Toward an Integral Interpretation of the Optical Steady-State Spectra of

Chem. B , 1997, 101 (51), pp 11280–11287 ... Chem. B 101, 51, 11280-11287 ..... Proceedings of the National Academy of Sciences 2009 106, 6134-6139 ...
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J. Phys. Chem. B 1997, 101, 11280-11287

Toward an Integral Interpretation of the Optical Steady-State Spectra of the FMO-Complex of Prosthecochloris aestuarii. 2. Exciton Simulations R. J. W. Louwe, J. Vrieze, A. J. Hoff, and T. J. Aartsma* Dep. of Biophysics, Huygens Laboratory, Leiden UniVersity, P.O. Box 9504, 2300 RA Leiden, The Netherlands ReceiVed: July 8, 1997; In Final Form: October 11, 1997X

We present a simultaneous simulation of various experimental steady-state spectra of the FMO-complex of green sulfur bacteria. The simulations are based on exciton calculations using a significantly lower dipolar interaction energy as compared to exciton calculations on the FMO-complex in the literature. Decrease of the interaction energy was suggested by comparing our results obtained with linear-dichroic absorbancedetected magnetic resonance spectroscopy with exciton simulations using parameters taken from literature. By considering a single subunit only, we arrive at a minimal set of parameters, consisting of reduced interaction energies between the bacteriochlorophyll molecules, seven different site energies, and a common line width for all transitions of 80 cm-1. With such a minimal set of parameters, we have achieved an unequalled match between the simulations and the experimental spectra, including the absorption, the linear dichroic, the circular dichroic, the triplet-minus-singlet, as well as the linear-dichroic triplet-minus-singlet spectra. We conclude that the structure in the various steady-state spectra is mainly determined by the variation in site energy and nearly all interaction energies are substantially less than the inhomogeneous width of the individual transitions within the QY band of the FMO-complex.

2. Introduction In the accompanying paper1 we presented results of absorbance-detected magnetic resonance (ADMR) experiments on the water-soluble bacteriochlorophyll (BChl) a protein complex, commonly referred to as the Fenna-Matthews-Olson (FMO)complex, of the green sulfur bacterium Prosthecochloris (Pr.) aestuarii. We found that the zero-field splitting (zfs-) parameters of the triplet state in the FMO-complex are identical to those observed for monomeric BChl a in organic solvents. Also, the polarization of the optical transition to the lowest excited singlet state at 827 nm is similar to what has been observed for monomeric BChl a in a range of organic solvents2, i.e., 0° and 90° with respect to the triplet y- and x-axes, respectively. Furthermore, the bandwidth of the microwave transitions in the ADMR spectrum is significantly smaller than in other pigmentprotein complexes. From these observations we concluded that the triplet state is localized on a single BChl, presumably the same BChl in all subunits. The triplet-minus-singlet (T-S) and the linear-dichroic, LD-(T-S) absorbance difference spectra could be simultaneously fitted to a sum of a limited number of Gaussian bands, each having a width of 80 cm-1 (fwhm). In addition to a bleaching centered at 827 nm, the T-S spectrum exhibits a bandshift of a transition at 814 nm towards longer wavelengths, and the bleaching of two bands, one centered at 805 nm and one at 800 nm. The transition involved in the bandshift is polarized more or less perpendicular to that at 827 nm. The bleaching centered at 805 nm, on the other hand, is polarized parallel to the bleaching of the 827 nm band. Exciton simulations of the T-S and the LD-(T-S) spectra, using parameter sets from the literature,3-5 display large discrepancies with the experimental spectra. In particular the bleaching at the longest wavelengths with a monomer polarization, and the limited number of spectroscopic changes that occur upon triplet formation are not reproduced by these simulations. * Author to whom correspondence should be addressed. X Abstract published in AdVance ACS Abstracts, November 15, 1997.

S1089-5647(97)02216-5 CCC: $14.00

Analysis of the discrepancies indicates that the interaction energies between the pigments in the FMO-complex are lower than assumed in the simulations in the literature. Furthermore, application of the full Hamiltonian using all 21 BChls of an FMO trimer, while the effect of disorder in the protein environment is neglected in the simulation, might contribute to these discrepancies. In our point of view, it is questionable whether the inter-subunit interactions are significant, considering their relative magnitude. Upon inspection of the dipolar interactions as calculated by Pearlstein, using a dipole strength of 51.6 D2 for monomer BChl,3 we find that more than 85% of the inter-subunit interactions is less than 5 cm-1. Only for a few distinct cases the inter-subunit interaction seems significant: 16 cm-1 for the pairwise interaction between the BChls 7, 14, and 21 and 21 cm-1 between BChls 2 and 19, BChls 5 and 9, and BChls 12 and 16. We estimate that the magnitude of the diagonal disorder is comparable to the inhomogeneous broadening of 80 cm-1. If we assume that the magnitude of the interaction energies as calculated by Pearlstein is correct, then for most of the complexes the variation in site energy between equivalent BChls of different subunits within a trimer as well as the intra-subunit interactions exceed the inter-subunit interactions by at least 1 order of magnitude. The fact that our ADMR-results1 point to a lower dipolar interaction energy than that calculated by Pearlstein provides further support for this argumentation. We conclude, therefore, that the distinctive features in the optical steady-state spectra are governed by the BChl site energy and dipole-dipole interactions within a single subunit. We emphasize that application of the full Hamiltonian of 21 BChls, as in refs 3-5, is not only unnecessary, it also leads to degeneracy within the trimer and symmetry effects which are not representative of the system if disorder is ignored, independent of the magnitude of the inter-subunit interactions. In ref 6 the technique of including static disorder has been described for exciton simulations and was applied to linear aggregates, while in refs 7 and 8 dynamic disorder was included in calculations on symmetric trimers and tetramers. In two © 1997 American Chemical Society

