Letter pubs.acs.org/JPCL
Molecular Level Design Principle behind Optimal Sizes of Photosynthetic LH2 Complex: Taming Disorder through Cooperation of Hydrogen Bonding and Quantum Delocalization Seogjoo Jang,* Eva Rivera, and Daniel Montemayor Department of Chemistry and Biochemistry, Queens College and the Graduate Center, City University of New York, 65-30 Kissena Boulevard, Flushing, New York 11367-1597, United States S Supporting Information *
ABSTRACT: The light harvesting 2 (LH2) antenna complex from purple photosynthetic bacteria is an efficient natural excitation energy carrier with well-known symmetric structure, but the molecular level design principle governing its structure−function relationship is unknown. Our all-atomistic simulations of nonnatural analogues of LH2 as well as those of a natural LH2 suggest that nonnatural sizes of LH2-like complexes could be built. However, stable and consistent hydrogen bonding (HB) between bacteriochlorophyll and the protein is shown to be possible only near naturally occurring sizes, leading to significantly smaller disorder than for nonnatural ones. Extensive quantum calculations of intercomplex exciton transfer dynamics, sampled for a large set of disorder, reveal that taming the negative effect of disorder through a reliable HB as well as quantum delocalization of the exciton is a critical mechanism that makes LH2 highly functional, which also explains why the natural sizes of LH2 are indeed optimal.
P
speculative suggestions without solid molecular-level basis due to the neglect of important physical features or the disorder that are known to be significant.11−13,20−22 In addition, no theoretical explanation is available regarding the physical stability of LH2-type complexes with nonnatural fold symmetries, for which only limited experimental evidence exists.23 Thus, the first question to be answered is whether nonnatural complexes can indeed be built and remain stable. We set out to investigate this issue through construction of all atomistic in silico models. LH2 is a cylindrically arranged membrane protein, where each symmetry unit (protomer) contains three bacteriochlorophylls (BChls) and two parallel apoprotein helices (α and β).1,11−13 Two BChls constituting the 850 nm band (B850) of LH2 are ligated to α and β helices, near the periplasmic ends, and are called α-BChl and β-BChl, respectively. The third BChl constituting the 800 nm band (B800) is ligated to the cytoplasmic end of the α-helix and located between two neighboring β helices. We chose the X-ray crystal structure of Rps. acidophila (pdb code 1NKZ),15 which has nine-fold symmetry (N = 9), as the template and constructed an allatomistic model for a native LH2 in membrane employing wellestablished computational methods.24,25 (See the Supporting Information (SI) for details.) Using the protomer of this as a building block, for the first time to the best of our knowledge, we have also constructed nonnatural models with N = 5−8 and
hotosynthetic organisms can achieve near-perfect quantum efficiency under an optimal condition.1 This is extraordinary because it typically requires electronic excitations to travel 100 nm length scale distances through rugged, fragile, and dynamic membrane protein environments. To what extent quantum coherence contributes to such superb capability remains controversial.2−6 Recent theoretical investigations7−10 suggest that photosynthetic light-harvesting systems have been optimized for efficient and robust energy transfer. However, detailed molecular level factors enabling such optimization remain poorly understood. A prominent example illustrating this status of matter is the photosynthetic unit (PSU) of purple bacteria,11 which attracts special attention due to its high organizational symmetry1,11−13 and potential as a template for biomimetic systems. The PSU contains only two types of antenna complexes called light harvesting 1 (LH1) and light harvesting 2 (LH2) with known X-ray crystal structures.14−16 Of these, LH2 serves as the major initiator and carrier of the excitation energy and is known to have particular sizes with only 8−10-fold symmetries,11,13,17 which is peculiar considering that membrane proteins of various sizes and fold symmetries can be found in nature. This raises the following fundamental question: Are such natural sizes of LH2 outcomes of simple molecular level structural constraints or an evolutionary optimization for light harvesting functionality? A thorough theoretical investigation reported in this letter elucidates the latter as the main factor but also demonstrates that molecular level structural constraints have a significant supporting role. While there have been interesting theoretical studies intended to explain the physics behind the natural sizes or fold symmetries of LH2,18,19 their conclusions remain largely © 2015 American Chemical Society
Received: January 14, 2015 Accepted: February 26, 2015 Published: February 26, 2015 928
DOI: 10.1021/acs.jpclett.5b00078 J. Phys. Chem. Lett. 2015, 6, 928−934
Letter
The Journal of Physical Chemistry Letters
Figure 1. Equilibrated structures of LH2-type complexes from 5-fold to 12-fold symmetries. Side views of α and β BChls of B850 are shown in blue and top views of BChls of B800 are shown in red.
