14206
J. Phys. Chem. 1996, 100, 14206-14217
Interexciton-State Relaxation and Exciton Localization in Allophycocyanin Trimers Maurice D. Edington, Ruth E. Riter, and Warren F. Beck* Department of Chemistry, Vanderbilt UniVersity, 5134 SteVenson Center, P.O. Box 1822-B, NashVille, Tennessee 37235 ReceiVed: February 9, 1996; In Final Form: May 30, 1996X
We have employed dynamic absorption, transient hole-burning, and discrete two-color pump-probe femtosecond spectroscopic methods to obtain a time-resolved view of exciton dynamics in trimers of allophycocyanin, the major component of the core of the phycobilisome in cyanobacteria. Allophycocyanin trimers contain a C3-symmetric array of phycocyanobilin (open-chain tetrapyrrole) dimers. The femtosecond time-resolved pump-probe spectra and single-wavelength transients observed in allophycocyanin preparations were interpreted with the aid of a series of calculated spectra, which are based on an assignment of the ground-state absorption spectrum in terms of exciton-coupled chromophore dimers. The observed and calculated time-resolved pump-probe spectra indicate that interexciton-state relaxation, a radiationless transfer of population between dimer exciton states, is responsible for a red shift of the spectra on the ∼30-fs time scale. The time evolution of the pump-probe spectra is inconsistent with a model accounting for the groundstate absorption spectrum in terms of pairs of uncoupled chromophores linked by subpicosecond Fo¨rster energy-transfer paths. On a slower time scale, extending from the 300-fs to ps delay range, the time-resolved spectra evolve in a manner consistent with localization of an exciton on one of the chromophores in a dimer. These results are to be compared with those of two-color anisotropy experiments that we previously described [J. Phys. Chem. 1995, 99, 15699-15704], which suggest time constants for interexciton-state relaxation and exciton-state dephasing of 10-30 fs and 280 fs, respectively. The present results suggest that exciton localization and exciton-state dephasing occur on similar time scales. We suggest that interexciton-state relaxation and exciton localization in allophycocyanin trimers provide a potent mechanism for directed energy transfer that arises from the energy-transfer coherence properties of chromophore dimers.
Introduction Photosynthetic organisms have evolved special antenna or light-harVesting chromoprotein systems to absorb the sun’s radiant energy and to transfer the captured energy efficiently to photosynthetic reaction centers, where a conversion to chemical potential energy occurs.1 The architecture of a lightharvesting protein might influence the dynamics of excitationenergy transfer by organizing the chromophores in a particular way. Several light-harvesting proteins have now been structurally characterized by X-ray crystallography,2-10 by electron diffraction,11 or by electron microscopy.12 The known structures exhibit an interesting clustering of the bound chromophores, which may lead to the formation of a set of exciton states owing to the admixture of isolated-chromophore electronic states. For instance, the LH2 system isolated from Rhodopseudomonas acidophila contains a “storage ring” structure made up of a 9-mer of strongly dipole-dipole coupled bacteriochlorophyll a dimers.9,13 The photophysics of a dimer or larger cluster of antenna chromophores in a light-harvesting protein is distinct from that of a similar set of isolated chromophores because of the likelihood that interexciton-state relaxation mediates relaxation of population to the lowest-energy exciton state on a time scale that is shorter than that involved in long-distance energy transfer by the Fo¨rster mechanism.14 Interexciton-state relaxation processes have been detected via hole-burning techniques at liquid helium temperatures in photosynthetic proteins by Small and co-workers.15-17 The time scale for transitions between exciton levels formed from admixture of levels from the seven chromophores in the bacteriochlorophyll a protein of ProsthX
Abstract published in AdVance ACS Abstracts, August 1, 1996.
