Calculation of chromophore excited state energy shifts in response to molecular dynamics of pigment-protein complexes

The absorption and energy transfer properties of photosynthetic pigments are strongly influenced by their local environment or “site.” Local electrostatic fields vary in time with protein and chromophore molecular movement and thus transiently influence the excited state transition properties of individual chromophores. Site-specific information is experimentally inaccessible in many light-harvesting pigment–proteins due to multiple chromophores with overlapping spectra. Full quantum mechanical calculations of each chromophores excited state properties are too computationally demanding to efficiently calculate the changing excitation energies along a molecular dynamics trajectory in a pigment–protein complex. A simplified calculation of electrostatic interactions with each chromophores ground to excited state transition, the so-called charge density coupling (CDC) for site energy, CDC, has previously been developed to address this problem. We compared CDC to more rigorous quantum chemical calculations to determine its accuracy in computing excited state energy shifts and their fluctuations within a molecular dynamics simulation of the bacteriochlorophyll containing light-harvesting Fenna–Mathews–Olson (FMO) protein. In most cases CDC calculations differed from quantum mechanical (QM) calculations in predicting both excited state energy and its fluctuations. The discrepancies arose from the inability of CDC to account for the differing effects of charge on ground and excited state electron orbitals. Results of our study show that QM calculations are indispensible for site energy computations and the quantification of contributions from different parts of the system to the overall site energy shift. We suggest an extension of QM/MM methodology of site energy shift calculations capable of accounting for long-range electrostatic potential contributions from the whole system, including solvent and ions.     

On the influence of pigment-protein interactions on energy transfer processes in photosynthetic membrane structures. 3. The FMO complex of Chlorobium tepidum at high pressure

The low-temperature absorption spectra of the Chlorobium tepidum FMO bacteriochlorophyll-protein complex at various pressures have been calculated within the framework of mini-exciton theory. The dependences of the Qy transition energies of the monomeric pigments on pressure have been found by means of functional minimization. This functional includes the parameters of both theoretical and experimental absorption spectra at low temperatures and various pressures. The dependences obtained are compared with those derived for the exciton transition energies, which have been obtained by deconvoluting absorption spectra with seven Gaussian components at each pressure. The pressure increase has been shown to result in the increased coupling energy between both the pigment molecules themselves and pigments and amino acid residues. The pigment molecules capable of binding histidines and water molecules have been shown to have the greatest and smallest responses to increased pressure, respectively. The couplings of Bchl molecules with the surrounding amino acid residues have been shown to change both the exciton delocalization index and the exciton distribution between the pigment molecules within the protein subunit; the increased pressure does not change these parameters significantly.     

Ultrafast absorption difference spectra of the Fenna-Matthews-Olson protein at 19 K: experiment and simulations.

We describe simulations of absorption difference spectra in strongly coupled photosynthetic antennas. In the presence of large resonance couplings, distinctive features arise from excited-state absorption transitions between one- and two-exciton levels. We first outline the theory for the heterodimer and for the general N-pigment system, and we demonstrate the transition between the strong and weak coupling regimes. The theory is applied to Fenna-Matthews-Olson (FMO) bacteriochlorophyll a protein trimers from the green photosynthetic bacterium Prosthecochloris aestuarii and then compared with experimental low-temperature absorption difference spectra of FMO trimers from the green bacterium Chlorobium tepidum.     

Orientation and excitonic interactions of the Fenna—Matthews—Olson bacteriochlorophyll a protein in membranes of the green sulfur bacterium Chlorobium tepidum

Linear and circular dichroism spectra of isolated bacteriochlorophyll a proteins (FMO proteins) and membrane vesicles containing FMO protein from the green sulfur bacterium Chlorobium tepidum were measured at room temperature and 77 K. The orientation of membranes and isolated FMO protein was obtained by gel squeezing. Linear dichroism (LD) data indicate that isolated FMO protein and membrane vesicles associated with the FMO protein are oriented in a similar way in a squeezed polyacrylamide gel. Both samples show a characteristic negative LD band around 814 nm with flanking positive bands at 802 and 824 nm ascribed to the Q_y excitonic transitions of BChl a of the FMO protein. This confirms that the C3 symmetry axis of the trimer is perpendicular to the membrane plane, which is supported by the model of the disc-like structure of FMO protein trimers of Cb. tepidum [Li Yi-Fen, Zhou W, Blankenship RE, and Allen JP (1997) J Mol Biol 272: 456–471]. The LD data are consistent with either BChl 3 or 6, but not 7 as the principal contributor to the low temperature band at 825 nm. The low temperature linear and circular dichroism spectra of FMO protein trimers from Chlorobium tepidum show significant differences from the low temperature LD and CD spectra of FMO protein trimers from Prosthecochloris aestuarii. The data are interpreted in terms of somewhat different pigment-protein and pigment-pigment interactions in the two complexes.     

