Dipole strengths in the chlorophylls

De novo design of proteins housing excitonically coupled chlorophyll special pairs

Natural photosystems couple light harvesting to charge separation using a 'special pair' of chlorophyll molecules that accepts excitation energy from the antenna and initiates an electron-transfer cascade. To investigate the photophysics of special pairs independently of the complexities of native photosynthetic proteins, and as a first step toward creating synthetic photosystems for new energy conversion technologies, we designed C2-symmetric proteins that hold two chlorophyll molecules in closely juxtaposed arrangements. X-ray crystallography confirmed that one designed protein binds two chlorophylls in the same orientation as native special pairs, whereas a second designed protein positions them in a previously unseen geometry. Spectroscopy revealed that the chlorophylls are excitonically coupled, and fluorescence lifetime imaging demonstrated energy transfer. The cryo-electron microscopy structure of a designed 24-chlorophyll octahedral nanocage with a special pair on each edge closely matched the design model. The results suggest that the de novo design of artificial photosynthetic systems is within reach of current computational methods.

Exciton interactions of chlorophyll tetramer in water-soluble chlorophyll-binding protein BoWSCP

The exciton interaction of four chlorophyll a (Chl a) molecules in a symmetrical tetrameric complex of the water-soluble chlorophyll-binding protein BoWSCP was analyzed in the pH range of 3-11. Exciton splitting ΔE = 232 ± 2 cm-1 of the Qy band of Chl a into two subcomponents with relative intensities of 78.1 ± 0.7 % and 21.9 ± 0.7 % was determined by a joint decomposition of the absorption and circular dichroism spectra into Gaussian functions. The exciton coupling parameters were calculated based on the BoWSCP atomic structure in three approximations: the point dipole model, the distributed atomic monopoles, and direct ab initio calculations in the TDDFT/PCM approximation. The Coulomb interactions of monomers were calculated within the continuum model using three values of optical permittivity. The models based on the properties of free Chl a in solution suffer from significant errors both in estimating the absolute value of the exciton interaction and in the relative intensity of exciton transitions. Calculations within the TDDFT/PCM approximation reproduce the experimentally determined parameters of the exciton splitting and the relative intensities of the exciton bands. The following factors of pigment-protein and pigment-pigment interactions were examined: deviation of the macrocycle geometry from the planar conformation of free Chl; the formation of hydrogen bonds between the macrocycle and water molecules; the overlap of wave functions of monomers at close distances. The most significant factor is the geometrical deformation of the porphyrin macrocycle, which leads to an increase in the dipole moment of Chl monomer from 5.5 to 6.9 D and to a rotation of the dipole moment by 15° towards the cyclopentane ring. The contributions of resonant charge-transfer states to the wave functions of the Chl dimer were determined and the transition dipole moments of the symmetric and antisymmetric charge-transfer states were estimated.

Short-Range Effects in the Special Pair of Photosystem II Reaction Centers: The Nonconservative Nature of Circular Dichroism

Photosystem II reaction centers extract electrons from water, providing the basis of oxygenic life on earth. Among the light-sensitive pigments of the reaction center, a central chlorophyll a dimer, known as the special pair, so far has escaped a complete theoretical characterization of its excited state properties. The close proximity of the special pair pigments gives rise to short-range effects that comprise a coupling between local and charge transfer (CT) excited states as well as other intermolecular quantum effects. Using a multiscale simulation and a diabatization technique, we show that the coupling to CT states is responsible for 45% of the excitonic coupling in the special pair. The other short-range effects cause a nonconservative nature of the circular dichroism spectrum of the reaction center by effectively rotating the electric transition dipole moments of the special pair pigments inverting and strongly enhancing their intrinsic rotational strength.

Thermal site energy fluctuations in photosystem I: new insights from MD/QM/MM calculations

Cyanobacterial photosystem I (PSI) is one of the most efficient photosynthetic machineries found in nature. Due to the large scale and complexity of the system, the energy transfer mechanism from the antenna complex to the reaction center is still not fully understood. A central element is the accurate evaluation of the individual chlorophyll excitation energies (site energies). Such an evaluation must include a detailed treatment of site specific environmental influences on structural and electrostatic properties, but also their evolution in the temporal domain, because of the dynamic nature of the energy transfer process. In this work, we calculate the site energies of all 96 chlorophylls in a membrane-embedded model of PSI. The employed hybrid QM/MM approach using the multireference DFT/MRCI method in the QM region allows to obtain accurate site energies under explicit consideration of the natural environment. We identify energy traps and barriers in the antenna complex and discuss their implications for energy transfer to the reaction center. Going beyond previous studies, our model also accounts for the molecular dynamics of the full trimeric PSI complex. Via statistical analysis we show that the thermal fluctuations of single chlorophylls prevent the formation of a single prominent energy funnel within the antenna complex. These findings are also supported by a dipole exciton model. We conclude that energy transfer pathways may form only transiently at physiological temperatures, as thermal fluctuations overcome energy barriers. The set of site energies provided in this work sets the stage for theoretical and experimental studies on the highly efficient energy transfer mechanisms in PSI.

