Jante M. Salverda, Frank van Mourik,, Gert van der Zwan, and Rienk van Grondelle*,

Transcription

1 J. Phys. Chem. B 2000, 104, Energy Transfer in the B800 Rings of the Peripheral Bacterial Light-Harvesting Complexes of Rhodopseudomonas Acidophila and Rhodospirillum Molischianum Studied with Photon Echo Techniques Jante M. Salverda, Frank van Mourik,, Gert van der Zwan, and Rienk van Grondelle*, Department of Biophysics and Physics of Complex Systems, VU Amsterdam, The Netherlands, Institut de Physique de la Matière Condensée, Faculté des Sciences, BSP, UniVersité de Lausanne, Switzerland, and Department of Analytical Chemistry and Applied Spectroscopy, Faculty of Exact Sciences, VU Amsterdam, The Netherlands ReceiVed: June 5, 2000; In Final Form: August 23, 2000 Eenergy transfer in the B800 ring of the LH2 antenna of the purple bacteria Rhodopseudomonas (Rps.) acidophila and Rhodospirillum (Rs.) molischianum was studied at room temperature using three-pulse echo peak shift (3PEPS) and transient grating (TG) techniques. From the transient grating experiments, we found the B800 f B850 energy transfer rates to be fs for both species. The anisotropy of the TG signal decays in about 1 ps for both species, which is ascribed to B800 f B800 energy transfer. The occurrence of B800 f B800 energy transfer was further substantiated by 3PEPS experiments. When measured over the whole B800 band, the initial peak shift of about 30 fs exhibited a fast <100 fs decay to about 10 fs due to the coupling to protein phonons, followed by a slow phase of about 1 ps, during which the peak shift decayed to 1-3 fs. Polarized 3PEPS experiments systematically resulted in smaller peak shift values for the third pulse polarized perpendicular to the first two than for the third pulse parallel to the first two. Furthermore, frequency-resolved 3PEPS experiments performed on LH2 of Rs. molischianum showed a large difference in peak shift decay rates when tuning over the B800 band. The blue peak shifts did not decay after the initial sub-100 fs phase, while red peak shifts decayed much faster than the whole band signal. All these observations confirm the presence of B800 f B800 energy transfer. Simulations using the Brownian oscillator model allowed the determination of an equilibration rate of 1100 fs for Rps. acidophila and 800 fs for Rs. molischianum. For a model in which the spectral equilibration in a ring occurs by single hopping steps between adjacent pigment molecules, these times correspond to 2.2 ps (Rps. acidophila) and 1.6 ps (Rs. molischianum) for a single step. Strong oscillations with a predominant frequency of 162 cm -1 are observed in the peak shift decays of both species. 1. Introduction 1.1. Light Harvesting and the B800 Ring. In photosynthesis, solar photons are converted into a stable transmembrane charge separation with a quantum efficiency of 90% or higher. To obtain such a high efficiency, all steps involved have to be extremely fast: charge separation occurs within 100 ps after a photon is absorbed. 1,2 Light is harvested by antenna complexes, membrane-bound proteins with photoactive cofactors such as (bacterio)chlorophyll and carotenoid pigments. The antennae transfer their excitation energy to a reaction center (RC) where initial charge separation is followed by a sequence of stabilizing electron-transfer steps. Photosynthetic purple bacteria are frequently used for studying excitation transfer in photosynthesis due to their relative simplicity and their suitability for genetic engineering. The different complexes involved in the process can be isolated to a high degree of purity while retaining their stability, and the * Corresponding author. Department of Biophysics and Physics of Complex Systems, VU Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands. rienk@nat.vu.nl. Department of Biophysics and Physics of Complex Systems, VU Amsterdam. Institut de Physique de la Matière Condensée, Université de Lausanne. Department of Analytical Chemistry and Applied Spectroscopy, VU Amsterdam. structure of several of the pigment-protein complexes involved is known to atomic resolution. Purple bacteria contain two types of light-harvesting antennaesthe core antenna LH1, which surrounds the RC, and the peripheral antenna LH2. The crystal structure of the RC was resolved more than 10 years ago for the two species Rhodopseudomonas (Rps.) Viridis 3 and Rhodobacter (Rb.) sphaeroides. 4,5 A few years ago, the structures of the LH2 antennae of Rhodopseudomonas (Rps.) acidophila 6 and Rhodospirillum (Rs.) molischianum 7 became known to a resolution of 2 Å, which generated an enormous increase of interest in the study of these complexes. For the LH1 antenna, only low-resolution models have been published so far. 8,9 The absorption spectra of the different components are carefully tuned from 800 to 850 nm for LH2, 875 nm for LH1, and 870 nm for the primary electron donor pair (P) of the RC. Energy transfer occurs from LH2 to LH1 on a picosecond time scale, 10,11 followed by relatively slow transfer from LH1 to the RC in several tens of picoseconds In this study, we will look at energy transfer in the peripheral antenna LH2. From the X-ray structure, this antenna is seen to consist of a ring of R-helical polypeptides, which are noncovalently bound to each other. The ring lies in the plane of the membrane with the R helices more or less perpendicular to it. For both Rps. acidophila and Rs. molischianum, the basic unit /jp002034z CCC: $ American Chemical Society Published on Web 11/01/2000

2 11396 J. Phys. Chem. B, Vol. 104, No. 47, 2000 Salverda et al. is a heterodimer of an R and a β polypeptide, which binds three bacteriochlorophylls (BChl) and one or two carotenoids (Car). Rps. acidophila contains nine of these basic units, and Rs. molischianum contains eight. Two of the BChls per basic unit (the Rβ-heterodimer) are sandwiched between the R and β polypeptide rings, with their tetrapyrrole planes perpendicular to the membrane plane. Together, all 18 (Rps. acidophila) or 16 (Rs. molischianum) of these BChls form a tightly coupled ring, which typically absorbs at 850 nm and is denoted as B850. Per basic unit one BChl is positioned at the outside of the ring, between the β polypeptides. The ring of 9 or 8 of these weakly coupled BChls, absorbs at 800 nm and is called B800. In the case of Rps. acidophila, the B800 pigments lie parallel to the membrane plane; in the case of Rs. molischianum, they are tilted by 30. From CD measurements [Frese et al., unpublished], it appears that all purple bacteria