Protein Arrangement Effects on the Exciton Dynamics in the PE555

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Protein Arrangement Effects on the Exciton Dynamics in the PE555 Complex Suryanarayanan Chandrasekaran, Karunakar Reddy Pothula, and Ulrich Kleinekathöfer J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b05803 • Publication Date (Web): 07 Sep 2016 Downloaded from http://pubs.acs.org on September 7, 2016

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The Journal of Physical Chemistry

Protein Arrangement Effects on the Exciton Dynamics in the PE555 Complex Suryanarayanan Chandrasekaran, Karunakar Reddy Pothula, and Ulrich Kleinekathöfer∗ Department of Physics and Earth Sciences, Jacobs University Bremen, Campus Ring 1, 28759 Bremen, Germany E-mail: [email protected] Phone: +49 421 200 3523

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Abstract The environmental coupling of the phycobiliprotein antenna complex PE555 and its excitonic energy transfer mechanisms are studied in detail. Molecular dynamics simulations were performed followed by calculations of the vertical transition energies along the classical ground-state trajectory. To this end, the distributions of energy levels for the PE555 complex were found to be similar to those of the PE545 complex despite the clear differences in the respective protein structures. In the PE555 complex the two αβ monomers are rotated by ∼73° compared to the PE545 structure leading to a water filled channel. Moreover, the connections between the bilins, which act as pigments in these aggregates, and the protein show clear differences in the two structures. Analyzing the coupling of the individual chromophores to the protein environment, however, yielded similar spectral densities in the two protein complexes. In addition, the partial transition charges of the involved bilins have been determined in order to calculate the electronic couplings using the transition charges from electrostatic potentials (TrESP) method. For comparison purposes, the couplings have been extracted using the pointdipole approximation as well. On average the coupling values predicted by the dipole approximation are slightly larger than those from the TrESP method leading to enhanced population decay rates as tested in ensemble-averaged wave packet dynamics. Moreover, the exciton dynamics in the PE555 structure is significantly slower than in the PE545 complex due to the smaller coupling values induced by the dissimilar arrangements of the monomers.

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Introduction While photosynthetic light harvesting sustains life on earth, 1 understanding the molecular details of biological complexes might help to improve the design and efficiency of (organic) solar cells. 2,3 Besides plants and bacteria, 4 also some algae use light harvesting as their primary source of energy. Among these algae are the unicellular cryptophyte algae, which live in all kinds of aqueous habitats from marine, brackish, to freshwater. Recently the interest in the light-harvesting apparatus of these algae increased, after long-lived quantum coherence had experimentally been observed in the Phycoerythrin 545 (PE545) antenna of Rhodomonas sp. CS24 marine algae. 5,6 These experiments followed the seminal 2D experiments on the FennaMatthews-Olson (FMO) complex observing long-lived quantum coherent oscillations for the first time. 7–9 By now, electronic 2D spectra have also been obtained, for example, for the cryptophyte complexes PE555 and PC645. 10,11 In addition, four-wave mixing, transient absorption and femtosecond stimulated Raman spectroscopy experiments have been performed to record ground- and excited-state coherences in different cryptophyte proteins. 12,13 Cryptophyte algae come in different colors stemming from a remarkable range of chemical versatile pigments called bilins. 14,15 A large variety of different compositions and chromic variations exists in cryptophycean phycobilin proteins. Among them are the phycoerythrins PE545, PE555, and PE566 as well as the phycocyanins PC569, PC577, PC612, PC630 and PC645. 14,16–20 The naming is according to the position of the absorption maximum of the native protein in units of nm. All these phycobilin proteins consist of two so-called α and β subunits, i.e., four subunits in total. In the present study we focus on the phycoerythrins and more specifically on PE555 which has quite some similarities with PE545. For both complexes crystal structures exist, i.e., for PE545 from Rhodomonas sp. CS24 at 0.97 ˚ A 21 and for PE555 from Hermiselmis andersenii at 1.8 ˚ A. 10 The structure of PE545 consists of 4 subunits (A, B, C and D) forming a dimer of two αβ monomers where the β subunits contain three phycoerythrobilins (PEBs) β50/61 (PEB 50/61B, 50/61D), β82 (PEB 82B, 82D) and β158 (PEB 158B, 158D) and the α part one dihydrobiliverdin, DBV, denoted α20 3