Calculation of pigment transition energies in the FMO protein

The Fenna-Matthews-Olson (FMO) protein of green sulfur bacteria represents an important model protein for the study of elementary pigment-protein couplings. We have previously used a simple approach [Adolphs and Renger (2006) Biophys J 91:2778-2797] to study the shift in local transition energies (site energies) of the FMO protein of Prosthecochloris aestuarii by charged amino acid residues, assuming a standard protonation pattern of the titratable groups. Recently, we have found strong evidence that besides the charged amino acids also the neutral charge density of the protein is important, by applying a combined quantum chemical/electrostatic approach [Müh et al. (2007) Proc Natl Acad Sci USA, in press]. Here, we extract the essential parts from this sophisticated method to obtain a relatively simple method again. It is shown that the main contribution to the site energy shifts is due to charge density coupling (CDC) between the pigments and their pigment, protein and water surroundings and that polarization effects for qualitative considerations can be approximated by screening the Coulomb coupling by an effective dielectric constant.     

Structure-based simulation of linear optical spectra of the CP43 core antenna of photosystem II

The linear optical spectra (absorbance, linear dichroism, circular dichroism, fluorescence) of the CP43 (PsbC) antenna of the photosystem II core complex (PSIIcc) pertaining to the S(0)?→?S(1) (Q(Y)) transitions of the chlorophyll (Chl) a pigments are simulated by applying a combined quantum chemical/electrostatic method to obtain excitonic couplings and local transition energies (site energies) on the basis of the 2.9?? resolution crystal structure (Guskov et al., Nat Struct Mol Biol 16:334-342, 2009). The electrostatic calculations identify three Chls with low site energies (Chls 35, 37, and 45 in the nomenclature of Loll et al. (Nature 438:1040-1044, 2005). A refined simulation of experimental spectra of isolated CP43 suggests a modified set of site energies within 143?cm(-1) of the directly calculated values (root mean square deviation: 80?cm(-1)). In the refined set, energy sinks are at Chls 37, 43, and 45 in agreement with earlier fitting results (Raszewski and Renger, J Am Chem Soc 130:4431-4446, 2008). The present structure-based simulations reveal that a large part of the redshift of Chl 37 is due to a digalactosyldiacylglycerol lipid. This finding suggests a new role for lipids in PSIIcc, namely the tuning of optical spectra and the creation of an excitation energy funnel towards the reaction center. The analysis of electrostatic pigment-protein interactions is used to identify amino acid residues that are of potential interest for an experimental approach to an assignment of site energies and energy sinks by site-directed mutagenesis.     

On the influence of pigment-protein interactions on the energy transfer processes in photosynthetic membrane structures

Low-temperature heterogeneous absorption and circular dichroism spectra of the Prosthecochloris aestuarii FMO complex were calculated within the framework of the mini-exciton theory including both the inhomogeneous distribution of exciton line frequencies and static random disorder of the pure electronic transitions of Bchl molecules. The frequencies of the Qy pure electronic transitions of Bchl molecules immobilized by the FMO complex polypeptides were found by minimization of a functional which links the parameters of the theoretical and experimental optical spectra. The interactions of Bchl molecules with surrounding amino acid residues was shown to change both the exciton delocalization index and exciton distribution between the pigment molecules in each exciton energetic state. As a consequence, the interlevel exciton relaxation processes, being accompanied by essential changes in the exciton distribution between pigment molecules, lead to the energy transfer within the FMO complex. The model spectra calculations within the framework of the static random disorder approach were shown to give unacceptable results.     