FMO-Complex of Prosthecochloris Aestuarii. 2. limited studies, we seperately included static- as well as dynamic disorder in exciton simulations on the FMO-complex, using only terms in the electronic Hamiltonian associated with the BChls of a single subunit (data not shown). Both studies showed that for a single subunit (no symmetry), inclusion of disorder does not noticably change the results of a particular simulation of the optical spectra. We have therefore reinvestigated in more detail the exciton simulations considering only a single subunit in the absence of disorder. For all the simulations we present in this paper, the electronic Hamiltonian is limited to terms associated with the BChls within a single subunit, the interaction energies are calculated in the point-dipole approximation, and a common line width of 80 cm-1 is assumed for all transitions. It seems reasonable to require that an exciton simulation with a minimal set of free parameters should reproduce the main features of the experimental spectra and that an extension of the simulations, such as increasing the number of free parameters by varying the line widths or inclusion of disorder, should only provide additional refinement of the simulations. To obtain a valid comparison with our results, the sets of parameters from the literature have been restricted in the same manner as well, in addition to the original simulations. We will compare our results with several experimental spectra, including the absorption, LD, CD, T-S, and both LD(T-S) spectra and present parameter sets that significantly improve the match between the simulated and experimental spectra as compared to other reports in the literature. 3. Materials and Methods The atomic coordinates of the FMO-complex9 were obtained from the Brookhaven National Databank. For exciton calculations, the dipole-dipole interaction between the various BChls was calculated in the point-dipole approximation.10 The QYtransition dipoles of the individual BChls were assumed to be oriented parallel to the axis running through the NI-NIII nitrogen-atoms of the BChl. (Note that these are the NB-ND nitrogen-atoms according to the crystallographic nomenclature.) The experimental LD and CD spectra have been taken from refs 11 and 12, respectively. 4. Theoretical Aspects 4.1. Implications of an Exciton Model for the T-S Spectrum. The application of exciton simulations to the analysis of absorption, LD- and CD-spectra has been described in detail elsewhere (see, for example, refs 10 and 13). Here we will briefly review some of the concepts involved before adressing the specific results of the exciton model for the T-S spectrum. In the exciton model the QY-absorption band consists of transitions from the ground state to a manifold of excited eigenstates (exciton states) of the complex. The eigenstates can be found by diagonalizing the electronic Hamiltonian containing the site energies of the individual pigments, and the pairwise interactions between pigments within the complex. Within this model, an excitation is formally delocalized over all pigments and the exciton states are described by an eigenvector consisting of a linear combination of the excited state wave functions of the individual pigments. The contribution of each pigment to the transition dipole movement of a particular exciton transition is given by the coefficients of the molecular wave functions in the corresponding eigenvector. The polarization of a particular transition from the ground- to an excited state is calculated by taking the vector sum of the dipole transition moments of the individual BChls, weighted by the coefficients. Delocalization is determined by the variation of site energies (diagonal disorder)

J. Phys. Chem. B, Vol. 101, No. 51, 1997 11281 within a complex, relative to the strength of the intermolecular interactions. Only in case of high symmetry, such as circular or linear aggregates, and in the absence of large disorder, the excitations are effectively delocalized over all pigments. In pigment-protein complexes like the FMO-complex, which do not have a high symmetry, it can be expected that an excitation will be effectively delocalized over a few pigments only. Also in this case, however, the polarization of the transitions to the excited states will generally be different than that of the transitions of the individual pigments. At sufficiently low temperature, optical excitation within the QY-manifold will be followed by downward energy transfer toward the lowest excited state of the complex. This state possesses the longest population lifetime compared to the other excited states within the manifold, because it can only decay to the electronic ground state. Due to this longer lifetime, the lowest excited state also has the highest triplet yield. The probability for triplet formation at a specific pigment scales with the degree of participation into the eigenvector of the lowest excited state. When two or more BChls contribute more or less equally to the lowest excited state, this results in triplet state formation at these BChls weighted by the coefficients in the eigenvector. Because every pigment has a specific environment, such a situation would result in a broadening of the ADMR-line. Experimentally, however, we observe remarkably narrow ADMR-lines in the FMO-complex. This observation implies that in the FMO-complex (a) the triplet state is always localized on the same BChl in each subunit, and (b) a single BChl contributes nearly all the oscillator strength to the lowest excited state of the FMO-complex. Within the exciton model, these conditions prevail when the triplet-carrying molecule is energetically isolated from the other BChls and/or the interaction energy between the triplet-carrying molecule and other BChls is small. The formation of a (localized) triplet state results in a completely new manifold of excited states, of which the eigenvalues can be found by diagonalizing the electronic Hamiltonian excluding the terms associated with the tripletcarrying BChl, because triplet-triplet transitions are far offresonance with respect to the QY-transitions in BChl a. Comparing the integrated dipole strength of the manifold of excited states with and without the presence of a triplet state, a net loss of dipole strength upon triplet formation will occur, predominantly at the transition(s) to which the triplet-carrying molecule contributes most. Thus, the loss of oscillator strength of the triplet-carrying molecule results in a shift of the exciton states in combination with a different contribution of the individual BChls to the various excited states. Experimentally, this is observed as a reorganization of dipole strength in the QY-manifold upon triplet formation and a change of polarization of the transitions to the excited states. 4.2. Exciton simulations on the FMO-Complex. As we discussed in the Introduction, the magnitude of the dipolar interaction energies as calculated by Pearlstein3 appears to be too large. The dipolar interaction energy depends on two mutually independent parameters, the dipole strength µ2, and the relative dielectric constant r. In ref 3, a dipole strength of 51.6 D2 is used, while in a subsequent paper, Lu and Pearlstein4 use 54.5 and 65.5 D2 to simulate two distinct sets of data. Gu¨len5 also uses a dipole strength of 54.5 D2. All these values appear to be comparable to the QY-dipole strength of 68.9 D2 calculated from the experimental absorption spectrum of the FMO-complex.14 Note that the FMO-dipole strength is much larger than the dipole strength of 37.6 and 41 D2 observed for monomeric BChl a in CCl415 and in acetone,16 respectively. The

