Theory of excitation energy transfer: from structure to function

Structural Basis for the Unusual Qy Red-Shift and Enhanced Thermostability of the LH1 Complex from Thermochromatium tepidum

While the majority of the core light-harvesting complexes (LH1) in purple photosynthetic bacteria exhibit a Q_y absorption band in the range of 870-890 nm, LH1 from the thermophilic bacterium Thermochromatium tepidum displays the Q_y band at 915 nm with an enhanced thermostability. These properties are regulated by Ca²⁺ ions. Substitution of the Ca²⁺ with other divalent metal ions results in a complex with the Q_y band blue-shifted to 880-890 nm and a reduced thermostability. Following the recent publication of the structure of the Ca-bound LH1-reaction center (RC) complex [Niwa, S., et al. (2014) Nature 508, 228], we have determined the crystal structures of the Sr- and Ba-substituted LH1-RC complexes with the LH1 Q_y band at 888 nm. Sixteen Sr²⁺ and Ba²⁺ ions are identified in the LH1 complexes. Both Sr²⁺ and Ba²⁺ are located at the same positions, and these are clearly different from, though close to, the Ca²⁺-binding sites. Conformational rearrangement induced by the substitution is limited to the metal-binding sites. Unlike the Ca-LH1-RC complex, only the α-polypeptides are involved in the Sr and Ba coordinations in LH1. The difference in the thermostability between these complexes can be attributed to the different patterns of the network formed by metal binding. The Sr- and Ba-LH1-RC complexes form a single-ring network by the LH1 α-polypeptides only, in contrast to the double-ring network composed of both α- and β-polypeptides in the Ca-LH1-RC complex. On the basis of the structural information, a combined effect of hydrogen bonding, structural integrity, and charge distribution is considered to influence the spectral properties of the core antenna complex.

Conformational control of cofactors in nature - the influence of protein-induced macrocycle distortion on the biological function of tetrapyrroles

Tetrapyrrole-containing proteins are one of the most fundamental classes of enzymes in nature and it remains an open question to give a chemical rationale for the multitude of biological reactions that can be catalyzed by these pigment-protein complexes. There are many fundamental processes where the same (i.e., chemically identical) porphyrin cofactor is involved in chemically quite distinct reactions. For example, heme is the active cofactor for oxygen transport and storage (hemoglobin, myoglobin) and for the incorporation of molecular oxygen in organic substrates (cytochrome P450). It is involved in the terminal oxidation (cytochrome c oxidase) and the metabolism of H2O2 (catalases and peroxidases) and catalyzes various electron transfer reactions in cytochromes. Likewise, in photosynthesis the same chlorophyll cofactor may function as a reaction center pigment (charge separation) or as an accessory pigment (exciton transfer) in light harvesting complexes (e.g., chlorophyll a). Whilst differences in the apoprotein sequences alone cannot explain the often drastic differences in physicochemical properties encountered for the same cofactor in diverse protein complexes, a critical factor for all biological functions must be the close structural interplay between bound cofactors and the respective apoprotein in addition to factors such as hydrogen bonding or electronic effects. Here, we explore how nature can use the same chemical molecule as a cofactor for chemically distinct reactions using the concept of conformational flexibility of tetrapyrroles. The multifaceted roles of tetrapyrroles are discussed in the context of the current knowledge on distorted porphyrins. Contemporary analytical methods now allow a more quantitative look at cofactors in protein complexes and the development of the field is illustrated by case studies on hemeproteins and photosynthetic complexes. Specific tetrapyrrole conformations are now used to prepare bioengineered designer proteins with specific catalytic or photochemical properties.

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.

Quantum Chemical Studies of Light Harvesting

The design of optimal light-harvesting (supra)molecular systems and materials is one of the most challenging frontiers of science. Theoretical methods and computational models play a fundamental role in this difficult task, as they allow the establishment of structural blueprints inspired by natural photosynthetic organisms that can be applied to the design of novel artificial light-harvesting devices. Among theoretical strategies, the application of quantum chemical tools represents an important reality that has already reached an evident degree of maturity, although it still has to show its real potentials. This Review presents an overview of the state of the art of this strategy, showing the actual fields of applicability but also indicating its current limitations, which need to be solved in future developments.