Dynamic Stark effect in β and γ carotenes induced by photoexcitation of bacteriochlorophyll c in chlorosomes from Chloroflexus aurantiacus

Chlorosomes of green bacteria can be considered as a prototype of future artificial light-harvesting devices due to their unique property of self-assembly of a large number of bacteriochlorophyll (BChl) c/d/e molecules into compact aggregates. The presence of carotenoids (Cars) in chlorosomes is very important for photoprotection, light harvesting and structure stabilization. In this work, we studied for the first time the electrochromic band shift (Stark effect) in Cars of the phototrophic filamentous green bacterium Chloroflexus (Cfx.) aurantiacus induced by fs light excitation of the main pigment, BChl c. The high accuracy of the spectral measurements permitted us to extract a small wavy spectral feature, which, obviously, can be associated with the dynamic shift of the Car absorption band. A global analysis of spectroscopy data and theoretical modeling of absorption spectra showed that near 60% of Cars exhibited a red Stark shift of ~ 25 cm^-1 and the remaining 40% exhibited a blue shift. We interpreted this finding as evidence of various orientations of Car in chlorosomes. We estimated the average value of the light-induced electric field strength in the place of Car molecules as ~ 10⁶ V/cm and the average distance between Car and the neighboring BChl c as ~ 10 Å. We concluded that the dynamics of the Car electrochromic band shift mainly reflected the dynamics of exciton migration through the chlorosome toward the baseplate within ~ 1 ps. Our work has unambiguously shown that Cars are sensitive indicators of light-induced internal electric fields in chlorosomes.

Determination of FRET orientation factor between artificial fluorophore and photosynthetic light-harvesting 2 complex (LH2)

The orientation factor of fluorescence resonance energy transfer (FRET) between photosynthetic light-harvesting 2 complex (LH2) and artificial fluorophore (Alexa Fluor 647: A647) was theoretically investigated. The orientation factor of 2/3, i.e., the isotropic mean, is widely used to predict the donor–acceptor distance from FRET measurements. However, this approximation seems inappropriate because the movement of A647 is possibly restricted by the bifunctional linker binding to LH2. In this study, we performed molecular dynamics (MD) simulations and electronic coupling calculations on the LH2-A647 conjugate to analyze its orientation factor. The MD results showed that A647 keeps a position approximately 26 Å away from the bacteriochlorophyll (BChl) assembly in LH2. The effective orientation factor was extracted from the electronic coupling calculated using the transition charge from electrostatic potential (TrESP) method. With MD snapshots, an averaged orientation factor was predicted to be 1.55, significantly different from the isotropic mean value. The analysis also suggested that the value of the refractive index employed in the previous studies is not suitable for this system. Furthermore, optimal orientations of A647 with larger orientation factors to improve FRET efficiency were searched using Euler angles. The present approach is useful for extending the applicability of FRET analysis.

Conformation of Light-Harvesting Complex II Trimer Depends upon Its Binding Site

The light-harvesting complex II (LHCII) trimer in plants functions as a major antenna complex and a quencher to protect it from photooxidative damage. Theoretical studies on the structure of an LHCII trimer have demonstrated that excitation energy transfer between chlorophylls (Chls) in LHCII can be modulated by its exquisite conformational fluctuation. However, conformational changes depending on its binding location have not yet been investigated, even though reorganization of protein complexes occurs by physiological regulations. In this study, we investigated conformational differences in LHCII by comparing published structures of an identical LHCII trimer in the three different photosystem supercomplexes from the green alga Chlamydomonas reinhardtii. Our results revealed distinct differences in Chl configurations as well as polypeptide conformations of the LHCII trimers depending on its binding location. We propose that these configurational differences readily modulate the function of LHCII and possibly lead to a change in excitation-energy flow over the photosynthetic supercomplex.

Structure-based model of fucoxanthin-chlorophyll protein complex: Calculations of chlorophyll electronic couplings

Diatoms are a group of marine algae that are responsible for a significant part of global oxygen production. Adapted to life in an aqueous environment dominated by the blue-green light, their major light-harvesting antennae-fucoxanthin-chlorophyll protein complexes (FCPs)-exhibit different pigment compositions than of plants. Despite extensive experimental studies, until recently the theoretical description of excitation energy dynamics in these complexes was limited by the lack of high-resolution structural data. In this work, we use the recently resolved crystallographic information of the FCP complex from Phaeodactylum tricornutum diatom [Wang et al., Science 363, 6427 (2019)] and quantum chemistry-based calculations to evaluate the chlorophyll transition dipole moments, atomic transition charges from electrostatic potential, and the inter-chlorophyll couplings in this complex. The obtained structure-based excitonic couplings form the foundation for any modeling of stationary or time-resolved spectroscopic data. We also calculate the inter-pigment Förster energy transfer rates and identify two quickly equilibrating chlorophyll clusters.

Theoretical Model of the Far-Red-Light-Adapted Photosystem I Reaction Center of Cyanobacterium Acaryochloris marina Using Chlorophyll d and the Effect of Chlorophyll Exchange

