An ab initio force field for the cofactors of bacterial photosynthesis

Architectures of photosynthetic RC-LH1 supercomplexes from Rhodobacter blasticus

The reaction center-light-harvesting complex 1 (RC-LH1) plays an essential role in the primary reactions of bacterial photosynthesis. Here, we present high-resolution structures of native monomeric and dimeric RC-LH1 supercomplexes from Rhodobacter (Rba.) blasticus using cryo-electron microscopy. The RC-LH1 monomer is composed of an RC encircled by an open LH1 ring comprising 15 αβ heterodimers and a PufX transmembrane polypeptide. In the RC-LH1 dimer, two crossing PufX polypeptides mediate dimerization. Unlike Rhodabacter sphaeroides counterpart, Rba. blasticus RC-LH1 dimer has a less bent conformation, lacks the PufY subunit near the LH1 opening, and includes two extra LH1 αβ subunits, forming a more enclosed S-shaped LH1 ring. Spectroscopic assays reveal that these unique structural features are accompanied by changes in the kinetics of quinone/quinol trafficking between RC-LH1 and cytochrome bc1. Our findings reveal the assembly principles and structural variability of photosynthetic RC-LH1 supercomplexes, highlighting diverse strategies used by phototrophic bacteria to optimize light-harvesting and electron transfer in competitive environments.

Molecular interactions of photosystem I and ZIF-8 in bio-nanohybrid materials

Bio-nanohybrid devices featuring natural photocatalysts bound to a nanostructure hold great promise in the search for sustainable energy conversion. One of the major challenges of integrating biological systems is protecting them against harsh environmental conditions while retaining, or ideally enhancing their photophysical properties. In this mainly computational work we investigate an assembly of cyanobacterial photosystem I (PS I) embedded in a metal-organic framework (MOF), namely the zeolitic imidazolate framework ZIF-8. This complex has been reported experimentally [Bennett et al., Nanoscale Adv., 2019, 1, 94] but so far the molecular interactions between PS I and the MOF remained elusive. We show via absorption spectroscopy that PS I remains intact throughout the encapsulation-release cycle. Molecular dynamics (MD) simulations further confirm that the encapsulation has no noticeable structural impact on the photosystem. However, the MOF building blocks frequently coordinate to the Mg2+ ions of chlorophylls in the periphery of the antenna complex. High-level quantum mechanical calculations reveal charge-transfer interactions, which affect the excitonic network and thereby may reversibly change the fluorescence properties of PS I. Nevertheless, our results highlight the stability of PS I in the MOF, as the reaction center remains unimpeded by the heterogeneous environment, paving the way for applications in the foreseeable future.

Combined Multireference-Multiscale Approach to the Description of Photosynthetic Reaction Centers

A first-principles description of the primary photochemical processes that drive photosynthesis and sustain life on our planet remains one of the grand challenges of modern science. Recent research established that explicit incorporation of protein electrostatics in excited-state calculations of photosynthetic pigments, achieved for example with quantum-mechanics/molecular-mechanics (QM/MM) approaches, is essential for a meaningful description of the properties and function of pigment-protein complexes. Although time-dependent density functional theory has been used productively so far in QM/MM approaches for the study of such systems, this methodology has limitations. Here we pursue for the first time a QM/MM description of the reaction center in the principal enzyme of oxygenic photosynthesis, Photosystem II, using multireference wave function theory for the high-level QM region. We identify best practices and establish guidelines regarding the rational choice of active space and appropriate state-averaging for the efficient and reliable use of complete active space self-consistent field (CASSCF) and the N-electron valence state perturbation theory (NEVPT2) in the prediction of low-lying excited states of chlorophyll and pheophytin pigments. Given that the Gouterman orbitals are inadequate as a minimal active space, we define specific minimal and extended active spaces for the NEVPT2 description of electronic states that fall within the Q and B bands. Subsequently, we apply our multireference-QM/MM protocol to the description of all pigments in the reaction center of Photosystem II. The calculations reproduce the electrochromic shifts induced by the protein matrix and the ordering of site energies consistent with the identity of the primary donor (ChlD1) and the experimentally known asymmetric and directional electron transfer. The optimized protocol sets the stage for future multireference treatments of multiple pigments, and hence for multireference studies of charge separation, while it is transferable to the study of any photoactive embedded tetrapyrrole system.