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between PE545 and PC645 on the one side and PC612 and PE555 on the other side naturally also lead to similarities in the inter-pigment distances and thus the excitonic couplings within the respective pairs (see Tab. 2 in Ref. 10). Moreover, in case of the PE545 complex all bilins in the β subunits are PEBs and the one pigment in the α subunit is a DBV, while in case of the PE555 protein the β50/61 pigment is a DBV and the other three are PEBs. 10 A slightly more subtle difference is in the bonding pattern of the bilins to the α and the β50/61 positions of the proteins. 14,18 The pigments are singly connected to the α subunits, while doubly connected to the β50/61 position in both cases. This finding is independent of the kind of bilin connected to either the α or β50/61 positions. Furthermore, the PEBs at the two other β positions are always singly connected. A large number of theoretical studies on light-harvesting aggregates have been performed especially on the FMO complex (see, for example, Ref. 22–28). The list of investigations on cryptophyte proteins is much smaller, however. The respective calculations have so far concentrated on the PC645 and PE545 complexes. In case of PC645, absorption and fluorescence spectra were modeled based on the available structure. 29 Later on, these results on the system Hamiltonian together with an estimate of the spectral density, i.e., the coupling to the protein environment, were employed in density matrix calculations to model the excitation energy transfer. 11,30 Moreover, a semi-classical exciton transfer theory has been applied to this complex. 31 At the same time, the PE545 complex has been investigated putting a larger emphasis on the coupling between exciton transfer and environmental modes. To this end, molecular dynamics (MD) simulations have been performed on the aggregate followed by QM/MM calculations of the excitation energies including polarization effects. 32 Subsequently, possible spatial correlations were studied. 33 Furthermore, spectral densities have been determined for this complex using a combination of MD simulations and QM/MM calculations 34,35 as well as the respective exciton dynamics. 36,37 Aim of the present study is to compare the results for spectral densities and exciton dynamics of the PE555 structure with those of the similar but different PE545 complex.

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Methods As described earlier for similar systems in more detail, 23,35,38–40 the present study started with a MD simulation of the PE555 complex (PDB ID code 4LMX 10 ) solvated in TIP3P water. The AMBER parm99SB 41,42 force field was employed for the protein while the force field for the bilins were constructed using GAFF. 43 These force fields have already been employed in the case of the previous study of the PE545 complex 35 though some of them had to be slightly modified due to the different connectivities to the surrounding protein. The system was equilibrated for 12 ns at 300 K and 1 atm using NAMD. 44 Subsequently, a constant volume run of 720 ps was performed in which the atomic coordinates were stored every 2 fs. This procedure lead to a total of 360.000 stored frames. Using a larger time step between the saved frames would lead to inaccuracies in the high-frequency regime of spectral densities. 45 As previously done for the PE545 complex to which we want to compare our present results, the energy gap between the ground and first excited state of the bilins were determined along the MD trajectory. Thus, we performed a ground-state MD with non-polarizable force fields and calculated the excited state long this trajectory using the ZINDO/S-CIS approach (Zerner Intermediate Neglect of Differential Orbital method with parameters for spectroscopic properties together with the configuration interaction scheme using single excitations only). 46 Although this semi-empirical approach has its limitations, we have recently shown that its results along a trajectory compare reasonably well to TDDFT calculations. 39 In the calculations of the vertical energies every bilin is treated separately within a QM/MM approach, i.e., the environment is taken into account by including all the partial charges in the force field. To this end, we employed the ORCA code 47 which has the scheme outlined in Ref. 48 implemented. Before each QM/MM calculation, we do actually move the respective bilin into the center of the simulation box since the MD part employs periodic boundary conditions but not the QM/MM calculations. The excitonic coupling between the pigments is determined with two different approaches 6


