}. We kept the difference E _{B820} ^{α} − E _{B820} ^{β} = 530 cm^{−1} as in the original LH2 parameters. In both rings we used the nearest and the secondnearest neighbor coupling. In B800 and B820 the nearest neighbor couplings are on the order of 30 and 300 cm^{−1}, respectively, and the coupling between monomers in different rings is on the order of 30 cm^{−1} (for more details see ref. 27). Using these parameters (with λ_{B800} = 110 cm^{−1}, τ_{B800} = 50 fs, σ_{B800} = 90 cm^{−1}, λ_{B820} = 100 cm^{−1}, τ_{B820} = 150 fs, and σ_{B820} = 150 cm^{−1}) resulted in a significant mismatch with the experimental absorption spectrum of LH3. Our calculations show that for the LH3 complex the antidiagonal width of the peaks is mostly governed by the chromophore homogeneous linewidth narrowed by the coupling. Consequently, the fact that the calculated antidiagonal width of the B820 peak was much larger than of the B800 peak suggested reduction of the B800 reorganization energy (as opposed to a possible change in disorder parameters) to account for the small homogeneous linewidth of the B800 peak. The shape of the B820 peak, on the other hand, clearly suggested a much larger reorganization energy. Thus, the model parameters were revised resulting in λ_{B800} = 30 cm^{−1} with τ_{B800} = 50 fs and static disorder σ_{B800} = 80 cm^{−1}. These parameters fit the B800 peak in both absorption and 2D spectra. A reasonable fit for the linear absorption spectrum and the 2D spectrum was obtained with B820 parameters of λ_{B820} = 300 cm^{−1}, τ_{B820} = 50 fs, and σ_{B820} = 215 cm^{−1}. During fitting we also adjusted the difference between the B820 site energies and introduced nonzero values of an additional external disorder Σ_{B820}. These changes yielded visible alterations of the 2D peak shape of the B820 band, but the differences were mostly suppressed when the spectrum was corrected for the experimental pulse shape. Therefore for our final parameters we chose the external disorder of both rings to be zero. Overall, the calculated 2D spectra reproduce rather well the main features of the experimental 2D spectra over the whole range of population times. The small homogeneous width of the B800 peak with respect to that of B820, the shift of the B820 peak below the diagonal of the 2D spectrum, and the position of the ESA features in the upper left and lower right corners of the 2D spectrum at T = 0 fs are well reproduced. Also, over the range T = 0 fs to T = 50 fs the decrease in the relative intensity of the B820 peak is reproduced. However, the prominent double peak feature, observed for T = 0–20 fs in experimental 2D spectra, does not appear in the simulations. This feature is likely caused by the overlap of the temporally chirped excitation pulses producing different pulse ordering not taken into account in simulations. At long population times T ≥ 1 ps we reproduce the main changes in the spectrum caused by the B800toB820 energy transfer. Remarkably, the agreement is very good also for the ESA features. Their positions in the spectra are replicated very well, although their intensity is smaller than in experiment. The calculated long time spectra are dominated by an energy transfer cross peak that is too intense, most likely as a result of the approximations used in our model, as described below.
Coupling in the B800 Ring.