Extracting the Excitonic Hamiltonian of the Fenna-Matthews-Olson Complex Using Three-Dimensional Third-Order Electronic Spectroscopy

We extend traditional two-dimensional (2D) electronic spectroscopy into a third Fourier dimension without the use of additional optical interactions. By acquiring a set of 2D spectra evenly spaced in waiting time and dividing the area of the spectra into voxels, we can eliminate population dynamics from the data and transform the waiting time dimension into frequency space. The resultant 3D spectrum resolves quantum beating signals arising from excitonic coherences along the waiting frequency dimension, thereby yielding up to 2n-fold redundancy in the set of frequencies necessary to construct a complete set of n excitonic transition energies. Using this technique, we have obtained, to our knowledge, the first fully experimental set of electronic eigenstates for the Fenna-Matthews-Olson (FMO) antenna complex, which can be used to improve theoretical simulations of energy transfer within this protein. Whereas the strong diagonal peaks in the 2D rephasing spectrum of the FMO complex obscure all but one of the crosspeaks at 77 K, extending into the third dimension resolves 19 individual peaks. Analysis of the independently collected nonrephasing data provides the same information, thereby verifying the calculated excitonic transition energies. These results enable one to calculate the Hamiltonian of the FMO complex in the site basis by fitting to the experimental linear absorption spectrum.     

How the molecular structure determines the flow of excitation energy in plant light-harvesting complex II

Excitation energy transfer in the light-harvesting complex II of higher plants is modeled using excitonic couplings and local transition energies determined from structure-based calculations recently (Müh et al., 2010). A theory is introduced that implicitly takes into account protein induced dynamic localization effects of the exciton wavefunction between weakly coupled optical and vibronic transitions of different pigments. Linear and non-linear optical spectra are calculated and compared with experimental data reaching qualitative agreement. High-frequency intramolecular vibrational degrees of freedom are found important for ultrafast subpicosecond excitation energy transfer between chlorophyll (Chl) b and Chla, since they allow for fast dissipation of the excess energy. The slower ps component of this transfer is due to the monomeric excited state of Chlb 605. The majority of exciton relaxation in the Chla spectral region is characterized by slow ps exciton equilibration between the Chla domains within one layer and between the lumenal and stromal layers in the 10-20 ps time range. Subpicosecond exciton relaxation in the Chla region is only found within the terminal emitter domain (Chls a 610/611/612) and within the Chla 613/614 dimer. Deviations between measured and calculated exciton state life times are obtained for the intermediate spectral region between the main absorbance bands of Chla and Chlb that indicate that besides Chlb 608 another pigment should absorb there. Possible candidates, so far not identified by structure-based calculations, but by fitting of optical spectra and mutagenesis studies, are discussed. Additional mutagenesis studies are suggested to resolve this issue.     

Ultrafast light harvesting dynamics in the cryptophyte phycocyanin 645.

Steady-state and femtosecond time-resolved optical methods have been used to study spectroscopic features and energy transfer dynamics in the soluble antenna protein phycocyanin 645 (PC645), isolated from a unicellular cryptophyte Chroomonas CCMP270. Absorption, emission and polarization measurements as well as one-colour pump-probe traces are reported in combination with complementary quantum chemical calculations of electronic transitions of the bilins. Estimation of bilin spectral positions and energy transfer rates aids in the development of a model for light harvesting by PC645. At higher photon energies light is absorbed by the centrally located dimer (DBV, beta50/beta61) and the excitation is subsequently funneled through a complex interference of pathways to four peripheral pigments (MBV alpha19, PCB beta158). Those chromophores transfer the excitation energy to the red-most bilins (PCB beta82). We suggest that the final resonance energy transfer step occurs between the PCB 82 bilins on a timescale estimated to be approximately 15 ps. Such a rapid final energy transfer step cannot be rationalized by calculations that combine experimental parameters and quantum chemical calculations, which predict the energy transfer time to be 40 ps.     

Near edge X-ray absorption fine structure spectroscopy (NEXAFS) of pigment–protein complexes: Peridinin–chlorophyll a protein (PCP) of Amphidinium carterae

Peridinin–chlorophyll a protein (PCP) is a unique water soluble antenna complex that employs the carotenoid peridinin as the main light-harvesting pigment. In the present study the near edge X-ray absorption fine structure (NEXAFS) spectrum of PCP was recorded at the carbon K-edge. Additionally, the NEXAFS spectra of the constituent pigments, chlorophyll a and peridinin, were measured. The energies of the lowest unoccupied molecular levels of these pigments appearing in the carbon NEXAFS spectrum were resolved. Individual contributions of the pigments and the protein to the measured NEXAFS spectrum of PCP were determined using a “building block” approach combining NEXAFS spectra of the pigments and the amino acids constituting the PCP apoprotein. The results suggest that absorption changes of the pigments in the carbon near K-edge region can be resolved following excitation using a suitable visible pump laser pulse. Consequently, it may be possible to study excitation energy transfer processes involving “optically dark” states of carotenoids in pigment–protein complexes by soft X-ray probe optical pump double resonance spectroscopy (XODR).     