Protein Effects on the Excitation Energies and Exciton Dynamics of the CP24 Antenna Complex

In this study, the site energy fluctuations, energy transfer dynamics, and some spectroscopic properties of the minor light-harvesting complex CP24 in a membrane environment were determined. For this purpose, a 3 μs-long classical molecular dynamics simulation was performed for the CP24 complex. Furthermore, using the density functional tight binding/molecular mechanics molecular dynamics (DFTB/MM MD) approach, we performed excited state calculations for the chlorophyll a and chlorophyll b molecules in the complex starting from five different positions of the MD trajectory. During the extended simulations, we observed variations in the site energies of the different sets as a result of the fluctuating protein environment. In particular, a water coordination to Chl-b 608 occurred only after about 1 μs in the simulations, demonstrating dynamic changes in the environment of this pigment. From the classical and the DFTB/MM MD simulations, spectral densities and the (time-dependent) Hamiltonian of the complex were determined. Based on these results, three independent strongly coupled chlorophyll clusters were revealed within the complex. In addition, absorption and fluorescence spectra were determined together with the exciton relaxation dynamics, which reasonably well agrees with experimental time scales.

PigmentHunter: A point-and-click application for automated chlorophyll-protein simulations

Chlorophyll proteins (CPs) are the workhorses of biological photosynthesis, working together to absorb solar energy, transfer it to chemically active reaction centers, and control the charge-separation process that drives its storage as chemical energy. Yet predicting CP optical and electronic properties remains a serious challenge, driven by the computational difficulty of treating large, electronically coupled molecular pigments embedded in a dynamically structured protein environment. To address this challenge, we introduce here an analysis tool called PigmentHunter, which automates the process of preparing CP structures for molecular dynamics (MD), running short MD simulations on the nanoHUB.org science gateway, and then using electrostatic and steric analysis routines to predict optical absorption, fluorescence, and circular dichroism spectra within a Frenkel exciton model. Inter-pigment couplings are evaluated using point-dipole or transition-charge coupling models, while site energies can be estimated using both electrostatic and ring-deformation approaches. The package is built in a Jupyter Notebook environment, with a point-and-click interface that can be used either to manually prepare individual structures or to batch-process many structures at once. We illustrate PigmentHunter's capabilities with example simulations on spectral line shapes in the light harvesting 2 complex, site energies in the Fenna-Matthews-Olson protein, and ring deformation in photosystems I and II.

Quantum chemical elucidation of a sevenfold symmetric bacterial antenna complex

The light-harvesting complex 2 (LH2) of purple bacteria is one of the most studied photosynthetic antenna complexes. Its symmetric structure and ring-like bacteriochlorophyll arrangement make it an ideal system for theoreticians and spectroscopists. LH2 complexes from most bacterial species are thought to have eightfold or ninefold symmetry, but recently a sevenfold symmetric LH2 structure from the bacterium Mch. purpuratum was solved by Cryo-Electron microscopy. This LH2 also possesses unique near-infrared absorption and circular dichroism (CD) spectral properties. Here we use an atomistic strategy to elucidate the spectral properties of Mch. purpuratum LH2 and understand the differences with the most commonly studied LH2 from Rbl. acidophilus. Our strategy exploits a combination of molecular dynamics simulations, multiscale polarizable quantum mechanics/molecular mechanics calculations, and lineshape simulations. Our calculations reveal that the spectral properties of LH2 complexes are tuned by site energies and exciton couplings, which in turn depend on the structural fluctuations of the bacteriochlorophylls. Our strategy proves effective in reproducing the absorption and CD spectra of the two LH2 complexes, and in uncovering the origin of their differences. This work proves that it is possible to obtain insight into the spectral tuning strategies of purple bacteria by quantitatively simulating the spectral properties of their antenna complexes.

Thermal site energy fluctuations in photosystem I: new insights from MD/QM/MM calculations

Cyanobacterial photosystem I (PSI) is one of the most efficient photosynthetic machineries found in nature. Due to the large scale and complexity of the system, the energy transfer mechanism from the antenna complex to the reaction center is still not fully understood. A central element is the accurate evaluation of the individual chlorophyll excitation energies (site energies). Such an evaluation must include a detailed treatment of site specific environmental influences on structural and electrostatic properties, but also their evolution in the temporal domain, because of the dynamic nature of the energy transfer process. In this work, we calculate the site energies of all 96 chlorophylls in a membrane-embedded model of PSI. The employed hybrid QM/MM approach using the multireference DFT/MRCI method in the QM region allows to obtain accurate site energies under explicit consideration of the natural environment. We identify energy traps and barriers in the antenna complex and discuss their implications for energy transfer to the reaction center. Going beyond previous studies, our model also accounts for the molecular dynamics of the full trimeric PSI complex. Via statistical analysis we show that the thermal fluctuations of single chlorophylls prevent the formation of a single prominent energy funnel within the antenna complex. These findings are also supported by a dipole exciton model. We conclude that energy transfer pathways may form only transiently at physiological temperatures, as thermal fluctuations overcome energy barriers. The set of site energies provided in this work sets the stage for theoretical and experimental studies on the highly efficient energy transfer mechanisms in PSI.