dominant HBs throughout the MD trajectories for N = 7−12. However, for N = 5 and 6, severe angle strains render the formation of such HBs highly unfavorable. As a result, intraprotomer BChl pairs adopt nearly antiparallel configurations, whereas interprotomer pairs form sharp angles corresponding to vertices of polygonal shapes, as shown in Figure 1. We believe this is not a result specific for the sequence of the protomer of Rps. acidophila but is a general feature of all LH2s because it originates from the bulky nature of tryptophan and tyrosine, the only two major residues that can form effective HB with BChls in hydrophobic environments. From the simulation trajectories of nonnatural complexes, we have also identified an alternative HB between the acetyl group of the β-BChl and the amine group of a tryptophan in the β-helix of the same protomer, which we call HB-β′. The probability for this new HB is nonnegligible for N = 8, 11, and 12, where HBβ′ appears to compete with HB-β and creates a new source of frustration. Figure 2a shows an example where all three types of HB are realized. Considering all options, we have identified eight possible scenarios of the HB, as listed in Table 1. From the MD trajectories for each complex, we were able to estimate relevant probabilities of different HB situations by evaluating an appropriate weighting function. (See the SI for a more detailed procedure.) The resulting probabilities are listed in Table 1. It is important to note that the probability to form the natural HB (Case 6) is near perfect for N = 9, 10 but is 200 cm−1. For N = 7, the formation of at least one of the HB-α and HB-β becomes a dominant event. As a result, the blue shift in the average excitation energy is much smaller than those for N = 5, 6. Still the probabilities to break HBs remain high, resulting in a significant amount of disorder in the excitation energy of the BChl. For N ≥ 8, the probability of having no HB becomes almost zero, but the disorder for N = 8 is about twice as large as it is for N = 9 and 10 due to significant probability to break HBβ. These situations virtually disappear for N = 9 and 10 but then reemerge for N ≥ 11, resulting in increased disorder. The plots shown in Figure 2b clearly demonstrate the sensitivity of the energetics to different HB situations for different complexes. The complexes with N = 9 and 10 have the two lowest values in both average shifts and the standard deviations of the disorder in the excitation energies of BChls. The electronic couplings between BChls are relatively insensitive to the variation of HB patterns. (See the SI.) To understand the effects of structural features and the disorder on exciton dynamics, we focus our attention to the B850 unit where the major effect of the symmetry number appears and the exciton resides most of the time. We have calculated exciton-transfer rates between two neighboring B850 units separated by a center-to-center distance Rinter(N), which can be expressed as
Figure 2. (a) Example of HB patterns for 4 BChls, αn−1, βn, αn, and βn+1 (shown sideways from the top in counterclockwise order) and their HB residues. The βn+1 BChl (at the bottom) exhibits the native HB to tyrosine (in green). The βn Bchl (second from the top) is adopting an alternate HB to a tryptophan (in red). Each of αn−1 and αn BChls is hydrogen-bonded to a tryptophan (in blue). (b) Average shifts of excitation energies due to HBs (top panel) and standard deviations of corresponding distributions of excitation energies (bottom panel). Lines are for visual guidance.