11282 J. Phys. Chem. B, Vol. 101, No. 51, 1997 FMO-dipole strength might be enhanced by hyperchromic effects (an increased QY-oscillator strength at the expense of decreased QX and Bx,y-oscillator strengths) as observed for BChl a oligomers.16 Although the FMO-dipole strength was determined by integrating the absorption spectrum from 650--870 nm and thus includes the major fraction of the vibrational bands, hole-burning17,18 and accumulated photon echo19 experiments show that the latter contribution is relatively small. Therefore we will use the experimentally observed value of 68.9 D2 in our calculations. For r ) 1 this value would yield even higher dipole-dipole interactions than those calculated by Pearlstein. In contrast to exciton simulations in the literature, however, we will also include screening by the protein, which is an important factor determining the magnitude of the dipolar interaction energy. When calculation of the dipole-dipole interaction is performed in formula units, as in ref 10, it is implicitly assumed that the relative dielectric constant r is unity, while in nonpolar proteins r might vary between 1 and 5.20 For the protein residues between various chromophores in photosynthetic RCs effective dielectric constants varying between 1 and 10 were calculated, using the results from Stark experiments.21 We will therefore use r as a free global fit parameter. Concerning the absolute scale of the experimental spectra other than the absorption spectrum, the following points are considered. We will use an arbitrary vertical scale for the simulation of the experimental LD-spectrum, considering that the orientation of the sample in the gel-pressing technique in these experiments does not necessarily yield a perfect orientation of the sample. The quality of the simulated LD-spectrum will therefore be evaluated by comparing the relative peak amplitudes with those in the experimental LD-spectrum. Since the rotational strength is proportional to the dipole strength, the vertical scale of the CD-spectrum is directly related to that of the absorption spectrum. The vertical scale of the simulated as well as that of the experimental T-S spectrum was determined by scaling the amplitude of the long-wavelength bleaching at 827 nm to the amplitude of the 825 nm band in the corresponding absorption spectrum, as most probably these bands both stem from the tripet-carrying BChl. The vertical scales of both LD-(T-S) spectra are directly related to that of the T-S spectrum by the dichroic ratio R as in eq 1 of ref 1. We found that an automatic search routine as described in refs 3 and 4 compensates for the absence of vibronic bands in the model by adjusting the site energies such that a significant fraction of the total dipole strength of the 0-0 transitions is relocated to the 770-795 nm wavelength region, which presumably also contains contributions of the vibronic bands. Furthermore, we found that such a routine compensates for the variation of the band positions in the absorption, T-S and LD(T-S) spectra1 by relocating a number of corresponding absorption bands to different wavelength regions, while the differences in the positions are presumably caused by a combination of disorder and energy transfer,1 which not have been accounted for in the exciton model employed here. These unwanted effects heavily influence the outcome of the exciton simulations based on automatic optimization of the parameters, and therefore we decided to manually adjust the parameters of a particular simulation in an interactive fit routine. 5. Results 5.1. Parameter Sets from the Literature. Before turning to new parameter sets, we first describe briefly the exciton simulations based on parameter sets from the literature and the experimental spectra. In Figures 1-6 a comparison of the

Louwe et al.

Figure 1. Comparison of the experimental absorption spectrum (circles) and the spectra simulated with two parameter sets from the literature and three parameter sets discussed in the text. Solid lines (I-V) represent the simulated absorption spectra using parameter set [D], [B], [A], the parameter set from Gu¨len5 and from Pearlstein,3 respectively. For the latter two parameter sets, simulations are also plotted with a Hamiltonian including the 7 BChls of a single subunit only and with an equal linewidth of 80 cm-1 for all transitions (broken lines). The simulated spectra using the parameter set from Gu¨len are shifted 20 cm-1 (∼1.3 nm) to longer wavelengths to adjust the minor discrepancy in wavelength calibration between the experimental datasets used here and in ref 5.

Figure 2. Comparison of the experimental LD-spectrum (from ref 11) with those obtained with the exciton calculations discussed in the text. Lines and ordering of simulations I-V as in Figure 1.

various experimental spectra with previous exciton simulations is presented together with our own results. Exciton simulations using the site energies from the parameter set of Gu¨len5 and from the parameter set in ref 3, representative for the exciton simulations presented by Pearlstein et al.,3,4 are plotted in curves IV and V of these figures. To calculate the orientation of the transitions with respect to the triplet axes in the above simulations using 21 BChls for the LD-(T-S) spectra, it is necessary to slightly alter the original parameter sets by including a small difference in site energy

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Figure 3. Comparison of the experimental CD-spectrum with those obtained with the exciton calculations discussed in the text. Experimental spectrum (dashed lines) from ref 12. Lines and ordering of simulations I-V as in Figure 1.

Figure 5. Comparison of the experimental LD-(T-S) spectrum, (|D| - |E| transition) with those obtained with the exciton calculations discussed in the text. Lines and ordering of simulations I-V as in Figure 1.

Figure 4. Comparison of the experimental T-S-spectrum, (|D| - |E| transition) with those obtained with the exciton calculations discussed in the text. Lines and ordering of simulations I-V as in Figure 1.