Contribution of bacteriochlorophyll conformation to the distribution of site-energies in the FMO protein

The structural data for the Fenna-Matthews-Olson (FMO) protein indicate that the bacteriochlorophylls (BChls) display a significant degree of conformational heterogeneity of their peripheral substituents and the protein-induced nonplanar skeletal deformations of the tetrapyrrole macrocycle. As electronic properties of chromophores are altered by such differences, a conformational effect may influence the site-energies of specific pigments and thus play a role in mediating the excitation energy transfer dynamics, but this has not yet been established. The difficulty of assessing this question is shown to be partly the result of the inability of the sequential truncation approach usually employed to account for interactions between the conformations of the macrocycle and its substituents and an alternative approach is suggested. By assigning the BChl atoms to meaningful atom groups and performing all possible permutations of partial optimizations in a full-factorial design, where each group is either frozen in the crystal geometry or optimized in vacuo, followed by excited state calculations on each resulting structure (PM6//ZIndo/S), the specific effects of the conformations of each BChl component as well as mutual interactions between the molecular fragments on the site-energy can be delineated. This factorial relaxation procedure gives different estimates of the macrocycle conformational perturbation than the approach of sequentially truncating the BChl periphery. The results were evaluated in the context of published site-energies for the FMO pigments from three species to identify how conformational effects contribute to their distribution and instances of cross-species conservation and functional divergence of the BChl nonplanarity conformational contribution are described.

Structure-Based Modeling of Fluorescence Kinetics of Photosystem II: Relation between Its Dimeric Form and Photoregulation

A photosystem II-enriched membrane (PSII-em) consists of the PSII core complex (PSII-cc) which is surrounded by peripheral antenna complexes. PSII-cc consists of two core antenna (CP43 and CP47) and the reaction center (RC) complex. Time-resolved fluorescence spectra of a PSII-em were measured at 77 K. The data were globally analyzed with a new compartment model, which has a minimum number of compartments and is consistent with the structure of PSII-cc. The reliability of the model was investigated by fitting the data of different experimental conditions. From the analysis, the energy-transfer time constants from the peripheral antenna to CP47 and CP43 were estimated to be 20 and 35 ps, respectively. With an exponential time constant of 320 ps, the excitation energy was estimated to accumulate in the reddest chlorophyll (Red Chl), giving a 692 nm fluorescence peak. The excited state on the Red Chl was confirmed to be quenched upon the addition of an oxidant, as reported previously. The calculations based on the Förster theory predicted that the excitation energy on Chl29 is quenched by ChlZD1(+), which is a redox active but not involved in the electron-transfer chain, located in the D1 subunit of RC, in the other monomer with an exponential time constant of 75 ps. This quenching pathway is consistent with our structure-based simulation of PSII-cc, which assigned Chl29 as the Red Chl. On the other hand, the alternative interpretation assigning Chl26 as the Red Chl was not excluded. The excited Chl26 was predicted to be quenched by another redox active ChlZD2(+) in the D2 subunit of RC in the same monomer unit with an exponential time constant of 88 ps.

Quantifying highly efficient incoherent energy transfer in perylene-based multichromophore arrays

Multichromophore perylene arrays were designed and synthesized to have extremely efficient resonance energy transfer, as confirmed by ultrafast spectroscopy.

Energy transfer efficiency in the chromophore network strongly coupled to a vibrational mode

Using methods from condensed matter and statistical physics, we examine the transport of excitons through the photosynthetic complex from a receiving antenna to a reaction center. Writing the equations of motion for the exciton creation-annihilation operators, we are able to describe the exciton dynamics, even in the regime when the reorganization energy is of the order of the intrasystem couplings. We determine the exciton transfer efficiency in the presence of a quenching field and protein environment. While the majority of the protein vibrational modes are treated as a heat bath, we address the situation when specific modes are strongly coupled to excitons and examine the effects of these modes on the energy transfer efficiency in the steady-state regime. Using the structural parameters of the Fenna-Matthews-Olson complex, we find that, for vibrational frequencies below 16 meV, the exciton transfer is drastically suppressed. We attribute this effect to the formation of a "mixed exciton-vibrational mode" where the exciton is transferred back and forth between the two pigments with the absorption or emission of vibrational quanta, instead of proceeding to the reaction center. The same effect suppresses the quantum beating at the vibrational frequency of 25 meV. We also show that the efficiency of the energy transfer can be enhanced when the vibrational mode strongly couples to the third pigment only, instead of coupling to the entire system.

Quantum mechanics of excitation transport in photosynthetic complexes: a key issues review

For a long time microscopic physical descriptions of biological processes have been based on quantum mechanical concepts and tools, and routinely employed by chemical physicists and quantum chemists. However, the last ten years have witnessed new developments on these studies from a different perspective, rooted in the framework of quantum information theory. The process that more, than others, has been subject of intense research is the transfer of excitation energy in photosynthetic light-harvesting complexes, a consequence of the unexpected experimental discovery of oscillating signals in such highly noisy systems. The fundamental interdisciplinary nature of this research makes it extremely fascinating, but can also constitute an obstacle to its advance. Here in this review our objective is to provide an essential summary of the progress made in the theoretical description of excitation energy dynamics in photosynthetic systems from a quantum mechanical perspective, with the goal of unifying the language employed by the different communities. This is initially realized through a stepwise presentation of the fundamental building blocks used to model excitation transfer, including protein dynamics and the theory of open quantum system. Afterwards, we shall review how these models have evolved as a consequence of experimental discoveries; this will lead us to present the numerical techniques that have been introduced to quantitatively describe photo-absorbed energy dynamics. Finally, we shall discuss which mechanisms have been proposed to explain the unusual coherent nature of excitation transport and what insights have been gathered so far on the potential functional role of such quantum features.