A theoretical model of the far-red-light-adapted photosystem I (PSI) reaction center (RC) complex of a cyanobacterium, Acaryochloris marina (AmPSI), was constructed based on the exciton theory and the recently identified molecular structure of AmPSI by Hamaguchi et al. (Nat. Commun., 2021, 12, 2333). A. marina performs photosynthesis under the visible to far-red light (400-750 nm), which is absorbed by chlorophyll d (Chl-d). It is in contrast to the situation of all the other oxygenic photosynthetic processes of cyanobacteria and plants, which contains chlorophyll a (Chl-a) that absorbs only 400-700 nm visible light. AmPSI contains 70 Chl-d, 1 Chl-d^', 2 pheophytin a (Pheo-a), and 12 carotenoids in the currently available structure. A special pair of Chl-d/Chl-d^' acts as the electron donor (P740) and two Pheo-a act as the primary electron acceptor A₀ as the counterparts of P700 and Chl-a, respectively, of Chl-a-type PSIs. The exciton Hamiltonian of AmPSI was constructed considering the excitonic coupling strength and site energy shift of individual pigments using the Poisson-TrESP (P-TrESP) and charge density coupling (CDC) methods. The model was constructed to fit the experimentally measured spectra of absorption and circular dichroism (CD) spectra during downhill/uphill excitation energy transfer processes. The constructed theoretical model of AmPSI was further compared with the Chl-a-type PSI of Thermosynechococcus elongatus (TePSI), which contains only Chl-a and Chl-a^'. The functional properties of AmPSI and TePSI were further examined by the in silico exchange of Chl-d by Chl-a in the models.

Structure of the stress-related LHCSR1 complex determined by an integrated computational strategy

Light-harvesting complexes (LHCs) are pigment-protein complexes whose main function is to capture sunlight and transfer the energy to reaction centers of photosystems. In response to varying light conditions, LH complexes also play photoregulation and photoprotection roles. In algae and mosses, a sub-family of LHCs, light-harvesting complex stress-related (LHCSR), is responsible for photoprotective quenching. Despite their functional and evolutionary importance, no direct structural information on LHCSRs is available that can explain their unique properties. In this work, we propose a structural model of LHCSR1 from the moss P. patens, obtained through an integrated computational strategy that combines homology modeling, molecular dynamics, and multiscale quantum chemical calculations. The model is validated by reproducing the spectral properties of LHCSR1. Our model reveals the structural specificity of LHCSR1, as compared with the CP29 LH complex, and poses the basis for understanding photoprotective quenching in mosses.

The structure of the moss P. patens light-harvesting complex stress-related 1 (LHCSR1) is determined using a multi-scale computational approach for investigations of its photoprotective function.

Active control of strong plasmon-exciton coupling in biomimetic pigment-polymer antenna complexes grown by surface-initiated polymerisation from gold nanostructures

Plexcitonic antenna complexes, inspired by photosynthetic light-harvesting complexes, are formed by attachment of chlorophylls (Chl) to poly(cysteine methacrylate) (PCysMA) scaffolds grown by atom-transfer radical polymerisation from gold nanostructure arrays. In these pigment–polymer antenna complexes, localised surface plasmon resonances on gold nanostructures are strongly coupled to Chl excitons, yielding hybrid light–matter states (plexcitons) that are manifested in splitting of the plasmon band. Modelling of the extinction spectra of these systems using a simple coupled oscillator model indicates that their coupling energies are up to twice as large as those measured for LHCs from plants and bacteria. Coupling energies are correlated with the exciton density in the grafted polymer layer, consistent with the collective nature of strong plasmon–exciton coupling. Steric hindrance in fully-dense PCysMA brushes limits binding of bulky chlorophylls, but the chlorophyll concentration can be increased to ∼2 M, exceeding that in biological light-harvesting complexes, by controlling the grafting density and polymerisation time. Moreover, synthetic plexcitonic antenna complexes display pH- and temperature-responsiveness, facilitating active control of plasmon–exciton coupling. Because of the wide range of compatible polymer chemistries and the mild reaction conditions, plexcitonic antenna complexes may offer a versatile route to programmable molecular photonic materials.

Excitons in pigment–polymer antenna complexes formed by attachment of chlorophyll to surface grafted polymers are coupled strongly to plasmon modes, with coupling energies twice those for biological light-harvesting complexes and active control of plasmon–exciton coupling.

Time-dependent atomistic simulations of the CP29 light-harvesting complex

Light harvesting as the first step in photosynthesis is of prime importance for life on earth. For a theoretical description of photochemical processes during light harvesting, spectral densities are key quantities. They serve as input functions for modeling the excitation energy transfer dynamics and spectroscopic properties. Herein, a recently developed procedure is applied to determine the spectral densities of the pigments in the minor antenna complex CP29 of photosystem II, which has recently gained attention because of its active role in non-photochemical quenching processes in higher plants. To this end, the density functional-based tight binding (DFTB) method has been employed to enable simulation of the ground state dynamics in a quantum-mechanics/molecular mechanics (QM/MM) scheme for each chlorophyll pigment. Subsequently, the time-dependent extension of the long-range corrected DFTB approach has been used to obtain the excitation energy fluctuations along the ground-state trajectories also in a QM/MM setting. From these results, the spectral densities have been determined and compared for different force fields and to spectral densities from other light-harvesting complexes. In addition, time-dependent and time-independent excitonic Hamiltonians of the system have been constructed and applied to the determination of absorption spectra as well as exciton dynamics.

Exciton properties and optical spectra of light harvesting complex II from a fully atomistic description

We present a fully atomistic simulation of linear optical spectra (absorption, fluorescence and circular dichroism) of the Light Harvesting Complex II (LHCII) trimer using a hybrid approach, which couples a quantum chemical description of the chlorophylls with a classical model for the protein and the external environment (membrane and water). The classical model uses a polarizable Molecular Mechanics force field, thus allowing mutual polarization effects in the calculations of the excitonic properties. The investigation is performed both on the crystal structure and on structures generated by a μs long classical molecular dynamics simulation of the complex within a solvated membrane. The results show that this integrated approach not only provides a good description of the excitonic properties and optical spectra without the need for additional refinements of the excitonic parameters, but it also allows an atomistic investigation of the relative importance of electronic, structural and environment effects in determining the optical spectra.

