Structure-Based Calculations of the Optical Spectra of the Light

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J. Phys. Chem. B 1999, 103, 6349-6356

6349

Structure-Based Calculations of the Optical Spectra of the Light-Harvesting Peridinin-Chlorophyll-Protein Complexes from Amphidinium carterae and Heterocapsa pygmaea Donatella Carbonera and Giovanni Giacometti* Dipartimento di Chimica-Fisica, UniVersita` di PadoVa, Via Loredan 2, I-35131 PadoVa, Italy

Ulderico Segre Dipartimento di Chimica, UniVersita` di Modena, Via Campi 183, 41100 Modena, Italy, and CSSMRE CNR, Via Loredan 2, 35131 PadoVa, Italy

Eckhard Hofmann Fakulta¨ t fu¨ r Biologie, UniVersita¨ t Konstanz, Postfach 55 60, 78434 Konstanz, Germany

Roger G. Hiller School of Biological Sciences, Macquarie UniVersity, New South Wales 2109, Australia ReceiVed: December 4, 1998

The molecular structure of the light-harvesting complex peridinin-chlorophyll-protein from the dinoflagellate Amphidinium carterae (A-PCP) provides the positions and orientations of the eight peridinin (Per) and two chlorophyll a (Chl) molecules in the complex whose apoprotein is 32 kD. We made structure-based calculations of the distinctive optical properties (absorption and CD spectra) of A-PCP and of the complex containing a ratio of four peridinin and one chlorophyll per complex (apoprotein ∼ 15 kD) obtained from the related species Heterocapsa pygmaea (H-PCP). The latter structure has not been determined but can be inferred from that of A-PCP. A point-monopole approximation was used to represent the low-energy transition of peridinin in the blue region of the spectrum and that of chlorophyll in the Soret region. Vibronic interactions are taken into account for peridinin because of the strong vibrational progression exhibited by the spectrum of the latter. From the calculations, we are able to simulate the absorption and CD spectra for H-PCP and A-PCP by using, in addition to the atomic coordinates taken from the A-PCP structure, one and only one set of parameters, adjusted for the small unit of four Per and one Chl common to both systems. In particular, the four peridinin site energies were assigned values in the range 18 500-19 500 cm-1, and those for the Bx and By transitions of chlorophyll a were given the common value 23 100 cm-1. The transition moments for peridinin were in the range 10.6-12.4 D, and those of the chlorophyll Bx and By transitions were 9.0 and 1.0 D, respectively. Each resolved vibronic transition was given the same Gaussian line width of 550 cm-1. Excitonic coupling among the different chromophores of the small cluster unit of the complex is not sufficient to describe the A-PCP optical properties. Intercluster interactions are necessary in order to reproduce the CD spectrum. The H-PCP spectrum, being practically identical to the former, is reproduced only if such interactions are maintained, meaning that the solution unit is a dimer of the monomeric polypeptide as previously inferred from the biochemical properties.

Introduction The photosynthetic apparatus of dinoflagellate Amphidinium carterae contains a water-soluble external antenna complex (APCP) made of a 32 kD polypeptide enclosing two pigment clusters comprising two chlorophyll a (Chl, II) and eight peridinin (Per, I) molecules total. The recent determination of the molecular structure of this protein using X-ray crystallography1 provides a structural basis for modeling the mechanism of excited-state energy coupling in this complex. The validity of the model can then be tested using comparisons of * Corresponding Author. E-mail: [email protected]. Fax: +39049-8275135.

predicted properties with those measured by steady-state optical spectroscopy. We had discussed absorption, CD, and T-S spectra of A-PCP and of the related complex from a different dinoflagellate species, Heterocapsa pygmaea (H-PCP), before the above X-ray structure was published.2

10.1021/jp9846429 CCC: $18.00 © 1999 American Chemical Society Published on Web 07/13/1999