S0022-3654(96)00454-6 CCC: $12.00
ecochloris aestuarii was shown to be on the order of 100 fs at 4.2 K through analysis of hole-burned line shapes.15 Interexciton-state relaxation mechanisms are thought to be involved in the 0 were normalized so that they summed to unity; the rise was instrumentresponse limited.) The same model was used to describe the 650-nm transient, with a1 ) -0.25 (a rising component), τ1 ) 310 fs, and a∞ ) 1.0.
fs time constant. The 650-nm rise transient can be described by a 310-fs time constant. At least 75% of the rise transient at 650 nm occurs in an instrument-limited manner. In addition, note that the largest signal encountered in the 650-nm transient is almost 3 times that observed in the 625-nm transient; this observation is consistent with the transient spectra shown in Figure 2. Transient Hole-Burning Experiments. The main deficiencies of the DA experiments described in Figures 2 and 3 involve the degenerate one-color pump-probe nature of the technique: the pump pulses are too broad in spectral range to excite specifically a given region of the ground-state absorption spectrum, and the probe pulses are not broad enough in spectral range to cover the entire width of the ground-state absorption and fluorescence-emission spectra. At the cost of time resolution, we could address these problems by performing THB experiments with narrow-band, 80-fs pump pulses and broadband probe pulses derived from a femtosecond continuum. The top panel of Figure 4 shows the continuous ground-state absorption and fluorescence-emission spectra of allophycocyanin overlaid with the spectrum of the 80-fs pump pulses used to obtain the time-resolved spectra shown in the bottom panel. The pump pulses were centered at 620 nm (fwhm ) 6-8 nm, as observed with 4-nm spectral band-pass) and were narrow enough in bandwidth that the sharper, 652-nm feature of the ground-state absorption was not directly excited, at least not to the considerable degree that occurred with the broad-band, temporally compressed pulses used in the DA experiments. As shown in the accompanying paper,33 under these pump and probe conditions the phycocyanobilin chromophores in the R subunits of C-phycocyanin initially exhibit transiently burned PB/SE holes. C-Phycocyanin contains phycocyanobilin chromophores bound in environments similar to the chromophore-
J. Phys. Chem., Vol. 100, No. 33, 1996 14209
Figure 4. THB spectra obtained in allophycocyanin trimers at several delay times (bottom panel) compared with the continuous ground-state absorption (dashed curve, top panel) and the continuous fluorescenceemission spectrum (black curve, top panel). The spectrum of the 620nm, 80-fs duration pump pulses used in these experiments is superimposed in the top panel (gray curve). The THB spectra (bottom panel) were observed with a 4-nm spectral band-pass. The ordinate for the bottom panel applies to the 10-ps spectrum; spectra obtained at other delays are offset arbitrarily vertically but are displayed with the same scaling factor. The dashed horizontal lines mark the baseline for each spectrum.
binding sites of allophycocyanin,10 so comparable intrinsic photophysics, pertaining only to the interaction of the chromophore with its protein environment and to intrachromophore dynamics, ought to be expected in allophycocyanin. The THB spectra shown in the bottom panel of Figure 4 are practically identical to the DA spectra shown in Figure 2; the pump-probe signal exhibits a single band in the 650-660-nm region and a 610-640-nm shoulder at early delay times. Within 2 ps, the shoulder has collapsed, and the 650-660-nm band has sharpened and increased in intensity at the same time, as was also observed in the DA experiments. The pump-probe signal observed in the 620-nm spectral region that was directly pumped is weaker than that observed in the 650-660-nm region at all probe delays. The spectral metamorphosis in the 610640-nm region associated with the decay observed at 625 nm and increase at 650 nm in the single-wavelength DA transients shown in Figure 3 over the 150-1000-fs regime is made more clear in these transient spectra. The THB spectra shown in Figure 4 contain additional details that were not observed in the DA experiments owing to the lack of sufficient probe spectral coverage. A weak SE feature in the 700-750-nm region appears to grow in and shift somewhat to the blue over the first 2 ps of delay at the same time as the 650-660-nm peak grows in intensity; this peak coincides with the tetrapyrrole vibrational transition evident from the shoulder that is observed in the fluorescence-emission spectrum (shown in the top panel). Additionally, the transient pump-probe spectra contain regions of net absorption in the 500-575- and 660-680-nm regions. We assign both of these regions to a broad (at least covering the 500-750-nm region) ESA band arising from S1 f Sn transitions. The accompanying
14210 J. Phys. Chem., Vol. 100, No. 33, 1996
Edington et al. Discussion
Figure 5. Two-color pump-probe transient obtained using 620-nm pump and 655-nm probe pulses, both of which had 80-fs pulse durations. The data points are shown superimposed with a fit function obtained with an iterative reconvolution program. The model used to 2 describe the transient was a∞ + ∑i)1 ai exp(-t/τi), where a1 ) -0.58, τ1 ) 485 fs, a2 ) -0.42, τ2 ) 35 fs, and a∞ ) 1.00 (where the rise components have normalized amplitudes ai < 0 summing to 1.00). Inset: Residual traces (data - fit): the top panel shows the residual obtained from a fit to the data (not shown) using the model a∞ + a1 exp(-t/τ1), where a1 ) -0.65, τ1 ) 432 fs, and a∞ ) 1.00 (the remaining rise is instrument response limited); the bottom panel shows the residual obtained from the fit to the data shown superimposed on the data points.