Excitation quenching in chlorophyll-carotenoid antenna systems: 'coherent' or 'incoherent'

Plants possess an essential ability to rapidly down-regulate light-harvesting in response to high light. This photoprotective process involves the formation of energy-quenching interactions between the chlorophyll and carotenoid pigments within the antenna of Photosystem II (PSII). The nature of these interactions is currently debated, with, among others, 'incoherent' or 'coherent' quenching models (or a combination of the two) suggested by a range of time-resolved spectroscopic measurements. In 'incoherent quenching', energy is transferred from a chlorophyll to a carotenoid and is dissipated due to the intrinsically short excitation lifetime of the latter. 'Coherent quenching' would arise from the quantum mechanical mixing of chlorophyll and carotenoid excited state properties, leading to a reduction in chlorophyll excitation lifetime. The key parameters are the energy gap, [Formula: see text] and the resonance coupling, J, between the two excited states. Coherent quenching will be the dominant process when [Formula: see text] i.e., when the two molecules are resonant, while the quenching will be largely incoherent when [Formula: see text] One would expect quenching to be energetically unfavorable for [Formula: see text] The actual dynamics of quenching lie somewhere between these limiting regimes and have non-trivial dependencies of both J and [Formula: see text] Using the Hierarchical Equation of Motion (HEOM) formalism we present a detailed theoretical examination of these excitation dynamics and their dependence on slow variations in J and [Formula: see text] We first consider an isolated chlorophyll-carotenoid dimer before embedding it within a PSII antenna sub-unit (LHCII). We show that neither energy transfer, nor the mixing of excited state lifetimes represent unique or necessary pathways for quenching and in fact discussing them as distinct quenching mechanisms is misleading. However, we do show that quenching cannot be switched 'on' and 'off' by fine tuning of [Formula: see text] around the resonance point, [Formula: see text] Due to the large reorganization energy of the carotenoid excited state, we find that the presence (or absence) of coherent interactions have almost no impact of the dynamics of quenching. Counter-intuitively significant quenching is present even when the carotenoid excited state lies above that of the chlorophyll. We also show that, above a rather small threshold value of [Formula: see text]quenching becomes less and less sensitive to J (since in the window [Formula: see text] the overall lifetime is independent of it). The requirement for quenching appear to be only that [Formula: see text] Although the coherent/incoherent character of the quenching can vary, the overall kinetics are likely robust with respect to fluctuations in J and [Formula: see text] This may be the basis for previous observations of NPQ with both coherent and incoherent features.

Reconstitution of 3-Acetyl Chlorophyll a into Light-Harvesting Complex 2 from the Purple Photosynthetic Bacterium Phaeospirillum molischianum

The manipulation of B800 bacteriochlorophyll (BChl) a in light-harvesting complex 2 (LH2) from the purple photosynthetic bacterium Phaeospirillum molischianum (molischianum-LH2) provides insight for understanding the energy transfer mechanism and the binding of cyclic tetrapyrroles in LH2 proteins since molischianum-LH2 is one of the two LH2 proteins whose atomic-resolution structures have been determined and is a representative of type-2 LH2 proteins. However, there is no report on the substitution of B800 BChl a in molischianum-LH2. We report the reconstitution of 3-acetyl chlorophyll (AcChl) a, which has a 17,18-dihydroporphyrin skeleton, to the B800 site in molischianum-LH2. The 3-acetyl group in AcChl a formed a hydrogen bond with β'-Thr23 in essentially the same manner as native B800 BChl a, but this hydrogen bond was weaker than that of B800 BChl a. This change can be rationalized by invoking a small distortion in the orientation of the 3-acetyl group in the B800 cavity by dehydrogenation in the B-ring from BChl a. The energy transfer from AcChl a in the B800 site to B850 BChl a was about 5-fold slower than that from native B800 BChl a by a decrease of the spectral overlap between energy-donating AcChl a and energy-accepting B850 BChl a.

Benchmark and performance of long-range corrected time-dependent density functional tight binding (LC-TD-DFTB) on rhodopsins and light-harvesting complexes

The chromophores of rhodopsins (Rh) and light-harvesting (LH) complexes still represent a major challenge for a quantum chemical description due to their size and complex electronic structure. Since gradient corrected and hybrid density functional approaches have been shown to fail for these systems, only range-separated functionals seem to be a promising alternative to the more time consuming post-Hartree-Fock approaches. For extended sampling of optical properties, however, even more approximate approaches are required. Recently, a long-range corrected (LC) functional has been implemented into the efficient density functional tight binding (DFTB) method, allowing to sample the excited states properties of chromophores embedded into proteins using quantum mechanical/molecular mechanical (QM/MM) with the time-dependent (TD) DFTB approach. In the present study, we assess the accuracy of LC-TD-DFT and LC-TD-DFTB for rhodopsins (bacteriorhodopsin (bR) and pharaonis phoborhodopsin (ppR)) and LH complexes (light-harvesting complex II (LH2) and Fenna-Matthews-Olson (FMO) complex). This benchmark study shows the improved description of the color tuning parameters compared to standard DFT functionals. In general, LC-TD-DFTB can exhibit a similar performance as the corresponding LC functionals, allowing a reliable description of excited states properties at significantly reduced cost. The two chromophores investigated here pose complementary challenges: while huge sensitivity to external field perturbation (color tuning) and charge transfer excitations are characteristic for the retinal chromophore, the multi-chromophoric character of the LH complexes emphasizes a correct description of inter-chromophore couplings, giving less importance to color tuning. None of the investigated functionals masters both systems simultaneously with satisfactory accuracy. LC-TD-DFTB, at the current stage, although showing a systematic improvement compared to TD-DFTB cannot be recommended for studying color tuning in retinal proteins, similar to some of the LC-DFT functionals, because the response to external fields is still too weak. For sampling of LH-spectra, however, LC-TD-DFTB is a viable tool, allowing to efficiently sample absorption energies, as shown for three different LH complexes. As the calculations indicate, geometry optimization may overestimate the importance of local minima, which may be averaged over when using trajectories. Fast quantum chemical approaches therefore may allow for a direct sampling of spectra in the near future.