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in the present study. As, for example, in the Förster approach describing exciton dynamics, the coupling can be assumed to be dominated by the Coulomb interaction and calculated using the point-dipole approximation (PDA). The necessary dipole moments are taken from the above described ZINDO/S-CIS calculations. To account for the charge distributions in a more detailed way, we also employed the TrEsp method (where TrEsp stands for transition charges from electrostatic potentials). 49,50 The transition densities have been determined in configuration interaction singles CIS/6-31G in vacuum using Gaussian 09 . 51 These calculations and results for the transition dipole moments are quite similar to those in Ref. 21 and also in Ref. 52 which includes environmental effects in the polarizable continuum method (PCM). Subsequently, the TrEsp charges have been extracted using version 3.3.8 of the program package Multiwfn 53 and are listed in Tab. S1. To account for environmental screening effects in the present study, we applied a constant screening factor of f = 0.69 to both PDA and TrEsp couplings. 50 One main result of the present study are spectral density calculations. These results can subsequently be employed in density matrix propagation schemes 54,55 or in ensemble averaged wave packet approaches 38,56 to determine the exciton dynamics. In the proper limit, the density matrix and ensemble averaged wave packet approaches do, of course, lead to the same results. 45 In the latter approach, the time-dependent Schrödinger equation is solved for the fluctuating Hamiltonian with the time divided into short time intervals during, which the Hamiltonian can be assumed to be constant. In the present calculations the length of the time intervals with constant Hamiltonian coincide with the time step of saving MD conformations. Assuming that these time intervals are short enough, this scheme yields the solution of the time-independent Schrödinger equation. To this end, the exciton dynamics can be determined assuming that the excitation was initially localized on one of the sites. Moreover, the calculation of this exciton dynamics was repeated many times with different starting positions along the MD trajectory and then averaged to yield an approximation of the ensemble average. This procedure is possible since the time for the exciton dynamics of

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Table 1: Transisiton dipole moments based on ZINDO/S-CIS for PDA and on CIS/6-31G for TrEsp averaged along the MD trajectory in units of Debye. site pigment ZINDO/S CIS/6-31G

1

2

3

4

5

6

7

8

PEB 20A

DBV 50/61B

PEB 82B

PEB 158B

PEB 20C

DBV 50/61D

PEB 82D

PEB 158D

10.31 9.375

13.87 12.678

10.59 9.290

10.31 9.573

10.16 9.672

13.69 11.603

10.49 9.376

10.26 9.728

as depicted in the inset. Actually, the other four pigments behave very similar, i.e., there is a splitting between the DBV and PEB DOS. This feature has already been observed in earlier studies on the PE545 complex. 32,35,37 Furthermore, the widths of the site energy DOS are very similar to those in the PE545 complex for the corresponding pigments. The average peak position of the pigments is actually not much different when comparing the PE545 and PE555 aggregates. We want to note in passing that for individual pigments, i.e., without taking excitonic couplings into account, the site energy DOS are proportional to the absorption of the individual pigments within the two-level approximation. 56 Thus, in this approximation the above statements on the DOS apply to the absorption spectra of the individual pigments as well. For example, the absorption line shape of the DBV pigments is very similar to those of the PEB bilins but shifted. For the PEB pigments this finding is consistent with the spectroscopic results 10,11 in that the energy shifts caused by the different bilin conformations are minimal. Experimentally the shift between the different bilin types is smaller than found here (see also discussion below). As described in the previous Methods section, the excitonic couplings are determined in two different ways: the PDA approach with transition dipole moments from the ZINDO/SCIS calculations and the more detailed and elaborate TrEsp scheme based in the present case on CIS/6-31G partial transition charges. Important properties concerning the coupling determinations are the transition dipole moments of the individual pigments which enter the PDA expression directly and can be constructed from the partial TrEsp charges as well. These values are given in Tab. 1. For the PDA approach, the average magnitude of the transition dipole of 11.21 D is almost identical to the experimental value of 11.25 D reported