with the protein. Then, the excitation energy was calculated by the time-dependent DFT (TD-DFT) method.28 For both DFT and TD-DFT, we have chosen the 6-31G(d,p) basis set and used the M06-2X functional,29 which is known to work well for HB systems. The results of calculations summarized in Table 2 suggest that the excitation energy of BChl is red-shifted by ∼0.06 eV due to the formation of stable HB, which is also consistent with the spectroscopic data on mutants lacking HB.11,30 To corroborate this estimate, we have also performed more extensive calculations utilizing different functionals for a case of β-BChl. The analysis of computational results, as detailed in SI, validates the results in Table 2 and in fact suggests that the estimate based on the M06-2X functional is a conservative one among those based on functionals of similar accuracy. By combining the estimate of 0.06 eV with the probabilities of different HB situations shown in Table 1, which were extracted from MD trajectories, it is possible to calculate the average shift in excitation energies of BChls and their standard deviations of disorder for each complex. Figure 2b shows the resulting data (see Table S5 in SI for actual data), the trends of which can be understood as follows. For N = 5 and 6, HB-α or
R inter(N ) = 2Rβ(N ) + lc
(1)
where Rβ(N) is the radius of the outer β-ring of the B850 complex or its analogue for different N (see SI) and lc is the nearest distance between the two B850 complex β-rings. Note
Table 1. Probabilities for Different Cases of HB Extracted from MD Trajectories N= case
H bonding
5
6
7
1 2 3 4 5 6 7 8
none HB-α HB-β′ HB-α,β′ HB-β HB-α,β HB-β,β′ HB-α,β,β′
0.61 0.14 0.20 0.05
0.37 0.22 0.02 0.04 0.10 0.25
0.17 0.08
0.16 0.51 0.07 0.01 930
8
9
0.15 0.01 0.14 0.01 0.69
0.01
10
11
12
0.10
0.10
0.09
0.08
0.01 0.94
0.01 0.96
0.74
0.73
0.04
0.03
0.07
0.09
DOI: 10.1021/acs.jpclett.5b00078 J. Phys. Chem. Lett. 2015, 6, 928−934
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The Journal of Physical Chemistry Letters
Figure 3. (a) Distribution of rates and the average population decay for lc = 2 nm and σ = 200 cm−1. The results for Markovian limit are shown in red dashed lines. (b) Average rates (on logarithmic scale) versus σ for different values of lc. Lines are for visual guidance. The results for Markovian limits are shown as dashed lines (T = 300 K) or dotted-dashed lines (T = 200 K).
that Rβ(N) depends on the symmetry number, N, but lc does not. On the basis of experimental data on inter-LH2 distances31,32 and the value of 2Rβ(9) = 5.5 nm obtained from the MD simulation (see SI), we estimate lc to be in the range of 2 to 3.7 nm. While calculation of inter-LH2 exciton transfer dynamics has been done before,33 the effects of distance and disorder remain poorly understood. Our method of quantum dynamical calculation is the generalized master equation for modular exciton density (GME-MED),34 which utilizes a nonMarkovian generalization of the multichromophoric Förster resonance energy transfer (MC-FRET)35 rate. The efficiency of the GME-MED makes it possible to repeat the calculation over a large number of realizations of the disorder and intercomplex distances. At the same time, it was demonstrated that34 the results of the GME-MED method can have accuracy comparable to that of the hierarchical equation of motion (HEOM) approach36 given that appropriate line shape theory is used. The same approach is used here. (See the SI for more details.) Figure 3a (upper panel) shows the distribution of effective rates (see SI for detailed procedure) extracted from an ensemble of 10 000 population dynamics for a pair of natural LH2s (N = 9) at lc = 2 nm. The ensemble was generated by a Gaussian distribution in the site excitation energy of each BChl with the standard deviation σ = 200 cm −1 , a value approximately in agreement with experimental results of typical ensemble spectroscopy.22 The distribution of rates due to the energetic disorder is surprisingly broad, spanning the range of 0.018 to 0.871 ps−1. This is consistent with the experimental observation of dispersive inter-LH2 exciton transfer kinetics at cryogenic temperature,37 where the disorder is significantly quenched. The lower panel of Figure 3a shows the average of the population dynamics. Despite the broad distribution of transfer rates, the exponential population dynamics based on the average rate, 0.241 ps−1, approximates the average population dynamics well except for a small discrepancy near the steady-state limit. The average rate is also close to an experimental estimate38 of 5 ps for inter-LH2 transfer time. We have also conducted similar calculations changing values of σ and lc. Figure 3b shows the rates averaged over 10 000