Coupling to Charge Transfer States is the Key to Modulate the Optical Bands for Efficient Light Harvesting in Purple Bacteria

The photosynthetic apparatus of purple bacteria uses exciton delocalization and static disorder to modulate the position and broadening of its absorption bands, leading to efficient light harvesting. Its main antenna complex, LH2, contains two rings of identical bacteriochlorophyll pigments, B800 and B850, absorbing at 800 and 850 nm, respectively. It has been an unsolved problem why static disorder of the strongly coupled B850 ring is several times larger than that of the B800 ring. Here we show that mixing between excitons and charge transfer states in the B850 ring is responsible for the effect. The linear absorption spectrum of the LH2 system is simulated by using a multiscale approach with an exciton Hamiltonian generalized to include the charge transfer states that involve adjacent pigment pairs, with static disorder modeled microscopically by molecular dynamics simulations. Our results show that sufficient inhomogeneous broadening of the B850 band, needed for efficient light harvesting, is only obtained by utilizing static disorder in the coupling between local excited and interpigment charge transfer states.

Structure-Based Theory of Fluctuation-Induced Energy Transfer in a Molecular Dyad

We present a microscopic theory for the description of fluctuation-induced excitation energy transfer in chromophore dimers to explain experimental data on a perylene biscarboximide dyad with orthogonal transition dipole moments. Our non-Condon extension of Förster theory takes into account the fluctuations of excitonic couplings linear and quadratic in the normal coordinates, treated microscopically by quantum chemical/electrostatic calculations. The modulation of the optical transition energies of the chromophores is inferred from optical spectra of the isolated chromophores. The application of the theory to the considered dyad reveals a two to three order of magnitude increase in the rate constant by non-Condon effects. These effects are found to be dominated by fluctuations linear in the normal coordinates and provide a structure-based qualitative interpretation of the experimental time constant for energy transfer as well as its dependence on temperature.

Computational Modeling of Exciton-Bath Hamiltonians for Light Harvesting 2 and Light Harvesting 3 Complexes of Purple Photosynthetic Bacteria at Room Temperature

Light harvesting 2 (LH2) complex is the primary component of the photosynthetic unit of purple bacteria that is responsible for harvesting and relaying excitons. The electronic absorption line shape of LH2 contains two major bands at 800 and 850 nm wavelength regions. Under low light conditions, some species of purple bacteria replace LH2 with light harvesting 3 (LH3), a variant form with almost the same structure as the former but with distinctively different spectral features. The major difference between the absorption line shapes of LH2 and LH3 is the shift of the 850 nm band of the former to a new 820 nm region. The microscopic origin of this difference has been the subject of some theoretical/computational investigations. However, the genuine molecular level source of such a difference is not clearly understood yet. This work reports a comprehensive computational study of LH2 and LH3 complexes so as to clarify different molecular level features of LH2 and LH3 complexes and to construct simple exciton-bath models with a common form. All-atomistic molecular dynamics simulations of both LH2 and LH3 complexes provide detailed molecular level structural differences of bacteriochlorophylls (BChls) in the two complexes, in particular, in their patterns of hydrogen bonding (HB) and torsional angles of the acetyl group. Time-dependent density functional theory calculation of the excitation energies of BChls for structures sampled from the MD simulations suggests that the observed differences in the HB and torsional angles cannot fully account for the experimentally observed spectral shift of LH3. Potential sources that can explain the actual spectral shift of LH3 are discussed, and their magnitudes are assessed through fitting of experimental line shapes. These results demonstrate the feasibility of developing simple exciton-bath models for both LH2 and LH3, which can be employed for large-scale exciton quantum dynamics in their aggregates.

Theory of Anisotropic Circular Dichroism of Excitonically Coupled Systems: Application to the Baseplate of Green Sulfur Bacteria

A simple exciton theory for the description of anisotropic circular dichroism (ACD) spectra of multichromophoric systems is presented that is expected to be of general use for the analysis of structure-function relationships of molecular aggregates such as photosynthetic light-harvesting antennae. The theory is applied to the baseplate of green sulfur bacteria. It is demonstrated that only the combined analysis of ACD and circular dichroism (CD) spectra for the present baseplate bacteriochlorophyll (BChl) a dimer allows for an unambiguous determination of the parameters of the exciton Hamiltonian from experimental data. The analysis of experimental absorption and linear dichroism spectra suggests that either the NMR structure has to be refined or in addition to the dimers seen in the NMR structure and in the CD and ACD spectra, BChl a monomers are present in the baseplate carotenosome sample. A refined dimer structure is presented, explaining all four optical spectra.

