Electromagnetic Study of the Chlorosome Antenna Complex of Chlorobium Tepidum

Electromagnetic Study of the Chlorosome Antenna Complex of Chlorobium tepidum

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Citation Valleau, Stéphanie, Semion K. Saikin, Davood Ansari-Oghol-Beig, Masoud Rostami, Hossein Mossallaei, and Alán Aspuru-Guzik. 2014. “Electromagnetic Study of the Chlorosome Antenna Complex of Chlorobium Tepidum.” ACS Nano 8 (4) (April 22): 3884–3894. doi:10.1021/nn500759k.

Published Version doi:10.1021/nn500759k

Citable link http://nrs.harvard.edu/urn-3:HUL.InstRepos:23603186

Terms of Use This article was downloaded from Harvard University’s DASH repository, and is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http:// nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of- use#OAP Electromagnetic study of the chlorosome antenna complex of Chlorobium-tepidum

Stéphanie Valleau,∗,† Semion K. Saikin,† Davood Ansari-Oghol-Beig,‡ Masoud Rostami,‡ Hossein Mossallaei,‡ and Alán Aspuru-Guzik∗,†

Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, USA, and CEM and Photonics Lab, Electrical and computer engineering department, Northeastern University, Boston, Massachusetts, USA

E-mail: [email protected]; [email protected]

Abstract indicates that the directionality of transfer is robust to structural variations while on the other hand, the Green sulfur bacteria is an iconic example of na- intensity of transfer can be tuned by structural vari- ture’s adaptation: thriving in environments of ex- ations. tremely low photon density, the bacterium ranks itself amongst the most efficient natural light- keywords: electrodynamics, chlorosome, an- harvesting organisms. The photosynthetic antenna tenna, field enhancement, spectra, classical complex of this bacterium is a self-assembled nanostructure, ≈ 60 × 150 nm, made of bacteriochlorophyll molecules. We study the system from a computational nanoscience perspective by using electrodynamic modeling with the goal of understanding its role as a nanoantenna. Three different nanostructures, built from two molec- HE life cycle of plants, photosynthetic bacteria ular packing moieties, are considered: a struc- T and algae is based on the harvesting of so- ture built of concentric cylinders of aggregated lar energy. In all of these organisms solar light is bacteriochlorophyll-d monomers, a single cylinder absorbed and processed by a photosynthetic sys- of bacteriochlorophyll-c monomers and a model tem. This unit typically consists of an aggregate e.g. for the entire chlorosome. The theoretical model of light absorbing molecules, bacteriochloro- captures both coherent and incoherent components phylls (BChls) (See Fig. 1, panel II). Photosyn- of exciton transfer. The model is employed to ex- thetic systems vary in composition and size, for tract optical spectra, concentration and depolariza- instance, their dimensions can range from tens ∼ 2 · 105 tion of electromagnetic fields within the chloro- to hundreds of nanometers with up to some, and fluxes of energy transfer for the struc- pigment molecules. Solar energy is transferred tures. The second model nanostructure shows the in these systems through molecular excitations largest field enhancement. Further, field enhance- known as excitons. Success in nature’s competi- ment is found to be more sensitive to dynamic tion for resources is crucial for the survival of pho- noise rather than structural disorder. Field depolar- totrophic organisms. Therefore, optimal efficiency ization however is similar for all structures. This of light absorption and energy transfer within the photosynthetic systems are essential characteris- ∗To whom correspondence should be addressed † tics. Harvard University Recently, much scientific effort has been de- ‡Northeastern University

1 I) NATURAL SYSTEM II) ATOMISTIC MODEL FOR THE CHLOROSOME R2 R3

O AB N N Mg x N N y HO COOR z R1 Roll structure - mutant Bacteriochlorophyll III) CLASSICAL DIPOLE MODELS - DIPOLE PACKING 20 nm a) b) c)

FMO 50 nm 12 nm 12 nm

Roll A - mutant Roll A - wild type

Figure 1: Panel I) - model of the photosynthetic units in the natural system of green sulfur bacteria - the main elements are the chlorosome, the baseplate and the FMO complexes which transfer excitons to the reaction center. Panel II): Atomistic model for the chlorosome (Ref. 2); in a) the chlorosome nanostructure consisting of two concentric rolls, roll A and B, is shown. Further, the reference system for the incoming field propagating along the x0 direction is indicated. In b) the molecular structure of a bacteriochlorophyll (BChl), the main building block of chlorosomes, is indicated. Here, the R, R1, R2 and R3 symbols represent molecular chains (not drawn for simplicity) which vary depending on the type of BChl. The grey arrow indicates the direction of the transition dipole for the first molecular optical transition. Panel III): three classical dipole models for the chlorosome nanostructure. In a) we see a slice of a single cylinder (full length ~30nm) and the molecular packing of BChl-d as obtained by Ganapathy, et al. (Ref. 2). In b) another type of packing using BChl-c molecules is shown (full length ~30nm). Finally in c) we show a slice of the model for the entire chlorosome nanostructure. This last structure is built using the packing motif of panel b). Due to the type of pigment molecules, structures b) and c) are denoted as “wild-type” structures. See Methods and Supporting Information for more details. voted to understanding the microscopic principles to the third and last element, the reaction center, which govern the efficiency of photosynthetic sys- where the exciton energy is employed in the syn- tems.1 Amongst these systems, green sulfur bacte- thesis of metabolic compounds. ria is one of the most widely studied. The photo- Similarly, in the nanostructure community, synthetic system of green sulfur bacteria consists much research has focused on the study of nano- of three main elements (See Fig. 1, panel I). The antennas.3–6 Various types of antennas have been first is the chlorosome: a large nanostructure ar- devised and studied7,8 in order to understand ray of BChl’s which functions as a light absorb- which materials and shapes are optimal to en- ing antennae. The second elements are interme- hance and direct radiation. Models for nonradia- diates (these include the baseplate and the Fenna- tive energy transfer between nanostructures have Matthews-Olson protein complex) which play the also been developed9 in an effort to answer these role of exciton bridges connecting the chlorosome questions.