paper shows that a similar broad phycocyanobilin ESA spectrum is observed in THB spectra obtained with preparations of R subunits of C-phycocyanin.33 The ESA spectrum observed here in allophycocyanin trimers appears to shift to the blue over the first few picoseconds of delay, causing evolution of both the 500-575- and 660-680-nm regions. Single-wavelength transients (not shown) obtained at various probe wavelengths using the same narrow-band pump and continuum-probe technique used for the time-resolved spectra shown in Figure 4 resemble those shown in Figure 3. The spectral evolution detected in terms of a single-exponential decay at 625 nm corresponds to a rise in the 650-660-nm probe region. The 650-660-nm band detected in the pump-probe spectra shown in Figure 4 rises initially with an instrumentresponse-limited rate to about two-thirds of the final amplitude. Two-Color Pump-Probe Experiments. In order to observe the rise of the 650-660-nm band observed in the DA and THB studies, we performed discrete two-color pump-probe experiments. Two-color experiments avoid complications from the coherence (four-wave mixing) feature39,40 that is typically observed when the pump and probe pulses are temporally overlapped in the sample in one-color experiments or in timeresolved spectroscopy experiments in the spectral region of the pump pulse.37 Figure 5 shows the two-color pump-probe transient obtained using 620-nm pump and 655-nm probe pulses, both of which were of 80-fs duration. The spectrum of the probe pulses was selected to overlap with the 650-660-nm band observed in the transient pump-probe spectra and to be offresonance from the pump pulses. Superimposed on the transient is a fitted curve obtained using an iterative reconvolution program. The transient is well described by two exponential rise components with time constants of 35 and 485 fs. Inclusion of the faster of the two rise components is required to obtain a satisfactory description of the early delay region of the transient. The inset in Figure 5 shows the residuals obtained from fits to the data using one (top) and two (bottom) rise components; the fit obtained using a single rise component exhibits marked deviations from the experimental trace in the -100-100-fs probe delay region.
We have observed two distinct phases of dynamic spectral evolution in the photosynthetic light-harvesting protein allophycocyanin following femtosecond excitation at 620 nm. The fast phase, occurring on the ∼30-fs time scale, is characterized by the formation of a 650-660-nm PB/SE band. The slower phase accompanies an increase in intensity of the 650-660nm band on the 400-fs time scale. These two phases of spectral evolution were also detected in discrete two-color pump-probe transients. In the following we will discuss the applicability of the Fo¨rster and exciton models in accounting for the observed spectral dynamics. We will also present calculated pump-probe absorption-difference spectra for a chromophore dimer system to aid in distinguishing between the two models. Evidence for Interexciton-State Relaxation from PumpProbe Spectra and Transients. Pump-probe and fluorescence transients with time constants on the 300-500-fs time scale were previously observed in allophycocyanin trimers by two groups.41-44 Calculations performed by Sauer and Scheer,45 based on the coordinates for the chromophores from the X-ray crystal structure,8 suggest that Fo¨rster energy transfer would occur between the R84 and β84 chromophores in C-phycocyanin on a similar time scale. On the basis of the structural analogy between allophycocyanin and C-phycocyanin, Sharkov and coworkers attributed the 440-fs PB decay measured in one-color pump-probe experiments with 70-fs pulses at 620 nm to Fo¨rster energy transfer between the R84 and β84 chromophores in allophycocyanin trimers.41 Using 230-fs excitation pulses at 618 nm and continuum-probe pulses spanning from 635 to 690 nm, Sharkov and co-workers43 recorded time-resolved pumpprobe spectra, which were interpreted as being consistent with the 440-fs PB kinetics they observed previously at 620 nm. They concluded that the observed evolution of the time-resolved spectrum was consistent with the Fo¨rster energy-transfer picture.43 Using a femtosecond fluorescence up-conversion technique, Xie and co-workers44 observed fluorescence anisotropy decays having time constants of 360 fs and 2.7 ps when excitation was made at 605 and 640 nm, respectively. Xie and co-workers44 specifically implicate a spectral red shift as contributing to the observed subpicosecond fluorescence anisotropy decay. The time-resolved