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average 11.21 10.16



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as is also the case for electrostatic partial charges in MD simulations. The TrEsp scheme has been tested extensively in several studies, for example, recently in Refs. 58 and 59. For large distances, the PDA results converge to those of the TrEsp approach if the underlying method for the charge determination is the same. As can be seen in Fig. 3, the average peak positions for the same coupling in the two approaches lie close while the distributions are broader in case of the PDA coupling. Only for the 2-6 coupling a large discrepancy between PDA and TrEsp values are found. In this case the PDA coupling between the two bilins DBV 50/61B and DBV 50/61D is found to be six times higher than the TRESP value showing that for certain configuations the PDA approximations is rather poor. 49 Interestingly, a similar large coupling is also observed in the case of the PE545 complex. In this protein the coupling between the PEB 50/61C and PEB 50/61D is found to be 10.625 meV within the PDA approximation (see Tab. S2). No TrEsp data is yet available for that complex. In both, the PE545 and the PE555 complex, the rather high coupling values are present between the two central pigments . The average values for the couplings are shown in Tab. 2 together with the site energies. These values can, for example, be employed in a density matrix propagation describing the exciton dynamics within the single-exciton manifold. The average values of the couplings for the PE555 are clearly smaller than those in the PE545 aggregate employed in Ref. 37 for the exciton dynamics and listed for completeness in the present supplementary material. Moreover, Harrop et al. 10 predicted the excitonic coupling for the PE555 complex using the Transition Density Cube Method 60 at the CIS/cc-pvtz level. Those data are listed in Tab. S3 using the present pigment enumeration and an environmental scaling factor of f = 0.69 for a better comparison with the present results. Qualitatively, there is a large degree of agreement with our results especially on the ordering and signs of the couplings. The values do, however, vary with the findings by Harrop et al. 10 having a larger magnitude in many cases. Part of the discrepancies might stem from the fact that our values are averaged of the MD trajectory while the data by Harrop et al. 10 is based on a single structure, i.e., the crystal structure.

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Table 2: Time-averaged Hamiltonian with the site energies on the diagonal including the shifts for the DBV pigments. The upper off-diagonal triangle is given by the TrEsp coupling while the lower off-diagonal triangle shows the PDA couplings. The coupling values are given in units of meV. site 1 2 3 4 5 6 7 8

1 2.317 0.778 0.925 3.045 -0.971 -0.517 0.610 0.227

2 1.215 2.222 -3.523 1.850 -0.218 6.201 1.521 0.249

3 0.895 -3.481 2.293 0.621 -0.552 1.513 0.290 0.194

4 2.243 1.176 0.597 2.341 0.247 0.269 -0.064 0.201

5 -0.902 -0.669 -0.415 0.314 2.346 1.130 1.010 3.088

6 -0.885 1.026 1.394 0.231 1.565 2.248 -3.317 2.138

7 0.804 1.423 0.267 -0.004 0.990 -3.336 2.267 0.609

8 0.303 0.199 0.211 0.199 2.471 1.646 0.599 2.332

Spectral densities Other than the average Hamiltonian, a key ingredient for density matrix calculations is the so-called spectral density. 56 These have previously been determined for complexes like LH2, 38,56 FMO 61–63 and PE545. 34,35 To this end, one first needs to determine the autocorrelation functions Cj (t) for pigment j based on the energy gaps ∆Ej (ti ) at time steps ti . The energy gap autocorrelation function for pigment j is defined as 56 1 X ∆Ej (ti + tk )∆Ej (tk ) . Cj (ti ) = N − i k=1 N −i

(1)

To be able to properly compare the PE545 and the PE555 spectral densities, exactly the same parameters have been employed to extract the spectral densities. So the autocorrelation functions were calculated over time lengths of 2 ps. For this purpose trajectory pieces of 4 ps length are necessary. The autocorrelation functions of the 180 trajectory pieces (720 ps divided into 4 ps pieces) are averaged and an exponential cut-off function for the autocorrelation function is used with a damping range of 1 ps for each sampling. Based on these auto-correlation functions, the spectral density Jj (ω) of pigment j can be determined