realizations of the Gaussian disorder in the excitation energy of BChl and random uniform distribution of the in-plane internal rotational angle of the second LH2. (See the SI for details.) Different values of the standard deviation, σ, and lc were tested at two temperatures, T = 300 and 200 K. As a side note, we want to clarify that examination of our results show that the averaging over the in-plane internal rotational angle of the second LH2 has negligible effects. This is because the variation of rates with the angle is substantially smaller than those due to the disorder in the site excitation energies and lc. In this sense, we find that the concept of robustness19 against rotation of LH2 does not have any significant effects once real effects of the disorder and variation of inter-LH2 distance are taken into consideration. Our assessment is also consistent with experimental data,39 which show that packing of LH2s is nonspecific with regard to the internal in-plane rotation of LH2s and does not require any specific points of contact. The monotonic decrease in average rates with the magnitude of the disorder, as shown in Figure 3, is not unusual but requires some explanation. Recent works8,9 have argued that an optimal amount of disorder is necessary to achieve the best performance. This can be true if there is a significant energy gap between the groups of donors and acceptors, which exceeds the range of the spectral density, or if the original system is structured to prevent efficient energy transfer. In these cases, the disorder can provide more favorable channels by narrowing the effective gap or by breaking unfavorable energetic/structural conditions. However, in aggregates of nearly degenerate complexes with good intercomplex electronic couplings, the disorder, in general, has negative effects because it lowers the chance of resonance and reduces the degree of quantum delocalization. This is the case for the aggregate of LH2s in the PSU and most likely for many synthetic biomimetic systems formed by self-assembly. Figure 3b suggests that the effects of the disorder are more dominant than those of temperature and the phonon dynamics of the surrounding protein environments under natural condition. This is because a qualitative change in the dependence on temperature can be seen for σ = 100 cm−1, which corresponds to about half the natural magnitude of the disorder. Comparison of GME-MED results with those based 931
DOI: 10.1021/acs.jpclett.5b00078 J. Phys. Chem. Lett. 2015, 6, 928−934
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disorder. Remarkably, the average rate remains relatively insensitive to N for both Models I and II. This is a combined effect of quantum delocalization of excitons and the disorder, which together wash away the effects of small discrepancies in structure and electronic couplings. However, our MD simulation results and the analysis of the HB pattern show that a uniform magnitude of the disorder for all values of N, as assumed in Models I and II, is not realistic. The results for Model III, which uses a realistic variation of the disorder with N due to changing HB patterns as listed in Table 3, show qualitatively different trends. The average rates for N ≤ 8 are much smaller than those for N = 9,10. The increase in the disorder for N ≥ 11 also leads to the reduction of average rates. Thus, the complexes with N = 9, 10 have the two highest interLH2 transfer rates. These results demonstrate that natural sizes of LH2 have indeed been optimized for the maximum interLH2 exciton transfer rate. The diffusion constant of the exciton through a uniformly distributed aggregate of LH2-type complexes, assuming fast intracomplex equilibration of exciton as confirmed experimentally,41 can be estimated by DN ≈ ⟨kN(ξ)⟩ξRinter(N)2, where the exact prefactor depends on the packing pattern. For the natural case (N = 9) with lc = 2 nm and σ = 200 cm−1, for which the distribution of rates are shown in Figure 3a, the corresponding value of the diffusion constant is 13.4 nm2/ps. This predicts that the exciton diffusion length during a nanosecond lifetime can be as long as 115 nm for compactly packed aggregates of LH2s, which is a remarkably long distance compared with those observed in organic photovoltaic devices. Figure 4b shows the trends of estimated diffusion constants with N. For both Models I and II, the diffusion constant increases slowly with N mainly due to size effects. For Model III, it is substantially smaller for 5 ≤ N ≤ 7, where stable HBs are predominantly not formed. This shows that the complexes with N ≤ 7 are relatively bad exciton harvesters and can be clearly ruled out. The estimated diffusion constants suggest that there may be modest advantages for having N ≥ 12. However, in reality, larger values of N can easily entail new sources of disorder and require more time for thermalization of the exciton, which can further delay inter-LH2 exciton transfer dynamics. Thus, the