2 It is interesting that nature has evolved to gener- of molecules. ate antennas in biological organisms as well. The The chlorosome antenna complexes are com- chlorosome nanostructure has dimensions of the posed of different types of BChls, namely BChl- order of hundreds of nanometers and works ex- c, BChl-d or BChl-e, with varying chemical com- actly like an antenna: it absorbs photons and trans- position according to the species in question. Be- mits them to the next subunits very efficiently. A cause of the large amount of disorder present in the question naturally arises: can energy transfer prin- natural system, the definitive structure for the com- ciples be deduced from the study of these natural plex is unknown. However, several models have systems and applied to the field of nano-antennas? been proposed.2,24–27 Recently, Ganapathy et al. 2 To begin to answer this question, in this paper, we determined the structure of a synthetic triple mu- investigate the electromagnetic properties of the tant chlorosome antennae, generated to mimic nat- chlorosome antenna complex. ural chlorosomes. This mutant structure replicated Previously, we investigated reduced models of various structural signatures of the natural chloro- this photosynthetic unit using open-quantum sys- some while, however, being less efficient in terms tem approaches coupled to ab-initio simulations. of growth rates at different light intensities respect Energy transfer was found to be a non-Markovian to the wild type chlorosome. Other experimental process10 which can be characterized by multiple efforts have been made in this direction using a timescales.11 Recently, some of us investigated a combination of NMR and X-Ray diffraction.28–30 reduced model of the entire photosynthetic system The structure by Ganapathy et al. will be the first atomistically, Ref. 12. We found energy transfer of three nanostructures which we will consider in to be robust to initial conditions and temperature. this work and their experimental findings inspire Other theoretical studies on energy transfer dy- the remaining two structures. The first structure namics as well as the spectroscopy of the antenna comprises a series of concentric cylinders of ag- complex have been carried out for small models gregated BChl-d molecules (Fig. 1 II-a and III-a). of the chlorosome structure13 using open-quantum We will consider both the case of a single cylin- system theories. Spectra were also obtained for der and of two concentric cylinders in this work. helical aggregates using the CES approximation The second system is a similar cylindrical array, and including the vibrational structure.14 In this built of BChl-c molecules rather than BChl-d (See paper, we present a new perspective: an electro- Fig. 1 III-b). This structure is obtained following dynamic study of the full chlorosome antenna. the findings of Ganapathy et al. 2 Finally we will The chlorosome antenna complex is composed consider a model for the entire chlorosome (panel of up to tens of thousands of BChls (see Fig. 1) III-c)) consisting of over 70000 BChl-c. More de- which makes it the largest of the photosyn- tail on these three structures can be found in the thetic antenna units known. This nanostructure Methods section. is thought to be the main element responsible for Using our recent algorithm to solve the elec- capturing photons at the extremely low photon tromagnetic equations,23 we efficiently compute densities of the bacteria’s environment.15,16 Quan- the induced polarization and fields of the three tum mechanical models, as employed in some of chlorosome structures. The role of different ini- the recent theoretical work on photosynthetic sys- tial excitations, i.e frequency and polarization of tems,10,11,17–21 cannot be used here due to the large the incoming field, are investigated. We also study size of the full chlorosome antenna complex. Elec- the field enhancement and field depolarization as trodynamic modeling thus provides a viable alter- a function of structural disorder and dynamical native. This approach can capture, within certain noise. Finally, we determine fluxes of energy approximations, both coherent and incoherent ex- transferred in time to acceptors located around the citation dynamics and has already been described antenna nanostructures. and employed in the simple case of a molecular dimer.22 Further, we have recently23 devised an algorithm to solve the electrodynamic equations very efficiently even in the presence of thousands

3 Results and discussion

Antenna spectra and resonances The chlorosome antennae absorbs incoming light in the visible range. The resulting spectrum shows resonances determined by the presence of molecular transitions at about 750 nm. The chloro- xy - Classical some aggregate resonances are shifted respect to 1 xy - Quantum z - Classical the pigment transitions due to the couplings be- z - Quantum tween monomers. In order to understand which re- 0.8 gions are of interest for energy transfer, we calcu- 0.6 lated the absorption and circular dichroism spectra of the structures. Due to the three-dimensional 0.4

arrangement of the dipoles in a cylindrical struc- Absorption [arb. u] ture, we expect there to be two components in 0.2 the absorption spectra, a z polarization compo- 0 nent, parallel to the main axis of the cylinder, -280 -240 -200 -160 and an in-plane xy component, orthogonal to the ∆ω [meV] a) main axis. Panel a) of Fig. 2 shows the computed absorption spectra for the roll structure III-a) of 0.8 Classical Fig. 1. The spectra were obtained using a semi- Quantum classical approach (see Methods) and using the 0.4 Fermi-Golden rule quantum approach. The spectra were broadened by adding disorder through the 0 rate Γ = 1 meV (See Eq. 1). As remarked pre- ) [arb. u] L -I viously in the literature (see e.g. Ref. 31) the R -0.4 quantum and classical spectra are simply shifted (I

(see Methods for more details). More importantly, -0.8 in both approaches we see the expected z and xy, components at about ∆ωz = −280 meV and -280 -240 -200 -160 ∆ω = [−260; −230] meV for the classical spec- ∆ω [meV] xy b) trum. A higher oscillator strength is observed for the z component. The range over which transi- Figure 2: Panel a) Absorption spectrum and its tions are observed is consistent with experiments32 components obtained using a classical electrody- though a direct comparison of the components namic approach and the quantum Fermi-Golden is not possible due to the large amount of noise rule approach. Panel b) Circular dichroism spec- present in the natural system. The CD spectra in trum (CD) obtained using the classical and quan- panel b) also follows the same trend1 as the exper- tum approaches. The spectra were broadened with imentally observed CD, Ref. 32, 33. The alter- disorder Γ = 1 meV, and the frequency axis nating negative and positive peaks in the CD spec- corresponds to the shift in energy respect to the tra are related to the orientation of the incoming monomer transition frequency. All spectra were ﬁeld respect to the helicity of the structure. These computed for structure III-a) in Fig. 1. spectra were also calculated for structure III-b) of Fig. 1 and these follow a similar pattern. The inter- and intra-molecular vibrations, interaction with the solvent, and other environmen-

1Note that the structure of Ref. 2 was chosen with opposite helicity in agreement with experimental ﬁndings.

