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.     

Photon echo studies of photosynthetic light harvesting

The broad linewidths in absorption spectra of photosynthetic complexes obscure information related to their structure and function. Photon echo techniques represent a powerful class of time-resolved electronic spectroscopy that allow researchers to probe the interactions normally hidden under broad linewidths with sufficient time resolution to follow the fastest energy transfer events in light harvesting. Here, we outline the technical approach and applications of two types of photon echo experiments: the photon echo peak shift and two-dimensional (2D) Fourier transform photon echo spectroscopy. We review several extensions of these techniques to photosynthetic complexes. Photon echo peak shift spectroscopy can be used to determine the strength of coupling between a pigment and its surrounding environment including neighboring pigments and to quantify timescales of energy transfer. Two-dimensional spectroscopy yields a frequency-resolved map of absorption and emission processes, allowing coupling interactions and energy transfer pathways to be viewed directly. Furthermore, 2D spectroscopy reveals structural information such as the relative orientations of coupled transitions. Both classes of experiments can be used to probe the quantum mechanical nature of photosynthetic light-harvesting: peak shift experiments allow quantification of correlated energetic fluctuations between pigments, while 2D techniques measure quantum beating directly, both of which indicate the extent of quantum coherence over multiple pigment sites in the protein complex. The mechanistic and structural information obtained by these techniques reveals valuable insights into the design principles of photosynthetic light-harvesting complexes, and a multitude of variations on the methods outlined here.     

Theoretical characterization of excitation energy transfer in chlorosome light-harvesting antennae from green sulfur bacteria

We present a theoretical study of excitation dynamics in the chlorosome antenna complex of green photosynthetic bacteria based on a recently proposed model for the molecular assembly. Our model for the excitation energy transfer (EET) throughout the antenna combines a stochastic time propagation of the excitonic wave function with molecular dynamics simulations of the supramolecular structure and electronic structure calculations of the excited states. We characterized the optical properties of the chlorosome with absorption, circular dichroism and fluorescence polarization anisotropy decay spectra. The simulation results for the excitation dynamics reveal a detailed picture of the EET in the chlorosome. Coherent energy transfer is significant only for the first 50 fs after the initial excitation, and the wavelike motion of the exciton is completely damped at 100 fs. Characteristic time constants of incoherent energy transfer, subsequently, vary from 1 ps to several tens of ps. We assign the time scales of the EET to specific physical processes by comparing our results with the data obtained from time-resolved spectroscopy experiments.     

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.     

Coherent phenomena in photosynthetic light harvesting: part one—theory and spectroscopy

The role of non-trivial quantum mechanical effects in biology has been the subject of intense scrutiny over the past decade. Much of the focus on potential “quantum biology” has been on energy transfer processes in photosynthetic light harvesting systems. Ultrafast laser spectroscopy of several light harvesting proteins has uncovered coherent oscillations dubbed “quantum beats” that persist for hundreds of femtoseconds and are putative signatures for quantum transport phenomena. This review describes the language and basic quantum mechanical phenomena that underpin quantum transport in open systems such as light harvesting and photosynthetic proteins, including the photosystem reaction centre. Coherent effects are discussed in detail, separating various meanings of the term, from delocalized excitations, or excitons, to entangled states and coherent transport. In particular, we focus on the time, energy and length scales of energy transport processes, as these are critical in understanding whether or not coherent processes are important. The role played by the protein in maintaining chromophore systems is analysed. Finally, the spectroscopic techniques that are used to probe energy transfer dynamics and that have uncovered the quantum beats are described with reference to coherent phenomena in light harvesting.     

Quantum-classical model of retinal photoisomerization reaction in visual pigment rhodopsin

A quantum-classical model of photoisomerization of the visual pigment rhodopsin chromophore is proposed. At certain (and more realistic) parameter value combinations, the model is shown to accurately reproduce a number of independent experimental data on the photoreaction dynamics: the quantum yield, the time to reach the point of conical intersection of potential energy surfaces, the termination time of the evolution of quantum subsystem, as well as the characteristic low frequencies of retinal molecular lattice fluctuations during photoisomerization. In addition, the model behavior is in good accordance with experimental data about coherence and local character of quantum transition.     

Insights into the mechanisms and dynamics of energy transfer in plant light-harvesting complexes from two-dimensional electronic spectroscopy

During the past two decades, two-dimensional electronic spectroscopy (2DES) and related techniques have emerged as a potent experimental toolset to study the ultrafast elementary steps of photosynthesis. Apart from the highly engaging albeit controversial analysis of the role of quantum coherences in the photosynthetic processes, 2DES has been applied to resolve the dynamics and pathways of energy and electron transport in various light-harvesting antenna systems and reaction centres, providing unsurpassed level of detail. In this paper we discuss the main technical approaches and their applicability for solving specific problems in photosynthesis. We then recount applications of 2DES to study the exciton dynamics in plant and photosynthetic light-harvesting complexes, especially light-harvesting complex II (LHCII) and the fucoxanthin-chlorophyll proteins of diatoms, with emphasis on the types of unique information about such systems that 2DES is capable to deliver. This article is part of a Special Issue entitled Light harvesting, edited by Dr. Roberta Croce.     