on MC-FRET shows that the net effect of non-Markovian dynamics is appreciable only for σ ≤ 50 cm−1, which is even smaller. Nonetheless, the variation of the average rate due to changes in the magnitude of the disorder, within its expected natural range (σ ≈ 150−250 cm−1), is modest compared with that due to lc. This is a consequence of the quantum delocalization of excitons within the B850 unit, which reduces the effect of the disorder through exchange narrowing mechanism.40 From a design principle point of view, this should be beneficial for easy control of exciton transfer rates because purple bacteria can simply use the arrangement and density of LH2s as major control variables without changing internal structures of LH2s. This also explains experimental observation of different aggregation patterns of LH2s depending on illumination condition.23,31 The effects of structural variation and the disorder on the exciton dynamics between nonnatural complexes were examined employing three sets of model parameters. (See the SI.) Model I represents the ideal case where all complexes retain the structural and energetic features of the natural B850 of Rps. acidophila (N = 9). Model II reflects the actual equilibrated structures of Figure 1. Thus, the structural parameters were determined from the average structures of the MD simulations, whereas the magnitudes of the disorder remain the same as those in Model I. Model III retains both features of the structure and the disorder obtained from our simulations and theoretical analysis. Thus, in Model III, each complex has a different magnitude of disorder reflecting a different HB pattern, as shown in Table 3. (See the SI for details of the calculation.) Table 3. Total Standard Deviations in the Excitation Energies of BChls for Different Values of N in Model III N −1
σ (cm )
5
6
7
8
9
10
11
12
279
309
298
237
200
198
223
220
Figure 4a shows the average rates, kN = ⟨kN(ξ)⟩ξ, where ξ represents each realization of the disorder and ⟨...⟩ξ denotes averaging over the ensemble of 10 000 realizations of the
Figure 4. (a) Average inter-LH2 rates (on logarithmic scale) versus N. Open circles connected by dotted lines represent Model I, filled circles connected by dotted-dashed lines represent Model II, and squares connected by solid lines represent Model III. Blue lines and symbols are for lc = 2 nm, red ones are for lc = 2.5 nm, and green ones are for lc = 3 nm. Lines are for visual guidance. (b) Diffusion constants (on logarithmic scale) versus N. All of the conventions are the same as in panel a. 932
DOI: 10.1021/acs.jpclett.5b00078 J. Phys. Chem. Lett. 2015, 6, 928−934
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The Journal of Physical Chemistry Letters actual trends for N ≥ 11 are likely to be less favorable than those shown in Figure 4b, and the modest enhancement of the diffusion constant for N = 12 seen in Figure 4b is not expected to materialize once all factors are taken into consideration. In summary, through a combination of in silico atomistic modeling, quantum calculations of the effects of HB on electronic excited states, and quantum dynamical simulation of inter-LH2 exciton transfer dynamics, we have identified a molecular level design principle explaining particular sizes and the performance of natural LH2 antenna complexes in purple bacteria. Our results for the natural LH2 complex (N = 9) are consistent with available spectroscopic data and provide deeper insights into molecular level factors controlling the inter-LH2 exciton transfer dynamics. The increase in intra-LH2 energetic disorder was shown to result in a monotonic decrease in average inter-LH2 exciton transfer rates. However, such a decrease in the vicinity of the natural magnitudes of the energetic disorder is milder than that due to physically observable variations of inter-LH2 distances. This is because quantum delocalization of excitons within LH2 mitigates the negative effects of the disorder significantly, which, in turn, allows purple bacteria to control inter-LH2 exciton transfer rates mainly through arrangement of LH2 complexes without changing their internal structures. Comparison of average exciton transfer rates for a series of LH2-type complexes (N = 5−12), with representative structures and model parameters, clearly demonstrates an important hidden energetic role of HB. Because of structural constraints of the major molecules involved, tryptophan and tyrosine, most stable and consistent HBs with the least amount of energetic disorder can be formed for complexes with symmetry number N ≈9, 10 (and possibly 8), for which the inter-LH2 exciton transfer rates become close to the maximum. Even though the formation of nonnatural LH2-type complexes are energetically possible, relative instability of HB and the resulting increase in the disorder of excitation energies of BChls make them inefficient in relaying excitons. Thus, the results here clarify that the observed optimal size of LH2 is an outcome of purple bacteria’s design principle to tame the negative effect of the disorder down to an acceptable level through stable HB formation as well as the quantum delocalization of the exciton.