Figure 6. Comparison of the experimental LD-(T-S) spectrum, (|D| + |E| transition) with those obtained with the exciton calculations discussed in the text. Lines and ordering of simulations I-V as in Figure 1.

between the corresponding sites of the different subunits to avoid degeneracy of the eigenstates. This degeneracy prohibits calculation of the orientation of the transition dipole moments with respect to the triplet axes. In contrast to the calculation of the LD-spectrum, where the plane of degeneracy is perpendicular to the orientation- (C3-) axis, for the LD-(T-S) spectrum, a solution with degenerate eigenstates leads to an undefined polarization of the corresponding transition dipole moments. The simulations using the original set of parameters3,4 reasonably reproduce the absorption- and CD-spectrum (Figures 1 and 3), but if the, in our opinion, excessively large variation of linewidths is removed and a common width of 80 cm-1 is assumed, significant deviations occur between the simulated and experimental CD-spectra, especially in the region 12 60012 800 cm-1. It was noted previously5 that an exciton simula-

tion using the parameter sets in refs 3 and 4 does not give an acceptable fit to the LD-spectrum nor to the T-S spectrum: these simulations are shown in curves IV and V of Figures 2 and 4, respectively. For further comments on these results we refer to ref 5. Although the parameter set presented by Gu¨len5 considerably improves the fit to the LD-spectrum, there are still substantial deviations between the experimental and simulated absorption and LD-spectra, especially considering the relative dipole strengths and polarization of the 825, 815, and 805 nm bands (Figures 1 and 2). Furthermore, the CD-spectrum cannot be reproduced using this set of parameters (Figure 3). Summarizing, we find that neither of the exciton simulations in refs 3-5 simultaneously reproduces the absorption-, LD-,

11284 J. Phys. Chem. B, Vol. 101, No. 51, 1997

Louwe et al.

TABLE 1: Orientation and Relative Strength of QY-Transition Dipole Momentsa state

1/N∑|µ bi|2

φC3

φQ(2)Y

φQ(2)X

φQ(3)Y

φQ(3)X

φQ(5)Y

φQ(5)X

φQ(6)Y

φQ(6)X

(1) (2) (3) (4) (5) (6) (7) (1+2) (1-2) (2+3) (2-3) (3+4) (3-4) (4+5) (4-5) (5+6) (5-6) (6+7) (6-7) (1+6) (1-6) (1+7) (1-7) (2+6) (2-6) (4+6) (4-6) (4+7) (4-7)

1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.4 0.6 1.7 0.3 0.7 1.3 1.2 0.8 0.6 1.4 1.5 0.5 1.4 0.6 1.9 0.1 0.7 1.3 1.5 0.5 1.9 0.1

16.8 74.6 109.4 23.4 94.3 69.1 10.8 43.9 49.1 92.1 43.6 60.9 141.5 57.0 38.3 75.0 104.9 39.5 129.1 39.1 55.6 9.6 94.0 57.7 93.2 42.1 56.9 12.7 98.2

63.8 0.0 48.7 60.9 20.0 109.0 83.4 31.9 121.9 24.4 65.6 17.9 83.8 23.1 111.0 55.7 41.0 97.0 116.3 86.1 43.9 73.6 25.6 54.5 35.5 84.6 37.9 72.0 35.0

29.3 88.2 134.9 29.0 103.0 36.2 24.8 57.8 37.4 111.7 26.7 81.9 171.8 65.2 29.4 57.8 128.0 9.0 95.8 7.6 86.5 25.2 95.6 43.8 118.4 11.4 86.2 23.8 94.1

106.4 48.7 0.0 105.9 40.4 154.1 120.2 77.2 153.0 24.4 114.4 53.0 37.0 71.7 145.1 97.3 7.8 143.9 113.6 134.3 54.5 113.5 52.6 101.9 16.7 133.2 52.6 113.5 59.8

28.5 39.6 87.7 23.4 55.4 73.5 49.3 13.8 84.1 63.6 27.6 37.4 123.4 16.6 73.9 38.5 80.3 57.3 111.7 46.6 56.1 38.9 51.2 24.8 72.6 45.5 52.0 36.3 54.2

82.2 20.0 40.4 78.3 0.0 113.9 102.5 50.7 139.5 21.0 77.5 36.9 69.5 39.2 129.2 57.0 33.0 111.0 101.0 99.2 59.4 92.3 13.1 62.6 34.3 96.8 53.8 90.4 22.6

158.9 103.0 55.9 161.1 88.0 136.7 154.5 133.0 132.0 79.4 162.4 108.6 19.3 126.0 140.9 129.5 63.0 160.0 79.8 168.8 101.1 159.0 94.8 145.1 72.0 167.3 102.3 161.7 95.4

64.3 109.0 154.1 61.9 113.9 0.0 59.6 86.3 44.1 132.2 45.8 110.8 149.2 87.6 46.0 57.0 147.0 29.8 60.2 32.1 122.1 61.4 101.5 54.5 144.5 30.9 120.9 59.9 94.4

49.5 20.4 68.9 45.0 33.7 88.7 70.3 20.8 105.8 44.6 45.6 27.5 102.5 6.9 95.7 38.4 61.1 78.0 108.5 66.6 53.9 59.9 30.3 34.3 55.8 64.8 48.2 57.6 35.3

a Dipole moments of the monomer BChls states and of those that would result from the interaction between two isolated, equally participating, BChls in the FMO-complex. The orientations (in degrees) are given with respect to the symmetry C3-axis, φC3, and to the triplet y- and x-axes of the triplet-carrying molecule i, φQ(i)Y, and φQ(i)X, respectively. This molecule is BChl 2, 3, 5, or 6 in parameter sets [A]...[D]; for each set the candidates for the 815 nm and for the 800/805 nm transition(s) are given in boldface and italics, respectively.