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based on a normal mode analysis of the respective potential energy surfaces of the pigments. In the present study, however, we do proceed with the above described MD-based approach. As in the case of FMO and PE545, our aim is to analyze the effects of the environmental fluctuations on the spectral densities. Therefore, spectral densities have been extracted from two different QM/MM calculations. In the first case, standard QM/MM calculations are performed with the QM part constituting of the respective bilin and using the timedependent positions of the partial charges of the environmental atoms. In the second case, however, the positions of the environmental charges are kept fixed to those of the first frame of the MD trajectory, i.e., the environmental fluctuations are frozen out. A representative piece of a trajectory is shown in Fig. 4. As in the case of PE545, 35 differences between the calculations with flexible and frozen environment are hardly visible. The results for the spectral densities with fluctuating and with frozen point charges are shown in Fig. S1. As already found for the similar PE545 complex 35 with the same pigments, there is almost no difference between the spectral densities with and without environmental fluctuations. Thus, the spectral densities almost completely result from intermolecular vibrations of the pigments. 35 Certainly it is very interesting to compare the spectral densities for the bilins in the PE545 and the PE555 complexes. Here one has to keep in mind that some of the DBV and PEB bilins traded places between the two proteins. Moreover, and as discussed in the Introduction, in the PE555 bonding pattern of the bilins to the α and the β50/61 positions of the proteins 14,18 is changed. The pigment is singly connected to the α subunit, while doubly connected to the β50/61 position in both cases. The PEBs at the two other β positions are always singly connected. When comparing the bilins from the two rather similar complexes, we do compare DBVs and PEBs with each other and if possible those at the same positions. As can be seen in Fig. 5, in such a comparison the respective pairs do show very similar spectral densities. In fact, it is impossible to state if the differences are statistically significant or simply are due to finite trajectory length or insufficient equilibration of the complex. The

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Based on the above results, one could either use the average Hamiltonian together with the spectral densities or an ensemble-averaged wave packet dynamics scheme to obtain the exciton dynamics in the PE555 complex. Those two approaches do lead to the same results in certain limiting cases but do usually involve different approximations. 45 Before performing the wave packet dynamics, we have shifted the PEB and DBV pigment site energies by −1500 cm−1 and +750 cm−1 , respectively. For the exciton dynamics only the relative shift between the two bilin types actually matters. The shift is the same as already introduce in case of PE545 37 due to the inaccuracy of the ZINDO/S-CIS approach to properly reproduce optical spectra. Shown in Fig. 6 are the wave packet dynamics for an exciton, which is initially located at one of the eight pigments. All eight different cases are actually displayed. The dynamics is shown up to a time of 6 ps at which the population has considerably relaxed but equilibrium is not reached yet. At the same time, we need to mention that the employed scheme of ensemble-averaged wave packet dynamics includes an implicit high-temperature limit, which leads to an equal population of 0.125 for all 8 sites at equilibrium which is non-physical by itself. It is evident that the open structure of PE555 leads to smaller couplings compared to PE545. For example, using the PDA approximation and comparing Tabs. 2 and S2 one finds that for the case of PE545 ten couplings are equal to or larger in absolute value than 2 meV while the same count for the PE555 complex leads to only five couplings of this size. Therefore, larger times are needed in the PE555 complex to reach the thermal equilibrium. As can be seen in Fig. 6 in case of PE555 this time is larger than 6 ps while in the PE545 complex this value is of the order of 2 ps. 37 In the present case, the population dynamics based on the PDA couplings reaches equilibrium faster due to the slightly larger coupling values given in Tab. 2. Using the PDA coupling both DBV pigments reach the equilibrium state on a similar time scale which is shorter that those of the PEB bilins. Because of smaller coupling values in the TrEsp approach, however, some couplings are smaller and the DBV 50/61B pigment shows a larger decay time. The relatively short decay times of

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the DBV pigments is mots likely due to their central location within the protein structure. Chromophores PEB 158B and PEB 158 D have the largest decay times which goes well beyond 6 ps. For some bilins like PEB 82B the populations decays simultaneously to all other pigments while for pigments like DBV 50/61B or PEB 82D the excitation first decays mainly to one other molecule before than spreading onto all pigments.