Excited state energy fluctuations in the Fenna-Matthews-Olson complex from molecular dynamics simulations with interpolated chromophore potentials

We analyze the environment-induced fluctuation of pigment excitation energies in the Fenna-Matthews-Olson (FMO) complex from various perspectives, by employing an interpolation-based all-atom potential energy model for describing realistic pigment vibrations. We conduct molecular dynamics simulations on a 100 ns timescale, which is an extent that can enclose the effect of static disorder, and demonstrate its timescale separation from fast dynamic disorder. We extract the spectral densities of the complex by considering both the site and the exciton bases. We show that exciton delocalization reduces the effective environmental fluctuation and rationalize this aspect based on a model of fluctuating molecular aggregates. We also obtained the spectral density of the lowest exciton state under low temperature conditions and show that it reasonably well reproduces the experimental result. Finally, by additionally performing non-equilibrium excited state trajectory simulations, we show that the system lies well within the linear response regime after photo-absorption and that the pigments do not visit anharmonic regions of the potential surface to a significant extent. This indicates that methodologies based on harmonic bath models are indeed reasonable approaches for describing the excited state dynamics of the FMO complex.

Exciton states and optical properties of the CP26 photosynthetic protein

The photosynthetic complex CP26, one of the minor antennae of the photosystem II, plays an important role in regulation of the excitation energy transfer in the PSII. Due to instability during isolation and purification, it remained poorly studied from the viewpoint of theoretical chemistry because of the absence of X-ray crystallography data. In this work, using the recently determined three-dimensional structure of the complex we apply the quantum chemical approach to study the properties of exciton states in it. Spectral properties, structure of exciton states and roles of the pigments in the complex and photosystem II are discussed.

Fine control of chlorophyll-carotenoid interactions defines the functionality of light-harvesting proteins in plants

Photosynthetic antenna proteins can be thought of as "programmed solvents", which bind pigments at specific mutual orientations, thus tuning the overall energetic landscape and ensuring highly efficient light-harvesting. While positioning of chlorophyll cofactors is well understood and rationalized by the principle of an "energy funnel", the carotenoids still pose many open questions. Particularly, their short excited state lifetime (<25 ps) renders them potential energy sinks able to compete with the reaction centers and drastically undermine light-harvesting efficiency. Exploration of the orientational phase-space revealed that the placement of central carotenoids minimizes their interaction with the nearest chlorophylls in the plant antenna complexes LHCII, CP26, CP29 and LHCI. At the same time we show that this interaction is highly sensitive to structural perturbations, which has a profound effect on the overall lifetime of the complex. This links the protein dynamics to the light-harvesting regulation in plants by the carotenoids.

Can Förster Theory Describe Stereoselective Energy Transfer Dynamics in a Protein-Ligand Complex?

Förster resonance energy transfer (FRET) reactions involving ligands and aromatic amino acids can substantially impact the fluorescence properties of a protein-ligand complex, an impact intimately related to the corresponding binding mode. Structural characterization of such binding events in terms of intermolecular distances can be done through the well-known R^-6 distance-dependent Förster rate expression. However, such an interpretation suffers from uncertainties underlying Förster theory in the description of the electronic coupling that promotes FRET, mostly related to the dipole-dipole orientation factor, dielectric screening effects, and deviations from the ideal dipole approximation. Here, we investigate how Förster approximations impact the prediction of energy transfer dynamics in the complex between flurbiprofen (FBP) and human serum albumin (HSA), as well as a model FBP-Trp dyad, in which recent observation of enantioselective fluorescence quenching has been ascribed to energy transfer from FBP to Trp. To this end, we combine classical molecular dynamics simulations with polarizable quantum mechanics/molecular mechanics calculations that allow overcoming Förster approximations. On the basis of our results, we discuss the potential of structure-based simulations in the characterization of drug-binding events through fluorescence techniques. Overall, we find an excellent agreement between theory and experiment both in terms of enantioselectivity and FRET times, thus strongly supporting the reliability of the binding modes proposed for the (S) and (R) enantiomers of FBP. In particular, we show that the dynamic quenching arises from a small fraction of drug bound to the secondary site of HSA at the interface between subdomains IIA and IIB, whereas the enantioselectivity arises from the larger flexibility of the (S)-FBP enantiomer in the binding pocket.

The carotenoid pathway: what is important for excitation quenching in plant antenna complexes?

Plant light-harvesting is regulated by the Non-Photochemical Quenching (NPQ) mechanism involving the slow trapping of excitation energy by carotenoids in the Photosystem II (PSII) antenna in response to high light.

Origin of non-conservative circular dichroism of the CP29 antenna complex of photosystem II

Structure-based explanation of the non-conservative circular dichroism spectrum of the photosynthetic antenna complex CP29 of photosystem II.

Coulomb couplings in solubilised light harvesting complex II (LHCII): challenging the ideal dipole approximation from TDDFT calculations

We investigate the coulomb coupling interactions of natural chromophores in the solubilised light harvesting complex II (LHCII) using DFT quantum chemistry calculations.