The B800 ring is formed by relatively weakly coupled BChls with a coupling energy of ≈30 cm^{−1} between the nearest neighbors. It has been therefore often modeled as a set of monomers that do not exhibit any mixing because of electronic coupling. Recently, it was suggested that the excitation dynamics within the B800 ring (23) and the shape of the linear absorption spectrum (29) cannot be explained unless the excitonic character of the ring is taken into account. In Fig. 3 we compare a calculated 2D spectrum by using an excitonic model of the B800 ring (Fig. 3 a) with one where excitonic mixing has been neglected (Fig. 3 b). In Fig. 3 a, the coupling was used to calculate the energies of the excitonic states, and the relaxation rates between these states were calculated by using modified Redfield theory. In Fig. 3 b, the same initial parameters were used, but no diagonalization was performed. The values of the coupling between different sites were used to calculate energy relaxation rates by generalized Förster theory. Besides the obvious lack of spectral narrowing when neglecting excitonic mixing and an overall shift of the spectrum (both of which could be compensated by changing the initial parameters) (Fig. 3 b), the most striking difference between the two 2D spectra that reveals the importance of electronic coupling is the asymmetry in the negative part of the 2D spectrum (Fig. 3 a). This antidiagonal asymmetry seems to be characteristic for a coupled excitonic system. The couplinginduced redistribution of energies and dipole strengths in LH3 favors ESA from the lower oneexciton states and is manifested as stronger negative features above the diagonal. Furthermore, because the electronic coupling does not change the actual line shape of the individual transitions (the energy gap correlation function is only multiplied by a narrowing factor) the difference of the absorption line shape between coupled and uncoupled B800 complexes is only caused by couplinginduced dipole strength redistribution in the disordered complexes. Such a distribution of transition dipoles could, in principle, result from the complex being composed of different types of uncoupled monomers, and, therefore, the linear absorption shape cannot conclusively reveal the presence of electronic coupling. The 2D spectrum, on the other hand, reveals the coupling either by the presence of cross peaks, e.g., as observed in the FennaMatthewsOlson complex (8) or by antidiagonal asymmetry, as in the case of B800 (and B820), much more conclusively. Because our modeling does not include any monomer states higher than Q_{Y} for BChl the good description of the 2D spectrum allows us to conclude that these higher excited states do not contribute significantly to the 2D spectra. It would, however, be desirable to measure the 2D spectrum of a monomeric BChl in protein environment (such as the B777 complex; ref. 31) to obtain a 2D image of the absorption of these higher excited states. Using these data, one could obtain quantitative information about couplings inside B800 directly from the spectral asymmetry of the 2D spectrum.
B800toB820 Energy Transfer Dynamics.
We calculated the rates of interring energy transfer by using the generalized Förster approach introduced by Scholes and Fleming (14) and Scholes (32) and similarly by Sumi (13), Mukai et al. (33), and Jang et al. (15) for molecular aggregates with small interchromophore distances. The overlap of spectral density and electronic coupling factor are calculated pairwise for statically disordered donor and acceptor states before ensemble averaging, and both the donor and acceptor are treated in an excitonic basis. The calculation of B800toB820 energy transfer rates and their application to the calculation of the long population time spectra (T = 1, 2, and 5 ps) based on the above parameters and the B800–B820 BChl couplings from ref. 27 resulted in somewhat faster rates of transition between the rings than observed in the experiment. The discrepancies between the calculated and the actual shape and amplitude of the relaxation crosspeak are most probably caused by the fact that we neglect the excitonic character of the B800–B820 coupling. This coupling is of the same order as that within B800, which, as shown above, has a significant impact on the 2D spectrum. Another source of the discrepancy is the factorization of the delay times in the response functions, resulting in the line shape of the crosspeak being unaffected by the population time. Also, dielectric screening of the protein that would slow the rate of energy transfer is not included (14).
Nevertheless, the overall rather good reproduction of the experimental 2D spectra by our minimal model suggests that the energy level structure corresponds well with that of the actual LH3 complex, enabling us to draw some conclusions about the internal dynamics of the system from our calculations. The ≈1ps energy transfer between BChl rings observed in both LH2 (and LH3) cannot be predicted by a traditional Förster calculation because the spectral overlap between the rings is too small. It has been suggested (14, 33) that energy transfer occurs from B800 into dark, higherlying states of B850 (B820). A 2D histogram of our calculated averaged energy transfer rates from B800 to B820 for 200 LH3 complexes is shown in Fig. 4 a. The highest rates are concentrated near the diagonal in the spectral region of the B800 band, that is, energy would transfer most quickly from B800 states into B820 states of similar energy. A histogram of the energy transfer rates for a single realization of the Hamiltonian is shown in Fig. 4 b. Inspection of many such singlecomplex calculations shows that the energy would transfer fastest from the eighth and ninth B800 states into the sixth to eighth exciton states of B820. These regions have vanishingly small dipole strength for both rings, in a direct disagreement with traditional Förster results. However, in the experiment only optically allowed states are populated in B800 and thus the fastest B800toB820 excitation energy transfer occurs from states where B800 absorbs strongly (first to fifth). It can be seen in Fig. 4 a that the range of fast rates extends well above the position of the B800 peak.