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ratory. S.J. thanks Benedetta Mennucci, Filipp Furche, Joseph Subotnik, and Qin Wu for discussion on TD-DFT calculation and Graham Fleming for helpful comments.
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(1) Blankenship, R. E. Molecular Mechansims of Photosynthesis; Blackwell Science: Oxford, 2002. (2) Engel, G. S.; Calhoun, T. R.; Read, E. L.; Ahn, T.-K.; Mancal, T.; Cheng, Y.-C.; Blankenship, R. E.; Fleming, G. R. Evidence for Wavelike Energy Transfer through Quantum Coherence in Photosynthetic Systems. Nature 2007, 446, 782−786. (3) 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. (4) Christensson, N.; Kauffmann, H.; Pullerits, T.; Mancal, T. Origin of Long-Lived Coherences in Light-Harvesting Complexes. J. Phys. Chem. B 2012, 116, 7449−7454. (5) Tiwari, V.; Peters, W. K.; Jonas, D. M. Electronic Resonance with Anti Correlated Pigment Vibrations Drives Photosynthetic Energy Transfer Outside the Adiabatic Framework. Proc. Natl. Acad. Sci. U.S.A. 2013, 110, 1203−1208. (6) Kassal, I.; Yuen-Zhou, J.; Rahimi-Keshari, S. Does Coherence Enhance Transport in Photosynthesis? J. Phys. Chem. Lett. 2013, 4, 362−367. (7) Rebentrost, P.; Mohseni, M.; Kassal, I.; Lloyd, S.; Aspuru-Guzik, A. Environment-Assisted Quantum Transport. New J. Phys. 2009, 11, 033003. (8) Caruso, F.; Chin, A. W.; Datta, A.; Huelga, S. F.; Plenio, M. B. Highly Efficient Energy Excitation Transfer in Light-Harvesting Complexes: The Fundamental Role of Noise-Assisted Transport. J. Chem. Phys. 2009, 131, 105106. (9) Wu, J. L.; Silbey, R. J.; Cao, J. General Mechanism of Optimal Energy Transfer Efficiency: A Scaling Theory of the Mean FirstPassage Time in Exciton Systems. Phys. Rev. Lett. 2013, 110, 200402. (10) Mohseni, M.; Shabani, A.; Lloyd, S.; Rabitz, H. Energy-Scales Convergence for Optimal and Robust Quantum Transport in Photosynthetic Complexes. J. Chem. Phys. 2014, 140, 035102. (11) Cogdell, R. J.; Gali, A.; Köhler, J. The Architecture and Function of the Light-Harvesting Apparatus of Purple Bacteria: From Single Molecules to in Vivo Membranes. Q. Rev. Biophys. 2006, 39, 227−324. (12) Sundstrom, V.; Pullerits, T.; vanGrondelle, R. Photosynthetic Light-Harvesting: Reconciling Dynamics and Structure of Purple Bacteria Lh2 Reveals Function of Photosynthetic Unit. J. Phys. Chem. B 1999, 103, 2327−2346. (13) Hu, X.; Ritz, T.; Damjanovic, A.; Autenrieth, F.; Schulten, K. Photosynthetic Apparatus of Purple Bacteria. Q. Rev. Biophys. 2002, 35, 1−62. (14) McDermott, G.; Prince, S. M.; Freer, A. A.; HawthornthwaiteLawless, A. M.; Paplz, M. Z.; Cogdell, R. J.; Issacs, N. W. Crystal Structure of an Integral Membrane Light-Harvesting Complex from Photosynthetic Bacteria. Nature 1995, 374, 517−521. (15) Papiz, M. Z.; Prince, S. M.; Howard, T.; Cogdell, R. J.; Isaacs, N. W. The Structure and Thermal Motion of the B800−850 LH2 Complex from Rps. Acidophila at 2.0 Å Resolution and 100 K: New Structural Features and Functionally Relevant Motions. J. Mol. Biol. 1995, 46, 1523−1538. (16) Roszak, A. W.; Howard, T. D.; Southall, J.; Gardiner, A. T.; Law, C. J.; Isaacs, N. W.; Cogdell, R. J. Crystal Structure of the RC-LH1 Core Complex from Rhodopseudomonas palustris. Science 2003, 302, 1969−1971. (17) Scheuring, S.; Rigaud, J.