4 tal fluctuations, generate a source of noise which also be determined by computing the field depo- needs to be taken into account when modeling larization. the system. Generally speaking, we can distin- guish between static/structural disorder and dy- Field concentration and depolarization namic noise based on the time scales of the associated fluctuations. Fluctuations related to struc- Plane wave incoming fields propagating along the tural disorder oscillate on a much longer timescale x direction (see Fig. 1 panel II-a), were used to compared to the dynamics of the system whereas study the electric field enhancement and depolar- dynamical noise fluctuations are more rapid. The ization from the dipole arrays of the chlorosome. noise source is the same for both types of disorder. Two different polarizations of the incoming field 0 In this model, one can include noise by introduc- are considered, along the y direction and along the 0 ing a molecular response function34 z direction, as shown in Fig. 1, panel II-a. The roll-A structure (Fig. 1; III-a), was em- 2 |~µ |2 ω |E~ | i,s i,s ployed to obtain the field enhancement κ = ~ χ (ω) = . (1) |E0| i,s Γ 2 2 ~ (ωi,s + i 2 ) − ω plots shown in Fig. 3. In these plots, we see the values of the scattered field calculated on a grid Here, ~µi,s is the transition dipole of the s − th orthogonal to the structure (panels a and b) and transition for the i − th molecule and ωi,s the cor- on a grid parallel to the structure (panels c and responding transition frequency. The dynamical d). By comparison of panels a) and b) we no- noise is accounted for by the rate constant, Γ, and tice a larger field enhancement when the incoming structural disorder can be included by introducing field is polarized along the z0 direction. This is ex- noise in the transition frequencies, ωi,s. Usually, pected due to the more favorable overlap with the ωi,s, is taken from a Gaussian distribution, and dipole orientations in the structure. The field en- structural disorder is characterized by the width of hancement overall is not very big in this case due the Gaussian, σ. to the large value of the noise Γ = 50 meV. We There is no straightforward way to quantify notice that the field is enhanced homogeneously in structural and dynamical noise in the localized the radial direction (panels b,d), for y0-polarized molecular basis experimentally. The sum of struc- incoming field. This trend supports the idea of ex- tural disorder, σ, and dynamic disorder, Γ, in the citon transfer in the radial direction. This feature is 2 exciton, delocalized energy basis corresponds to observed even when including structural disorder. the linewidth of the absorption spectrum. The For the z0-polarized incoming field (panels a,c), overall disorder in the localized site basis should we see enhancement radially but also at the edges be of the same order of magnitude. In this case of the structure (panel c) this suggests that exci- the linewidth is ≈ 70 meV both for the BChl- tons may be transfered between layers and at the c monomeric spectrum and for the Chlorosome edges amongst neighboring substructures. In the 35 spectrum. next section, we look at how κ varies with noise and structural disorder. Induced fields In Fig. 4, we show contour plots of the depo- . larization η = |E~ | − |E~ | |E~ | of the elec- Within the electromagnetic framework, we can ob- k ⊥ tain information on the exciton transfer proper- tric field on a horizontal grid across the structures. ties from the induced polarizations. Indeed, once Panel a) and b) indicate η computed for the roll A the nanostructure interacts with an incoming plane structure (Fig. 1; III-a) while panels c) and d) cor- wave, the induced polarizations generate fields and respond to calculations for the chlorosome model 4 thus transport can be quantified in terms of field structure with 7 · 10 molecules (Fig. 1; III-c). enhancement. The directionality of transport can In panels a) and c) the depolarization is calculated for a z0-polarized incoming field and in pan- 2The exciton basis corresponds to the basis of delocalized els b) and d) for a y0-polarized incoming field. The energy states which is obtained by diagonalizing the Hamil- depolarization, η, was also computed for the wild tonian in the localized molecular basis.

5 a) b)

c) d)

Figure 3: Panel a) Base ten logarithm of the electric field enhancement, log10 κ, calculated on a grid orthogonal to the roll structure in Fig. 1, III-a). The dynamical noise rate is Γ = 50 meV, the initial field excitation frequency is shifted by ∆ω = 0.23 eV (see Fig. 2). The polarization of the initial field is along the z0 direction. Panel b), same as panel a) but for external field polarized along the y0 direction. Panel c) same as panel a) but here field is calculated on a grid parallel to the longest axis of the roll and at a distance of r = 80 A˚from the origin. Panel d) same as panel c) but for y0-polarization.

6 a) b)

c) d) ~ ~ . ~ Figure 4: Panel a) Depolarization of electric field η = |E|k − |E|⊥ |E| calculated on a grid orthogonal to the roll structure in Fig. 1, III-a). The dynamical noise rate is Γ = 50 meV, the initial field excitation frequency is shifted by ∆ω = ω0 −ωext = 0.23 eV (See Fig. 2). The polarization of the initial field is along the z0 direction. Panel b), same as panel a) but for y0-polarization of the external field. Panels c) and d), same as a) and b) but for the wild type chlorosome model structure III-c) with ∆ω = ω0 −ωext = 0.22 eV.

7 type roll-A structure (Fig. 1; III-b) and the pattern is analogous to that shown here in panels a) and b) for structure III-a. For these two cylindrical structures, the z0-polarized incoming field is not significantly depolarized, this is probably due to the fact that the dipoles’ z-component is largest. For the third model chlorosome structure, we see in panel c) that the field gets depolarized in an interesting pattern which most likely originates 0 from the dipole packing at the edges. For the y - Γ = 0.1 meV Γ = 1 meV polarized incoming field, the depolarization pat- 5 Γ = 10 meV Γ = 25 meV tern is similar for all three structures (panels b, d) Γ = 50 meV and the field remains polarized for specific direc- ~1/r 3