Manipulating Excited-State Dynamics of Individual Light-Harvesting Chromophores through Restricted Motions in a Hydrated Nanoscale Protein Cavity

Manipulating the photophysical properties of light-absorbing units is a crucial element in the design of biomimetic light-harvesting systems. Using a highly tunable synthetic platform combined with transient absorption and time-resolved fluorescence measurements and molecular dynamics simulations, we interrogate isolated chromophores covalently linked to different positions in the interior of the hydrated nanoscale cavity of a supramolecular protein assembly. We find that, following photoexcitation, the time scales over which these chromophores are solvated, undergo conformational rearrangements, and return to the ground state are highly sensitive to their position within this cavity and are significantly slower than in a bulk aqueous solution. Molecular dynamics simulations reveal the hindered translations and rotations of water molecules within the protein cavity with spatial specificity. The results presented herein show that fully hydrated nanoscale protein cavities are a promising way to mimic the tight protein pockets found in natural light-harvesting complexes. We also show that the interplay between protein, solvent, and chromophores can be used to substantially tune the relaxation processes within artificial light-harvesting assemblies in order to significantly improve the yield of interchromophore energy transfer and extend the range of excitation transport. Our observations have implications for other important, similarly sized bioinspired materials, such as nanoreactors and biocompatible targeted delivery agents.

An efficient implementation of the localized operator partitioning method for electronic energy transfer

The localized operator partitioning method [Y. Khan and P. Brumer, J. Chem. Phys. 137, 194112 (2012)] rigorously defines the electronic energy on any subsystem within a molecule and gives a precise meaning to the subsystem ground and excited electronic energies, which is crucial for investigating electronic energy transfer from first principles. However, an efficient implementation of this approach has been hindered by complicated one- and two-electron integrals arising in its formulation. Using a resolution of the identity in the definition of partitioning, we reformulate the method in a computationally efficient manner that involves standard one- and two-electron integrals. We apply the developed algorithm to the 9-((1-naphthyl)-methyl)-anthracene (A1N) molecule by partitioning A1N into anthracenyl and CH2-naphthyl groups as subsystems and examine their electronic energies and populations for several excited states using configuration interaction singles method. The implemented approach shows a wide variety of different behaviors amongst the excited electronic states.

Generalized master equation with non-Markovian multichromophoric Förster resonance energy transfer for modular exciton densities

A generalized master equation (GME) governing quantum evolution of modular exciton density (MED) is derived for large scale light harvesting systems composed of weakly interacting modules of multiple chromophores. The GME-MED offers a practical framework to incorporate real time coherent quantum dynamics calculations of small length scales into dynamics over large length scales, and also provides a non-Markovian generalization and rigorous derivation of the Pauli master equation employing multichromophoric Förster resonance energy transfer rates. A test of the GME-MED for four sites of the Fenna-Matthews-Olson complex demonstrates how coherent dynamics of excitonic populations over coupled chromophores can be accurately described by transitions between subgroups (modules) of delocalized excitons. Application of the GME-MED to the exciton dynamics between a pair of light harvesting complexes in purple bacteria demonstrates its promise as a computationally efficient tool to investigate large scale exciton dynamics in complex environments.

Dynamic protein conformations preferentially drive energy transfer along the active chain of the photosystem II reaction centre

One longstanding puzzle concerning photosystem II, a core component of photosynthesis, is that only one of the two symmetric branches in its reaction centre is active in electron transfer. To investigate the effect of the photosystem II environment on the preferential selection of the energy transfer pathway (a prerequisite for electron transfer), we have constructed an exciton model via extensive molecular dynamics simulations and quantum mechanics/molecular mechanics calculations based on a recent X-ray structure. Our results suggest that it is essential to take into account an ensemble of protein conformations to accurately compute the site energies. We identify the cofactor CLA606 of active chain as the most probable site for the energy excitation. We further pinpoint a number of charged protein residues that collectively lower the CLA606 site energy. Our work provides insights into the understanding of molecular mechanisms of the core machinery of the green-plant photosynthesis.