belong to one of two classes with different B800 orientations, which are represented by these two species. As seen in the structure, the B850 pigments are in close contact with each other, with a center-to-center distance of about 9 Å within the basic unit and close to 10 Å between the neighboring BChls from different units. Because of these short distances, the excitonic coupling between the transition dipoles of the lowest excited state, Q y, which lie in the plane of the ring, is rather large, about 300 cm ,16 This coupling tends to delocalize the excitation over the whole B850 ring, but this effect is counteracted by dynamic and static disorder, for instance, in the site energies. The combined effect of electronic coupling and disorder results in a delocalization of the excitation over a few (2 or 3) pigments Energy transfer or, in the excitonic picture, relaxation to the lowest exciton levels, takes place in 100 fs, according to fluorescence depolarization, 22 pump-probe, 23,24 and three-pulse (photon) echo peak shift (3PEPS) 25 measurements. For LH1, a variety of experiments has shown that the energy transfer events occur on very similar time scales The B800s are as far as 20 Å apart from each other and 17 Å from the nearest B850, causing the excitation to be localized on monomeric BChls. Energy transfer from B800 to B850 is well established to occur in fs at room temperature for many different species At low temperature, it is somewhat slower, with rates found between 1.1 and 1.8 ps 30,32-34 but probably close to 1 ps at 77K. 33 It has been a subject of much discussion in recent years whether any energy transfer occurs between the B800s before the excitation is transferred to B850. At low temperature, energy transfer between B800 pigments is relatively well established and has been observed by several authors. Originally, B800 energy transfer was proposed on the basis of the observed polarization of the B800 emission. 35 From spectrally resolved pump-probe studies, 30,33,36,37 a variation in decay rate over the B800 band was found, with the fastest rate, 0.5 ps, at the blue side and the slowest, 1.5 ps, at the red side. Also, a finite rise time was observed in the bleaching of the red edge of the B800 band following excitation in the blue edge. These findings were confirmed by spectral hole-burning studies, 32,38,39 in which a variation of the hole width over the B800 absorption band was found. Clearly, inhomogeneity plays a very important role. Single-molecule spectra taken at 1.2 K demonstrate this inhomogeneity straightforwardly, as the spectrum of a single LH2 molecule around 800 nm is shown to consist of several narrow ( 1 nm) peaks at wavelengths ranging from 785 to 810 nm. Remarkably, in these spectra, no variation of the line width over the B800 band was observed, in contrast to the pumpprobe 30,33,36,37 and hole-burning 32,38,39 results. At room temperature, the occurrence of B800 intraband transfer is much more a matter of debate. Different techniques and models are needed to deal with B800 T B800 energy transfer compared with cryogenic temperatures. Due to the large homogeneous line width of the pigments ( 150 cm -144 ) at room temperature, frequency-selective excitation is seriously hampered. Furthermore, both uphill and downhill energy transfer, if any, will proceed at comparable rates. In polarized pumpprobe experiments, several authors 36,45,46 find anisotropy decay times which they attribute to B800 T B800 energy transfer. Hess et al. 45 and Kennis et al. 46 find a value of ps for this time, whereas Ma et al. 36 find faster rates of 400 to 800 fs at varying wavelengths. Hess et al. 45 and Joo et al. 44 observe isotropic transient absorption decay times of 300 fs, which they attribute to vibrational relaxation. In their 3PEPS experiment, Joo et al. 44 detect a 600 fs peak shift decay time, but they attribute this to B800 f B850 transfer. Jimenez et al. 22 find a decay time of 350 fs for the anisotropy of B850 fluorescence after B800 excitation, which they interpret as due to B800 intraband energy transfer. By others, Jimenez s observation is cited as evidence both for 2 and against 44 B800 intraband transfer. Altogether, the picture is confusing both with respect to the presence of B800 T B800 transfer and the time which should be attributed to it. For a review of this debate, see also Sundström et al. 2 In this study, we describe a set of 3PEPS experiments on the B800 band of LH2 of Rps. acidophila and Rs. molischianum. To search specifically for evidence of B800 intraband energy transfer, we use both polarized and frequency-selective detection of the echo signal. A transient grating (TG) experiment was also performed at both polarizations, with and without frequencyresolved detection The Three-Pulse Echo Peak Shift and Transient Grating Methods. In the 3PEPS experiment, a sequence of three laser pulses, each with a slightly different direction of propagation k 1, k 2,ork 3, is focused onto the sample. We will describe the principle of this experiment using the impulsive limit. A fourth pulse, the photon echo, is emitted in the direction k 3 - k 2 + k 1 at a time τ after the third pulse, with τ being the delay between the first two pulses. The time-integrated intensity of the echo is measured as a function of the delay τ, with the delay T between the second and third pulse, also known as population time, as a parameter. The distance of the maximum of this signal (further referred to as the echo) from τ ) 0, the peak shift, is then determined as a function of T. The decay of the peak shift with T reflects all processes which lead to frequency changes of the excited pigments, described as ω(t), within the spectral window of the used pulses. This can be explained by the following argument. Pulses 1 and 2 generate a frequency-dependent modulation of the excited-state population within the laser bandwidth, a so-called frequency grating, which has spacing proportional to 1/τ. The modulation depth and width of this grating will be affected by changes in the transition frequencies of the pigments within the laser bandwidth, rather like in a transient hole-burning experiment. The amplitude of the grating also decays due to population transfer to pigments absorbing outside the laser window, but this does not affect the peak shift. Because the intraband frequency changes efface a fine grating more easily, an increasingly widespaced grating is needed to survive when longer T values are used. As a more widely spaced grating corresponds to a smaller delay between pulses 1 and 2, this means that the echo intensity