Million-atom molecular dynamics simulations reveal the interfacial interactions and assembly of plant PSII-LHCII supercomplex

Protein-protein interface interactions dictate efficient excitation energy transfer from light-harvesting antennas to the photosystem II (PSII) core. In this work, we construct a 1.2 million atom-scale model of plant C₂S₂-type PSII-LHCII supercomplex and perform microsecond-scale molecular dynamics (MD) simulations to explore the interactions and assembly mechanisms of the sizeable PSII-LHCII supercomplex. We optimize the nonbonding interactions of the PSII-LHCII cryo-EM structure using microsecond-scale MD simulations. Binding free energy calculations with component decompositions reveal that hydrophobic interactions predominantly drive antenna-core association and the antenna-antenna interactions are relatively weak. Despite the positive electrostatic interaction energies, hydrogen bonds and salt bridges mainly provide directional or anchoring forces for interface binding. Analysis of the roles of small intrinsic subunits of PSII suggests that LHCII and CP26 first interact with small intrinsic subunits and then bind to the core proteins, whereas CP29 adopts a one-step binding process to the PSII core without the assistance of other factors. Our study provides insights into the molecular underpinnings of the self-organization and regulation of plant PSII-LHCII. It lays the framework for deciphering the general assembly principles of photosynthetic supercomplexes and possibly other macromolecular structures. The finding also has implications for repurposing photosynthetic systems to enhance photosynthesis.

Chemistry of Lipoquinones: Properties, Synthesis, and Membrane Location of Ubiquinones, Plastoquinones, and Menaquinones

Lipoquinones are the topic of this review and are a class of hydrophobic lipid molecules with key biological functions that are linked to their structure, properties, and location within a biological membrane. Ubiquinones, plastoquinones, and menaquinones vary regarding their quinone headgroup, isoprenoid sidechain, properties, and biological functions, including the shuttling of electrons between membrane-bound protein complexes within the electron transport chain. Lipoquinones are highly hydrophobic molecules that are soluble in organic solvents and insoluble in aqueous solution, causing obstacles in water-based assays that measure their chemical properties, enzyme activities and effects on cell growth. Little is known about the location and ultimately movement of lipoquinones in the membrane, and these properties are topics described in this review. Computational studies are particularly abundant in the recent years in this area, and there is far less experimental evidence to verify the often conflicting interpretations and conclusions that result from computational studies of very different membrane model systems. Some recent experimental studies have described using truncated lipoquinone derivatives, such as ubiquinone-2 (UQ-2) and menaquinone-2 (MK-2), to investigate their conformation, their location in the membrane, and their biological function. Truncated lipoquinone derivatives are soluble in water-based assays, and hence can serve as excellent analogs for study even though they are more mobile in the membrane than the longer chain counterparts. In this review, we will discuss the properties, location in the membrane, and syntheses of three main classes of lipoquinones including truncated derivatives. Our goal is to highlight the importance of bridging the gap between experimental and computational methods and to incorporate properties-focused considerations when proposing future studies relating to the function of lipoquinones in membranes.

Comparison of proton transfer paths to the QA and QB sites of the Rb. sphaeroides photosynthetic reaction centers

The photosynthetic bacterial reaction centers from purple non-sulfur bacteria use light energy to drive the transfer of electrons from cytochrome c to ubiquinone. Ubiquinone bound in the Q_A site cycles between quinone, Q_A, and anionic semiquinone, Q_A^·-, being reduced once and never binding protons. In the Q_B site, ubiquinone is reduced twice by Q_A^·-, binds two protons and is released into the membrane as the quinol, QH₂. The network of hydrogen bonds formed in a molecular dynamics trajectory was drawn to investigate proton transfer pathways from the cytoplasm to each quinone binding site. Q_A is isolated with no path for protons to enter from the surface. In contrast, there is a complex and tangled network requiring residues and waters that can bring protons to Q_B. There are three entries from clusters of surface residues centered around HisH126, GluH224, and HisH68. The network is in good agreement with earlier studies, Mutation of key nodes in the network, such as SerL223, were previously shown to slow proton delivery. Mutational studies had also shown that double mutations of residues such as AspM17 and AspL210 along multiple paths in the network presented here slow the reaction, while single mutations do not. Likewise, mutation of both HisH126 and HisH128, which are at the entry to two paths reduce the rate of proton uptake.