6350 J. Phys. Chem. B, Vol. 103, No. 30, 1999

We are now in a position to reexamine quantitatively that discussion by attempting to reproduce the steady-state spectra using the three-dimensional structure of A-PCP. A-PCP consists of a trimer of monomers each containing a 312 residue peptide with 2 molecules of digalactosyldiacylglycerol (DGDG) being an integral part of the structure together with a number of resident water molecules. The NH2 and COOH terminal halves of the monomer polypeptide form almost identical domains related by a 2-fold local symmetry axis. Each domain consists of eight R-helical segments appearing in antiparallel pairs making a sort-of half-boat of which the four different pairs constitute respectively the deck, the bow (or stern), and the two sides which are inclined in such a way as to form the keel of the ship. The two domains generate by juxtaposition a central, hydrophobic space of about 23 × 23 × 53 Å3 filled with the pigments. The latter occurs in two clusters of one chlorophyll and four peridinin molecules related to each other by the local 2-fold axis (Figure 1). The closest distances between pigments belonging to the two different clusters are greater than those between pigments within a single cluster. Intracluster edge-to-edge distances between peridinins are in the range 4-11 Å, and the conjugated regions of all peridinins are in van der Waals contact with the tetrapyrrole ring of chlorophyll. The distance between the chlorophylls of the two clusters is 17.4 Å. The interchromophoric distances between units of the trimer are all much larger. H-PCP (whose structure analysis is in progress) is related to A-PCP in such a way as it possesses the same pigment stoichiometric ratio but its peptide unit is about half the size of that of A-PCP and contains only half the pigments.3,4 The almost complete homology between the two large regions of the A-PCP peptide, consisting of the four helices making the sides of each half-boat (residues 37-114 and 200-276 respectively), and the large homology of these protein regions with the analogous one of the H-PCP peptide (residues 40-108)4 suggest a very similar structure of the latter in relation to the former. The overall identity of the H-PCP monomer with that of the N and C terminal domains of A-PCP is ∼90%. This view is supported by the great similarity of the optical properties (absorption, CD, and T-S spectra) of the two proteins.2 The absorption spectra of A-PCP and H-PCP (Figure 2) consist of an intense absorption at 450-550 nm and a small band at 670 nm. The short-wavelength region is due to the carotenoid and to the chlorophyll Soret bands which overlap at the short-wavelength side. A vibrational progression is evident, similar to that present in the spectrum of peridinin in ethanol

Carbonera et al.

Figure 1. Scheme of the chromophore clusters in H-PCP (above) and A-PCP (below). Peridinins are shown without the saturated heads. Chlorophylls are shown without the phityl chain. A scheme of the peptide chain is shown below each cluster with omologous regions indicated with solid straight lines. Peridinin labels are as in ref 1.

Figure 2. Low-temperature (77 K) absorption spectra of A-PCP and H-PCP (experimental conditions as in ref 2). Insert: Low-temperature (77 K) peridinin absorption spectrum in ethanol (from ref 20) and simulation (see text). Solid line: experiment. Dashed line: simulation.

(insert in Figure 2). The long-wavelength region is due to the Qy chlorophyll band. There is no evidence of significant band narrowing or of additional components in the low-temperature spectra.2 The assignment of the absorption features is possible on the basis of the comparison with the peridinin spectrum in ethanol. The maxima at 526 and 491 correspond to the 0-0 and 0-1 components of a vibrational progression which shows up to four components in the peridinin solution spectrum. The features at shorter wavelengths overlap with the chlorophyll Soret transition, which peaks at 440 nm. As one can see, the PCP spectrum in the peridinin absorption region is only slightly wider than the monomer spectrum and the regularity of the vibrational progression is less evident.

Spectra of Peridinin-Chlorophyll-Protein Complexes

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The CD spectra of the two proteins exhibit a distinctive, seemingly conservative spectrum in the short-wavelength absorption region (negative at long wavelength) and a negative rotational band at the place of the chlorophyll Qy absorption. At low temperatures, the CD spectra reveal a feature in the form of a distinct shoulder at 510 nm. The absorption maximum in the Soret region corresponds rather well to a characteristic hole in the CD spectra.2 The objective of the present investigation is to interpret quantitatively the spectroscopic properties of the PCP proteins using the three-dimensional structure of A-PCP derived from X-ray crystallography and a suitable simple model of excitedstate energy coupling among the single set of eight peridinin and two chlorophyll molecules, belonging to the monomeric unit of the protein trimer. While our paper was in preparation, a study by Pilch and Pawlikowski5 came to our attention where the authors calculate CD and absorption spectra of H-PCP according to an exciton model similar to the one that will be described below. However, these authors do not compare their results with the resolved crystal structure of A-PCP, do not discuss the relationships of the latter with the structure of H-PCP, and neglect in their model the peridinin-chorophyll interactions that will be shown to be essential in order to rationalize the spectra and are of extreme relevance to the antenna function of these complexes. Theoretical Model Various theoretical approaches to excited-state energy coupling in natural photosynthetic systems have been discussed in the past6-8 and more recently have been reutilized and reviewed.9,10 We shall use essentially a model that has been again recently employed by Sauer et al.11 to discuss the problem of the LH2 bacteriochlorophyll-protein complex. Some additions have been made to the model that were necessary in order to take into account the strong vibronic character of the PCP spectra, a feature that is not important, for example, in the LH2 study. First, two different chemical species have to be included; second, the model must also consider the vibronic interactions due to the presence of an outstanding vibrational progression in the spectrum of peridinin; third, the Soret transitions of the chlorophyll must be included owing to their closeness in energy with the carotenoids transition. In fact, if we limit ourselves to the interpretation of the high-energy region of the spectrum (500-450 nm), the Qy and Qx chlorophyll transitions may safely be neglected in the interaction calculation. The vibrational structure of the band must be taken into account in the calculation as the transition dipole has to be considered partitioned among the different components of the progression according to their Franck-Condon factors. The analysis of this problem and the correct procedures to be followed in the calculations have been discussed in the pioneering days of optical molecular spectroscopy by Moffitt,12 Simpson,13 and others. The individual molecules have vibronic eigenstates that are perturbed by interchromophore interactions. The Hamiltonian for the assembly of N molecules is given by