Cofactor-mediated energy and electron transfer in photosystem II occurs preferentially through one branch of the reaction centre, despite there being a symmetric path available. Here, the authors use computational methods to determine the influence of protein conformation on this selectivity.

From localized excited States to excitons: changing of conceptions of primary photosynthetic processes in the twentieth century

A short description of two theories of the primary photosynthetic processes is given. Generally accepted in 1950s-1990s, the localized excited states theory has been changed to the modern exciton theory. Appearance of the new experimental data and the light-harvesting complex crystal structure are reasons why the exciton theory has become important. The bulk of data for the old theory and outstanding experiments that have been the driving force for a new theory are discussed in detail.

Photosynthetic light harvesting: excitons and coherence

Photosynthesis begins with light harvesting, where specialized pigment-protein complexes transform sunlight into electronic excitations delivered to reaction centres to initiate charge separation. There is evidence that quantum coherence between electronic excited states plays a role in energy transfer. In this review, we discuss how quantum coherence manifests in photosynthetic light harvesting and its implications. We begin by examining the concept of an exciton, an excited electronic state delocalized over several spatially separated molecules, which is the most widely available signature of quantum coherence in light harvesting. We then discuss recent results concerning the possibility that quantum coherence between electronically excited states of donors and acceptors may give rise to a quantum coherent evolution of excitations, modifying the traditional incoherent picture of energy transfer. Key to this (partially) coherent energy transfer appears to be the structure of the environment, in particular the participation of non-equilibrium vibrational modes. We discuss the open questions and controversies regarding quantum coherent energy transfer and how these can be addressed using new experimental techniques.

Excitons in the LH3 complexes from purple bacteria

The noncovalently bound and structurally identical bacteriochlorophyll a chromophores in the peripheral light-harvesting complexes LH2 (B800-850) and LH3 (B800-820) from photosynthetic purple bacteria ensure the variability of the exciton spectra in the near-infrared (820-850 nm) wavelength region. As a result, the spectroscopic properties of the antenna complexes, such as positions of the maxima in the exciton absorption spectra, give rise to very efficient excitation transfer toward the reaction center. In this work, we investigated the possible molecular origin of the excitonically coupled B820 bacteriochlorophylls in LH3 using femtosecond transient absorption spectroscopy, deconvolution of steady-state absorption spectra, and modeling of the electrostatic intermolecular interactions using a charge density coupling approach. Compared to LH2, the upper excitonic level is red-shifted from 755 to 790 nm and is associated with an approximate 2-fold decrease of B820 intrapigment coupling. The absorption properties of LH3 cannot be reproduced by only changing the B850 site energy but also require a different scaling factor to be used to calculate interpigment couplings and a change of histidine protonation state. Several protonation patterns for distinct amino acid groups are presented, giving values of 162-173 cm(-1) at 100 K for the intradimer resonance interaction in the B820 ring.

Understanding photosynthetic light-harvesting: a bottom up theoretical approach

We discuss a bottom up approach for modeling photosynthetic light-harvesting. Methods are reviewed for a full structure-based parameterization of the Hamiltonian of pigment-protein complexes (PPCs). These parameters comprise (i) the local transition energies of the pigments in their binding sites in the protein, the site energies; (ii) the couplings between optical transitions of the pigments, the excitonic couplings; and (iii) the spectral density characterizing the dynamic modulation of pigment transition energies and excitonic couplings by protein vibrations. Starting with quantum mechanics perturbation theory, we provide a microscopic foundation for the standard PPC Hamiltonian and relate the expressions obtained for its matrix elements to quantities that can be calculated with classical molecular mechanics/electrostatics approaches including the whole PPC in atomic detail and using charge and transition densities obtained with quantum chemical calculations on the isolated building blocks of the PPC. In the second part of this perspective, the Hamiltonian is utilized to describe the quantum dynamics of excitons. Situations are discussed that differ in the relative strength of excitonic and exciton-vibrational coupling. The predictive power of the approaches is demonstrated in application to different PPCs, and challenges for future work are outlined.

Two-Dimensional Electronic Spectroscopy Reveals Ultrafast Downhill Energy Transfer in Photosystem I Trimers of the Cyanobacterium Thermosynechococcus elongatus

Two-dimensional electronic spectroscopy (2DES) was used to investigate the ultrafast energy-transfer dynamics of trimeric photosystem I of the cyanobacterium Thermosynechococcus elongatus. We demonstrate the ability of 2DES to resolve dynamics in a large pigment-protein complex containing ∼300 chromophores with both high frequency and time resolution. Monitoring the waiting-time-dependent changes of the line shape of the inhomogeneously broadened Qy(0-0) transition, we directly observe downhill energy equilibration on the 50 fs time scale.

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.