pump-probe spectra reported in this paper allow us to draw significant conclusions that were not evident from the spectra obtained by Sharkov and co-workers43 owing to their limited time resolution and spectral coverage. The 30fs time resolution of the DA experiments allows us to refine the time scale for the formation of the 650-660-nm PB/SE band. It is evident from the 0-fs spectrum shown in Figure 2 that the 650-660-nm band is almost completely formed during the duration of the pump-probe temporal overlap. Although a small increase in the intensity of the band occurs on the 400fs time scale, the initial formation of the band occurs too rapidly to be attributed to the 440-fs kinetics measured by Sharkov and co-workers. The broad spectral coverage of the continuumprobe pulses (500-800 nm) used in the THB experiments in this study allows for a more complete visualization of the timeresolved spectrum, which aids considerably in the analysis of transition strengths. It is likely that the 440-fs kinetics measured by Sharkov and co-workers43 is associated with the time evolution of the 610640-nm PB shoulder observed at early probe delay times in Figures 2 and 4. The decay of the shoulder and the increase in intensity of the 650-660-nm PB/SE band both occur on the 300-500-fs time scale, as indicated by the 625- and 650-nm single-probe-wavelength transients shown in Figure 3. If Fo¨rster
Exciton Relaxation and Localization in Allophycocyanin energy-transfer mechanisms are involved on the 300-500-fs time scale, then we would expect to observe a comparable change in intensity (or spectral area) in both of the regions probed. The results shown in Figure 3 and the time-resolved spectra shown in Figures 2 and 4 indicate that the decrease in the 625-nm region is much smaller in intensity than the overall increase in intensity in the 650-nm region. Thus, our results argue against the involvement of Fo¨rster energy-transfer on the subpicosecond time scale in allophycocyanin trimers. Recent work performed in our laboratory prompts the suggestion that the dynamic spectral evolution observed in allophycocyanin trimers involves radiationless decay processes associated with exciton states.28 Using a discrete two-color technique with 80-fs pump (620 nm) and probe pulses (640 nm), we observed two phases of anisotropy decay from an initial value in the 0.58-0.70 range. The first phase of decay to an anisotropy r ) 0.4 was described by a 10-30-fs time constant; subsequent decay of the anisotropy to a terminal value of 0.15 occurred on the 300-1000-fs time scale. The 300-1000-fs anisotropy decay occurs on a time scale quite comparable to that associated with the spectral evolution observed in the timeresolved pump-probe spectra shown in Figures 2 and 4. The anisotropy decay was interpreted using the theory developed by Wynne and Hochstrasser46 and by Knox and Gu¨len.47 The theory, as analyzed by van Amerongen and Struve,48 predicts that an initial anisotropy r(0) ) 0.7 will be observed if the two chromophores of a molecular dimer are coherently excited by a spectrally broad femtosecond laser pulse. Dephasing of the exciton states is accompanied by decay of the large initial anisotropy; van Amerongen and Struve48 showed that the rapid phase of anisotropy decay from r g 0.4 reports the time constant for interexciton-state relaxation, 2Γ ) γ + γ′, where γ and γ′ represent the rate constants for upward and downward population transfer. The slower phase of anisotropy decay from r ) 0.4 occurs with a rate constant similar to that expected for Fo¨rster energy-transfer between the dimer chromophores in the weak coupling limit.48 On that basis, we made the prediction28 that a fast red shift should be observed in a time-resolved pump-probe experiment with allophycocyanin trimers. If the excitation pulses prepare an excess of population in the upper exciton state, then interexciton-state relaxation would cause a red shift as the population equilibrates in the lower exciton state. At first glance, the prompt appearance of the 650-660-nm PB/SE band following 620-nm excitation would appear to be consistent with this expectation. If exciton states are involved, however, it is possible that strong ESA in the 620-nm region might arise from transitions populating doubly excited exciton states, making the pump-probe signal appear weak in this region. Struve and coworkers analyzed the strongly dipolar pump-probe spectra observed in the bacteriochlorophyll a protein isolated from Prosthecochloris aestuarii in terms of ESA arising from transitions between singly and doubly excited exciton states.49 Mathematical