H)

HK + V ∑ K

(1)

where HK are the local Hamiltonians, which can be different from the isolated molecule Hamiltonians, and V is the interchromophore potential. In the approximation where only one excited state (φ′K) for the Kth chromophore is considered, the excited electronic states of the unperturbed Hamiltonian are

given as

ψK ) φ1...φ′K...φN

(2)

while the vibronic states are

ψKV ) φ1χ(1)00...φ′Kχ(K)1V...φNχ(N)00

(3)

where χ(K)eV is the Vth vibrational state of the eth electronic state of the Kth molecule. The Hamiltonian matrix elements are, therefore, given by

〈ψKV|H|ψK′V′〉 ) (νK + Vν0(K))δKK′δVV′ + VKK′SKV SK′V′

(4)

where νK and ν0(K) are, respectively, the electronic and vibrational frequencies of the Kth molecule, VKK′ is the electrostatic interaction between the transition dipole moments of two distinct molecules (VKK ) 0), and

SKV2 ) |〈χ(K)00|χ(K)1V〉|2

(5)

is the Franck-Condon factor of the Vth vibrational state. Peridinin, as a typical carotenoid, possesses two low-lying electronic excited states (S1 and S2) of which only the higher is connected to the ground state (S0) by a dipole-allowed transition. The latter (S2) is therefore the only peridinin state considered in the calculations. The excited state is further divided into a progression of vibrational states whose energy intervals are determined from the known peridinin absorption spectrum. In Figure 2, the room-temperature peridinin spectrum is simulated by a linear combination of four Gaussians

I(ν) )

∑i ai exp[-[(ν - νi)/δ]2]

(6)

with the same line width (δ) of 850 cm-1, separated by equal intervals (∆νi) of 1360 cm-1 and coefficients (ai) equal to 0.97, 1.0, 0.68, and 0.44. For the chlorophyll a molecule, we consider only the Soret excited states. The Soret region of chlorophyll a in ether shows an intense peak at 428 nm accompanied by a satellite band at 409 nm.14 The main peak is assigned to a doubly degenerate Bx, By transition and the hump at higher energies to a transition of uncertain assignments, on the basis of molecular orbital calculations.15 We will neglect the latter considering that its energy is larger by 1450 cm-1 with respect to the upper limit of the region (23 000-17 000 cm-1) than we are considering. For the same reason we will not include in the calculation the 0-0 Qy transition lying at 15 120 cm-1. The complete vibronic set of the Qx transition and the upper vibronic components of the Qy transition are also not included because of their very small intensity. Using the above assumptions and provided necessary parameters, the Hamiltonian is diagonalized and the eigenvalues and eigenfunctions for the excitonic states are determined. By using the excitonic wave functions and the values of the electric dipole transition moments, which are among the necessary parameters for the diagonalization, one calculates the new resulting transition dipoles and the excitonic absorption spectrum. Rotational strengths can also be calculated from the transition moments and the position and orientation of the chromophores. To rely as little as possible on fitted parameters, we take the zero-order transition dipoles from the solution spectra data. The value for the transition moment of the peridinin-allowed transition is taken as 12 D, with the direction along the long

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Carbonera et al.

molecular axis.16 For chlorophyll a Bx and By transition moments, we accept the analysis by Weiss15 and use a value of about 9 D, which is indicated by the experimental intensity of the degenerate Bx and By transitions. From an analysis of the fluorescence polarization data, the intensity of the overlapped transitions results largely from the Bx transition.15 The dipole direction of the latter is that between the two nitrogen atoms of rings II and IV in II.17 The quantitative partition of intensity among Bx and By transitions is, however, uncertain from the polarization experiments; hence, it will be treated as an adjustable parameter in refining the calculations. The coordinates used to define the positions of individual atoms contain all the knowledge required to describe all details of the interchromophore distances and the chromophore orientations and are obtained from the crystallographic refinement. The pairwise potential energies (VKK′) could be calculated using the simple point dipole approximation, which would avoid the necessity of assuming a charge distribution on the molecules. This approach can produce serious errors if the interchromophore distances are not sufficiently large relative to the chromophore dimensions. In the case of the PCP clusters, interchromophore distances are often much smaller than the overall dimension of even the smaller conjugated part of the chromophores where the electronic excitation is localized. It is therefore imperative to use an alternative approach that distributes the transition moment over the spatial region of the electronic orbitals involved. We then adopted the following models for the two kinds of chromophore. For peridinin we used ground- and excited-state π-electron Hu¨ckel wave functions to calculate a set of point monopoles to be assigned to each atom of the conjugated part of the molecule. These values reflect an effective change in charge density at each atom involved when the molecule goes from the ground state to the excited state, and they serve to distribute the electrical interactions over the peridinin chain. Some authors11 split the p orbital associated with each atom contributing to the π orbitals into two parts, above and below the plane of the conjugated system, and assign half of the charge to a monopole above and half below the plane. In a number of test calculations (not shown) performed on the PCP pigment cluster, we never found any difference using the two procedures. All calculations were subsequently done with unsplit monopoles. For the chlorophyll Bx and By transitions, the approximation we used is more drastic because the detailed transition monopole distribution over the tetrapyrrol ring in the Bx and By states is not easy to calculate with simple methods owing to the necessity of including configuration interaction in the computations. We then decided to simulate the two transition moments simply by putting two opposite charges onto the two corresponding couples of nitrogen atoms defining the x and y directions, respectively. The value of the charge is a variable parameter. In such a way, we again overcome the point dipole approximation and may also consider the effect of the approximation on the results by assuming a number of distributions of the charges. We again checked by representative test calculations (not shown) that for different distributions giving the same value of the total dipole moment, the final results were not significantly different. The nondiagonal interaction matrix elements (VKK′) are calculated as the sum of the Coulomb interactions of all the monopoles. Thus,