) ~1/r tions, perhaps those corresponding to where other κ 0

substructures might be found. The observed depo- Log( larization patterns ensure that a photon of arbitrary polarization will be transferred to the next layer -5 following the radial direction. The observed robustness to structural variations 80 100 120 140 of the field polarization is in agreement with re- r [angstrom] cent experimental findings by Tian et al., Ref. a) 36. In this work the authors used 2D fluorescence polarization microscopy on a series of wild σ = 0 meV σ = 15 meV type chlorosomes of C-tepidum grown in homo- 5 σ = 30 meV geneous conditions. They found that all spectral σ = 60 meV ~1/r 3 properties were homogeneous independent of the ~1/r ) selected chlorosome and their results suggested κ 0

that BChl molecules must possess a distinct or- Log( ganization within the chlorosomes. A similar organization is present in our model structures and it appears that even when adding structural disor- -5 der, the overall transition dipole moment components are not significantly modified and the largest 80 100 120 140 r [angstrom] component remains along the z axis thus leading b) to the field polarization patterns we have obtained. It would be interesting to obtain a theoretical esti- Figure 5: Scaling of field enhancement κ with dy- mate of the modulation depth for each of the three namical noise, (panel a)) and structural disorder structures so as to compare to these experimental (panel b)) for the roll-A structure (Fig. 1; III-a) as a findings. function of distance r from the center of the struc- ˚ ture (rcenter = 0 A). The incoming field is polarized along the z0 direction. Scaling of field enhancement with disorder In Fig. 5 we show the scaling of the field enhancement κ as a function of distance from the center of the structure (panel III-a of Fig. 1) for different values of structural disorder and dynamical noise. In panel a) the field intensity as a function of distance is shown for different values of dynamical noise. We notice that as dynamical noise increases, the

8 1 field scaling tends to go as ∼ r , but there are dif- tors, R(t), can be obtained from the divergence P ~ ferent slopes of the scaling on shorter distances. of the pointing vector as R(t) = acc Eacc(t) · In panel b), the scaling as a function of structural d ~ dt ~pacc(t), where Eacc is the electric field at the ac- disorder σ is investigated at fixed small Γ. In this ceptor at time t and ~pacc is the induced polarization 1 case the trend of the field is ∼ r3 . It is not im- of the acceptor at time t. This approach has been mediately clear to us why a different scaling with discussed in Ref. 22. respect to r is observed in the case of dynamical In Fig. 7, panel a), we show these fluxes of en- versus structural disorder, however it is interest- ergy as a function of time, R(t), for transfer from a ing that perhaps nature may tune one or the other roll of donors (structure III-a of Fig. 1) to a dipole type of disorder to modify the intensity of energy acceptor positioned at different distances from the transferred through structural variations. The dis- center of the cylinder. The dipole acceptor is ori- tance amongst substructures has experimentally2 ented vertically along the main axis of the cylin- been determined to be rphys ∼ 2 nm. The slope of der and has transition frequency ωacc = 1.51 eV, the fields around this distance is not homogeneous in the region where the roll absorbs (see Fig. 2). as a function of Γ. In the case of structural disor- The external field which interacts with donors is der, at about rphys, we notice (Fig. 5, panel b) that polarized along the z0 direction. The energy flux a similar slope is observed with a smaller variation is normalized by the number of donor molecules in intensity respect to panel a). 2 squared, Ndonor. In these calculations, the dy- In Fig. 6, we plot the field enhancement κ at namic disorder rate Γ = 50 meV. We notice that the biological distance rphys for the two cylindri- the energy flux R(t) does not decrease monotoni- cal structures (panels III-a and III-b of Fig. 1) as cally with distance, in fact there are some distances a function of dynamical noise (panel a) and struc- more favorable for transfer. This can be explained tural disorder (panel b). It appears that dynamical by the fact that the components of the field at each noise has the strongest effect. In such large struc- distance are not the same but may rotate. This ef- tures it is more likely that the main source of dis- fect can be thought of as some type of coherence order is actually structural disorder however. This between acceptor and donor. means that overall the excitation energy transfer is We also computed the flux of energy trans- quite robust to disorder. Further, for all values of Γ fered between two concentric cylindrical struc- and σ, the enhancement is larger for the wild type tures (Structure of Fig. 1, panel II-a) for an exter- structure. This suggest that the dipole arrangement nal field polarized along the z0 direction. The re- of the wild type structure leads to higher efficiency sulting fluxes are shown in Fig. 7, panel b) for two in terms of field enhancement. This is also ob- different values of the dynamic rate constant Γ. served at the physiological distance, rphys, relevant Here, RA indicates the flux when roll-A (the roll for transport. with the smaller diameter) is the acceptor and roll- B the donor and RA indicates the opposite case. Energy flux When Γ = 50 meV, i.e. the incoherent limit, the fluxes from roll-A and B are equivalent, as ex- The main role of the chlorosome is that of trans- pected and decay within 300 fs. When the disorder mitting the collected solar energy: it is therefore is decreased, the flux is much larger and decays important to investigate how fast energy is trans- fully only after about 800 fs. Further, in this case ferred amongst these nanostructures. In our elec- the fluxes are different in each direction (from roll- trodynamic model, the energy flow can be ob- A to B and from B to A). This model however does tained from the induced fields and polarizations. not account for relaxation, therefore the estimated In particular, one defines some acceptor molecules fluxes should be considered upper bounds of the which are not initially excited by the incoming actual rates. field and some donor molecules which are excited by the incoming field and later interact with the acceptors. The rates of energy flow absorbed by the accep-

9 4 4 Roll A Roll A Roll A - wild type Roll A - wild type 2 2

0 (r~2nm)] (r~2nm)] κ κ

log[ log[ 0 -2

-4 -2 0 10 20 30 40 50 0 15 30 45 60 Γ [meV] σ [meV] a) b) Figure 6: Panel a) scaling of field enhancement κ with dynamical noise rate Γ for each structure, at a distance of rphys = 2 nm. Panel b) scaling of field with structural disorder σ for each structure, at a 0 distance of rphys = 2 nm. The incoming field is polarized along the z direction. Roll-A and Roll-A wild type, correspond to the structures in panels III-a) and b) of Fig. 1.