3 Peripheral Bacterial Light-Harvesting Complexes J. Phys. Chem. B, Vol. 104, No. 47, maximum gets closer to zero τ. Thus, the decay of the peak shift as a function of T reflects the loss of correlation, averaged over all pigments, between the excitation frequency at the time of pulse 2 and the frequency at the time of pulse 3. We note that for the case of nonzero pulse widths, the overlap of the pulses in time, leading to different time ordering, must explicitly be accounted for (see section 4). The fluctuating frequency ω i - (t) of each pigment i can be described as ω i (t) ) ω eg + ω i (t) + ɛ i (1.1) with ω eg the ensemble average of the transition frequency, ω i - (t) the fluctuation of the transition frequency for pigment i, and ɛ i the static deviation of w i (t) from average, i.e., the inhomogeneous broadening. The average frequency correlation of the ensemble is then described by the two-point frequency correlation function M(t) ) ω(0) ω(t) ω(0) 2 (1.2) The transient grating technique is a special case of the threepulse echo, with the first two pulses set at τ ) 0 and the signal intensity scanned as a function of the population time T. The first two pulses now create a spatial population grating in the sample due to interference between the beams which intersect at a small angle. The decay of this grating reflects the loss of excited-state population from within the laser spectrum. This spatial grating is also created in the 3PEPS experiment, of course, but in that experiment, the amplitude decay, which is caused by population transfer, is not considered (as mentioned above). Also at nonzero delays between pulses 1 and 2, the phase of this grating will be different for each frequency, leading to canceling contributions. The 3PEPS technique, originally developed for the study of solid-state dynamics, became increasingly popular in the field of liquid dynamics as sub-100 fs lasers were developed. For monomeric solutes in solvents, the peak shift decay reflects the coupling of the solute electronic transition to various solvent relaxation processes. From 3PEPS and other experiments, these solvent relaxation processes were shown to occur over a whole range of time scales, 47,48 thereby demonstrating the limited usefulness of the standard (Bloch) model, which factors all dynamics in an infinitely fast homogeneous contribution and an infinitely slow inhomogeneous contribution. Several more sophisticated models were developed, such as the Kubo theory 49 and the Brownian oscillator model, which will be used here. In the Brownian oscillator model, each frequency-affecting process is defined by its characteristic time scale and the strength of its coupling to the electronic transition. Several studies on dye molecules in liquids have shown how relaxation processes can be identified with this technique. 54,55 In the case of pigment protein complexes, the protein will act as a solvent, reacting to the excitation of the pigment via electron-phonon coupling. Further contributions to the decay of the frequency correlation function M(t), such as inter- and intramolecular vibrations of the excited pigments, also have to be taken into account. The most important difference between a pigment in a protein and a solute in a solvent is the coupling between the pigments leading to energy transfer. In the most often used approach, 25,44,56 the energy transfer is incorporated by taking ω i (t) (eq 1.1) to describe a two-level electron-hole system which migrates among the pigments, rather than a single fixed pigment. During the migration, the electron-hole pair samples the inhomogeneous distribution, so the ɛ i term in eq 1.1 becomes a time-dependent quantity. The diffusive character of energy transfer implies an exponential decay term of M(t), which is added to the sum of Brownian oscillators. In fact, the electron-hole system is analogous to a solute in a liquid, with the exponential term analogous to an overdamped oscillator. This analogy, which allows for the use of modeling methods derived for liquid systems, explains how the Brownian oscillator (BO) model came to be used for photosynthetic systems. However, it is unclear whether this is physically justified. Recently, a different approach to third-order nonlinear spectroscopy, using exciton annihilation and creation operators, was developed by Mukamel and co-workers, 57 which can be applied to strongly coupled systems such as B850 and LH1. For more weakly coupled systems such as B800, a model was developed by Yang and Fleming, 58 which describes the system as two twolevel systems, a donor and an acceptor, with uncorrelated frequency fluctuations. In this paper, we will employ the more widely used old model. We will discuss the validity of the obtained results by comparing them to calculations based on a simplified form of the formalism of Yang and Fleming This Study. As mentioned above, in this work, we specifically search for evidence of B800 intraband transfer. We have attempted to separate a possible energy transfer contribution to the 3PEPS signal from protein dynamics contributions by measuring at both parallel and perpendicular polarization of the third pulse. If any energy transfer takes place, we expect to see a difference in peak shift decay between both polarizations, since energy transfer will change the polarization drastically because of the different orientations of the pigments involved. Moreover, we applied frequency-resolved detection of the echo signal. Possible downhill energy transfer between B800s would then show up as a difference between blue and red detected peak shift decays. Furthermore, a transient grating experiment was carried out as an alternative way of looking at B800 excitedstate dynamics. Also in this experiment, frequency-selective and polarized detection of the signal was applied. From the polarized transient grating signals, we have calculated the anisotropy decay, which is taken to reflect B800 f B800 energy transfer. The overall decay of the transient grating will display the B800 population decay due to B800 f B850 energy transfer. In the following section, we will discuss the experimental setup and methods. In section 3, we will discuss the results qualitatively. After introducing the mathematics of the models used in section 4, we will proceed to present simulations of the measured peak shift curves, which will allow for more quantitative statements. Concluding remarks will follow in section Experimental Procedure The experimental setup is shown in Figure 1. A standard 3PEPS configuration was used, similar to that described elsewhere. 25,44 As a source of ultrashort pulses, we used a commercial 20 fs Titanium Sapphire laser (Coherent MIRA Seed). A cavity dumper (Coherent) was built into the laser cavity to reduce the repetition rate from 76 MHz to 150 khz. The rate has to be reduced to avoid the buildup of carotenoid triplet states, which live for about 1 µs. Together with the use of a flow cell, lowering the repetition rate also reduces possible heat damage to the sample. The wavelength of the laser can be tuned from 770 to 840 nm by changing the position of the mode-locking slit across the beam profile. For our experiment, the central wavelength is tuned to 800 nm to match the absorption of B800. In Figure 2, the laser spectrum is shown together with the absorption spectrum of the LH2 of Rps. acidophila which was used for