VKK′ )

∑ ∑FKnFK′m/|(rKn - rK′m)| n∈K m∈K′

(7)

where  is the dielectric constant and FKn is the monopole at atom n of the transition dipole of molecule K and the condition K * K′ must hold. The interaction energy is then scaled by the factors necessary to reproduce the dipole strenghts (dK, dK′) of the two connected unperturbed vibronic transitions. The dielectric constant relative to that of the medium is taken as 1 both for peridinin and chlorophyll transitions, in consideration of the use of “experimental” quantities for the transition moments. VKK′ are inserted into eq 4, and the Franck-Condon factors are taken as proportional to the intensity of the vibrational component. In this way, the exciton interaction is correctly weighted among the different vibrational components.12,13 The Hamiltonian matrix on the basis of the vibronic states (|ψKV>) is diagonalized numerically, and the set of eigenvalues (νJ) and eigenvectors

|ΨJ> )

∑ |ψKV>CKV,J

(8)

KV

is obtained. Then the stick absorption and CD spectra are simulated by computing for each excitonic transition (νJ) the dipole strength (DJ) and the rotational strength (RJ) by the means of the well-known expressions18,19

DJ ) 〈Ψ0|d|ΨJ〉‚〈ΨJ|d|Ψ0〉 )

∑ ∑ {dK‚dL}CKV,JCLw,JSKVSLw KV Lw

(9)

RJ ) Im 〈Ψ0|d|ΨJ〉‚〈ΨJ|m|Ψ0〉 )

∑ ∑ {dK‚(rK - rL) × dL}CKV,JCLw,JSKVSLw KV Lw

(π/λ)

(10)

The stick spectra are then completed with Gaussian forms in order to simulate the true inhomogeneously broadened spectra. The band shapes of the absorption and CD spectra predicted by this theoretical model critically depend on the relative strength of the energy parameters entering in the Hamiltonian equation (1). For a degenerate cluster, it is possible to distinguish two limiting situations: in the strong coupling limit, the electrostatic interaction (|V|) between the molecular transition dipoles is much larger than the vibrational progression energy (ν0), while the weak coupling limit is realized in the opposite case. In the intermediate cases, the band shapes are to be computed by solving numerically the eigenvalue equation for the complete vibronic Hamiltonian, but in the limit cases, approximate solutions can be obtained by a perturbative procedure. In the strong coupling regime, the overall band shape can be approximated by convoluting the pure electronic transitions with the monomer vibrational progression. On the other hand, when |V| is small with respect to ν0, the different vibronic transitions overlap in a spectral region of the order of the vibrational bandwidth. In the latter case, the different molecular pairs of a cluster of interacting chromophores contribute to the overall spectral intensity in an additive way. Results We first calculated the Hu¨ckel molecular orbitals of the peridinin molecule in order to get a realistic picture of charge distribution changes following the electronic transition. The S0S2 transition of carotenoids is assigned, as is well-known, to the HOMO-LUMO π-electron transition. To get the molecular orbitals, we used different sets of Hu¨ckel parameters, chosen in the usual ranges, and we verified that the differences were always negligible as far as the simulation of the optical spectra was concerned. In fact, even a simple linear polyene model of

Spectra of Peridinin-Chlorophyll-Protein Complexes

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TABLE 1: Hu1 ckela HOMO-LUMO Transition Monopoles for the Conjugated Part of the Peridinin Moleculeb 7

8

9

11

12

13

14

15

16

17

18

19

20

21

22

23

+0.16

-0.01

+0.15

-0.02

+0.13

-0.05

+0.11

-0.08

+0.08

-0.11

+0.05

-0.13

+0.02

-0.15

+0.01

-0.16

a

Parameters: R ) 0; β ) 1; atoms O3, O4, C10, neglected. b Atomic numeration in first row, from ref 1.