Conclusions radial direction and at the edges of the cylinders (depending of the incoming field polarization), We have analyzed the chlorosome antenna com- which would enable exciton transport to neighbor- plex in the green sulfur bacteria Chlorobium- ing structures and to other layers. The field de- tepidum using an electrodynamic model. Three polarization also supports transport to neighbor- structures were considered as models for the nating layers. Finally, transport has been quantified ural chlorosome complex. Each antenna structure by calculating the flux of electromagnetic energy shows robustness to structural variations. This ef- transferred between the cylindrical structure and a fect was seen in the values of the field enhance- dipole acceptor. In this case there is a specific dis- ment which is much more sensitive to noise than tance which maximizes transport. One can think to structural disorder. of it in terms of coherence amongst the donor field At the physiological distance, the minimum dis- polarization and the acceptor molecule dipole ori- tance observed for packing amongst nanostruc- entation. The timescale for the flux of energy tures, the field enhancement trend follows differ- transfer is roughly 300 fs which is an upper bound ent slopes as a function of disorder. Therefore no to the true timescale, in fact the model does not clear trend regarding variations of induced fields account for relaxation. We also computed these and polarization as a function of disorder can be fluxes of energy for transfer amongst cylindrical deduced. However, at this same distance, the wild structures and found that depending on dynamic type nanostructure antenna shows larger field en- noise, it is enhanced in the radial direction. This hancement. This suggests that the molecular pack- study opens the road to the possibility of creating ing can be tuned to maximize transport proper- antennae that mimic this type of natural system. ties. A preferential direction for transfer is ob- For instance, we could consider the idea of the served consistently for all structures for specific chlorosome outside of its natural environment: if polarizations. This suggests that this type of struc- one could devise a nanoantenna based on the structure acts as a concentrator by enhancing trans- tural arrangement of dipoles in the chlorosome, port for specific photon polarizations. This is also how efficient would it be? confirmed by the patterns of field depolarization which strongly depend on initial field polarization but not on structural variations. In particular we observe that the field is concentrated in the

10 Methods

Physical model of the chlorosome structure In this section, we describe the structures employed as models of the chlorosome in more de- tail. In both of the molecular packing motifs -4 4×10 employed to construct the chlorosome structures, r = 0.9 nm r = 1.8 nm BChl molecules are stacked in columns such that r = 5 nm r = 10 nm the oxygen from the hydroxyl, OH, group of one -4 3×10 molecule, see Fig. 1 panel II-b), binds to the Mg atom of the next molecule.37 The columns of BChl ) [eV/fs]

t molecules couple to each other through OH ··· O

R( -4 1×10 hydrogen bonds thus forming two dimensional layers (this is shown in Fig. 8). These layers are then folded to form cylinders or curved lamel- 33 0 0 100 200 300 400 500 lar structures. Two distinct types of layer fold- t [fs] ing have been proposed previously. In Ref. 2 a) the authors suggested that BChl layers are folded such that BChl columns form concentric rings.

6.0 This structure was obtained by ﬁtting the 2D nu- R ; Γ = 50 meV A clear magnetic resonance (NMR) spectra of mu- Γ RB ; = 50 meV Γ tant Chlorobium tepidum bacteria which produce RA ; = 10 meV Γ chlorosomes with BChl-d molecules. This pack- 4.0 RB ; = 10 meV ing motif was also supported by cryo-electron mi- 30

) [eV/fs] croscopy images. The ﬁrst structure we consider t

R( 2.0 (III-a in Fig. 1) comes from these studies. In con- trast, in Ref. 38 the same group of authors used a different folding pattern, where BChl columns are 0.0 parallel to the cylinder’s symmetry axis. The lat- 0 200 400 600 800 t [fs] ter structure was also supported by 2D NMR stud- b) ies of a different mutant bacteria, which is more Figure 7: Panel a) Flux of energy transferred from similar to wild-type species (the chlorosome was roll-A (Fig. 1, III-a) to a single dipole acceptor, packed with BChl-c). The choice of these cylin- z drical structures is also bolstered by recent 2D ﬂu- oriented along the direction and located at var- 36 ious distances r from the outside of the roll along orescence polarization microscopy experiments. the radial direction, here Γ = 50 meV. Panel b) We used this second type of folding to obtain Flux of energy transferred from roll-A to roll-B, the second structure, i.e III-b in Fig. 1. Finally, the layer structures are packed inside of an ellip- RB(t) and from roll-B to roll-A, RA(t) for different values of the dynamic noise constant Γ. The soidal shaped body: the chlorosome. While the incoming ﬁeld is polarized along the z0 direction. chlorosome may contain multiple rolls packed in parallel,39 here we use a different model (structure III-c in in Fig. 1) which is composed of concentric rolls.33 This concentric assembly is in-line with the cryo-EM images.30 More details on this structure are given in the Supporting information. In the electromagnetic model, each molecule is represented by a transition dipole, in particular we

11 sition s is approximately described by an electronic transition dipole ~µn,s (for the n − th molecule),34,43,44 and the frequency of the transition is taken to be ωn,s = n,s/~. The expression for the overall electric field at the n − th molecule ~ located at ~xn is the sum of the internal field Eint Figure 8: Two columns of BChl molecules linked which comes from the interactions with all other ~ together through a network of hydrogen bonds. dipoles and the external field Eext, ~ ~ ~ E(t, ~xn) = Eint(t, ~xn) + Eext(t, ~xn). (3) use the Qy transition dipole. The frequency of the 40 transition is taken to be ω0 = 1.904eV for BChl- In particular, in the case of classical dipoles this d and ω0 = 1.881eV for BChl-c as obtained ex- equation can be written as34 perimentally. The dipole intensity is taken to be µ = 5.48 D, following the values given in litera- ~ 2 X ~ E(t, ~xn) = 4πk G (~xm, ~xn)·~pn +Eext(t, ~xn). ture, e.g. Ref. 41, 42, 39. m6=n (4) Polarizability model Here, ~pn is the induced electric dipole moment at molecule n due to the electric field and the con- The system considered is an array of aggregated stant k is the magnitude of the wavevector of the BChl monomers (as shown in Fig. 1). In quantum incident light. The free-space Green’s function models, a Hamiltonian in the molecule localized tensor G includes all interactions amongst dipoles basis |ni is often used to describe this type of sys- and is directly proportional to the field at point ~x tem due to a dipole oscillating at position ~xn. It is ex- pressed as ˆ X X H0 = n |ni hn|+ Jnm (|ni hm| + |mi hn|) . n n