-L.; Sturgis, J. N. Variable LH2 Stoichiometry and Core Clustering in Native Membranes of Rhodospirillum Photometrical. J. Mol. Biol. 2004, 23, 4127−4133. (18) Tei, G.; Nakatani, M.; Ishihara, H. Starategy of Ring-Shaped Aggregates in Excitation Energy Transfer for Removing DisorderInduced Shielding. New J. Phys. 2013, 15, 063032.
ASSOCIATED CONTENT
S Supporting Information *
Detailed theoretical methods and data. This material is available free of charge via the Internet at http://pubs.acs.org.
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REFERENCES
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the Office of Basic Energy Sciences, Department of Energy (DE-SC0001393), the National Science Foundation (CHE-0846899 & CHE-1362926), and the Camille Dreyfus Teacher Scholar Award. We acknowledge computational support by the CUNY High Performance Computing Center, Queens College Center for Computational Infrastructure for the Sciences, and the Center for Functional Nanomaterials at Brookhaven National Labo933
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The Journal of Physical Chemistry Letters (19) Cleary, L.; Chen, H.; Chuang, C.; Silbey, R. J.; Cao, J. Optimal Fold Symmetry of LH2 Rings on a Photosynthetic Membrane. Proc. Natl. Acad. Sci. U.S.A. 2013, 110, 8537−8542. (20) Scholes, G. D.; Fleming, G. R. On the Mechanism of Light Harvesting in Photosynthetic Purple Bacteria: B800 to B850 Energy Transfer. J. Phys. Chem. B 2000, 104, 1854−1868. (21) Novoderezhkin, V. I.; Stuart, T. A. C.; van Grondelle, R. Dynamics of Exciton Relaxation in LH2 Antenna Probed by Multipulse Nonlinear Spectroscopy. J. Phys. Chem. A 2011, 115, 3834−3844. (22) Jang, S.; Silbey, R. J.; Kunz, R.; Hofmann, C.; Köhler, J. Is There Elliptic Distortion in the Light Harvesting Complex 2 of Purple Bacteria? J. Phys. Chem. B 2011, 115, 12947−12953. (23) Scheuring, S.; Sturgis, J. N. Atomic Force Microscopy of Bacterial Photosynthetic Apparatus: Plain Pictures of an Elaborate Machinery. Photosynth. Res. 2009, 102, 197−211. (24) Damjanović, A.; Kosztin, I.; Kleinekathöfer, U.; Schulten, K. Excitons in a Photosynthetic Light-Harvesting System: A Combined Molecular Dynamics, Quantum Chemistry, And Polaron Model Study. Phys. Rev. E 2002, 65, 031919. (25) Olbrich, C.; Kleinekathöfer, U. Time-Dependent Atomistic View on the Electronic Relaxation in Light Harvesting System II. J. Phys. Chem. B 2010, 114, 12427−12437. (26) Kohn, W.; Sham, L. J. Self Consistent Equations Including Exchange and Correlation Effects. Phys. Rev. 1965, 140, A1133− A1138. (27) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; et al. Gaussian 09, revision