4 11398 J. Phys. Chem. B, Vol. 104, No. 47, 2000 Salverda et al. Figure 1. Experimental setup. An Ar + laser pumps a cavity-dumped Ti:sapphire laser, which yields 30 fs pulses with a wavelength of 800 nm and a bandwidth of 30 nm. The beam is split twice to obtain three pulses, which can be delayed with respect to each other. The three beams are focused into the same spot in the sample, each beam entering at a slightly different angle. The two photon echoes exit the sample under two separate angles determined by the geometry of the incident beams (see text) and are detected by two photodiodes, each connected to a lock-in amplifier. our experiments. The pulse spectrum has a width (fwhm) of about 30 nm and amply covers the B800 absorption band, so no selection effects are to be expected. An autocorrelation of 50 fs is measured, implying that the pulses are nearly transformlimited when a Gaussian pulse shape is assumed. At the sample, the total energy per shot is about 2 nj. Directly after the laser, an external LaKL21 prism compressor corrects for the group velocity dispersion (GVD) of the setup. After compression, the beam is split in three with beam splitters, with all beams having approximately equal energy. All three beams are delayed by travelling via retroreflectors on translation stages. Pulses 1 and 2 travel via motorized translation stages (Newport stepper motor MM3000), so their delays can be varied. After the delay path, the three beams are aligned parallel to each other at a distance of about 1 cm, forming an equilateral triangle, and they are focused onto the sample. The sample is contained in a quartz flow cuvette of only 0.2 mm path length to ensure that no reabsorption takes place after the focus, where the echo signal is generated. For a more accurate determination of the peak shift, the echo corresponding to pulse 2 (with wavevector k 2 ) is also detected. The echoes with vectors k S ) k 3 + k 2 - k 1 and k S ) k 3 - k 2 + k 1 are detected in a timeintegrated fashion by photodiodes. To reduce noise, we connected the diodes to lock-in amplifiers, for which a chopper in beam 2 is used as reference. The original beams are blocked after the sample to reduce scattering onto the detectors. For the polarized measurements, waveplates are positioned in all three beams to set their polarization. The orientation of the waveplate in beam 3 can be varied with a motorized rotator. Frequency selection is achieved by placing interference filters in front of the detecting photodiodes. Two filters with bandwidths of 7 nm and central wavelengths of 818 and 797 nm are used. The filters were tilted with respect to the beam to set the wavelengths of maximum transmission to 810 and 790 nm, respectively. The time resolution is not affected by the bandwidth reduction because the filter only lengthens the echo signal, which is already detected time-integrated. The sample consists of detergent isolated LH2 complexes of Rps. acidophila strain and Rs. molischianum, isolated and purified as described elsewhere. 6,7 The complexes are dissolved in a standard phosphate buffer with 20 mm HEPES and a ph of 8. Some excess detergent was added to a total of 0.2% LDAO to avoid aggregation. To remove any remaining large aggregates, we placed a sub-0.45 µm filter into the flow circuit. The sample is circulated through the flow circuit at a speed of cm/s by a peristaltic pump. The maximum absorbance is 0.3, chosen to balance the intensity of the signal against deformation of it from reabsorption and against the use of large amounts of the sample. To check if any photodamage had occurred, we measured the absorption spectrum before and after the experiments. No changes could be detected. 3. Results Figure 2. Absorption spectrum (solid line) of the detergent-isolated LH2 of Rps. acidophila (strain 10050) and laser spectrum (dotted line). Three-pulse echo (3PE) signals were measured for both Rs. molischianum and Rps. acidophila at about 50 values of the population time T, with the third pulse at parallel polarization. For the third pulse perpendicular, the 3PE signals were measured at three values of T. For each value of the population time, a number of fast scans was averaged to obtain a good signal-tonoise ratio. For Rs. molischianum only, the 3PEPS experiment was repeated with selective detection of the blue and red edges of the B800 band, both at parallel polarization of the third pulse. Transient grating signals were measured for both polarizations and with and without frequency selection, for Rs. molischianum and Rps. acidophila Transient Grating. In Figure 3, transient grating (TG) curves are shown for both species at all combinations of polarization and detection frequency. In each plot, the curves for both polarizations are shown together, with the parallel signal being the largest. At T ) 0, the ratio between the parallel and perpendicular signals is about 9:1. All transient grating traces decay almost monoexponentially. At early times, a coherent coupling artifact is superposed on the transient grating signal, with a relative amplitude varying from one measurement to the next. A very small oscillatory contribution, which is not further considered here, can be discerned during the first 1000 fs of the decay. Within 1 to 2 ps, the signals decay to a constant, finite level as B800 transfers its excitation to B850. Because excited B850 (denoted as B850*) displays excited-state absorption around 800 nm, it generates also a small TG signal, which does not decay on the time scale of the experiment. This contribution is larger at longer wavelengths, so it shows up most clearly in the 810 nm signals. Since the B850* grating results from absorption, it has an opposite phase to the grating constituted by the B800 bleaching,