12 Optical properties here, Ek is the k − th eigenvalue of the Hamilto- nian given in Eq. 2 and ~µ is it’s transition dipole. Linear absorption In this case resonances in the aggregate spectrum 2 2 2 Using the formalism introduced in “Polarizability will be obtained as the roots of Ωagg,k = Ek/~ = 2 model” section, an equation for the induced elec- (ωmol +γ ˜k) . The expression given in Eq. 9 is tric dipole ~p on each molecule can be obtained as a the one used to compute the quantum absorption function of the index of refraction.34,43 In the limit spectrum shown in Fig. 2. We see that respect to of the dipole approximation, the expression for the the classical case (Eq. 8), the frequencies squared 2 molar extinction coefficient is then are shifted by γ˜k: this comes from the absence of counter rotating terms in the classical response 4πω X = − N ImA ~u ·~u , (6) function.31 In fact, in classical electromagnetics abs 3000 · ln(10)c av ij i j ij only one type of time ordering of interactions between photons and molecules is allowed. For op- ~µi with ~ui = . Here the matrix A is defined as |~µi| tical frequencies the counter-rotating term only gives a small shift, however it becomes important −1 δij for long wavelengths, for instance, in microwave Aij = + Dij , (7) χi cavities. It should be noted that the counter- rotating term is still partly included in our model with Dij = ~ui · Gij · ~uj, the term which includes through the susceptibility functions of the single dipole-dipole interactions and χi the molecular re- molecules. However, its contribution to the inter- sponse function as defined in Eq. 1. In the limit molecular interaction is not accounted for. An- of static dipole interactions, the tensor G takes the other way to see how the shift arises is by compar- 3~e~e−1 simple form Gij ≡ G (~xi, ~xj) = r3 . ison of the eigenstates of a quantum Hamiltonian To better understand where resonances occur, we with the normal modes for a set of driven coupled can look at the eigenvalues of A. For zero dy- classical oscillators. The comparison can be made namical noise rate Γ and for identical molecules after applying the Dirac mapping and realistic cou- (~µk ≡ ~µ, ωk = ωmol) we see that resonances are pling (RCA) approximation. This approach has the roots of been discussed in Ref. 45. The two approaches 2 become equivalent in the limit where the couplings 2 2 |µ˜| Ωagg,k ≡ ωmol + 2 γkωmol. (8) are small compared to the monomer transition fre- ~ quency γk ≪ ωmol. Here, γk is the k − th eigenvalue of G. We can |~µ|2 define γk =γ ˜k to get proper units of energy ~ Circular dichroism 2 2 for the coupling. Thus Ωagg,k ≡ ωmol + 2˜γkωmol. In this expression it is clear that the aggregate res- Circular dichroism is another important optical onances will be shifted respect to the molecular quantity which can help identify the correct structure of a system. It can also be obtained both clas- transition frequency ωmol and this shift will depend on the coupling between monomers, here captured sically and quantum mechanically. Following the classical approach34 of the previous sections, one by γk. Eq. 6 was employed to compute the linear absorption spectrum shown in Fig. 2. A simi- can arrive at the following expression for the molar lar approach, the CES method, has also been used ellipticity for excitonic systems14 and leads essentially to the X same equations that are used in the present work. θ = − CijImAij. (10) Now, in the quantum case, the simplest approach ij to obtain the absorption spectrum consists in ap- Here we have used the standard definition of CD, plying Fermi’s Golden rule as the difference between left polarized and right

(qtm) 4πω X 2 (ω) = |µ˜| πδ (E − ω) , (9) abs 3c k ~ k

13 polarized intensity. The matrix C is deﬁned as References

6ω2N 1. Blankenship, R. E. Molecular Mechanisms C = av (~u × ~u ) · (~x − ~x ) (11) ij c2 i j i j of Photosynthesis; World Scientific: London, 2002. in the absence of any magnetic dipoles or polarizations. Here, ~xi corresponds to the position of the 2. Ganapathy, S.; Oostergetel, G. T.; Wawrzy- i − th molecule respect to the origin. niak, P. K.; Reus, M.; Gomez Maqueo Similarly, in the quantum case one finds (see e.g. Chew, A.; Buda, F.; Boekema, E. J.; Ref. 46) that in the exciton basis, i.e. the basis Bryant, D. A.; Holzwarth, A. R.; de Groot, H. in which the Hamiltonian of Eq. 2 is diagonal, the J. M. Alternating Syn-Anti Bacteriochloro- rotation strength associated with the exciton level phylls Form Concentric Helical Nanotubes in J is Chlorosomes. Proc. Natl. Acad. Sci. 2009, 106 2 , 8525–8530. 6ω Nav X R = − σ σ (~u × ~u ) · (~x − ~x ) . J c2 Ji Jk i j i j 3. Devilez, A.; Stout, B.; Bonod, N. Compact ik (12) Metallo-Dielectric Optical Antenna for Ul- The coefficients σ are the coefficients of the ma- tra Directional and Enhanced Radiative Emis- trix S which diagonalizes the Hamiltonian of the sion. ACS nano 2010, 4, 3390–3396. system. Eq. 10 and eq. 12 are used in this work to 4. King, N. S.; Knight, M. W.; Large, N.; Good- compute the circular dichroism spectra shown in man, A. M.; Nordlander, P.; Halas, N. J. Ori- Fig. 2. enting Nanoantennas in Three Dimensions To Control Light Scattering Across a Dielectric Supporting Information Available: A figure interface. Nano Lett. 2013, 13, 5997–6001. and detailed description of the third model struc- 5. Novotny, L.; van Hulst, N. Antennas for Light. ture for the chlorosome are included in the sup- Nat. Photonics 2011, 5, 83–90. porting information. This material is available free of charge via the Internet at http://pubs.acs.org. 6. Knight, M. W.; Sobhani, H.; Nordlander, P.; Halas, N. J. Photodetection with Active Opti- Acknowledgments cal Antennas. Science 2011, 332, 702–704. 7. Knight, M. W.; Liu, L.; Wang, Y.; Brown, L.; The authors would like to thank A. Eisfeld for Mukherjee, S.; King, N. S.; Everitt, H. O.; useful discussions. S. V. acknowledges support Nordlander, P.; Halas, N. J. Aluminum Plas- from the Center for Excitonics, an Energy Fron- monic Nanoantennas. Nano Lett. 2012, 12, tier Research Center funded by the U.S. Depart- 6000–6004. ment of Energy, Office of Science and Office of Basic Energy Sciences under Award Number DE- 8. Schuller, J.; Barnard, S. E.; Cai, W.; SC0001088 as well as support from the Defense Jun, Y. C.; White, J. S.; Brongersma, M. L. Advanced Research Projects Agency under award Plasmonics for Extreme Light Concentration number N66001-10-1-4060. S.K.S. and A.A.-G. and Manipulation. Nat. Mater. 2010, 9, 193– acknowledge Defense Threat Reduction Agency 204. grant HDTRA1-10-1-0046. D. A.-O.-B., M. R. and H. M. are grateful to the U.S. Air Force Of- 9. Hernández-Martínez, P. L.; Govorov, A. O.; fice of Scientific Research (AFOSR) Grant No. Demir, H. V. Generalized Theory of Förster- FA9550-10-1-0438, for the support of this work. Type Nonradiative Energy Transfer in Nanos- tructures with Mixed Dimensionality. J. Phys. Chem. C 2013, 117, 10203–10212.