Structure Prediction of Self-Assembled Dye Aggregates from Cryogenic Transmission Electron Microscopy, Molecular Mechanics, and Theory of Optical Spectra

Cryogenic transmission electron microscopy (cryo-TEM) studies suggest that TTBC molecules self-assemble in aqueous solution to form single-walled tubes with a diameter of about 35 Å. In order to reveal the arrangement and mutual orientations of the individual molecules in the tube, we combine information from crystal structure data of this dye with a calculation of linear absorbance and linear dichroism spectra and molecular dynamics simulations. We start with wrapping crystal planes in different directions to obtain tubes of suitable diameter. This set of tube models is evaluated by comparing the resulting optical spectra with experimental data. The tubes that can explain the spectra are investigated further by molecular dynamics simulations, including explicit solvent molecules. From the trajectories of the most stable tube models, the short-range ordering of the dye molecules is extracted and the optimization of the structure is iteratively completed. The final structural model is a tube of rings with 6-fold rotational symmetry, where neighboring rings are rotated by 30° and the transition dipole moments of the chromophores form an angle of 74° with respect to the symmetry axis of the tube. This model is in agreement with cryo-TEM images and can explain the optical spectra, consisting of a sharp red-shifted J-band that is polarized parallel to to the symmetry axis of the tube and a broad blue-shifted H-band polarized perpendicular to this axis. The general structure of the homogeneous spectrum of this hybrid HJ-aggregate is described by an analytical model that explains the difference in redistribution of oscillator strength inside the vibrational manifolds of the J- and H-bands and the relative intensities and excitation energies of those bands. In addition to the particular system investigated here, the present methodology can be expected to aid the structure prediction for a wide range of self-assembled dye aggregates.

Distinguishing the roles of energy funnelling and delocalization in photosynthetic light harvesting

Photosynthetic complexes improve the transfer of excitation energy from peripheral antennas to reaction centers in several ways. In particular, a downward energy funnel can direct excitons in the right direction, while coherent excitonic delocalization can enhance transfer rates through the cooperative phenomenon of supertransfer. However, isolating the role of purely coherent effects is difficult because any change to the delocalization also changes the energy landscape. Here, we show that the relative importance of the two processes can be determined by comparing the natural light-harvesting apparatus with counterfactual models in which the delocalization and the energy landscape are altered. Applied to the example of purple bacteria, our approach shows that although supertransfer does enhance the rates somewhat, the energetic funnelling plays the decisive role. Because delocalization has a minor role (and is sometimes detrimental), it is most likely not adaptive, being a side-effect of the dense chlorophyll packing that evolved to increase light absorption per reaction center.

Towards an ab initio description of the optical spectra of light-harvesting antennae: application to the CP29 complex of photosystem II

Light-harvesting pigment-protein complexes (PPC) represent the fundamental units through which the photosynthetic organisms absorb sunlight and funnel the energy to the reaction centre for carrying out the primary energy conversion reactions of photosynthesis. Here we apply a multiscale computational strategy to a specific PPC present in the photosystem II of plants and algae (CP29) to investigate in what detail should the environment effects due to protein and membrane/solvent be included for an accurate description of optical spectra. We find that a refinement of the crystal structure is needed before any meaningful quantum chemical calculations of pigment transition energies can be performed. For this purpose we apply classical molecular dynamics simulations of the PPC within its natural environment and we perform ab initio computations of the exciton Hamiltonian of the complex, including the environment either implicitly by the polarizable continuum model (PCM) or explicitly using the polarizable QM/MM methodology (MMPol). However, PCM essentially leads to an unspecific redshift of all transition energies, and MMPol is able to reveal site-specific changes in the optical properties of the pigments. Based on the latter and the excitonic couplings obtained within a polarizable QM/MM methodology, optical spectra are calculated, which are in good qualitative agreement with experimental data. A weakness of the approach is however found in the overestimation of the fluctuations of the excitonic parameters of the pigments along the MD trajectory. An explanation for such a finding in terms of the limits of the force fields commonly used for protein cofactors is presented and discussed.

An ‘all pigment’ model of excitation quenching in LHCII

This work presents the first all-pigment microscopic model of a major light-harvesting complex of plants and the first attempt to capture the dissipative character of the known structure.

Constrained geometric dynamics of the Fenna-Matthews-Olson complex: the role of correlated motion in reducing uncertainty in excitation energy transfer

The trimeric Fenna-Mathews-Olson (FMO) complex of green sulphur bacteria is a well-studied example of a photosynthetic pigment-protein complex, in which the electronic properties of the pigments are modified by the protein environment to promote efficient excitonic energy transfer from antenna complexes to the reaction centres. By a range of simulation methods, many of the electronic properties of the FMO complex can be extracted from knowledge of the static crystal structure. However, the recent observation and analysis of long-lasting quantum dynamics in the FMO complex point to protein dynamics as a key factor in protecting and generating quantum coherence under laboratory conditions. While fast inter- and intra-molecular vibrations have been investigated extensively, the slow, conformational dynamics which effectively determine the optical inhomogeneous broadening of experimental ensembles has received less attention. The following study employs constrained geometric dynamics to study the flexibility in the protein network by efficiently generating the accessible conformational states from the published crystal structure. Statistical and principle component analyses reveal highly correlated low frequency motions between functionally relevant elements, including strong correlations between pigments that are excitonically coupled. Our analysis reveals a hierarchy of structural interactions which enforce these correlated motions, from the level of monomer-monomer interfaces right down to the α-helices, β-sheets and pigments. In addition to inducing strong spatial correlations across the conformational ensemble, we find that the overall rigidity of the FMO complex is exceptionally high. We suggest that these observations support the idea of highly correlated inhomogeneous disorder of the electronic excited states, which is further supported by the remarkably low variance (typically <5%) of the excitonic couplings of the conformational ensemble.