Excitation energy transfer in the LHC-II trimer: a model based on the new 2.72 Å structure

Energy transfer of the light harvesting complex LHC-II trimer, extracted from spinach, was studied in the Q(y) region at room temperature by femtosecond transient absorption spectroscopy. Configuration interaction exciton method [Linnanto et al. (1999) J Phys Chem B 103: 8739-8750] and 2.72 A structural information reported by Liu et al. was used to calculate spectroscopic properties and excitation energy transfer rates of the complex. Site energies of the pigments and coupling constants of pigment pairs in close contact were calculated by using a quantum chemical configuration interaction method. Gaussian random variation of the diagonal and off-diagonal exciton matrix elements was used to account for inhomogeneous broadening. Rate calculations included only the excitonic states initially excited and probed in the experiments. A kinetic model was used to simulate time and wavelength dependent absorption changes after excitation on the blue side of the Q(y) transition and compared to experimentally recorded rates. Analysis of excitonic wavefunctions allowed identification of pigments initially excited and probed into later. It was shown that excitation of the blue side of the Q(y) band of a single LHC-II complex results in energy transfer from chlorophyll b's of the lumenal side to chlorophyll a's located primarly on one of the monomers of the stromal side.     

Pump-probe anisotropies of Fenna-Matthews-Olson protein trimers from Chlorobium tepidum: a diagnostic for exciton localization?

Exciton calculations on symmetric and asymmetric Fenna-Matthews-Olson (FMO) trimers, combined with absorption difference anisotropy measurements on FMO trimers from the green bacterium Chlorobium tepidum, suggest that real samples exhibit sufficient diagonal energy disorder so that their laser-excited exciton states are noticeably localized. Our observed anisotropies are clearly inconsistent with 21-pigment exciton simulations based on a threefold-symmetric FMO protein. They are more consistent with a 7-pigment model that assumes that the laser-prepared states are localized within a subunit of the trimer. Differential diagonal energy shifts of 50 cm(-1) between symmetry-related pigments in different subunits are large enough to cause sharp localization in the stationary states; these shifts are commensurate with the approximately 95 cm(-1) inhomogeneous linewidth of the lowest exciton levels. Experimental anisotropies (and by implication steady-state linear and circular dichroism) likely arise from statistical averaging over states with widely contrasting values of these observables, in consequence of their sensitivity to diagonal energy disorder.     

Near edge X-ray absorption fine structure spectroscopy (NEXAFS) of pigment-protein complexes: peridinin-chlorophyll a protein (PCP) of Amphidinium carterae

Peridinin-chlorophyll a protein (PCP) is a unique water soluble antenna complex that employs the carotenoid peridinin as the main light-harvesting pigment. In the present study the near edge X-ray absorption fine structure (NEXAFS) spectrum of PCP was recorded at the carbon K-edge. Additionally, the NEXAFS spectra of the constituent pigments, chlorophyll a and peridinin, were measured. The energies of the lowest unoccupied molecular levels of these pigments appearing in the carbon NEXAFS spectrum were resolved. Individual contributions of the pigments and the protein to the measured NEXAFS spectrum of PCP were determined using a “building block” approach combining NEXAFS spectra of the pigments and the amino acids constituting the PCP apoprotein. The results suggest that absorption changes of the pigments in the carbon near K-edge region can be resolved following excitation using a suitable visible pump laser pulse. Consequently, it may be possible to study excitation energy transfer processes involving “optically dark” states of carotenoids in pigment-protein complexes by soft X-ray probe optical pump double resonance spectroscopy (XODR).     

Theory of optical spectra of photosystem II reaction centers: location of the triplet state and the identity of the primary electron donor

Based on the structural analysis of photosystem II of Thermosynechococcus elongatus, a detailed calculation of optical properties of reaction-center (D1-D2) complexes is presented applying a theory developed previously. The calculations of absorption, linear dichroism, circular dichroism, fluorescence spectra, all at 6 K, and the temperature-dependence of the absorption spectrum are used to extract the local optical transition energies of the reaction-center pigments, the so-called site energies, from experimental data. The site energies are verified by calculations and comparison with seven additional independent experiments. Exciton relaxation and primary electron transfer in the reaction center are studied using the site energies. The calculations are used to interpret transient optical data. Evidence is provided for the accessory chlorophyll of the D1-branch as being the primary electron donor and the location of the triplet state at low temperatures.     