5 Peripheral Bacterial Light-Harvesting Complexes J. Phys. Chem. B, Vol. 104, No. 47, Figure 3. TG signals obtained for LH2 of Rps. acidophila (A-C) and Rs. molischianum (D-F). The signals were measured with a 790 nm filter (A,D) or a 810 nm filter (C,F) placed behind the sample or without a filter (B,E). In each plot, the signal obtained with all pulses polarized parallel (large) is shown together with the signal obtained with the third pulse polarized perpendicular to the first two (small). TABLE 1: Exponential Fits of Transient Grating Signals wavelength (nm) τ par (fs) τ perp (fs) Rps. acidophila whole band Rs. molischianum whole band XXX Figure 4. Monoexponential fits (dotted line) to the TG signals (solid line) measured without a filter for Rps. acidophila (a) and Rs. molischianum (b). In each graph, both parallel and perpendicular polarizations are shown (see Figure 3). To avoid contamination by the coherent coupling artifact, the fits ignored the first 100 fs after T ) 0. leading to a shallow minimum at around 1.5 ps, when both contributions are comparable in size and cancel each other. As a first approximation, single exponentials were fit to all transient grating signals. To avoid contamination of the time constant by the coherent coupling artifact, the curves were fit from 100 fs onward. An infinite second lifetime was included to account for the B850* absorption. Examples of the fits are shown in Figure 4 for the TG signals measured at both polarizations without frequency selection. The results of the fits to all 12 curves are given in Table 1. Decay of the gratings takes place in fs, corresponding to a fs excited-state lifetime of B800. For Rps. acidophila, this value agrees well with rates found by others at room temperature. 36,46 For Rs. molischianum, only B800 f B850 transfer rates measured at low temperature have been published so far. 39 The room-temperature rate of 700 fs, which we obtain in this work, is remarkably similar to the rates known for Rps. acidophila and Rb. sphaeroides, considering the difference in orientation of the B800 pigments. Compared to the Rps. acidophila structure (to which the Rb. sphaeroides structure is probably similar [Frese et al., unpublished]), the chlorin rings of the B800s in Rs. molischianum are tilted out of the membrane plane by 30 and rotated by 90, corresponding to a 30 tilt and a 90 rotation of the Q y transition. Calculations show that both configurations have an orientation factor of the same magnitude [Wendling, M., personal communication]. When the Förster equation is used together with the point dipole approximation, the calculated coupling strength between B800 and B850 should be similar in both species, which is in line with our findings. At a distance of 17 Å between the pigments, the point dipole approximation should be allowed. 60 However, for the absolute value of the rate to be reproduced reasonably well, it is crucial that the excitonic and vibronic structures of the B850 band and

6 11400 J. Phys. Chem. B, Vol. 104, No. 47, 2000 Salverda et al. its disorder are included properly. 39,60 From the blue to the red edge of the B800 band, the decay seems to get slightly faster. This could reflect better energy transfer B850 from the red B800s. However, it is most likely due to the larger B850* contribution in the 810 nm traces. Thus, the point at which the two gratings cancel is reached earlier, leading to an apparently faster decay. Because of the large interference minimum, which is neglected in the fit, the residuals are also largest for the red curves. The Rs. molischianum TG signal with perpendicular polarization could not even be fit at all. The transient grating signals measured at perpendicular polarization mostly decay more slowly than those detected parallel, even with the B850* contribution being relatively stronger at perpendicular polarization. This trend is most obvious in the 790 nm traces with parallel decay times of fs and perpendicular decay times of 550 fs. This suggests that energy transfer between the B800s, changing the orientation of the excited state, does occur. To look at this in more detail, we have made an analogy between the transient grating and the more common pump-probe experiment. Both of these reflect population decay, with the transient grating approximately quadratic and the pump-probe linear in the population. Because of interference terms, the transient grating is not exactly quadratic with either the B800 or B850 population, but for the moment, we will ignore this. To look at the polarization change as a measure of energy transfer between differently oriented pigments, one calculates the anisotropy, r, of a pump-probe signal as r ) I VV - I VH I VV + 2I VH (3.1) The decay time constant, τ dep, of the anisotropy can be related to the hopping time, τ hop, with τ hop τ dep ) 4(1 - cos 2 R) (3.2) with R)360/N and N the number of pigments (or effective sites) in a ring. Note that this expression only holds true when the anisotropy decay is wavelength independent. For the transient grating, the equivalent of this anisotropy is obtained by replacing I VV and I VH in eq 3.1 with the square root of the transient grating signals TG VV and TG VH (note that in the TG experiment, the first subscript refers to the polarization of the first two pulses, while the second subscript is the polarization of the third pulse). We expect this to yield a better result than the pump-probe equivalent because in the TG signal the small B850 contribution is positive whereas in the pump-probe experiment this contribution is negative. In the pump-probe signal, this leads to a zero-crossing where the anisotropy is not defined. The resulting anisotropy decays are shown in Figure 5 for the TG decays measured without frequency selection together with monoexponential fits. The results of fits for all six anisotropy traces are given in Table 2. The anisotropies decay in about 1 ps from an initial value of 0.4 to a final value of We think that the anisotropy decay can be taken to represent mostly B800 T B800 transfer. The B850 signal is also depolarized, but it is too small to contribute much on a sub-picosecond time scale, especially for the blue and whole band signals. For the two curves shown in Figure 5, we find a decay time of 700 fs for Rps. acidophila and 900 fs for Rs. Figure 5. Anisotropy of the TG signals (solid line) measured without a filter and the monoexponential