14 10. Fujita, T.; Brookes, J. C.; Saikin, S. K.; Electronic Energy Transfer in Photosynthetic Aspuru-Guzik, A. Memory-Assisted Exci- Light-Harvesting Complexes. Phys. Chem. ton Diffusion in the Chlorosome Light- Chem. Phys. 2012, 14, 10094–10108. Harvesting Antenna of Green Sulfur Bacteria. J. Phys. Chem. Lett. 2012, 3, 2357–2361. 19. Ritschel, G.; Roden, J.; Strunz, W. T.; Aspuru- Guzik, A.; Eisfeld, A. Absence of Quan- 11. Fujita, T.; Huh, J.; Saikin, S. K.; tum Oscillations and Dependence on Site En- Brookes, J. C.; Aspuru-Guzik, A. Theo- ergies in Electronic Excitation Transfer In retical Characterization of Excitation Energy the Fenna–Matthews–Olson Trimer. J. Phys. Transfer in Chlorosome Light-Harvesting Chem. Lett. 2011, 2, 2912–2917. Antennae from Green Sulfur Bacteria. Photosynth. Res., in press 2014, 20. Shim, S.; Rebentrost, P.; Valleau, S.; Aspuru- Guzik, A. Atomistic Study of the Long-Lived 12. Huh, J.; Saikin, S. K.; Brookes, J.; Valleau, S.; Quantum Coherences in the Fenna-Matthews- Fujita, T.; Aspuru-Guzik, A. Atomistic Study Olson Complex. Biophys. J. 2012, 102, 649– of Energy Funneling in the Light-Harvesting 660. Complex of Green Sulfur Bacteria. J. Am. Chem. Soc. 2014, 136, 2048–2057. 21. Valleau, S.; Eisfeld, A.; Aspuru-Guzik, A. On the Alternatives for Bath Correlators and 13. Prokhorenko, V. I.; Steensgaard, D. B.; Spectral Densities from Mixed Quantum- Holzwarth, A. R. Exciton Theory for Classical Simulations. J. Chem. Phys. 2012, Supramolecular Chlorosomal Aggregates: 1. 137, 224103(1)–224103(13). Aggregate Size Dependence of the Linear Spectra. Biophys. J. 2003, 85, 3173–3186. 22. Zimanyi, E. N.; Silbey, R. J. Uniﬁed Treat- ment of Coherent and incoherent Electronic 14. Eisfeld, A.; Kniprath, R.; Briggs, J. S. The- Energy Transfer Dynamics using Classical ory of the Absorption and Circular Dichro- Electrodynamics. J. Chem. Phys. 2010, 133, ism Spectra of Helical Molecular Aggre- 144107(1)–144107(10). gates. J. Chem. Phys. 2007, 126, 104904(1)– 104904(13). 23. Ansari-Oghol-Beig, D.; Rostami, M.; Cher- nobrovkina, E.; Saikin, S.; Valleau, S.; Mosal- 15. Beatty, J. T.; Overmann, J.; Lince, M. T.; laei, H.; Aspuru-Guzik., A. Parametric Hierar- Manske, A. K.; Lang, A. S.; Blanken- chical Matrix Approach for the Wideband Op- ship, R. E.; Van Dover, C. L.; Martin- tical Response of Large-Scale Molecular Ag- son, T. A.; Plumley, F. G. An Obligately Pho- gregates. J. App. Phys. 2013, 114, 164315(1)– tosynthetic Bacterial Anaerobe from a Deep- 164315(10). Sea Hydrothermal Vent. Proc. Natl. Acad. Sci. 2005, 102, 9306–9310. 24. van Rossum, B.-J.; Steensgaard, D. B.; Mul- der, B. G. J., F. M. and; Schaffner, K.; 16. Overmann, J.; Cypionka, H.; Pfennig, N. An Holzwarth, A. R.; de Groot, H. J. M. Reﬁned Extremely Low-Light-Adapted Phototrophic Model of the Chlorosomal Antennae of the Sulfur Bacterium from the Black Sea. Limnol. Green Bacterium Chlorobium Tepidum from Oceanog. 1992, 37, 150–155. Proton Chemical Shift Constraints Obtained With High-Field 2d and 2-D Mas Nmr Dipo- 17. Ishizaki, A.; Fleming, G. R. Theoretical Ex- lar Correlation Spectroscopy. Biochem. 2001, amination of Quantum Coherence in a Pho- 40, 1587–1595. tosynthetic System at Physiological Tempera- ture. Proc. Natl. Acad. Sci. 2009, 106, 17255– 25. de Boer, I.; Matysik, J.; Erkelens, K.; 17260. Sasaki, S.; Miyatake, T.; Yagai, S.; Tami- 18. Pachón, L. A.; Brumer, P. Computational aki, H.; Holzwarth, A. R.; de Groot, H. Methodologies and Physical insights into J. M. Mas Nmr Structures of Aggregated

15 Cadmium Chlorins Reveal Molecular Con- Urban, V. S.; Aspuru-Guzik, A. Tempera- trol of Self-Assembly of Chlorosomal Bacte- ture and Carbon Assimilation Regulate the riochlorophylls. J. Phys. Chem. B 2004, 108, Chlorosome Biogenesis in Green Sulfur Bac- 16556–16566. teria. Biophys. J. 2013, 105, 1346–1356.