CD-, T-S, and LD-(T-S) spectra. In the previous paper,1 where we reported ADMR results on the FMO-complex, we discussed the discrepancies between the T-S and LD-(T-S) spectra and the simulations using either of the parameter sets from refs 3-5 (Curves IV and V of Figures 4-6). We concluded that these discrepancies mainly stem from an overestimation of the interaction energy between the BChls in the FMO-complex. 5.2. New Parameter Sets. 5.2.1. Four Possible Parameter Sets. As described above, we restrict ourselves to the minimal set of parameters for a FMO-subunit, reducing the number of elements in the electronic Hamiltonian from (21×21) to (7×7). In addition, a major simplification occurs in the search for a set of site energies because the number of dipolar interactions with substantial magnitude within a subunit is limited. We find that in addition to the interactions between nearest neighbours, in particular the pair-wise interactions between BChl pairs (1,6), (2,6), (4,6), and (4,7) are significant. Another simplification is suggested by the LD-(ADMR) results, which show that the lowest excited state is mainly composed of the contribution from a single molecule and that this BChl appears to be energetically isolated. We interpret the 825 nm band in the absorption- and LD-spectrum, and the bleaching at 827 nm in the T-S spectrum as originating from this energetically isolated BChl only. Therefore, the polarization of the 825 nm band in the LD-spectrum directly indicates which molecules are candidates to account for the absorption band at this wavelength. The observed anisotropy of ∼0.2 at 825 nm dictates that the transition dipole moment belonging to this band is oriented approximately perpendicular to the C3-axis, which is the orientation axis in the LD-absorption experiment. Table 1 lists the orientation of the QY-axes of the individual BChls with respect to the C3-axis. We find that only BChls 2, 3, 5, or 6 (numbering according to ref 22) have an orientation corre-

sponding more or less to the polarization of the 825 nm absorption band, which breaks down the possible sets of parameters into four groups. This break down serves as a basis for searching new parameter sets as we will discuss below. The set of parameters for which BChl 2, 3, 5, or 6 has the lowest site energy in the exciton simulations will be denoted as set [A], [B], [C] or [D], respectively. 5.2.2. Spectral Properties of Candidate Transitions. We proceed as follows in searching for a set of site energies. The exciton splitting of an isolated BChl-pair is proportional to J/∆E, J being the dipolar interaction between the two BChls, and ∆E the difference in their site energies. The relatively low interaction energy suggests, therefore, that the structure of the QY-band in the experimental spectra results mainly from the differences in site energies of the BChls in the FMO-complex. We expect that a reasonable estimate of the site energies of the various BChls can be made if we only consider the properties of the transitions of the individual BChls and of transitions resulting from strongly interacting pairs of BChls. Mathematically this approximation is equivalent to the assumption that the triplet-carrying BChl only interacts with this individual BChl or BChl pair. In that case, the electronic Hamiltonian can (partly) be written in block-diagonal form and that part can be diagonalized separately. Comparison of these monomer and dimer properties with the characteristic features observed in the experimental absorption-, LD-, T-S, and LD-(T-S) spectra yields candidates for transitions in a specific wavelength region. First we list the various properties of the monomer- and dimeric transitions mentioned above, for every base set [A]...[D] separately. Table 1 lists the polarization of the transitions with respect to the C3-axis and to the triplet axes, and in Table 2 the frequency shift and change in dipole strength upon triplet formation are shown. These numbers were obtained by diagonalizing a Hamiltonian consisting of the site energies and dipolar

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TABLE 2: Frequency Shift ∆ν and Change in Dipole Strength ∆|µ b|2 a [A]: (2) f BChlT state (1) (2) (3) (4) (5) (6) (7) (1+2) (1-2) (2+3) (2-3) (3+4) (3-4) (4+5) (4-5) (5+6) (5-6) (6+7) (6-7) (1+6) (1-6) (1+7) (1-7) (2+6) (2-6) (4+6) (4-6) (4+7) (4-7)

∆ν

(∆|µ b|2)

-18.6

(-4.7)

-2.0 -0.1 -0.0 -0.3 -0.1

(+2.5) (+0.5) (+0.3) (-0.5) (+0.1)

-1.8 -0.5 -0.1 -0.0 -0.2 -0.1 -0.3 -0.1 -5.1 -13.7 -5.7 -12.9

(-3.2) (-0.2) (-1.0) (+0.1) (-0.5) (+1.1) (+0.2) (+0.2) (+1.3) (+3.6) (+6.3) (-1.7)

-0.4 -0.0 -0.2 -0.0

(-0.2) (+0.3) (-0.6) (-0.0)

[B]: (3) f BChlT ∆ν

(∆|µ b|2)

-0.1 -2.0

(-0.2) (+2.5)

-5.6 -0.0 -0.2 -0.0 -1.8 -0.6

(+1.7) (-0.1) (+1.1) (-0.1) (-1.0) (-1.2)

-3.6 -2.3 -0.1 -0.1 -0.1 -0.1 -0.0 -0.2 -0.0 -0.0 -0.4 -1.8 -4.1 -1.9 -3.2 -2.5

(+2.1) (-2.8) (-0.1) (-1.1) (-0.7) (-0.3) (-0.3) (-0.6) (+0.3) (-0.1) (+0.3) (-4.1) (-4.3) (+1.4) (-2.6) (+0.5)

[C]: (5) f BChlT ∆ν

(∆|µ b|2)

-0.1 -0.0 -0.0 -8.7

(+0.1) (+0.3) (-0.1) (-1.6)

-16.4 -0.0 -0.1 -0.0 -0.0 -0.0 -4.9 -4.0

(-4.1) (+0.1) (-0.8) (+0.2) (-0.1) (-0.1) (+4.2) (-1.7)

-7.8 -8.8 -6.2 -10.3 -0.0 -0.1 -11.8 -4.4 -0.2 -23.0 -5.6 -3.5

(+3.9) (-0.2) (+3.1) (+1.0) (+0.0) (-0.2) (-2.2) (+6.4) (+0.3) (+4.2) (+0.4) (+1.1)

[D]: (6) f BChlT ∆ν

(∆|µ b|2)

-0.4 -0.3 -0.2 -0.7 -16.4

(-0.8) (-0.5) (+1.1) (-1.1) (-4.1)