fits (dotted line) for Rps. acidophila (a) and Rs. molischianum (b). The anisotropies were calculated from the square roots of the TG signals, as described in the text. TABLE 2: Exponential Fits of Transient Grating Anisotropy wavelength (nm) τ (fs) amplitude residual anisotropy Rps. acidophila whole band Rs. molischianum whole band molischianum. These times correspond well with pump-probe anisotropy decay times found by others for B800 at room temperature, 45,46 which they also ascribed to B800 T B800 transfer. The initial anisotropy we observe is close to the theoretical maximum value of 0.4, which indicates that any possible ultrafast (sub-100 fs) dynamics does not lead to depolarization. For Rs. molischianum, the final value of 0.03 is clearly lower than that for Rps. acidophila, With the Rs. molischianum B800 Q y s tilted at an angle of about 30 with respect to the membrane plane, an anisotropy lower than 0.01 should be expected after equilibration between the B800s has taken place. Transfer to B850, with its Q y transition almost in the membrane plane, should lead to an increase again at later times. In Figure 5b, a slight increase can be seen, but the fits do not take this into account. For Rps. acidophila, the final anisotropy is close to the minimum of 0.1 for randomization within a plane Three-Pulse Echo Peak Shift. Typical examples of 3PE scans are shown in Figure 6. The left plot shows the signal at T ) 0 fs and the right plot the signal at T ) 200 fs. Also shown are the Gaussian fits used to determine the peak shift value. As can be seen in Figure 6, the shape of the signal is not entirely Gaussian at very short times T. We estimate that this results in an uncertainty of 2-3 fs in the value of the peak shift. At intermediate times, the Gaussian fits match the signal almost perfectly, thereby decreasing the uncertainty. However, at long times T, the low signal intensity makes the fits less reliable again, so the uncertainty is considered to be 2-3 fs over the whole range for the sake of simplicity. In Figure 7, the peak shift curves measured at parallel polarization are shown. The peak shift decay is similar for both species, with Rs. molischianum decaying slightly faster and to a lower final value. The initial peak shift is 30 fs for both species. This relatively high value suggests that the coupling between pigment and protein is weak compared to the coupling between a dye and a liquid solvent. For dyes in solvent, an initial

7 Peripheral Bacterial Light-Harvesting Complexes J. Phys. Chem. B, Vol. 104, No. 47, Figure 6. Examples of three-pulse photon echo (3PE) signals (solid line) obtained for LH2 of Rs. molischianum. Shown are two scans in which the integrated echo intensity is measured as a function of the delay τ between the first two pulses for the delay times T ) 0fs(a) and T ) 200 fs (b). The peak shift values were obtained from these curves by fitting them with Gaussians (dotted line; see also the text). Figure 7. Peak shift decay as a function of the population time T measured over the total B800 band. The curves show the peak shift for the parallel polarization of the third pulse obtained for LH2 of Rps. acidophila (dotted line) and Rs. molischianum (solid line). The points show the peak shifts measured at three selected population times, with the third pulse polarized perpendicular to the first two, for Rps. acidophila (4) and Rs. molischianum (b) peak shift of fs is generally obtained with comparable pulse lengths. 54,55 In that case, the dephasing is so fast compared to the pulse duration that the measurement at T ) 0 already probes a partially relaxed situation. In our experiment, dephasing due to electron-phonon coupling is probably responsible for the decay of the peak shift from the initial value of 30 fs to about fs on a sub-100 fs time scale. After the initial dephasing, a slower decay process leads to a peak shift value of a few femtoseconds in less than a picosecond. This decay process is partly obscured by pronounced oscillatory features. For both species, these oscillations look very similar in amplitude and frequency. In section 4, we will discuss these oscillations more extensively. The results of the perpendicular polarization measurements are also shown in Figure 7 as separate points. All six points lie below the curves measured at parallel polarization. Furthermore, this difference is somewhat larger at later times. Apparently, a population is probed by the perpendicular polarization measurements whose change of transition frequency is larger than that for the population probed at parallel polarization. The easiest explanation for this observation is that the population probed with the third pulse perpendicular has been formed after energy transfer between pigments with different orientations has taken Figure 8. Peak shift decay as a function of the population time T measured for the LH2 of Rs. molischianum with frequency-selective detection. All three experiments were performed with parallel polarization of the laser pulses only. The peak shift decay detected at 790 nm (dashed line) is shown together with the peak shift decay measured at 810 nm (dotted line). The measurement without filter (solid line) is shown for comparison. place. From the transient grating measurements, it is clear that the B850 excited state absorption is too small to show up clearly in the 3PEPS signal at these population times, all three of which are below 1 ps. Therefore, we conclude that energy transfer must be taking place between different B800 pigments. In Figure 8, frequency-selective peak shift decay curves for the B800 ring of LH2 of Rs. molischianum are shown. The curves for the blue edge, 790 nm, and the red edge, 810 nm, are both averages of two measuring sessions. The uncertainty in these curves is about 3 fs, judging from the difference between these two sessions. The difference between the three signals in Figure 8 is remarkable, with the blue curve not showing any decay after the initial drop to about 10 fs. By contrast, the red peak shift curve decays faster than the peak shift measured over the whole band. This difference shows that it is unlikely that a protein relaxation process can be responsible for the picosecond decay of the peak shift from 10 fs to a few femtoseconds; otherwise, this decay would show up at all wavelengths. Most likely, at 790 nm, pigments are detected which absorb to the blue of the maximum and have not yet transferred their energy to more red pigments. We estimate the difference between the energy transfer rate from 790 to 810 nm and the back rate to be at least a factor of 2 at room temperature, so downhill energy transfer is still dominant. Support for our energy transfer hypothesis comes from the observation by Yu et al. 61 that the B820 subunit of the LH1 antenna, in which no energy transfer occurs, also has a large residual peak shift, like the peak shift observed by us at 790 nm. The peak shift of the intact LH1 antenna, which does show energy transfer, decays to 1 or 2 fs on a time scale of a few hundred femtoseconds. 