26. Psencík, J.; Ikonen, T. P.; Laurinmäki, P.; Mer- 34. DeVoe, H. Optical Properties of Molecular ckel, M. C.; Butcher, S. J.; Serimaa, R. E.; Aggregates. II Classical Theory of the Refrac- Tuma, R. Lamellar Organization of Pigments tion, Absorption, and Optical Activity of So- in Chlorosomes, the Light Harvesting Com- lutions and Crystals. J. Chem. Phys. 1965, 43, plexes of Green Photosynthetic Bacteria. Bio- 3199–3208. phys. J. 2004, 87, 1165–1172. 35. Shibata, Y.; Saga, Y.; Tamiaki, H.; Itoh, S. Po- 27. Hohmann-Marriott, M. F.; Blankenship, R. E.; larized Fluorescence of Aggregated Bacteri- Roberson, R. W. The Ultra Structure of ochlorophyll C and Baseplate Bacteriochloro- Chlorobium Tepidum Chlorosomes Revealed phyll a in Single Chlorosomes Isolated from By Electron Microscopy. Photosynth. Res. Chloroﬂexus Aurantiacus. Biochemistry 2007, 2005, 86, 145–154. 46, 7062–7068.

28. Egawa, A.; Fujiwara, T.; Mizoguchi, T.; Kak- 36. Tian, Y.; Camacho, R.; Thomsson, D.; itani, Y.; Koyama, Y.; Akutsu, H. Structure of Reus, M.; Holzwarth, A. R.; Scheblykin, I. G. the Light-Harvesting Bacteriochlorophyll C Organization of Bacteriochlorophylls in In- Assembly in Chlorosomes from Chlorobium dividual Chlorosomes from Chlorobaculum Limicola Determined By Solid-State Nmr. Tepidum Studied by 2-Dimensional Polariza- Proc. Natl. Acad. Sci. 2007, 104, 790–805. tion Fluorescence Microscopy. J. Am. Chem. Soc. 2011, 133, 17192–17199. 29. Linnanto, J. M.; Korppi-Tommola, J. E. I. In- vestigation on Chlorosomal Antenna Geome- 37. Holzwarth, A. R.; Schaffner, K. On the Struc- tries: Tube, Lamella and Spiral-Type Self- ture of Bacteriochlorophyll Molecular Aggre- Aggregates. Photosynth. Res. 2008, 96, 227– gates in the Chlorosomes of Green Bacteria. a 245. Molecular Modelling Study. Photosynth. Res. 1994, 41, 225–233. 30. Oostergetel, G. T.; Reus, M.; Gomez Maqueo Chew, A.; Bryant, D. A.; Boekema, E. J.; 38. Ganapathy, S.; Oostergetel, G. T.; Reus, M.; Holzwarth, A. R. Long-Range Organization Tsukatani, Y.; Gomez Maqueo Chew, A.; of Bacteriochlorophyll in Chlorosomes of Buda, F.; Bryant, D. A.; Holzwarth, A. R.; Chlorobium Tepidum Investigated By Cryo- de Groot, H. J. M. Structural Variabil- Electron Microscopy. FEBS lett. 2007, 581, ity in Wild-Type and Bchq Bchr Mutant 5435–9. Chlorosomes of the Green Sulfur Bacterium Chlorobaculum Tepidum. Biochemistry 2012, 31. Mahan, G. D. Davydov Splittings in An- 51, 4488–4498. thracene. J. Chem. Phys. 1964, 41, 2930– 2933. 39. Prokhorenko, V. I.; Steensgaard, D. B.; Holzwarth, A. R. Exciton Dynamics in the 32. Martiskainen, J.; Linnanto, J.; Aumanen, V.; Chlorosomal Antennae of the Green Bacte- Myllyperkiö, P.; Korppi-Tommola, J. Excita- ria Chloroﬂexus Aurantiacus and Chlorobium tion Energy Transfer in Isolated Chlorosomes Tepidum. Biophys. J. 2000, 79, 2105–2120. from Chlorobaculum tepidum and Prosthe- cochloris aestuarii. Photochem. Photobiol. 40. Linnanto, J.; Korppi-tommola, J. Spectro- 2012, 88, 675–683. scopic Properties of Mg-Chlorin , Mg- 33. Tang, J. K. H.; Saikin, S. K.; Pingali, S. V.; Bacteriochlorin , and Bacteriochlorophylls a , Enriquez, M. M.; Huh, J.; Frank, H. A.;

16 b , c , d , e , f , g , and h Studied by Semiempir- ical and Ab initio MO / CI Methods. J. Phys. Chem. 2001, 3855–3866.

41. Knox, R. S.; Spring, B. Q. Dipole Strengths in the Chlorophylls. Photochemistry and Photo- biology 2003, 77, 497–501.

42. Adolphs, J.; Renger, T. How Proteins Trig- ger Excitation Energy Transfer in the Fmo Complex of Green Sulfur Bacteria. Biophys. J. 2006, 91, 2778–2797.

43. Keller, D.; Bustamante, C. Theory of the interaction of Light With Large Inhomoge- neous Molecular Aggregates. I. Absorption. J. Chem. Phys. 1986, 84, 2961–2971.

44. Keller, D.; Bustamante, C. Theory of the interaction of Light With Large Inhomoge- neous Molecular Aggregates. Ii. Psitype Cir- cular Dichroism. J. Chem. Phys. 1986, 84, 2972–2980.

45. Briggs, J. S.; Eisfeld, A. Coherent Quan- tum States from Classical Oscillator Ampli- tudes. Phys. Rev. A 2012, 85, 052111(1)– 052111(10).

46. Somsen, O. J. G.; van Grondelle, R.; van Amerongen, H. Spectral Broadening of in- teracting Pigments: Polarized Absorption By Photosynthetic Proteins. Biophys. J. 1996, 71, 1934–1951.