D.01; Gaussian, Inc.: Wallingford, CT, 2009. (28) Runge, E.; Gross, E. K. U. Density-Functional Theory for Time Dependent Systems. Phys. Rev. Lett. 1984, 52, 997−1000. (29) Zhao, Y.; Truhlar, D. G. The M06 Suite of Density Functionals for Main Group Thermochemistry, Thermochemical Kinetics, Noncovalent Interactions, Excited States, And Transition Elements: Two New Functionals and Systematic Testing of Four M06-Class Functionals and 12 Other Functionals. Theor. Chem. Acc. 2008, 120, 215−241. (30) Beekman, L. M. P.; Frese, R. N.; Fowler, G. J. S.; Picorel, R.; Cogdell, R. J.; van Stokkum, I. H. M.; Hunter, C. N.; van Grondelle, R. Characterization of the Light-Harvesting Antennas of Photosynthetic Purple Bacteria by Stark Spectroscopy. 2. Lh2 Complexes: Influence of the Protein Environment. J. Phys. Chem. B 1997, 101, 7293−7301. (31) Scheuring, S.; Sturgis, J. N. Chromatic Adaptation of Photosynthetic Membranes. Science 2005, 309, 484−487. (32) Sumino, A.; Dewa, T.; Noji, T.; Nakano, Y.; Watanabe, N.; Hildner, R.; Bosch, N.; Kohler, J.; Nango, M. Influence of Phospholipid Composition on Self-Assembly and Energy-Transfer Efficiency It Networks of Light Harvesting 2 Complexes. J. Phys. Chem. B 2013, 117, 10395−10404. (33) Strümpfer, J.; Schulten, K. The Effect of Correlated Bath Fluctuations on Exciton Transfer. J. Chem. Phys. 2011, 134, 095102. (34) Jang, S.; Hoyer, S.; Fleming, G. R.; Whaley, K. B. Generalized Master Equation with Non-Markovian Multichromophoric Föroster Resonance Energy Transfer for Modular Exciton Densities. Phys. Rev. Lett. 2014, 113, 188102. (35) Jang, S.; Newton, M. D.; Silbey, R. J. Multichromophoric Förster Resonance Energy Transfer. Phys. Rev. Lett. 2004, 92, 218301. (36) Ishizaki, A.; Fleming, G. R. Unified Treatment of Quantum Coherent and Incoherent Hopping Dynamics in Electronic Energy Transfer: Reduced Hierarchy Equation Approach. J. Chem. Phys. 2009, 130, 234111. (37) Timpmann, K.; Woodbury, N. W.; Freiberg, A. Unraveling Exciton Relaxation and Energy Transfer in LH2 Photosynthetic Antennas. J. Phys. Chem. B 2000, 104, 9769−9771. (38) Agarwal, R.; Rizvi, A. H.; Prall, B. S.; Olsen, J. D.; Hunter, C. N.; Fleming, G. R. Nature of Disorder and Inter-Complex Energy Transfer in LH2 at Room Temperature: A Three Pulse Photon Echo Peak Shift Study. J. Phys. Chem. A 2002, 106, 7573−7578.
(39) Scheuring, S.; Goncalves, R. P.; Prima, V.; Sturgis, J. N. The Photosynthetic Apparatus of Rhodopseudomonas palustris: Structures and Organization. J. Mol. Biol. 2006, 358, 83−96. (40) Jang, S.; Dempster, S. E.; Silbey, R. J. Characterization of the Static Disorder in the B850 Band of LH2. J. Phys. Chem. B 2001, 105, 6655−6665. (41) Harel, E.; Engel, G. Quantum Coherence Spectroscopy Reveals Complex Dynamics in Bacterial Light Harvesting Complex 2. Proc. Natl. Acad. Sci. U.S.A. 2012, 109, 706−711.
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DOI: 10.1021/acs.jpclett.5b00078 J. Phys. Chem. Lett. 2015, 6, 928−934