Framework for Calculated Pump-Probe Spectra. In order to consider the possibility that ESA to doubly excited exciton states makes the pump-probe signal appear weak in the 620-nm region most strongly pumped in all the experiments we described, we have calculated time-resolved pump-probe spectra that would arise from a pair of coupled phycocyanobilin chromophores with various exciton-state population distributions. The mathematical framework used here to calculate time-resolved absorption-difference spectra for the case of a coupled dimer of chromophores is also used to test the idea advanced by Sharkov and co-workers42,43 that fast Fo¨rster energy transfer between two uncoupled chromophores can
J. Phys. Chem., Vol. 100, No. 33, 1996 14211
Figure 6. Electronic energy levels for a chromophore dimer in the uncoupled (dipole-dipole interaction energy V12 ) 0) and coupled (V12 < 0) cases. In the uncoupled limit, the energy levels are those arising from single excitations of one or the other of the two chromophores (sites); “e” denotes that a given chromophore has been excited (S0 f S1) from its ground electronic state “g”. In the coupled case, the upper and lower exciton (delocalized) states |+〉 and |-〉 arise from symmetric and antisymmetric linear combinations of the |eg〉 and |ge〉 site states (for V12 < 0). The doubly excited state |ee〉 corresponds to the state reached when both chromophores in the dimer are excited.
explain the time evolution of the observed spectra discussed above. The model developed here allows us to explore the effect of varying the transition dipole interaction between the two chromophores in a dimer on the ground-state absorption spectrum and on the time-resolved absorption-difference spectra. Figure 6 shows the energy level scheme for a chromophore dimer that we used in these calculations. The singly excited chromophore dimer states present in the absence of a dipoledipole interaction are labeled |eg〉 and |ge〉, while the ground and doubly excited states are represented as |gg〉 and |ee〉, respectively. When the transition dipole-dipole interaction is turned on, the singly excited dimer states become the “exciton” states |+〉 and |-〉, which arise from symmetric and antisymmetric linear combinations of the singly excited “site” states |eg〉 and |ge〉. The energies of the exciton states |+〉 and |-〉 can be calculated by diagonalizing the Hamiltonian matrix
[
E V H ) V1 E12 12 2
]
where E1 and E2 are the energies for the two site states |eg〉 and |ge〉, respectively, and the transition dipole-dipole interaction energy V12 ) (µ1µ2)R12-3 - (µ1R12)(R12µ2)R12-5. In the preceding equation, µi represents the transition dipole moment for the isolated chromophore in site i, and R12 represents the distance between the two sites. The eigenvectors obtained by solving the eigenvalue problem describe the exciton states |+〉 ) c1|eg〉 + c2|ge〉 and |-〉 ) d1|eg〉 + d2|ge〉. The dipole strength Dij for transitions between the states shown in Figure 6 is proportional to the square of the matrix element 〈i|µ1 + µ2)|j〉, which depends on the angle θ12 between the transition dipoles. The dipole-dipole interaction distributes the dipole strength arising from the two chromophore sites so that transitions from the ground state to either of the singly-excited exciton states are, in general, not of equivalent strength.50 As will be shown below, this distribution of dipole strength, as revealed by the shape of the ground-state absorption spectrum, defines the shapes of the time-resolved pump-probe spectra. Interpretation of the Ground-State Absorption Spectrum. As required by the X-ray crystal structure of allophycocyanin,10 which contains only two distinct types of chromophores, we suggest that the ground-state absorption spectrum of allophy-
14212 J. Phys. Chem., Vol. 100, No. 33, 1996 cocyanin can be adequately described in terms of two overlapping transitions, as shown in Figure 1. The two bands arise from the degenerate |gg〉 f |+〉 and and |gg〉 f |-〉 transitions of the three chromophore dimers. In making this assignment, we assume that dimer-dimer transition-dipole interactions can be neglected owing to the relatively large distances between dimers. We modeled the absorption band for each transition using a line shape constructed as the sum of log-normal (asymmetric Gaussian)51 line shapes for the main and 0 f 1 vibronic bands. The log-normal line shapes were arbitrarily given asymmetry factors of 1.4, resulting in broader tails to high energy. The lower-energy band shown in Figure 1 is composed of a main transition and a weaker vibronic transition positioned about 1500 cm-1 to