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) <i>a</i> 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 <i>a</i> monomers are present in the baseplate carotenosome sample. A refined dimer structure is presented, explaining all four optical spectra

Hole-Burning Spectroscopy on Excitonically Coupled Pigments in Proteins: Theory Meets Experiment

A theory for the calculation of resonant and nonresonant hole-burning (HB) spectra of pigment–protein complexes is presented and applied to the water-soluble chlorophyll-binding protein (WSCP) from cauliflower. The theory is based on a non-Markovian line shape theory (Renger and Marcus J. Chem. Phys. 2002, 116, 9997) and includes exciton delocalization, vibrational sidebands, and lifetime broadening. An earlier approach by Reppert (J. Phys. Chem. Lett. 2011, 2, 2716) is found to describe nonresonant HB spectra only. Here we present a theory that can be used for a quantitative description of HB data for both nonresonant and resonant burning conditions. We find that it is important to take into account the excess energy of the excitation in the HB process. Whereas excitation of the zero-phonon transition of the lowest exciton state, that is, resonant burning allows the protein to access only its conformational substates in the neighborhood of the preburn state, any higher excitation gives the protein full access to all conformations present in the original inhomogeneous ensemble. Application of the theory to recombinant WSCP from cauliflower, reconstituted with chlorophyll <i>a</i> or chlorophyll <i>b</i>, gives excellent agreement with experimental data by Pieper et al. (J. Phys. Chem. B 2011, 115, 4053) and allows us to obtain an upper bound of the lifetime of the upper exciton state directly from the HB experiments in agreement with lifetimes measured recently in time domain 2D experiments by Alster et al. (J. Phys. Chem. B 2014, 118, 3524)

Electrostatic Asymmetry in the Reaction Center of Photosystem II

The exciton Hamiltonian of the chlorophyll (Chl) and pheophytin (Pheo) pigments in the reaction center (RC) of photosystem II is computed based on recent crystal structures by using the Poisson–Boltzmann/quantum-chemical method. Computed site energies largely confirm a previous model inferred from fits of optical spectra, in which Chl_D1 has the lowest site energy, while that of Pheo_D1 is higher than that of Pheo_D2. The latter assignment has been challenged recently under reference to mutagenesis experiments. We argue that these data are not in contradiction to our results. We conclude that Chl_D1 is the primary electron donor in both isolated RCs and intact core complexes at least at cryogenic temperatures. The main source of asymmetry in site energies is the charge distribution in the protein. Because many small contributions from various structural elements have to be taken into account, it can be assumed that this asymmetry was established in evolution by global optimization of the RC protein

Revealing the Functional States in the Active Site of BLUF Photoreceptors from Electrochromic Shift Calculations

Photoexcitation with blue light of the flavin chromophore in BLUF photoreceptors induces a switch into a metastable signaling state that is characterized by a red-shifted absorption maximum. The red shift is due to a rearrangement in the hydrogen bond pattern around Gln63 located in the immediate proximity of the isoalloxazine ring system of the chromophore. There is a long-lasting controversy between two structural models, named Q63_A and Q63_J in the literature, on the local conformation of the residues Gln63 and Tyr21 in the dark state of the photoreceptor. As regards the mechanistic details of the light-activation mechanism, rotation of Gln63 is opposed by tautomerism in the Q63_A and Q63_J models, respectively. We provide a structure-based simulation of electrochromic shifts of the flavin chromophore in the wild type and in various site-directed mutants. The excellent overall agreement between experimental and computed data allows us to evaluate the two structural models. Compelling evidence is obtained that the Q63_A model is incorrect, whereas the Q63_J is fully consistent with the present computations. Finally, we confirm independently that a keto–enol tautomerization of the glutamine at position 63, which was proposed as molecular mechanism for the transition between the dark and the light-adapted state, explains the measured 10 to 15 nm red shift in flavin absorption between these two states of the protein. We believe that the accurateness of our results provides evidence that the BLUF photoreceptors absorption is fine-tuned through electrostatic interactions between the chromophore and the protein matrix, and finally that the simplicity of our theoretical model is advantageous as regards easy reproducibility and further extensions

Theory of FRET “Spectroscopic Ruler” for Short Distances: Application to Polyproline

Förster resonance energy transfer (FRET) is an important mechanism for the estimation of intermolecular distances, e.g., in fluorescent labeled proteins. The interpretations of FRET experiments with standard Förster theory relies on the following approximations: (i) a point-dipole approximation (PDA) for the coupling between transition densities of the chromophores, (ii) a screening of this coupling by the inverse optical dielectric constant of the medium, and (iii) the assumption of fast isotropic sampling over the mutual orientations of the chromophores. These approximations become critical, in particular, at short intermolecular distances, where the PDA and the screening model become invalid and the variation of interchromophore distances, and not just orientations, has a critical influence on the excitation energy transfer. Here, we present a quantum chemical/electrostatic/molecular dynamics (MD) method that goes beyond all of the above approximations. The Poisson-TrEsp method for the ab initio/electrostatic calculation of excitonic couplings in a dielectric medium is combined with all-atom molecular dynamics (MD) simulations to calculate FRET efficiencies. The method is applied to analyze single-molecule experiments on a polyproline helix of variable length labeled with Alexa dyes. Our method provides a quantitative explanation of the overestimation of FRET efficiencies by the standard Förster theory for short interchromophore distances for this system. A detailed analysis of the different levels of approximation that connect the present Poisson-TrEsp/MD method with Förster theory reveals error compensation effects, between the PDA and the neglect of correlations in interchromophore distances and orientations on one hand and the neglect of static disorder in orientations and interchromophore distances on the other. Whereas the first two approximations are found to decrease the FRET efficiency, the latter two overcompensate this decrease and are responsible for the overestimation of the FRET efficiency by Förster theory