16 conjugated carbon atoms gave similar results to those for peridinin, and all calcutations were finally performed in this way. Table 1 shows the atomic transition monopoles obtained from the Hu¨ckel calculation. The shifts of transition frequency in going from the solvent, where the absorption spectrum of the single molecules is known, to the specific protein medium must be evaluated as a set of input parameters. We start from the assumption that the shift experienced by any transition is independent of the specific position of the molecule in the complex; thus, we will have a common shift for all eight peridinin transitions and another common shift for the degenerate B bands of the two chlorophylls. The upper state vibrational frequency of peridinin is taken, as already noted, as equal to that of the monomer (1360 cm-1). The calculations were made in steps on assemblies of different portions of the eight peridinin-two chlorophyll double cluster with the purpose of discovering the relevant interactions with relation to the spectral features. The sequence of small clusters was the following: (a) all six different pairs of peridinin molecules which are contained in one cluster and all four peridinin-chlorophyll pairs belonging to the same cluster; (b) all four possible groups of three peridinin and one chlorophyll molecules belonging to the same cluster; (c) the full cluster of four peridinin and one chlorophyll molecule; (d) the complete double cluster of eight peridinin and two chlorophyll molecules belonging to the peptide monomer. The values of the transition moments and frequencies which were used in these partial calculations are dper ) 11.5 D and dchl ) 9.2 D and νper ) 18 800 cm-1 and νchl ) 22 900 cm-1. For chlorophyll, the cumulative transition moment intensity for the two degenerate Soret Bx and By bands has been taken from ref 14 and was assigned completely to the Bx transition. The smaller By component is less important for the interactions and will be employed only for the complete final calculation. (a) Peridinin-Peridinin and Peridinin-Chlorophyll Pairs. The six possible peridinin pairs have mutual orientations and distances quite different from each other. Two pairs (Per1Per2) and (Per3-Per4) [see Figure 1] have the closest distances of their polyene chains of less than 4 Å. The crossing angle within each pair is about 56° ( 6° except for Per1 and Per3, which are parallel to within 5°, and for Per2 and Per4, which are perpendicular. The latter flank the chlorophyll-tetrapyrrole system on opposite sides, defining a plane that is tilted by 30° from that of the chlorophyll macrocycle. The conjugated regions of all peridinins are in van der Waals contact with the tetrapyrrole ring of chlorophyll. Table 2 illustrates the calculated electronic interactions for the 10 pairs of molecules.The largest Per-Per interactions are found between pairs 1-2 and 3-4, but the remaining interactions are not negligible. Additionally, the chlorophyll interacts at relevant levels with each peridinin, except the notable case of peridinin 2. Figures 3 and 4 illustrate the CD spectra expected for the pigment pairs. The absorption spectra are not affected much by the exciton interactions (not shown) as evident also from the experimental spectra, and the CD spectra clearly retain the band structure showing peridinin vibronic components and the

TABLE 2: Electronic Interactions of Peridinin-Peridinin and Peridinin-Chlorophyll Pairsa Per-Per

1-2

1-3

1-4

2-3

2-4

3-4

int. energy angle Per-Chl Bx int. energy angle

334 52.1 1 179.5 33.1

136.5 4.9 2 47.1 11.8

167 52.8 3 254.5 37.2

180 49.0 4 270.4 82.8

91 90.2

265.75 57.7

a Assumed dipoles: dper ) 11.2 D; dchl ) 9.2 D. Energies in cm-1. Assumed transition frequencies for single molecules: νper ) 18 800 cm-1, νchl ) 22 900 cm-1.

Figure 3. Per-Per pair CD simulated spectra (see text).

Figure 4. Per-Chl pair simulated CD spectra (see text).

chlorophyll Soret band. They are clearly affected by the geometry of the pigment pairs both in sign and intensity. The pair interactions Per1-Per3 and Per2-Chl, for instance, contribute very little to the CD spectra, and this will be reflected in the complete cluster spectrum. The spectra are expected to be almost additive over the pair interactions in view of the fact that the largest possible interaction is only of the order of onefourth of the vibronic intervals in the single pigment frequencies and the weak coupling limit is a good approximation. (b) Groups of Three Peridinin and One Chlorophyll Molecules. Figure 5 illustrates the four possible 3Per-1Chl

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Carbonera et al. TABLE 3: Intercluster Interaction Energies (cm-1) cluster 2 cluster 1 Per1 Per2 Per3 Per4 Chl Bx

Per1

Per2

Per3

Per4

Chl Bx

29.5 41.3 39.4 1.7 -12.9

38.0 136.6 91.6 5.8 61.7

40.6 92.2 84.2 20.2 130.7

1.7 7.8 21.85 -10.9 -16.8

-7.6 61.3 133.3 -16.0 90.6

Figure 5. Three peridinin-one chlorophyll groups simulated CD spectra (see text).