25 The peak shift decay curve measured for B820 by Yu et al. actually looks remarkably similar to the 790 nm peak shift curve for B800 shown in Figure 8. In summary, from the peak shift measurements shown in Figures 7 and 8, we conclude that the B800 energy transfer takes place at room temperature and that it is responsible for the peak shift decay to a value of a few femtoseconds on a 1 ps time scale, which is seen in the non-frequency-selective measurements. 4. Simulations and Discussion In this section, we present numerical simulations of the measured signals discussed in the previous section. All simula-

8 11402 J. Phys. Chem. B, Vol. 104, No. 47, 2000 Salverda et al. The response functions are expressed as functions of g(t), with R 1 ) R 4 ) exp{-g*(t 1 ) + g(t 2 ) - g*(t 3 ) - g(t 1 + t 2 ) - g(t 2 + t 3 ) + g*(t 1 + t 2 + t 3 )} (4.6) R 2 ) R 3 ) exp{-g(t 1 ) + g*(t 2 ) - g*(t 3 ) + g(t 1 + t 2 ) + g*(t 2 + t 3 ) - g(t 1 + t 2 + t 3 )} (4.7) Figure 9. Schematic outline of the pulse sequence in the 3PEPS experiment. The parameters as used in the numerical integration are indicated (see text). tions of the peak shift curves are based on the nonlinear response theory described by Mukamel. 62 To obtain the frequency correlation function M(t) used in this formalism, we used two simple models, the Brownian oscillator (BO) model 50-53,62 and the modified electron-hole (MEH) model, 58 which will be described below. The transient gratings were only simulated with a simple model describing B800 f B850 transfer, without any reference to nonlinear response theory. This model will be described in more detail in section 4.2. In section 4.1, we will first review the key features of the nonlinear response formalism as it was used in the numerical code for the 3PEPS simulations Three-Pulse Echo Simulation Method. Photon echo and transient grating signals are two of many third-order nonlinear responses of a medium to applied external electric fields. For both signals, we have three incident optical pulse electric fields E 1, E 2, and E 3, each of which has a single interaction with the medium. These three interactions result in a reactant polarization of the sample, the third-order polarization P (3). The 3PE signal S(τ,T) is proportional to the square of this polarization in the direction k S ) k 3 - k 2 + k 1, measured timeintegrated as S(τ, T) ) - P (3) (t,τ,t) 2 dt (4.1) A diagram showing the pulse sequence and the definition of the relevant time intervals is shown in Figure 9. The third-order response of the sample to electric fields is determined by the third-order response functions R 1 - R 4 and their complex conjugates [see ref 62 for details]. These functions allow us to calculate the polarization P (3) (see below). They can be related straightforwardly to the frequency correlation function M(t).At high temperature, when all fluctuations ω are much slower than ω L ) kt/p, this function has the form M(t) ) ω(0) ω(t) ω(0) 2 as mentioned in the Introduction. From M(t), we can calculate the line shape function g(t) g(t) ) ω 2 0 t ( 0 τ 1M(τ2 )dτ 2 )dτ 1 + iλ 0 t (1 - M(τ1 )) dτ 1 with 2λ the Stokes shift, related to ω via λ ) ω2 2kT (4.2) (4.3) (4.4) The line shape function g(t) is directly related to the absorption line profile σ(ω) via the Fourier transform σ A (ω) Re - e -i(ω - ω eg )t e -g(t) dt (4.5) The time variables used in these expressions, t 1, t 2, and t 3, are the intervals between the three interaction points and the time t at which the echo is emitted (see the diagram in Figure 9). With the three fields E 1, E 2, and E 3 peaking at times -τ - T, -T, and 0, respectively, we calculate the polarization as follows: P (3) (k S,t,τ,T) ) ( i)1 R i (t 1,t 2,t 3 )E 3 (k 3,t - t 3 )E 2 (k 2,t + T - t 3 - t 2 ) E 1 (k 1,t + T + τ - t 3 - t 2 - t 1 )) dt 1 dt 2 dt 3 (4.8) For nonzero pulse duration, we thus have to integrate over the pulse profiles. From eq 4.1 and the ensemble averaging (over all molecular orientations) of the response functions R i,wenow find the echo signal S(τ,T). The transient grating is a special case of this formula, obtained from eq 4.8 with τ ) 0. With two polarizations e 1 and e 2 for the first two pulses and the third pulse, respectively, the direction of P, e P, can be calculated e P ) e 2 + 2e 1 (e 1 e 2 ) (4.9) This leads to a polarization-dependent prefactor for S(τ,T), given by e 2 + 2e 1 (e 1 e 2 ) 2 ) 1 + 8(e 1 e 2 ) 2 (4.10) For the third pulse parallel to the first two, this factor equals 9, while for the third pulse perpendicular to the first two, we get 1. This explains the 9:1 ratio of intensities of the initial transient grating and three-pulse echo signals. This, of course, leads to an initial value of 0.4 for the TG anisotropy, as defined in section 3.1. To calculate the frequency correlation function M(t) for our system, we used two approaches, which will be described below. As a basis, we used the Brownian oscillator (BO) model described in the Introduction, which takes M(t) to be the sum of a number of independent contributions from damped oscillators. A Gaussian term was added to describe the fastest decay component of M(t), which is due to electron-phonon coupling, giving M(t) ) { ω 2 g e -(t2 /τ 2) g + ω 2 i,e e -(t/τi,e) + i ω 2 j,o e -(t/τj,o) cos(ω j t + φ j )} j ω 2 k k In this equation, the subscripts g, e, and o denote the Gaussian, exponential, and oscillatory contributions, respectively. The sums over i and j are partial sums over the exponential or oscillatory terms, whereas the sum over k includes all processes which contribute to M(t). The ω 2 factors describe the ensemble-averaged coupling strength of each process. Note that 1 (4.11)