Suppressing Energy Loss due to Triplet Exciton Formation in Organic Solar Cells: The Role of Chemical Structures and Molecular Packing

In the most efficient solar cells based on blends of a conjugated polymer (electron donor) and a fullerene derivative (electron acceptor),ultrafast formation of charge‐transfer (CT) electronic states at the donor‐acceptor interfaces and efficient separation of these CT states into free charges, lead to internal quantum efficiencies near 100%. However, there occur substantial energy losses due to the non‐radiative recombinations of the charges, mediated by the loweset‐energy (singlet and triplet) CT states; for example, such recombinations can lead to the formation of triplet excited electronic states on the polymer chains, which do not generate free charges. This issue remains a major factor limiting the power conversion efficiencies (PCE) of these devices. The recombination rates are, however, difficult to quantify experimentally. To shed light on these issues, here, an integrated multi‐scale theoretical approach that combines molecular dynamics simulations with quantum chemistry calculations is employed in order to establish the relationships among chemical structures, molecular packing, and non‐radiative recombination losses mediated by the lowest‐energy charge‐transfer states.     

Insight into the structural dynamics of light sensitive proteins from time-resolved crystallography and quantum chemical calculations

The structural dynamics underlying molecular mechanisms of light-sensitive proteins can be studied by a variety of experimental and computational biophysical techniques. Here we review recent progress in combining time-resolved crystallography at X-ray free electron lasers and quantum chemical calculations to study structural changes in photoenzymes, photosynthetic proteins, photoreceptors, and photoswitchable fluorescent proteins following photoexcitation.     

Electronic excited states and excitation transfer kinetics in the Fenna-Matthews-Olson protein of the photosynthetic bacterium Prosthecochloris aestuarii at low temperatures

The molecular structure-function relationship of the Fenna-Matthews-Olson light-harvesting complex of the photosynthetic green bacterium Prosthecochloris aestuarii has been investigated. It has been assumed that the electronic excited states responsible for the function (transfer of electronic excitation energy) result from the dipole-dipole interactions between the bacteriochlorophyll molecules bound to the polypeptide chain of the complex at a specific three-dimensional geometry. The molecular structure-electronic excited states relationship has been addressed on the basis of simultaneous simulations of several spectroscopic observations. Current electronic excited state models for the Fenna-Matthews-Olson complex have generally been based on obtaining an optimal match between the information contents of the optical steady-state spectra and the bacteriochlorophyll organization. Recent kinetic and spectral information gathered from ultrafast time-resolved measurements have not yet been used effectively for further refinement of the excited state models and for quantification of the relation between the excited states and the energy transfer processes. In this study, we have searched for a model that not only can explain the key features of several steady-state spectra but also the temporal and spectral evolution observed in a recent absorption difference experiment and we have discussed the implications of this model for equilibration of the electronic excitation energy in systems at low temperatures. Received: 12 June 1998 / Revised version: 19 October 1998 / Accepted: 30 November 1998     

On the origin of cancer: can we ignore coherence?

A growing number of inconsistencies have accumulated within the genetically deterministic paradigm of the origin of cancer. Among them the most important are the nonspecific nature of cancer mutations and the non-cell-autonomous factors of cancer initiation and progression. Epigenetic aspects of cancer and cancer systems biology represent novel approaches to cancer aetiology and converge in the notion that cancer is characterized by a nonspecific progressive destabilization of multiple molecular pathways. The coherent behaviour of certain cellular subsystems has been theoretically predicted for a long time to have a general role in coordinating biological processes. However, it has only recently gained major scientific interest when it was measured on photosynthetic complexes at physiological temperatures and confirmed to have a direct effect over the dynamics of the energy transfer. Several theoretical and experimental considerations suggest that cancer might be associated with the absence or impairment of the proper coherent dynamics in certain biological structures, most notably in the microtubules. We review those models and suggest that impaired coherence might largely contribute to the progressive destabilization of the molecular and gene regulatory networks, thus connecting different non-genetic aspects of cancer.     