Figure 7. “Best fit” simulation (see text) of absorption and CD spectra of A-PCP (solid lines). Experimental spectra from ref 2, superimposed as single mark curves.

TABLE 4: Final Parameters Used in the Calculationsa,b cm-1

ν, d, D Figure 6. Dotted lines: (a) 4Per-1Chl cluster simulated CD spectrum (see text); (b) 8Per-2Chl double cluster simulated CD spectrum (see text). Solid lines: (a) H-PCP experimental CD spectrum at 20 K; (b) A-PCP experimental CD spectrum at 20 K.

group calculations, showing how the different pair interactions add up to give significantly different CD spectra for the four different complexes. The additivity behavior mentioned above is clearly visualized in the CD intensities. The comparison with the experimental CD spectrum illustrates how the peridinin spectral region is rather well reproduced in its shape while the Soret chlorophyll region shows a calculated negative rotational strength, opposite to the experimental one. The corresponding absorption spectra are not shown because, as before, they are not greatly affected by the interactions to be of interest in the discussion of the incomplete clusters. (c) Cluster of Four Peridinins and One Chlorophyll. We finally come to the computation for the total 4Per-1Chl cluster, to be compared with the experimental H-PCP and A-PCP spectra. The resulting spectral simulation for the CD spectrum is shown in Figure 6a. It is quite clear that the theoretical CD spectrum reproduces the experimental features of the lowfrequency region (peridinin bands), as was already expected from the small clusters simulations, but the chlorophyll Soret region has a much too negative rotational strength. (d) Complete Double Cluster of Eight Peridinins and Two Chlorophylls. We go one more step with the calculation and examine the full dimer of eight peridinin and two chlorophyll molecules, as contained in A-PCP. It is clear from Figure 6b that the high-frequency region of the CD spectrum is now described in a much better way, meaning that intercluster peridinin-peridinin and/or peridinin-chlorophyll interactions

Per1

Per2

Per3

Per4

Chl Bx

Chl By

18 400 11.7

20 600 10.6

19 300 12.3

18 700 12.4

23 100 9.0

23 100 1.0

a The dipole moment values include also the reduction factor due to the medium dielectric constant. b Parameters not contained in this table are the same as those used in the partial calculations.

are necessary to account for all the spectral features. If we examine the intercluster VKK′ matrix elements (Table 3), we see the most relevant interactions between the pairs Per2-Per2′ and Per3-ChlBx′ of about 130 cm-1, and a few others of about 90 cm-1. These long-range interactions seem to determine the CD spectral form in the 25 000-cm-1 region. The comparison with the experimental absorption and CD spectra is already quite satisfactory for the latter as shown in Figure 6b, but a much better fit of both spectra can be obtained by small variations of some of the parameters involved. Most important in this procedure was to allow different zero-order frequencies and different transition dipoles for different peridinins as expected if the differing site effect of the protein medium is not negligible. The variations were allowed only for the intracluster differences, while the local symmetry for the two clusters was retained for the medium effect, and peridinins with the same position in each cluster were given the same zeroorder frequency and transition moment. Also, the chlorophyll By transition has been introduced, assigned to it some of the Soret region intensity but still maintaining the degeneracy with the Bx transition. Figure 7 shows the “best fit” obtained, and Table 4 gives the parameters values. Discussion The main result of this investigation is that a simple model of electronic dipole-dipole interaction among peridinin molecules and among peridinin and chlorophyll a molecules, which takes into account vibronic effects under the Franck-Condon