Conclusions
We report a combined experimental and theoretical study of the 2D electronic photon echo spectra of the bacterial photosynthetic complex LH3. This study represents only the second photosynthetic system studied by 2D electronic spectroscopy to our knowledge. The 2D spectra measured for different population times reveal ultrafast dynamics within the B820 BChl ring of LH3 and enable the extraction of detailed information about energy transfer from the B800 to the B820 ring. Modeling based on a minimal Frenkel Hamiltonian results in a rather good agreement with the experiment, reproducing most of the features of 2D spectra. This minimal model extended with a more flexible lineshape theory provides means for quantitative comparison of experiment and theory. We have demonstrated that the couplings between BChls in a highly symmetric structure such as LH3, which eliminates crosspeaks by forbidding certain electronic transitions, can reveal themselves by asymmetry of the 2D spectrum. The simulations of B800toB820 energy transfer rates confirm the breakdown of conventional Förster theory in this system and show that generalized Förster theory is necessary to describe light harvesting in complex multichromophoric systems.
Materials and Methods
Sample Preparation.
Rps. acidophila strain 7050 was grown anaerobically on Pfennig’s media at a low light intensity (≈10 μmol·s^{−1}·m^{−2}) and at 303 K. Membranes were solubilized with the detergent lauryl dimethylamine Noxide, and the LH3 was separated from LH1/RC “core” complex by discontinuous sucrose density gradients. The complex was then purified by ionexchange and gel filtration chromatography. All 2D experiments were done in a 0.2mm quartz cuvette placed in the liquid nitrogen cryostat. Sample concentration was adjusted to achieve ≈0.3 OD at 804.5 nm. Absorption spectra were measured before and after 2D experiments to ensure that no substantial sample degradation took place.
Experimental Setup, Data Acquisition, and Evaluation.
2D electronic spectra were measured by using a diffractive opticbased inherently phasestabilized fourwave mixing setup. The details of the setup, data acquisition, and analysis can be found in refs. 4 and 5. In brief, a homebuilt Ti:sapphire regenerative amplifier seeded by a homebuilt Ti:sapphire oscillator produced 40fs pulses at a 3kHz repetition rate. The spectrum of the pulses was centered at 808 nm with an FWHM of 34 nm. The spectral resolution of the setup in detection frequency, ω _{t} , and coherence frequency, ω_{τ}, was 2 and 42 cm^{−1}, respectively. The excitation density of the pulses at the sample space was 8 × 10^{13} photons per pulse^{−1}·cm^{−2}. All measurements were performed at 77 K to accentuate separated contributions from the two BChl rings within LH3 and to avoid rapid sample degradation. All beams used in the experiments were polarized parallel to each other.
Data analysis was performed by using Fourier transformations resulting in 2D spectra with undefined absolute phase. For determination of the absolute phase, frequencyresolved transient electric field amplitude measurements (analogous to pumpprobe measurements) were performed separately for population times T ranging from 0 to 5 ps. The 2D spectral phasing procedure using the projectionslice theorem was carried out as described (5). To obtain a reasonable match, the constant phase factor was varied within 0.3 rad, and the timing correction was within 4 fs for different population times.
A more detailed description of sample preparation and experimental methods can be found in Supporting Text, which is published as supporting information on the PNAS web site.
Acknowledgments
R.J.C. and A.T.G. thank the Biotechnology and Biological Sciences Research Council for financial support. T.B. thanks the German Science Foundation for an Emmy Noether fellowship. This work was supported by the Director, Office of Science, Office of Basic Energy Sciences, Chemical Sciences Division of the U.S. Department of Energy under Contract DEAC0376SF00098.
Footnotes
 ^{¶}To whom correspondence should be addressed. Email: grfleming{at}lbl.gov

↵ ^{‡}Present address: Physikalisches Institut, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany.

Author contributions: D.Z. and G.R.F. designed research; D.Z., E.L.R., T.M., and T.B. performed research; T.M., T.B., A.T.G., and R.J.C. contributed new reagents/analytic tools. D.Z., E.L.R., and T.M. analyzed data; and D.Z., E.L.R., T.M., A.T.G., and G.R.F. wrote the paper.

Conflict of interest statement: No conflicts declared.

This paper was submitted directly (Track II) to the PNAS office.
 Abbreviations:
 BChl,
 bacteriochlorophyll;
 ESA,
 excitedstate absorption;
 LH2,
 lightharvesting complex II;
 LH3,
 lightharvesting complex III.
 © 2006 by The National Academy of Sciences of the USA
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