Developing polarized protein-specific charges for protein dynamics: MD free energy calculation of pKa shifts for Asp26/Asp20 in thioredoxin

Ab initio quantum mechanical calculation of protein in solution is carried out to generate polarized protein-specific charge(s) (PPC) for molecular dynamics (MD) stimulation of protein. The quantum calculation of protein is made possible by developing a fragment-based quantum chemistry approach in combination with the implicit continuum solvent model. The computed electron density of protein is utilized to derive PPCs that represent the polarized electrostatic state of protein near the native structure. These PPCs are atom-centered like those in the standard force fields and are thus computationally attractive for molecular dynamics simulation of protein. Extensive MD simulations have been carried out to investigate the effect of electronic polarization on the structure and dynamics of thioredoxin. Our study shows that the dynamics of thioredoxin is stabilized by electronic polarization through explicit comparison between MD results using PPC and AMBER charges. In particular, MD free-energy calculation using PPCs accurately reproduced the experimental value of pK_a shift for ionizable residue Asp²⁶ buried inside thioredoxin, whereas previous calculations using standard force fields overestimated pK_a shift by twice as much. Accurate prediction of pK_a shifts by rigorous MD free energy simulation for ionizable residues buried inside protein has been a significant challenge in computational biology for decades. This study presented strong evidence that electronic polarization of protein plays an important role in protein dynamics.     

Calculations of protein circular dichroism from first principles

Understanding the relationship between the amino acid sequence of a protein and its unique, compact 3D structure is one of the grand challenges in molecular biophysics. One particularly exciting approach is time-resolved electronic circular dichroism (CD) spectroscopy, which offers resolution on a nanosecond (or faster) time scale, although it does not provide the spatial resolution of techniques like X-ray crystallography or NMR. The thrust of our work is to underpin fast time scale spectroscopic studies of protein folding with a stronger theoretical foundation. Ultimately, we seek to use molecular dynamics simulations to study the influence of conformational dynamics and conformational transitions on the electronic CD spectra of proteins. We discuss how improved quantum chemical models of individual chromophores, including aromatic sidechains, can be incorporated into calculations of the electronic structure of proteins and their CD.     

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.     

Overview of simulation studies on the enzymatic activity and conformational dynamics of the GTPase Ras

Over the last 40 years, we have learnt a great deal about the Ras onco-proteins. These intracellular molecular switches are essential for the function of a variety of physiological processes, including signal transduction cascades responsible for cell growth and proliferation. Molecular simulations and free energy calculations have played an essential role in elucidating the conformational dynamics and energetics underlying the GTP hydrolysis reaction catalysed by Ras. Here we present an overview of the main lessons from molecular simulations on the GTPase reaction and conformational dynamics of this important anti-cancer drug target. In the first part, we summarise insights from quantum mechanical and combined quantum mechanical/molecular mechanical simulations as well as other free energy methods and highlight consensus viewpoints as well as remaining controversies. The second part provides a very brief overview of new insights emerging from large-scale molecular dynamics simulations. We conclude with a perspective regarding future studies of Ras where computational approaches will likely play an active role.     

Quantum transport in the FMO photosynthetic light-harvesting complex

The very high light-harvesting efficiency of natural photosynthetic systems in conjunction with recent experiments, which showed quantum-coherent energy transfer in photosynthetic complexes, raised questions regarding the presence of non-trivial quantum effects in photosynthesis. Grover quantum search, quantum walks, and entanglement have been investigated as possible effects that lead to this efficiency. Here we explain the near-unit photosynthetic efficiency without invoking non-trivial quantum effects. Instead, we use non-equilibrium Green’s functions, a mesoscopic method used to study transport in nano-conductors to compute the transmission function of the Fenna–Matthews–Olson (FMO) complex using an experimentally derived exciton Hamiltonian. The chlorosome antenna and the reaction center play the role of input and output contacts, connected to the FMO complex. We show that there are two channels for which the transmission is almost unity. Our analysis also revealed a dephasing-driven regulation mechanism that maintains the efficiency in the presence of varying dephasing potentials.     

高等植物体内激子相干迁移与俘获

依据所建立的色素分子排列和取向的新型结构模型,利用激发能传递的广义主方程理论,提出了高等植物体内激子相干迁移与俘获的点阵理论,研究了静态荧光量子产额、定态能量传递速率和荧光强度的变化规律。指出激子相干迁移有助于活体的激发能转移与俘获,并且它有可能是活体内激子寿命的限制因素之一。     

Dynamics and diffusion in photosynthetic membranes from rhodospirillum photometricum

Photosynthetic organisms drive their metabolism by converting light energy into an electrochemical gradient with high efficiency. This conversion depends on the diffusion of quinones within the membrane. In purple photosynthetic bacteria, quinones reduced by the reaction center (RC) diffuse to the cytochrome bc(1) complex and then return once reoxidized to the RC. In Rhodospirillum photometricum the RC-containing core complexes are found in a disordered molecular environment, with fixed light-harvesting complex/core complex ratio but without a fixed architecture, whereas additional light-harvesting complexes synthesized under low-light conditions pack into large paracrystalline antenna domains. Here, we have analyzed, using time-lapse atomic force microscopy, the dynamics of the protein complexes in the different membrane domains and find that the disordered regions are dynamic whereas ordered antennae domains are static. Based on our observations we propose, and analyze using Monte Carlo simulations, a model for quinone diffusion in photosynthetic membranes. We show that the formation of large static antennae domains may represent a strategy for increasing electron transfer rates between distant complexes within the membrane and thus be important for photosynthetic efficiency.