Spectra of Peridinin-Chlorophyll-Protein Complexes approximation, is able to reconstruct the features of absorption and CD spectra of the Amphidinium carterae PCP by using only structural and spectroscopic data provided by the recently resolved X-ray structure of the complex and by the absorption spectra of monomeric peridinin and chlorophyll a in organic solvents. An immediate general comment on the quantitative features of this result is that the old interpretation of the CD spectra of PCP systems20 as due to a quite strong peridinin-peridinin interaction (of the order of the distance between the peaks of the positive and negative rotational strengths, which amounts to more than 2000 cm-1) must be replaced by a view in which all peridinin pair interactions (except the 1-3 pair) contribute to the CD with energies of much smaller magnitude (100-300 cm-1), and the spread of the spectrum over almost 5000 cm-1 is mainly due to the outstanding vibrational progression. The detailed significance of the calculated A-PCP absorption and CD spectra may be better understood starting at first with a comparison of the spectra obtained in the calculations (both partial and complete) performed on the basis of the simple model of common transition frequency and moment for all eight peridinin molecules of the complex. The absorption spectrum has been neglected in this first part of the analysis because it appears to be much less affected by the interactions than the CD spectrum, and its consideration was postponed until the global best-fit adjustment. Once the common peridinin wavelength transition is fitted to satisfy the chromophore band shift when going from organic solvent to protein medium (∼700 cm-1 to the red for peridinin and ∼300 cm-1 in the same direction for chlorophyll a), the CD spectrum already shows some of the outstanding experimental features in the peridinin absorption region. The validity of the weak coupling limit is quite apparent from the results of the partial calculations. In the calculation on the minimal complete unit of four peridinins and one chlorophyll, the main peak and the shoulder of negative rotational strength are clearly evident and the positive region appears well described up to 21 000 cm-1, although somewhat red-shifted and with too much relative intensity compared to the experimental data. In this region, on the other hand, the effects due to the chlorophyll Soret bands are certainly present and the latter region (22 000-23 000 cm-1) is quite at variance with the experimental spectrum. It is, however, quite evident that as soon as the Chl-Chl and Chl-Per intercluster interactions are considered, the calculation produces large effects, leading to an acceptable fit. The Soret region is now positive, it shows clearly the characteristic hole near 22 500 cm-1, and the blue-side peridinin region is also better described. It may be noticed that this already acceptable spectral fit is obtained with practically no adjusted parameters (except the frequency shifts due to the medium), as the transition moments have been evaluated from literature spectra of the monomeric chromophores in organic solvents and only a common Gaussian line width has been used for each excitonic transition. Mention is in order here of the experiments on H-PCP. The peptide unit of this complex is about one-half of the A-PCP molecular weight and contains just four peridinin molecules and one chlorophyll molecule. The sequence analogies between the small H-PCP peptide and each of the two halves of the A-PCP peptide4 suggest that the H-PCP pigments cluster is structurally very similar to each of the two A-PCP clusters, related by the local 2-fold symmetry. The absorption and CD spectra obtained on H-PCP samples20 are extremely similar in shape to those obtained from A-PCP. On the basis of the comparison between the calculated CD spectra of the four peridinins-one Chl cluster

J. Phys. Chem. B, Vol. 103, No. 30, 1999 6355 and its dimer based on A-PCP structural elements, one would expect quite a different CD spectral shape for H-PCP compared with A-PCP. This is clearly not the case, the two experimental spectra being almost identical. We must conclude that, also in the case of H-PCP solutions, we are in the presence of a dimer which is formed through a highly specific noncovalent interaction of two peptide units to form a complex having the same structural characteristics as A-PCP. There is already evidence that H-PCP is a dimer in the original purification by Prezelin,21 and this has been confirmed by several authors. The molecular mass determined by size-exclusion chromatography was 3540 kD for both A-PCP and H-PCP, but on SDS-PAGE, H-PCP gave a single band of 15.5 kD compared with 32 kD for A-PCP and for another PCP obtained from Gonyaulax. In some Symbiodinium species, apoproteins of 15.5 and 32 kDa have been reported from the same isolates,22 with those 15.5 kDa being associated with PCP forms of low pI. Again, only species of ∼35 kD were observed by size-exclusion chromatography. Although the main features of the CD spectrum of PCP proteins are already quite well described by the simplified model used in the calculations for the partial chromophore groupings, it has been felt necessary to complete the simulation, on one hand, by taking care that the absorption spectral shape also is correctly reproduced and, on the other hand, by making some reasoned variations of the parameters in order to get an improved global best fit. The results of those have been shown in the last part of the Results section, and we now discuss the significance of the variations. Different transition frequencies and moments are in fact expected for each peridinin belonging to the same cluster because of their varied positions with respect to the protein; on the other hand, given the local 2-fold symmetry existing between the two clusters, the frequencies and moments have been taken to be equal for the corresponding molecules of the two clusters; for the same reason, no difference was assigned to the two chlorophyll molecules. In A-PCP, there are in fact differences also among the sites of the corresponding chromophores in the two clusters owing to the noncomplete homology of the C-terminal and N-terminal sequences of the single peptide, but one may consider them as having only higher order effects. The problem of adjusting in a rational way the frequency variations to achieve a best fit has been discussed by Pearlstein for the case of the seven bacteriochlorophyll a molecules of the well-known FMO antenna protein.9 His procedure has been followed whenever possible, and the best fitting was judged by eye in the same way. We also tried an analysis of the environment of each peridinin by searching the nearest-neighbor charged and aromatic amino acid side chains in order to uncover specific interactions as possible causes of variations in the peridinin transition frequency. However, as in the cited case of FMO, uncertainties in the degree of ionization of charged residues and the general difficulty of estimating collective, long-range electrostatic effects inside the proteins make this analysis of only limited value, and the empirical search of a fit is still the most valuable method. It may well be that experiments using the technique of persistent nonphotochemical hole burning will be helpful in a further assessment of the adjusted frequencies. The electrical dipoles assigned to each peridinin transition have also been varied within a limited range and adjusted for the best fit. This is justified on two grounds: first, the transition moments contain an implicit medium dielectric constant that can be site dependent; second, peridininchlorophyll interactions also occur through higher energy charge-transfer states. The latter may be a source of hyperchro-