Red/Green Color Tuning of Visual Rhodopsins: Electrostatic Theory Provides a Quantitative Explanation

We present a structure-based theory of the long-wavelength (red/green) color tuning in visual rhodopsins and its application to the analysis of site-directed mutagenesis experiments. Using a combination of electrostatic and molecular-mechanics methods, we explain the measured mutant-minus-wild-type absorption shifts and conclude that the dominant mechanism of the color tuning in these systems is electrostatic pigment–protein coupling. An important element of our analysis is the independent determination of protonation states of titratable residues in the wild type and the mutant protein as well as the self-consistent reoptimization of hydrogen atom positions, which includes the relaxation of the hydrogen bonding network and the reorientation of water molecules. On the basis of this analysis, we propose a “dipole-orientation rule” according to which both the position and the orientation of a polar group introduced in the protein environment determine the direction of the transition energy shift of the retinal chromophore

Photosystem II Does Not Possess a Simple Excitation Energy Funnel: Time-Resolved Fluorescence Spectroscopy Meets Theory

The experimentally obtained time-resolved fluorescence spectra of photosystem II (PS II) core complexes, purified from a thermophilic cyanobacterium Thermosynechococcus vulcanus, at 5–180 K are compared with simulations. Dynamic localization effects of excitons are treated implicitly by introducing exciton domains of strongly coupled pigments. Exciton relaxations within a domain and exciton transfers between domains are treated on the basis of Redfield theory and generalized Förster theory, respectively. The excitonic couplings between the pigments are calculated by a quantum chemical/electrostatic method (Poisson-TrEsp). Starting with previously published values, a refined set of site energies of the pigments is obtained through optimization cycles of the fits of stationary optical spectra of PS II. Satisfactorily agreement between the experimental and simulated spectra is obtained for the absorption spectrum including its temperature dependence and the linear dichroism spectrum of PS II core complexes (PS II-CC). Furthermore, the refined site energies well reproduce the temperature dependence of the time-resolved fluorescence spectrum of PS II-CC, which is characterized by the emergence of a 695 nm fluorescence peak upon cooling down to 77 K and the decrease of its relative intensity upon further cooling below 77 K. The blue shift of the fluorescence band upon cooling below 77 K is explained by the existence of two red-shifted chlorophyll pools emitting at around 685 and 695 nm. The former pool is assigned to Chl45 or Chl43 in CP43 (Chl numbering according to the nomenclature of Loll et al. <i>Nature</i> <b>2005</b>, <i>438</i>, 1040) while the latter is assigned to Chl29 in CP47. The 695 nm emitting chlorophyll is suggested to attract excitations from the peripheral light-harvesting complexes and might also be involved in photoprotection

Calculating Optical Absorption Spectra of Thin Polycrystalline Organic Films: Structural Disorder and Site-Dependent van der Waals Interaction

We propose a new approach for calculating the change of the absorption spectrum of a molecule when moved from the gas phase to a crystalline morphology. The so-called gas-to-crystal shift ΔE<i>_m</i> is mainly caused by dispersion effects and depends sensitively on the molecule’s specific position in the nanoscopic setting. Using an extended dipole approximation, we are able to divide ΔE_<i>m</i>= −<i>QW</i>_<i>m</i> in two factors, where <i>Q</i> depends only on the molecular species and accounts for all nonresonant electronic transitions contributing to the dispersion while <i>W</i>_m is a geometry factor expressing the site dependence of the shift in a given molecular structure. The ability of our approach to predict absorption spectra is demonstrated using the example of polycrystalline films of 3,4,9,10-perylenetetracarboxylic diimide (PTCDI)

Normal Mode Analysis of the Spectral Density of the Fenna–Matthews–Olson Light-Harvesting Protein: How the Protein Dissipates the Excess Energy of Excitons

We report a method for the structure-based calculation of the spectral density of the pigment–protein coupling in light-harvesting complexes that combines normal-mode analysis with the charge density coupling (CDC) and transition charge from electrostatic potential (TrEsp) methods for the computation of site energies and excitonic couplings, respectively. The method is applied to the Fenna–Matthews–Olson (FMO) protein in order to investigate the influence of the different parts of the spectral density as well as correlations among these contributions on the energy transfer dynamics and on the temperature-dependent decay of coherences. The fluctuations and correlations in excitonic couplings as well as the correlations between coupling and site energy fluctuations are found to be 1 order of magnitude smaller in amplitude than the site energy fluctuations. Despite considerable amplitudes of that part of the spectral density which contains correlations in site energy fluctuations, the effect of these correlations on the exciton population dynamics and dephasing of coherences is negligible. The inhomogeneous charge distribution of the protein, which causes variations in local pigment–protein coupling constants of the normal modes, is responsible for this effect. It is seen thereby that the same building principle that is used by nature to create an excitation energy funnel in the FMO protein also allows for efficient dissipation of the excitons’ excess energy

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