Discussion and Conclusions While the PE545 complex has been studied to some extend, 32,33,35,37,52,65–67 much less is known about the similar but different aggregate PE555. 10 The PE545 dimer is in what has been called a “closed” form, in which the two central β50/61 chromophores are in physical contact. 10 In the structure of the PE555, however, the αβ dimer is rotated by ∼73° compared to the closed form and is in a so-called “open” conformation. This leads to a water-filled channel, which separates the central β50/61 chromophores. As has been shown previously for PE545 and confirmed here for PE555, the site energy fluctuations are quite insensitive to the external fluctuation leading to distributions of the site energies and to spectral densities which are quite similar in the two complexes. This finding also leads to the fact that the spectral densities of the individual pigments are quite comparable when taking into account that some of the DBV bilins have traded placed with PEB chromophores. At the same time one has to keep in mind that with the present approach one can only determine the spectral density. In order to get hold on slower (quasi-)static disorder one would have to perform much longer simulations. Likely a coarse-grained approach would have to be employed to get access to longer time scale. So far, static disorder is usually added in a semi-empirical fashion. 68 The different spatial arrangements of the pigments in the open structure PE555 and the closed structure PE545 leads, however, to altered distances and in turn changed coupling values. Several couplings are smaller in the PE555 than in the PE545 complex. A clear

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consequence of this finding is the much slower relaxation dynamics in the PE555 complex with more than 6 ps compared to 2-3 ps in the PE545 aggregate. Interestingly, this change in dynamics does affects all bilins in a rather similar way and not only, for example, the central β50/61 chromophore pair. An important difference between the PE545 and the PE555 complexes is the fact the energetically lowest-lying pigments, i.e., the DBVs, are located differently in the respective proteins. Whereas in PE545 the DBVs are at peripheral sites, which could facilitate energy transfer to other proteins after relaxation inside one complex, in the PE555 the location of the DBVs in the center of the complex (although in an ”open” form) could actually make inter-protein transfer more difficult. Inspecting Tab. 2, however, one can observe that the site energies of the two peripheral bilins PEB 82B/D are close in average energy to those of the DBV pigments in the PE555 complex. Note that this fact is only true after the shift between the two types of bilins was introduced in order to roughly reproduce the experimental absorption spectrum. Thus, a significant part of the excitation energy might actually stay at the peripheral PEB 82B/D bilins especially when one keeps in mind that due to the large site energy fluctuations the locations of the excitons are rather flexible. Beyond the presented analysis, the current data allows for extended calculations based on the time-averaged Hamiltonian, the spectral densities and/or the time-dependent Hamiltonian. Since the spectral densities are almost completely independent from the environmental fluctuation of the individual chromophore as already discussed in more detail elsewhere, 35,37 these could be employed for other complexes involving the same pigments as well. The couplings, however, will have to be recomputed for each complex individually though for that purpose a calculation based on the crystal structure might be sufficient. The dynamical simulations, so far have been proven to be quite insensitive to the fluctuations in the couplings.

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Supporting Information Available Supporting tables and figures on TrEsp charges, excitonic couplings and spectral density comparisons.

This material is available free of charge via the Internet at http://pubs.

acs.org/.

Acknowledgements We are thankful to Mortaza Aghtar for fruitful discussions. This work has been supported by grant KL 1299/12-1 of the Deutsche Forschungsgemeinschaft (DFG) and by the Deutscher Akademischer Austausch Dienst (DAAD).

References (1) Blankenship, R. E. Molecular Mechanisms of Photosynthesis; Blackwell Science, 2008. (2) Blankenship, R. E.; Tiede, D. M.; Barber, J.; Brudvig, G. W.; Fleming, G.; Ghirardi, M.; Gunner, M. R.; Junge, W.; Kramer, D. M.; Melis, A. et al. Comparing Photosynthetic and Photovoltaic Efficiencies and Recognizing the Potential for Improvement. Science 2011, 332, 805–809. (3) Scholes, G. D.; Fleming, G. R.; Olaya Castro, A.; van Grondelle, R. Lessons from Nature About Solar Light Harvesting. Nat. Chem. 2011, 3, 763–764. (4) Hu, X.; Ritz, T.; Damjanović, A.; Autenrieth, F.; Schulten, K. Photosynthetic Apparatus of Purple Bacteria. Q. Rev. Biophys. 2002, 35, 1–62. (5) Collini, E.; Wong, C. Y.; Wilk, K. E.; Curmi, P. M. G.; Brumer, P.; Scholes, G. D. Coherently Wired Light-harvesting in Photosynthetic Marine Algae at Ambient Temperature. Nature 2010, 463, 644–647.

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Graphical TOC Entry

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Protein Arrangement Effects on the Exciton Dynamics in the PE555

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