6356 J. Phys. Chem. B, Vol. 103, No. 30, 1999 mic effects, and a slightly changed transition dipole may effectively describe such a situation. Line widths could also be chosen as fitting parameters, as was done by Pearlstein who, for FMO, used different ones for both absorption and CD spectra as well as for different chromophore sites. Given the arbitrariness of the choices, we preferred to use a single average line width for both types of spectra and for each chromophore and site. We note that interactions outside the minimal double A-PCP cluster of eight peridinins and two chlorophylls, appropriate if the trimeric unit found in the crystal was present in solution, were not considered. In fact, for the FMO system, such trimeric interactions are essential for describing the CD spectrum.9 In our case, there is no good, clear evidence that the trimer exists in solution concentrations used to obtain the experimental spectra, and the largest intermonomer interactions are much smaller than the 16-cm-1 one giving rise to the effect in the FMO antenna. Conclusion It appears likely that the absorption and CD spectra of both Amphidinium carterae PCP (apoprotein 32 kD) and Heterocapsa pygmaea PCP (apoprotein 15.5 kD) are understood in terms of interactions among the eight peridinin and two chlorophyll a molecules grouped in two symmetrically related clusters of four peridinins and one chlorophyll. This is a result of a treatment of the vibronic interaction which represents substantially a weak coupling limit as shown by the additivities of the pair interactions effects on the CD spectrum and as suggested by the small ratio of the largest dipole-dipole interaction to the outstanding vibrational frequency of peridinin. It is noteworthy that a quite acceptable fit is obtained with few adjustable parameters, and these are all within small ranges from quantities inferred from experiment. Further substantiation of this double cluster interaction model comes from the study of triplet-triplet energy transfer within the carotenoid chromophores described in the following paper23 in this issue.

Carbonera et al. Acknowledgment. This investigation was supported in part by Italian MURST under program BIOSTRUTT and by EC Contract No. ERB FMRX-CT98-0214 (DG 12-MZLS); both agencies are gratefully acknowledged. References and Notes (1) Hofmann, E.; Wrench, P. M.; Sharples, F. P.; Hiller R. G., Welte, W.; Diederichs, K. Science 1996, 272, 1788-1791. (2) Carbonera, D.; Giacometti, G.; Segre, U. J. Chem. Soc., Faraday Trans. 1996, 92, 989-993. (3) Song, P. S.; Koka, P.; Prezelin, B. B.; Haxo, F. T. Biochemistry 1976, 15, 4422-4427. (4) Sharples, F. P.; Wrench, P. M.; Ou, K.; Hiller, R. G. Biochim. Biophys. Acta 1996, 1276, 117-123. (5) Pilch, M.; Pawlikowski, M. J. Chem. Soc., Faraday Trans. 1998, 94, 227-232. (6) Scherz, A.; Parson, W. W. Biochim. Biophys. Acta 1984, 766, 666678. (7) Knapp, E. W.; Scherer, P. O. J.; Fischer, S. F. Biochim. Biophys. Acta 1986, 852, 295. (8) Won, Y.; Friesner, R. A. J. Phys. Chem. 1988, 92, 2208-2214. (9) Pearlstein, R. M. Photosynth. Res. 1992, 31, 213-226. (10) Pearlstein, R. M. In Chlorophylls; Scheer, H., Ed.; CRC Press: Boca Raton, FL, 1991; pp 1047-1078. (11) K.Sauer, K.; Cogdell, R. J.; Prince, S. M.; Freer, A.; Isaacs, N. W.; Scheer, H. Photochem. Photobiol. 1996, 64, 564-576. (12) Witkowski, A.; Moffitt, W. J. Chem. Phys. 1960, 33, 872-875. (13) Simpson, W. T.; Peterson, D. L. J. Chem. Phys. 1957, 26, 588593. (14) Eisner, U. P.; Linstead, R. P. J. Chem. Soc. 1955, 3749. (15) Weiss, C. J. Molec. Spectrosc. 1972, 37-80. (16) Andersson, P. O.; Gillbro, T.; Ferguson, L.; Cogdell, R. J. Photochem. Photobiol. 1991, 54, 353-360. (17) Gouterman, M. J. Mol. Spectrosc. 1961, 6, 138. (18) Barron, L. D. Molecular light scattering and Optical actiVity; Cambridge University: Cambridge, 1982. (19) Hemenger, R. P. J. Chem. Phys. 1978, 68, 1722. (20) Koka, P.; Song, P.-S. Biochim. Biophys. Acta 1977, 495, 220231. (21) Prezelin, B. B.; Haxo, F. T. Planta 1976, 128, 133-141. (22) Iglesias-Prieto, R.; Govind, N. S.; Trench, R. K. Proc. R. Soc. London, Ser. B 1991, 246, 275-283. (23) Carbonera, D.; Giacometti, G.; Segre, U.; Angerhofer, A.; Gross, U. J. Phys. Chem. 1999, following paper in this issue.