Native electrospray mass spectrometry reveals the nature and stoichiometry of pigments in the FMO photosynthetic antenna protein

The nature and stoichiometry of pigments in the Fenna-Matthews-Olson (FMO) photosynthetic antenna protein complex were determined by native electrospray mass spectrometry. The FMO antenna complex was the first chlorophyll-containing protein that was crystallized. Previous results indicate that the FMO protein forms a trimer with seven bacteriochlorophyll a in each monomer. This model has long been a working basis to understand the molecular mechanism of energy transfer through pigment/pigment and pigment/protein coupling. Recent results have suggested, however, that an eighth bacteriochlorophyll is present in some subunits. In this report, a direct mass spectrometry measurement of the molecular weight of the intact FMO protein complex clearly indicates the existence of an eighth pigment, which is assigned as a bacteriochlorophyll a by mass analysis of the complex and HPLC analysis of the pigment. The eighth pigment is found to be easily lost during purification, which results in its partial occupancy in the mass spectra of the intact complex prepared by different procedures. The results are consistent with the recent X-ray structural models. The existence of the eighth bacteriochlorophyll a in this model antenna protein gives new insights into the functional role of the FMO protein and motivates the need for new theoretical and spectroscopic assignments of spectral features of the FMO protein.     

Chemical oxidation of the FMO antenna protein from Chlorobaculum tepidum

Effect of chemical oxidation by ferricyanide on bacteriochlorophyll a (BChl a) in the Fenna–Matthews–Olson protein (FMO) was studied using absorbance and fluorescence spectroscopy at ambient and cryogenic temperatures. Partially selective oxidation of pigments bound to the antenna complex was achieved and the probable absorption wavelength corresponding to the recently discovered bacteriochlorophyll No. 8 of 806 nm was obtained by comparative analysis of the effect of chemical oxidation and the effect of different isolation procedures. Formation of a stable product identified as a chlorophyll a derivative occurred upon chemical oxidation. This new pigment remained bound within the pigment–protein complex, and exhibited an efficient energy transfer to BChl a. Furthermore, complex effects of the pigment oxidation upon the fluorescence yield of the FMO protein were observed. Utility of this approach based on chemical modifications for the investigation of the native regulatory mechanisms involved in the energy transfer in the FMO protein is discussed.     

Electron transfer in reaction center core complexes from the green sulfur bacteria Prosthecochloris aestuarii and Chlorobium tepidum

Electron transfer in reaction center core (RCC) complexes from the green sulfur bacteria Prosthecochloris aestuarii and Chlorobium tepidum was studied by measuring flash-induced absorbance changes. The first preparation contained approximately three iron-sulfur centers, indicating that the three putative electron acceptors F(X), F(A), and F(B) were present; the Chl. tepidum complex contained on the average only one. In the RCC complex of Ptc. aestuarii at 277 K essentially all of the oxidized primary donor (P840(+)) created by a flash was rereduced in several seconds by N-methylphenazonium methosulfate. In RCC complexes of Chl. tepidum two decay components, one of 0.7 ms and a smaller one of about 2 s, with identical absorbance difference spectra were observed. The fast component might be due to a back reaction of P840(+) with a reduced electron acceptor, in agreement with the notion that the terminal electron acceptors, F(A) and F(B), were lost in most of the Chl. tepidum complexes. In both complexes the terminal electron acceptor (F(A) or F(B)) could be reduced by dithionite, yielding a back reaction of 170 ms with P840(+). At 10 K in the RCC complexes of both species P840(+) was rereduced in 40 ms, presumably by a back reaction with F(X)(-). In addition, a 350 micros component occurred that can be ascribed to decay of the triplet of P840, formed in part of the complexes. For P840(+) rereduction a pronounced temperature dependence was observed, indicating that electron transfer is blocked after F(X) at temperatures below 200 K.     

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.     

Femtosecond energy transfer and spectral equilibration in bacteriochlorophyll a--protein antenna trimers from the green bacterium Chlorobium tepidum.

Femtosecond energy transfer processes in a bacteriochlorophyll a-protein antenna complex from the green sulfur bacterium Chlorobium tepidum have been studied by one-color, two-color, and broadband absorption difference spectroscopy. Much of the spectral excitation equilibration in this antenna occurs with 350 to 450 fs kinetics. The anisotropy decay functions r(t) exhibit two major lifetime components, 100 to 130 fs and 1.7 to 2.0 ps. The short component lifetimes may represent single-step energy transfer kinetics in this antenna; the long component is similar to the anisotropy decay observed in earlier picosecond pump-probe experiments.