-3.2 -0.0 -0.6 -0.0 -0.6 -0.9 -0.1 -5.5 -10.7

(+2.4) (+0.0) (+1.0) (+0.2) (-0.9) (-0.9) (+0.7) (-0.5) (+4.7)

-0.4 -3.1

(-0.7) (-1.1)

-0.5 -2.9

(-1.4) (-0.4)

a Shift in ∆ν and change in ∆|µ b|2 upon triplet formation of monomeric excited states and of exciton states resulting from the interaction between two isolated, equally participating, BChls in the FMO-complex. Candidates (including a preselection from Table 1) for 815 nm transition(s) are given in boldface; candidates for 800/805 nm transition(s) are given in italics.

interactions associated with the triplet-carrying molecule, together with those of an additional BChl or BChl-pair. For the triplet-carrying molecule a site energy of 12120 cm-1 has been used, while for an additional BChl 12 400 cm-1 and a BChlpair 12 400 and 12 410 cm-1 have been used. In this initial approximation it is thus assumed that both BChls in a pair contribute more or less equally to the dimeric exciton state. Note, that a transition of a specific BChl-pair, e.g., (1+2), is always accompanied by a complementary transition (1-2) which has to be taken into consideration as well, except when the latter transition has a strongly reduced dipole strength. 5.2.3. Experimentally ObserVed Criteria for Candidate Transitions. The criteria to select a candidate for the 815 nm and 805 and 800 nm transitions are found by considering the characteristic features of the absorption-, LD-, T-S, and LD(T-S) spectra. Because part of the chirality observed in the experimental CD-spectra may be related to pigment-protein interactions, we will only consider afterward how well the CDspectra are reproduced by the various simulations. Although the absorption band at 825 nm will be dominated by the transition dipole moment of the tripet-carrying molecule, it may be expected that some of the dipole strength of the tripetcarrying molecule is distributed over other transitions, considering that the oscillator strength of the 825 nm band seems to be less than 1/7 of the total integrated oscillator strength. Coupling with the other BChls, however, should not significantly alter the orientation of the transition dipole moment associated with the lowest excited state of the triplet-carrying molecule. The transition dipole moment(s) responsible for the absorption bands around 815 nm are expected to be oriented more or less parallel to the C3-axis (see below). Of these transitions, those that are observable in the experimental T-S and LD-(T-S) spectra are polarized perpendicular to the 825 nm transition

dipole moment and thus parallel to the triplet x -axis.1 Upon triplet formation, these transitions mainly display a frequency shift towards longer wavelengths, while the change in dipole strength and/or polarization of these transitions appears to be negligible. A considerable fraction of the total integrated dipole strength in the absorption spectrum is located around 815 nm, while only in this wavelength region a large negative band is observed in the LD-spectrum. Since we assume that the characteristic features in the various spectra are governed by the difference in site energies of the BChls, we conclude from the orientation of the transition dipole moments of the individual BChls in Table 1, that BChls 1, 4, and 7 contribute mainly to the transition(s) absorbing at 815 nm. If these BChls would contribute significantly to the transitions at other wavelengths, then large negative features would be observed in the LDspectrum outside the 815 nm wavelength region, in contrast to the experimental results which show positive, small LD-signals at wavelengths outside the 815 nm region. To account for the remaining dipole strength in the absorption spectrum, three of the BChls 2, 3, 5, and 6 must contribute mainly to the transitions absorbing around 805 nm and 800 nm, the fourth BChl being assigned to the 825 nm band. This assignment is in agreement with the orientations of the transition dipole moments of those BChls in Table 1, considering the small, positive LD-signals mentioned above. The transitions absorbing at 800 and 805 nm predominantly show a loss in dipole strength upon triplet formation and are oriented parallel to the 825 nm transition. 5.2.4. Selection of Candidates and Optimization of Site Energies. By comparing the experimentally observed features and the properties of the candidate-transitions as listed in Tables 1 and 2, a selection is made for the start values for the site energies of the various BChls. After this initial approximation,

11286 J. Phys. Chem. B, Vol. 101, No. 51, 1997

Louwe et al.

TABLE 3: Site energiesa (Left Part) Given as Deviation from 12 350 cm-1 and Interaction Energies (Right Part) BChl 1 2 3 4 5 6 7

[A]

[B]

[D]

1

2

3

4

5

6

7

-30 -30 0 -94 5 -6 6 -14 -12 -200 85 30 -94 30 7 2 12 5 90 -220 90 5 30 -51 -1 -9 1 90 -30 -30 -6 7 -51 -63 -17 -59 250 220 -30 6 2 -1 -63 88 -3 -50 100 -200 -14 12 -9 -17 88 38 -30 80 0 -12 5 1 -59 -3 38

a In units of cm-1 for best simultaneous simulations using parameter sets [A], [B], or [D] (BChl 2, 3, or 6 as triplet carrying molecule).

these site energies are further manually adjusted in the exciton simulations until the best fit is obtained. In this final step the magnitude of the interaction energy is changed simultaneously by adjusting the value for the dielectric constant r. For all sets of parameters, we found the best results using the in ViVo dipole strength of 68.9 D2 in combination with r ≈ 2.4 considering all spectra simultaneously. For parameter set [A], we find that transitions (1), (7), (1+7), and (4+7) are candidates for the 815 nm transition, referring to the orientation of the transition dipole moments listed in Table 1. Considering that only transitions (1) and (1+7) of those transitions display a significant frequency shift (Table 2), we select transitions (1) and/or (1+7) as candidates for the 815 nm region, not taking into account the change in dipole strength that these transitions display upon triplet formation. Although we did not observe a change in dipole strength in the Gaussian fit in the 815 nm region of the experimental results,1 the overlap of several transitions can possibly mask this effect. For the 805 nm transition, only transition (3+4) appears to display the observed loss of dipole strength upon triplet formation, in combination with an orientation with respect to both the C3axis as well as the triplet axes, which agrees more or less with the polarizations observed in this wavelength region. The fact that the complementary transition (3-4) is not affected by triplet formation and therefore does not show up in the T-S spectra, seems to support this choice. Using the above-selected start values, we first tried to find optimal site energies for the BChls by using a Hamiltonian excluding BChls 5 and 6. In this manner, the transitions associated with BChls 5 and 6 do not interfere in evaluating the fit of the simulation to the experimental spectra. After this optimization we include BChls 5 and 6 again and optimize all site energies. The results are plotted in curve III of Figures 1-6 together with the experimental spectra; the corresponding site energies are presented in Table 3.