The atomistic modeling of light-harvesting complexes from the physical models to the computational protocol

The function of light-harvesting complexes is determined by a complex network of dynamic interactions among all the different components: the aggregate of pigments, the protein, and the surrounding environment. Complete and reliable predictions on these types of composite systems can be only achieved with an atomistic description. In the last few decades, there have been important advances in the atomistic modeling of light-harvesting complexes. These advances have involved both the completeness of the physical models and the accuracy and effectiveness of the computational protocols. In this Perspective, we present an overview of the main theoretical and computational breakthroughs attained so far in the field, with particular focus on the important role played by the protein and its dynamics. We then discuss the open problems in their accurate modeling that still need to be addressed. To illustrate an effective computational workflow for the modeling of light harvesting complexes, we take as an example the plant antenna complex CP29 and its H111N mutant.

Electron Transport Lipids Fold Within Membrane-Like Interfaces

Lipoquinones, such as ubiquinones (UQ) and menaquinones (MK), function as essential lipid components of the electron transport system (ETS) by shuttling electrons and protons to facilitate the production of ATP in eukaryotes and prokaryotes. Lipoquinone function in membrane systems has been widely studied, but the exact location and conformation within membranes remains controversial. Lipoquinones, such as Coenzyme Q (UQ-10), are generally depicted simply as "Q" in life science diagrams or in extended conformations in primary literature even though specific conformations are important for function in the ETS. In this study, our goal was to determine the location, orientation, and conformation of UQ-2, a truncated analog of UQ-10, in model membrane systems and to compare our results to previously studied MK-2. Herein, we first carried out a six-step synthesis to yield UQ-2 and then demonstrated that UQ-2 adopts a folded conformation in organic solvents using 1H-1H 2D NOESY and ROESY NMR spectroscopic studies. Similarly, using 1H-1H 2D NOESY NMR spectroscopic studies, UQ-2 was found to adopt a folded, U-shaped conformation within the interface of an AOT reverse micelle model membrane system. UQ-2 was located slightly closer to the surfactant-water interface compared to the more hydrophobic MK-2. In addition, Langmuir monolayer studies determined UQ-2 resided within the monolayer water-phospholipid interface causing expansion, whereas MK-2 was more likely to be compressed out and reside within the phospholipid tails. All together these results support the model that lipoquinones fold regardless of the headgroup structure but that the polarity of the headgroup influences lipoquinone location within the membrane interface. These results have implications regarding the redox activity near the interface as quinone vs. quinol forms may facilitate locomotion of lipoquinones within the membrane. The location, orientation, and conformation of lipoquinones are critical for their function in generating cellular energy within membrane ETS, and the studies described herein shed light on the behavior of lipoquinones within membrane-like environments.

Structure of the stress-related LHCSR1 complex determined by an integrated computational strategy

Light-harvesting complexes (LHCs) are pigment-protein complexes whose main function is to capture sunlight and transfer the energy to reaction centers of photosystems. In response to varying light conditions, LH complexes also play photoregulation and photoprotection roles. In algae and mosses, a sub-family of LHCs, light-harvesting complex stress-related (LHCSR), is responsible for photoprotective quenching. Despite their functional and evolutionary importance, no direct structural information on LHCSRs is available that can explain their unique properties. In this work, we propose a structural model of LHCSR1 from the moss P. patens, obtained through an integrated computational strategy that combines homology modeling, molecular dynamics, and multiscale quantum chemical calculations. The model is validated by reproducing the spectral properties of LHCSR1. Our model reveals the structural specificity of LHCSR1, as compared with the CP29 LH complex, and poses the basis for understanding photoprotective quenching in mosses.

The structure of the moss P. patens light-harvesting complex stress-related 1 (LHCSR1) is determined using a multi-scale computational approach for investigations of its photoprotective function.

Effect of protein matrix on CP29 spectra and energy transfer pathways

We investigate energy transfer pathways between strongly coupled chlorophylls (Chls) in the CP29 (LHCII B4.1) antenna complex of Pisum sativum, including the possibility of higher energy states. We test for the environmental effects caused by the protein, membrane and solvent using a hybrid QM/MM approach. Classical molecular dynamics simulations of the full CP29 complex embedded in a DOPC membrane have been performed, followed by calculations of the time dependent DFT spectra of all Chls at several timesteps. The relative orientations of transition dipole moments (TDMs) were specifically analyzed, including and excluding the point charge field (PCF) of the surrounding environment. The PCF is found to drastically shift the spectra of specific Chls, while the majority of Chls is mostly unaffected. The net effect on the sum spectrum is however found to be negligible: The few strong changes in Chl spectra cancel each other due to being opposite in sign. We further find that the spectra of the Chls coordinating to water show a blue shift upon introduction of the environment. Conversely, the spectra of the Chls coordinating to glutamine show a red shift upon activation of the PCF. As the main influence of the PCF for tuning the couplings, we identify the energetic position of the individual chromophores. The fine-tuning, especially for states energetically above the Qy state, is however controlled by the changes in the TDM orientations. We also find an indication for the PCF to steer potentially harmful high energy excitations away from the PSII core complex.

