Theory of Excitation Energy Transfer and Optical Spectra of Photosynthetic Systems

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.

On uncorrelated inter-monomer Förster energy transfer in Fenna-Matthews-Olson complexes

The Fenna-Matthews-Olson (FMO) light-harvesting antenna protein of green sulfur bacteria is a long-studied pigment-protein complex which funnels energy from the chlorosome to the reaction centre where photochemistry takes place. The structure of the FMO protein from Chlorobaculum tepidum is known as a homotrimeric complex containing eight bacteriochlorophyll a per monomer. Owing to this structure FMO has strong intra-monomer and weak inter-monomer electronic coupling constants. While long-lived (sub-picosecond) coherences within a monomer have been a prevalent topic of study over the past decade, various experimental evidence supports the presence of subsequent inter-monomer energy transfer on a picosecond time scale. The latter has been neglected by most authors in recent years by considering only sub-picosecond time scales or assuming that the inter-monomer coupling between low-energy states is too weak to warrant consideration of the entire trimer. However, Förster theory predicts that energy transfer of the order of picoseconds is possible even for very weak (less than 5 cm^-1) electronic coupling between chromophores. This work reviews experimental data (with a focus on emission and hole-burned spectra) and simulations of exciton dynamics which demonstrate inter-monomer energy transfer. It is shown that the lowest energy 825 nm absorbance band cannot be properly described by a single excitonic state. The energy transfer through FMO is modelled by generalized Förster theory using a non-Markovian, reduced density matrix approach to describe the electronic structure. The disorder-averaged inter-monomer transfer time across the 825 nm band is about 27 ps. While only isolated FMO proteins are presented, the presence of inter-monomer energy transfer in the context of the overall photosystem is also briefly discussed.

Temperature-dependent vibrational and conformational dynamics of photosystem II membrane fragments from spinach investigated by elastic and inelastic neutron scattering

Vibrational and conformational protein dynamics of photosystem II (PS II) membrane fragments from spinach were investigated by elastic and inelastic incoherent neutron scattering (EINS and IINS). As to the EINS experiments, the average atomic mean square displacement values of PS II membrane fragments hydrated at a relative humidity of 57% exhibit a dynamical transition at ~230K. In contrast, the dynamical transition was absent at a relative humidity of 44%. These findings are in agreement with previous studies which reported a "freezing" of protein mobility due to dehydration (Pieper et al. (2008) Eur. Biophys. J. 37: 657-663) and its correlation with an inhibition of electron transfer from Q(A)(-) to Q(B) (Kaminskaya et al. (2003) Biochemistry 42, 8119-8132). IINS spectra of a sample hydrated at a relative humidity of 57% show a distinct Boson peak at ~7.5meV at 20K, which shifts towards lower energy values upon temperature increase to 250K. This unexpected effect is interpreted in terms of a "softening" of the protein matrix along with the onset of conformational protein dynamics as revealed by the EINS experiments. Information on the density of vibrational states of pigment-protein complexes is important for a realistic calculation of excitation energy transfer kinetics and spectral lineshapes and is often routinely obtained by optical line-narrowing spectroscopy at liquid helium temperature. The data presented here demonstrate that IINS is a valuable experimental tool in determining the density of vibrational states not only at cryogenic, but also at nearly physiological temperatures up to 250K. This article is part of a Special Issue entitled: Photosynthesis Research for Sustainability: from Natural to Artificial.

Quantum chemical description of absorption properties and excited-state processes in photosynthetic systems

The theoretical description of the initial steps in photosynthesis has gained increasing importance over the past few years. This is caused by more and more structural data becoming available for light-harvesting complexes and reaction centers which form the basis for atomistic calculations and by the progress made in the development of first-principles methods for excited electronic states of large molecules. In this Review, we discuss the advantages and pitfalls of theoretical methods applicable to photosynthetic pigments. Besides methodological aspects of excited-state electronic-structure methods, studies on chlorophyll-type and carotenoid-like molecules are discussed. We also address the concepts of exciton coupling and excitation-energy transfer (EET) and compare the different theoretical methods for the calculation of EET coupling constants. Applications to photosynthetic light-harvesting complexes and reaction centers based on such models are also analyzed.

Introduction to theory/modeling methods in photosynthesis

Theory and molecular modeling play an increasingly important role in complementing the experimental findings and supporting the interpretation of the data. Owing to the increase in computational power combined with the development of more efficient methods, computer simulations and modeling have emerged as primary ingredients of modern scientific inquiry. Here, we introduce the methods that in our view bring the largest promises in photosynthesis research, indicate how they have already contributed, and can in the near future assume a significant role in this field. Particular emphasis is given to density functional theory and its combination with molecular dynamics simulations. We point out the need for a multi-scale approach in facing the challenging task of describing processes which cover several orders of magnitude both in the time scale and in the size of the systems of interest.

Theory of excitation energy transfer: from structure to function

This mini-review summarizes our current theoretical knowledge about excitation energy transfer in pigment-protein complexes. The challenge for theory lies in the complexity of these systems and in the fact that the pigment-pigment and the pigment-protein interactions are of equal magnitude. The first part of this review contains an introduction to the theory of light harvesting and to structure- based calculations of the parameters of the theory. The second part provides a discussion of the standard Förster and Redfield theories of excitation energy transfer, which are valid in the limit of weak and strong pigment-pigment coupling, respectively. Afterward, we provide a description of recent extensions of the standard theories and discuss challenging problems to be solved in the future.

Fluorescence lifetimes: fundamentals and interpretations

Fluorescence measurements have been an established mainstay of photosynthesis experiments for many decades. Because in the photosynthesis literature the basics of excited states and their fates are not usually described, we have presented here an easily understandable text for biology students in the style of a chapter in a text book. In this review we give an educational overview of fundamental physical principles of fluorescence, with emphasis on the temporal response of emission. Escape from the excited state of a molecule is a dynamic event, and the fluorescence emission is in direct kinetic competition with several other pathways of de-excitation. It is essentially through a kinetic competition between all the pathways of de-excitation that we gain information about the fluorescent sample on the molecular scale. A simple probability allegory is presented that illustrates the basic ideas that are important for understanding and interpreting most fluorescence experiments. We also briefly point out challenges that confront the experimenter when interpreting time-resolved fluorescence responses.