For parameter set [B] we find, referring to Tables 1 and 2, that transition (4) is the best candidate for the 815 nm transition, while transitions (5-6) and/or (2-6) are implicated in the 800-805 nm region. Possibly the spectra in this wavelength region consist of a combination of the latter transitions, either by mixing or by spectral overlap. After optimization of the site energies as described above, we note that especially with parameter set [B] the various phenomena observed in the experimental spectra are very well reproduced. The site energies of the complete set of BChls are listed in Table 3, and the results of the spectral simulations are plotted in curve II of Figures 1-6. There are no obvious candidates for the various transitions in parameter set [C] nor in [D]. For both parameter sets, the relatively large interaction between BChls 5 and 6 dominates a simulation of the T-S spectra. This interaction is large compared to the interaction between these two BChls and the other BChls. Although triplet formation on either one of the BChls 5 or 6 yields a shift towards longer wavelengths of the other BChl as is observed in the 815 nm region of the T-S spectrum, the orientations of the dipole transition moments of BChls 5 and 6 are approximately perpendicular to that observed for the 815 nm transition in the LD spectrum as well as to those observed in both LD-(T-S) spectra (see Table 1 and 2). Only for parameter set [D] we obtained a set of site energies that gave reasonable results, such that the relatively large interaction between BChls 5 and 6 was masked by other shifts in the T-S spectra (Table 3, curve I of Figures 1-6). 6. Discussion and Conclusions We find three parameter sets, [A], [B], and [D], that improve the existing exciton simulations considerably (Table 3, Figures 1-6). However, although all simulations in Figure 1 seem to reproduce more or less the absorption spectrum, a closer inspection shows that only the simulation using parameter set [B] accurately predicts the relative peak amplitudes of the 825, 814, 805, and 800 nm bands. In addition, the relative peak amplitudes of the simulated LD-spectrum (Figure 2) completely concur with those of the experimental LD-spectrum in contrast to the other simulations presented in this figure. The simulation of the (T-S)- and both LD-(T-S) spectra (Figures 4-6), also show that parameter set [B] yields the best results, especially with respect to the following points: (a). Inspection of the amplitude of the 827 nm bands in the LD(T-S) spectra relative to that in the T-S spectrum shows that the experimental polarization of the transition to the lowest excited state is most accurately reproduced using parameter set

TABLE 4: Eigenvalues νa, Dipole Strengths µ2, and Eigenvectors Resulting from the Simulation Using Parameter Set [B] BChl ν [cm-1]

µ2 [D2]

1

2

3

4

5

6

7

12 112 (825.6) 12 266 (815.2) 12 293 (813.5) 12 396 (806.7) 12 457 (802.7) 12 496 (800.2) 12 634 (791.5)

46.7 151.5 57.2 89.3 90.7 11.7 35.5

-0.066 0.845 -0.220 0.015 0.130 -0.464 -0.018

-0.116 0.449 -0.133 -0.143 -0.336 0.795 0.043

0.955 0.037 -0.268 -0.111 0.009 0.057 0.014

0.259 0.252 0.794 0.348 -0.261 -0.007 -0.223

0.035 0.027 0.243 -0.293 -0.310 -0.199 0.847

0.027 0.020 -0.166 0.818 0.236 0.187 0.459

0.042 0.136 0.382 -0.300 0.807 0.272 0.139

12 266 (815.3) 12 280 (814.3) 12 393 (806.9) 12 457 (802.8) 12 495 (800.3) 12 634 (791.5)

0.0 128.6 74.8 72.6 92.4 10.0 35.0

-0.000 0.865 -0.113 0.038 0.128 -0.469 -0.017

With triplet on BChl 3 -0.000 1.000 0.471 0.000 -0.116 -0.000 -0.150 -0.000 -0.333 0.000 0.793 0.000 0.041 0.000

0.000 0.139 0.875 0.315 -0.258 0.009 -0.221

0.000 -0.000 0.233 -0.302 -0.311 -0.197 0.848

0.000 0.030 -0.116 0.823 0.240 0.198 0.460

0.000 0.093 0.374 -0.329 0.807 0.269 0.139

a

In wavenumbers; values between brackets are the corresponding wavelengths. Contributions larger than 50 % are shown in bold.