higher energy. The 1500 cm-1 spacing is consistent with the spacing of the main and vibronic bands observed in the continuous fluorescence-emission spectrum44 (see Figure 4) and with Raman spectra obtained by Lutz and co-workers.52,53 The higher-energy band is described by the same vibronic structure used to describe the lower-energy band, but the line width parameter for the main and vibronic transitions was made much larger, to the same extent; no vibronic structure is discernible in the resulting line shape because the breadth of the line exceeds the 1500 cm-1 offset of the vibronic band. Attempts to fit the spectrum with Gaussian line shapes, as used by Csatorday and co-workers26 prior to the determination of the X-ray crystal structures of C-phycocyanin or allophycocyanin, did not produce satisfactory results; the number of Gaussian spectral components required is not consistent with what is known about the number and types of chromophores present in allophycocyanin trimers and the overall 3-fold symmetry of the system.10 The two composite absorption line shapes used in Figure 1 are described by center energies (for the main transition) of approximately 16 050 and 15 300 cm-1; the lower-energy line has a width of 470 cm-1, while the broader, higher-energy line has a width of 1700 cm-1. Although the same shape functions are used to describe the vibronic structure for both bands, the width of the higher-energy band is almost 4 times that of the lower energy band. The relationship 1/T2 ) 1(2T1) + 1/T2′, where T2 and T2′ represent the effective and pure dephasing times and T1 is the lifetime of the excited state,54 suggests that the broader line width is required because the lifetime for the upper state is shorter than for the lower state. This idea is consistent with the suggestion that interexciton-state relaxation on the 10-30-fs time scale occurs in allophycocyanin trimers. Calculated Pump-Probe Spectra, V12 < 0. We next performed a manual search to determine the parameters that control the distribution of the summed oscillator strength provided by the two chromophores into the two bands that contribute to the ground-state absorption spectrum: the chromophore site energies E1 and E2, the transition dipole-dipole interaction V12, the angle between the transition moments θ12, and the relative magnitudes of the two transition moments µ1 and µ2. The areas of the two bands shown in Figure 1 were taken as the dipole strengths for the |gg〉 f |+〉 and |gg〉 f |-〉 transitions since Dab ) |〈Ψb|µ|Ψa〉|2 ) 9.28 × 10-3∫(/ν) dν (in debye).50 The bands shown correspond to the assumption that µ1 ) µ2, the interaction energy V12 ) -220 cm-1, and θ12 ) 55°. Although this interaction energy is unexpectedly large compared to the value of -110 cm-1 that was estimated previously from the circular dichroism spectrum,26 use of smaller interaction energies require an assumption that µ1 * µ2; as an example, for V12 of -110 cm-1 and θ12 ) 45°, µ1/µ2 is ∼1.5, which may be too large a difference in transition moment for
Edington et al. the two phycocyanobilin chromophores to be reasonable. Of course, the spectrum in Figure 1 is also consistent with two uncoupled chromophores with µ1/µ2 of ∼2. These three cases cannot be distinguished on the basis of an analysis of the groundstate absorption spectrum alone. The parameter space might be narrowed by attempting to fit the circular dichroism (CD) spectrum at the same time; however, because the phycocyanobilin chromophores are chiral, in addition to the circular dichroism arising from the transition dipole-dipole interaction in the chromophore dimer there is an intrinsic contribution to the CD spectrum that cannot be incorporated into a simple calculation.55 Given the relative dipole strengths for the two bands assigned to the |gg〉 f |+〉 and |gg〉 f |-〉 transitions, it is possible to calculate a consistent set of dipole strengths for the ESA and SE transitions. The time-resolved pump-probe spectrum is then calculated as the sum of contributions from PB, ESA, and SE. We have simplified the calculation (in effect, by excluding holeburning effects at early delays from consideration since they are not observed in the DA or THB spectra) by assuming that the PB spectrum is shaped like the continuous absorption spectrum. Thus, PB contributes a spectrum shaped like that of the ground-state absorption shown in Figure 1 in all cases; owing to the sharing of the |gg〉 ground state by both exciton states, the PB spectrum contains contributions from both transitions even though only one of the two exciton states might be prepared by the pump pulse. ESA arising from |+〉 f |ee〉 and |-〉 f |ee〉 transitions involves excitation by the probe pulse of the unexcited chromophore in the dimer. In the V12 ) 0 uncoupled chromophore case, ESA due to |eg〉 f |ee〉 or |ge〉 f |ee〉 transitions exactly cancels the PB spectrum of the chromophore that was not initially excited; thus, the line shape employed for ESA should be that for the unexcited site in the V12 ) 0 case. We have extrapolated this concept to the V12 * 0 cases by making the ESA line shape that of the unexcited exciton absorption transition, placed at the calculated energy corresponding to the difference between the energies of the |ee〉 and |+〉 or |-〉 states; using ESA line shapes or line widths other than these produced calculated spectra that were markedly inconsistent with the experimental spectra. Stimulated emission from either the |+〉 or |-〉 states carries the same dipole strength as the absorption |gg〉 f |+〉 and |gg〉 f |-〉 transitions;50 in the calculations that follow, the line shape for the SE component from a given state was initially determined by a mirror reflection of the absorption line shape around the band energy, with a Stokes shift of zero. We will have more to say about the possibility of a dynamic Stokes shift later. Figure 7 compares the transient pump-probe spectra for the V12 ) -220 cm-1 case that would be expected to arise from population in the |+〉 and |-〉 exciton states and from population localized on the lower energy chromophore site. The three calculated time-resolved spectra shown in Figure 7 arise from the same quantity of excited-state population. In each case, the component spectra arising from PB, ESA, and SE are superimposed with the overall (sum) spectrum. An additional ESA component, arising from probe-excited transitions from the state in question to higher singlet states Sn, is included in the calculation. This ESA would account for the regions of net ESA observed in the time-resolved spectra shown in Figure 4 in the 500-575- and 660-680-nm regions. (The ESA to doubly-excited states |ee〉 involves sharper transitions by the unexcited chromophore in a given dimer to its first excited singlet state S1.) The intensity and position of this Sn ESA band was kept the same in all of the calculations. Thus, the time evolution of the time-resolved pump-probe spectra shown in
Exciton Relaxation and Localization in Allophycocyanin
Figure 7. Calculated pump-probe absorption-difference spectra for the phycocyanobilin chromophore dimers in allophycocyanin trimers, with the assumption that the two chromophores exhibit equivalent transition dipole moments for the S0 f S1 transition and that the dipoledipole interaction strength V12 ) -220 cm-1: (a) for population in the |+〉 exciton state; (b) for a Boltzmann population distribution over the |+〉 and |-〉 exciton states; (c) for population localized on the |eg〉 site. The details of the calculations and assumptions required to generate these spectra are discussed in the text. In each case, the thick solid curve represents the net spectrum, which was determined by the sum of the contributions from PB (thin solid curve), SE (dashed curve), ESA arising from transitions to the doubly excited state |ee〉 (dotted curve), and ESA arising from transitions to higher singlet states Sn (dash-dotted curve). The line shapes for each component contributing to the net spectrum were determined as discussed in the text. The intensity axes for the three cases are directly comparable.
Figures 2 and 4 involves changes either in the ESA to doublyexcited states |ee〉 or in SE from the exciton states to the ground state |gg〉. ESA to Sn states does not exhibit a significant time evolution in the R subunit of C-phycocyanin, as shown in the accompanying paper.33 Figure 7a shows that the net pump-probe spectrum expected to arise from the |+〉 state is characterized by a broad PB/SE band centered near 620 nm and a sharper region of net absorption in the 650-660-nm range. A very broad band in the 700800-nm region arises from SE. Note that the experimental timeresolved spectra (Figures 2 and 4) do not at all resemble the calculated pump-probe spectrum shown in Figure 7a. Rather, the earliest spectra resemble the calculated spectrum shown in Figure 7b. This is the spectrum that would arise from a Boltzmann population distribution over both exciton states; note that most of the population would reside on the |-〉 state because the energy gap is larger than kT. This spectrum is characterized by an intense PB/SE peak in the 650-660-nm range and a 610640-nm shoulder. The regions of net ESA in this spectrum, in the 675-710-nm region in the red and the