9 Peripheral Bacterial Light-Harvesting Complexes J. Phys. Chem. B, Vol. 104, No. 47, the sum over k of ω k 2 could still be related to the Stokes shift as described in eq 4.4, although more commonly, the energy transfer contribution is excluded from the Stokes shift. In eq 4.11, one exponential will describe energy transfer with rate τ i,e, but possibly, exponentials can be used to describe other processes such as overdamped vibrational relaxation of the pigment or spectral diffusion of the protein. However, in our simulations, we only needed an exponential for the energy transfer, with rate τ e, with coupling strength ω e equal to the inhomogeneous broadening. The (damped) oscillatory terms in eq 4.11 represent specific vibrational modes of the chromophore and bath molecules. A nonzero phase shift φ j was needed to account for the vibrations being set in motion before T ) 0by the first pulse. The assumption on which the BO model is based, that all processes are independent, is obviously oversimplified. In a proper description, the rate of losing frequency information via one-pigment relaxation should be added to the rate of transferring the excitation to a neighboring pigment via energy transfer. If the frequency of the neighboring pigment is assumed to be uncorrelated to that of the originally excited pigment, M(t) becomes zero as soon as energy transfer occurs. The M(t) of the originally excited pigment, described with the BO model, should then be multiplied with its population amplitude. This approach was later described as the modified electron-hole model (MEH) by Yang and Fleming 58 (note that in ref 58, the BO model is termed the electron-hole or EH model, hence the additive modified ). As Yang and Fleming explain, this model is not physically correct because the system is still described as a single two-level system. In a more exact approach in the same paper, they describe energy transfer as a jump from a donor to an acceptor, both of which contribute to the echo signal. At early (sub-100 fs) times and for systems with many processes on the same time scale, the exact model and the MEH model differ significantly, but for B800, within the time range we are interested in, the deviation is expected to be minimal. We obtain for the MEH model M(t) ) M mon (t)e -(T/τ ET) with M mon (t) describing the originally excited monomeric pigment and e -(t/τ ET ) the decay of its population through energy transfer with rate τ ET. With M mon (t) from eq 4.11, we have M(t) ) e -(t/τet) { ω 2 g e -(t2 /τ 2) g + ω 2 i,e e -(t/τi,e) + i 1 ω 2 j,o e -(t/τj,o) cos(ω j t + φ j )} j (4.12) which leads to a decay of the peak shift τ* with population time T τ*(t) ) τ* mon (T)e -(T/τ ET) ω 2 k k (4.13) (4.14) To compare both methods, we will first simulate our measured peak shift decays with the BO model. With the obtained parameters, we will calculate τ* mon (T), which will include a non decaying term with the same coupling strength as that of the exponential which was used to describe energy transfer in the BO model. This nondecaying term represents the inhomogeneous broadening. The monomeric peak shift decay obtained this way will be multiplied with an exponential e -(t/τ ET ), with τ ET equal to the exponential decay time τ e from the BO model simulations. If necessary, the parameters will be adapted slightly to obtain a better fit. To calculate the peak shift for a given set of parameters, we first calculated g(t) as a numerical function via a straightforward integration program. A separate program is used to calculate R 1 - R 4 from g(t). The polarization P (3) is calculated from R 1 - R 4 with a Monte Carlo routine, in which a large number of random t 1, t 2, and t 3 combinations is used to perform the integration over the pulse profiles. In this calculation, the cases for which t 1, t 2, and t 3 correspond to a reversal in the timeordering of the pulses are explicitly considered. Note that also in this case the phase-matching condition must be fulfilled. For example at k S ) k 3 + k 2 - k 1, the 3PE signal corresponding to the time-order pulse 3 first, then pulse 1, then pulse 2 will also be detected. Just as in the measurements, the echo profile S(τ) is calculated for a limited number of T values, and the peak shift τ*(t) is determined by fitting a Gaussian to S(τ). The resulting peak shift curve is compared to the experimental curve. Unfortunately, a run with one set of parameters takes approximately 20 min; therefore optimization has to be performed by hand. To avoid the canceling effects which can result from using too many parameters, we have attempted to limit the various contributions to M(t) to one Gaussian, one exponential (or constant), and one oscillation. Once a set of parameters is obtained which reproduces the peak shift satisfactorily, the absorption spectrum can be calculated from g(t) with eq 4.5. Note that the population decay due to the B800 f B850 transfer, which should not influence the peak shift, is not incorporated in this simulation. Therefore, the same method could not be used for the simulation of the TG signals. Those are performed with a model that only considers population decay and will be described below Transient Grating. We have tried to estimate the effect of the B850 excited-state absorption contribution to the shape of the TG signal and the B800 f B850 transfer time which could be derived from this signal. A very simple model was used with I TG (T) ) B800 (B800(λ)e -(T/τ B800) - B850*(1 - e -(T/τ B800) )) 2 dλ (4.15) The B800 spectrum B800(λ) was taken to be a Gaussian, and the B850* absorption was taken to be independent of wavelength within the range of interest, taken from about 775 to 825 nm in this simulation to cover the B800 band completely. The energy transfer time, denoted as the B800 excited-state lifetime τ B800 and the amplitude of B850* relative to the peak amplitude of B800(λ) could be varied. For the transfer time, the value obtained from the single-exponential fits in section 3.1 is taken as a starting point. Note that now the real B800 f B850 transfer time is used, as opposed to half this time, which came out of the exponential fits. The transfer times we find are clearly at least 10%, and often 30%, larger than the times found from the exponential fits. The larger the B850* contribution is, the bigger this difference. For the parallel signals, with no frequency selection, we have a transfer time of 800 fs for Rps. acidophila and 1000 fs for Rs. molischianum. In Table A1 of the Appendix, the transfer times and B850* amplitudes are given for all transient grating curves. In Figure A1 of the Appendix, examples of TG simulations are shown. In section 3.1, we found 600 fs for Rps. acidophila and 700 fs for Rs. molischianum, which must be lower limits to the real values. However, we want to stress that the values obtained from the simulations using eq 4.15 are also only an indication.