FMO-Complex of Prosthecochloris Aestuarii. 2. [B]. We calculate 11° and 77° with respect to the triplet yTand xT axes, respectively, for the orientation of this transition using parameter set [B]. This is very close to the experimentally observed values (0-10° and 80-90°). Parameter set [A] yields 19° and 70°, and parameter set [D] yields 23° and 68° for these numbers, respectively. (b). Only parameter set [B] predicts a bleaching at ∼805 nm and a band shift around 815 nm upon triplet formation. From a comparison of the dipole strengths and the eigenvalues resulting from this simulation for the singletand triplet part in Table 4, respectively, more subtle details of this bandshift may be derived. For example, in addition to a bandshift of the 813.5 nm transition to 814.3 nm upon triplet formation, a reorganization of the dipole strengths is calculated for the 813.5 nm and 815.2 nm transitions, the latter not shifting upon triplet formation. The combined result of these changes yields the single bandshift described by the phenomological description of the Gaussian fit in the accompanying paper.1 The simulation using parameter set [B] is the only one that reproduces the long-wavelength side of the CD-spectrum (see Figure 3). Although the spectral position of the bands at higher energies is not correct, the overall result for this simulation of the CD-spectrum is comparable with the simulation from Pearlstein,3 which employed a significantly larger number of free parameters and a variation in line widths that seems to lack experimental support. Since the best fit to the experimental spectra is clearly obtained using parameter set [B], only for this parameter set the contributions of the BChls to the various exciton transitions with and without the presence of a triplet state in the FMOcomplex are listed in Tables 3 and 4, respectively. The probability density of an excitation on a particular BChl is given by the square of the corresponding term in an eigenvector. Inspection of Table 4 shows that the contributions to the various exciton states are more or less dominated by a single BChl and that the degree of delocalization is smaller than obtained by previous exciton simulations. This result will be especially important for calculations concerning energy transfer in the complex. It seems plausible that the deviations between the experimental spectra and the simulations can be significantly reduced by the inclusion of vibrational bands, in combination with allowing some lifetime-broadening of the linewidths at the highest energies in the exciton simulation, as the population relaxation time of the highest excited states within the QYmanifold is ∼50 fs,23,24 corresponding to a linewidth of approximately 110 cm-1. Furthermore, both a different dipole strength for the individual BChls and variation of the dielectric constant over the protein might further improve the fit between the simulations and the experimental data, although the validity of such an approach would be difficult to judge. The objective of this study, however, is to obtain a minimal set of parameters for the FMO-complex to adequately describe the characteristic features in the optical steady-state spectra. Only after verification of the site energies by independent experiments, such as

J. Phys. Chem. B, Vol. 101, No. 51, 1997 11287 site-directed mutagenesis, would an increase of freely adjustable parameters seem worthwhile to explain the remaining, relatively small discrepancies. We conclude that parameter set [B] yields the best simultaneous simulation of the optical steady state-spectra of the FMOcomplex at this moment. Moreover, the most prominent features in the experimental spectra are satisfactorily reproduced by a minimal set of free parameters. This minimal set of parameters consists of a common linewidth for all transitions, the site energies for the BChls within one subunit only, the in ViVo dipole strength of µ2 ) 68.9 D2 and a reduced interaction energy compared to previous exciton simulations through a dielectric constant of r ) 2.4. The latter reflects screening by the protein, and seems more realistic than r ) 1 that has been implicitly used in previous exciton simulations on the FMO-complex. Acknowledgment. This investigation was supported by the Life Science Foundation (SLW) and the Foundation for Chemical Research (SON), financed by the Netherlands Organization for Scientific Research (NWO), and by the European Community (Contract FMRX-CT96-0081). We acknowledge Prof. J. Amesz for his critical comments on the manuscript prior to publication. References and Notes (1) Louwe, R. J. W.; Vrieze, J.; Hoff, A. J.; Aartsma, T. J. J. Phys. Chem. 1997, 101, 7221. (2) Vrieze, J.; Hoff, A. J. Chem. Phys. Lett. 1995, 237, 493. (3) Pearlstein, R. M. Photosynth. Res. 1992, 31, 213. (4) Lu, X.; Pearlstein, R. M. Photochem. Photobiol. 1993, 57, 86. (5) Gu¨len, D. J. Phys. Chem. 1996, 100, 17683. (6) Fidder, H.; Knoester, J.; Wiersma, D. A. J. Chem Phys. 1991, 11, 7880. (7) Reineker, P.; Warns, Ch.; Neidlinger, Th.; Barvı´k, I. Chem. Phys. 1993, 177, 715. (8) Warns, Ch.; Barvı´k, I.; Reineker, P.; Neidlinger, Th. Chem. Phys. 1995, 194, 117. (9) Tronrud, D. E.; Schmidt, M. F.; Matthews, B. W. J. Mol. Biol. 1986, 188, 443. (10) Pearlstein, R. M. In Chlorophylls; Scheer, H., Ed.; CRC Press: Boca Raton 1991; p 1047. (11) van Mourik, F.; Verwijst, R. R.; Mulder, J. M.; van Grondelle, R. J. Phys. Chem. 1994, 98, 10307. (12) Vasmel, H.; Swarthoff, T.; Kramer, H. J. M.; Amesz, J. Biochim. Biophys. Acta 1983, 725, 361. (13) Davydov, A. S., Ed. Theory of Molecular Excitons; Plenum Press: New York, 1971. (14) Olson, J. M. In The Chlorophylls; Vernon, L. P., Seeley, G. R., Eds.; Academic Press: New York 1966; p 413. (15) Sauer, K.; Lindsay Smith, J. R.; Schultz, A. J. J. Am. Chem. Soc. 1966, 88, 2681. (16) Scherz, A.; Parson, W. W. Biochim. Biophys. Acta 1984, 766, 653. (17) Johnson, S. G.; Small, G. J. J. Phys. Chem. 1991, 95, 471. (18) Franken, E. M.; Neerken, S.; Louwe, R. J. W.; Amesz, J.; Aartsma, T. J. Submitted for publication. (19) Louwe, R. J. W.; Aartsma, T. J. J. Phys. Chem. B 1997, 101, 7221. (20) Rees, D. C. J. Mol. Biol. 1980, 141, 323 and references therein. (21) Steffen, M. A.; Lao, K.; Boxer, S. G. Science 1994, 264, 810. (22) Fenna, R. E.; Matthews, B. W.; Olson, J. M.; Shaw, E. K. J. Mol. Biol. 1974, 84, 231. (23) Vulto, S. I. E.; Streltsov, A.; Aartsma, T. J. J. Phys. Chem. B 1997, 101, 4845. (24) Buck, D. E.; Savikhin, S; Struve, W. S. Biophys. J. 1997, 72, 24.