Theoretical study on excited states of bacteriochlorophyll a in solutions with density functional assessment

The excited-state properties of bacteriochlorophyll (BChl) a in triethylamine, 1-propanol, and methanol are investigated with the time-dependent density functional theory by using the quantum mechanical and molecular mechanical reweighting free energy self-consistant field method. It is found that no prevalent density functionals can reproduce the experimental excited-state properties, i.e., the absorption and reorganization energies, of BChl a in the solutions. The parameter μ in the range-separated hybrid functional is therefore optimized to reproduce the differences of the absorption energies in the solutions. We examine the origin of the differences of the absorption energies in the solutions and find that sensitive balance between contributions of structural changes and solute-solvent interactions determines the differences. The accurate description of the excitation with the density functional with the adjusted parameter is therefore essential to the understanding of the excited-state properties of BChl a in proteins and also the mechanism of the photosynthetic systems.

Towards a structure-based exciton Hamiltonian for the CP29 antenna of photosystem II

The exciton Hamiltonian pertaining to the first excited states of chlorophyll (Chl) a and b pigments in the minor light-harvesting complex CP29 of plant photosystem II is determined based on the recent crystal structure at 2.8 Å resolution applying a combined quantum chemical/electrostatic approach as used earlier for the major light-harvesting complex LHCII. Two electrostatic methods for the calculation of the local transition energies (site energies), referred to as the Poisson-Boltzmann/quantum chemical (PBQC) and charge density coupling (CDC) method, which differ in the way the polarizable environment of the pigments is described, are compared and found to yield comparable results, when tested against fits of measured optical spectra (linear absorption, linear dichroism, circular dichroism, and fluorescence). The crystal structure shows a Chl a/b ratio of 2.25, whereas a ratio between 2.25 and 3.0 can be estimated from the simulation of experimental spectra. Thus, it is possible that up to one Chl b is lost in CP29 samples. The lowest site energy is found to be located at Chl a604 close to neoxanthin. This assignment is confirmed by the simulation of wild-type-minus-mutant difference spectra of reconstituted CP29, where a tyrosine residue next to Chl a604 is modified in the mutant. Nonetheless, the terminal emitter domain (TED), i.e. the pigments contributing mostly to the lowest exciton state, is found at the Chl a611-a612-a615 trimer due to strong excitonic coupling between these pigments, with the largest contributions from Chls a611 and a612. A major difference between CP29 and LHCII is that Chl a610 is not the energy sink in CP29, which is presumably to a large extent due to the replacement of a lysine residue with alanine close to the TED.

Electromagnetic study of the chlorosome antenna complex of Chlorobium tepidum

Green sulfur bacteria are an iconic example of nature's adaptation: thriving in environments of extremely low photon density, the bacterium ranks itself among the most efficient natural light-harvesting organisms. The photosynthetic antenna 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 molecular packing moieties, are considered: a structure built of concentric cylinders of aggregated bacteriochlorophyll d monomers, a single cylinder of bacteriochlorophyll c monomers, and a model for the entire chlorosome. The theoretical model captures both coherent and incoherent components of exciton transfer. The model is employed to extract optical spectra, concentration and depolarization of electromagnetic fields within the chlorosome, and fluxes of energy transfer for the structures. The second model nanostructure shows the largest field enhancement. Further, field enhancement is found to be more sensitive to dynamic noise rather than structural disorder. Field depolarization, however, is similar for all structures. This indicates that the directionality of transfer is robust to structural variations, while on the other hand, the intensity of transfer can be tuned by structural variations.

Chlorophyll modifications and their spectral extension in oxygenic photosynthesis

Chlorophylls are magnesium-tetrapyrrole molecules that play essential roles in photosynthesis. All chlorophylls have similar five-membered ring structures, with variations in the side chains and/or reduction states. Formyl group substitutions on the side chains of chlorophyll a result in the different absorption properties of chlorophyll b, chlorophyll d, and chlorophyll f. These formyl substitution derivatives exhibit different spectral shifts according to the formyl substitution position. Not only does the presence of various types of chlorophylls allow the photosynthetic organism to harvest sunlight at different wavelengths to enhance light energy input, but the pigment composition of oxygenic photosynthetic organisms also reflects the spectral properties on the surface of the Earth. Two major environmental influencing factors are light and oxygen levels, which may play central roles in the regulatory pathways leading to the different chlorophylls. I review the biochemical processes of chlorophyll biosynthesis and their regulatory mechanisms.

Toward Ab Initio Optical Spectroscopy of the Fenna-Matthews-Olson Complex

We present progress toward a first-principles parametrization of the Hamiltonian of the Fenna-Matthews-Olson pigment-protein complex, a molecule that has become key to understanding the role of quantum dynamics in photosynthetic exciton energy transfer. To this end, we have performed fully quantum mechanical calculations on each of the seven bacteriochlorophyll pigments that make up the complex, including a significant proportion of their protein environment (more than 2000 atoms), using linear-scaling density functional theory exploiting a recent development for the computation of excited states. Local pigment transition energies and interpigment coupling between optical transitions have been calculated and are in good agreement with the literature consensus. Comparisons between simulated and experimental optical spectra point toward future work that may help to elucidate important design principles in these nanoscale devices.