Bridging Carotenoid-to-Bacteriochlorophyll Energy Transfer of Purple Bacteria LH2 With Temperature Variations: Insights From Conformational Changes

Photosynthesis is a key process for converting light energy into chemical energy and providing food for lives on Earth. Understanding the mechanism for the energy transfers could provide insights into regulating energy transfers in photosynthesis and designing artificial photosynthesis systems. Many efforts have been devoted to exploring the mechanism of temperature variations affecting the excitonic properties of LH2. In this study, we performed all-atom molecular dynamics (MD) simulations and quantum mechanics calculations for LH2 complex from purple bacteria along with its membrane environment under three typical temperatures: 270, 300, and 330 K. The structural analysis from validated MD simulations showed that the higher temperature impaired interactions at N-terminus of both α and β polypeptide helices and led to the dissociation of this hetero polypeptide dimer. Rhodopin-β-D-glucosides (RG1) moved centripetally with α polypeptide helices when temperature increased and enlarged their distances with bacteriochlorophylls molecules that have the absorption peak at 850 nm (B850), which resulted in reducing the coupling strengths between RG1 and B850 molecules. The present study reported a cascading mechanism for temperature regulating the energy transfers in LH2 of purple bacteria.

Time-dependent atomistic simulations of the CP29 light-harvesting complex

Light harvesting as the first step in photosynthesis is of prime importance for life on earth. For a theoretical description of photochemical processes during light harvesting, spectral densities are key quantities. They serve as input functions for modeling the excitation energy transfer dynamics and spectroscopic properties. Herein, a recently developed procedure is applied to determine the spectral densities of the pigments in the minor antenna complex CP29 of photosystem II, which has recently gained attention because of its active role in non-photochemical quenching processes in higher plants. To this end, the density functional-based tight binding (DFTB) method has been employed to enable simulation of the ground state dynamics in a quantum-mechanics/molecular mechanics (QM/MM) scheme for each chlorophyll pigment. Subsequently, the time-dependent extension of the long-range corrected DFTB approach has been used to obtain the excitation energy fluctuations along the ground-state trajectories also in a QM/MM setting. From these results, the spectral densities have been determined and compared for different force fields and to spectral densities from other light-harvesting complexes. In addition, time-dependent and time-independent excitonic Hamiltonians of the system have been constructed and applied to the determination of absorption spectra as well as exciton dynamics.

Ultrafast structural changes within a photosynthetic reaction centre

Photosynthetic reaction centres harvest the energy content of sunlight by transporting electrons across an energy-transducing biological membrane. Here we use time-resolved serial femtosecond crystallography¹ using an X-ray free-electron laser² to observe light-induced structural changes in the photosynthetic reaction centre of Blastochloris viridis on a timescale of picoseconds. Structural perturbations first occur at the special pair of chlorophyll molecules of the photosynthetic reaction centre that are photo-oxidized by light. Electron transfer to the menaquinone acceptor on the opposite side of the membrane induces a movement of this cofactor together with lower amplitude protein rearrangements. These observations reveal how proteins use conformational dynamics to stabilize the charge-separation steps of electron-transfer reactions.

Normal mode analysis of spectral density of FMO trimers: Intra- and intermonomer energy transfer

The intermolecular contribution to the spectral density of the exciton-vibrational coupling of the homotrimeric Fenna-Matthews-Olson (FMO) light-harvesting protein of green sulfur bacteria P. aestuarii is analyzed by combining a normal mode analysis of the protein with the charge density coupling method for the calculation of local transition energies of the pigments. Correlations in site energy fluctuations across the whole FMO trimer are found at low vibrational frequencies. Including, additionally, the high-frequency intrapigment part of the spectral density, extracted from line-narrowing spectra, we study intra- and intermonomer exciton transfer. Whereas the intrapigment part of the spectral density is important for fast intramonomer exciton relaxation, the intermolecular contributions (due to pigment-environment coupling) determine the intermonomer exciton transfer. Neither the variations of the local Huang-Rhys factors nor the correlations in site energy fluctuations have a critical influence on energy transfer. At room temperature, the intermonomer transfer in the FMO protein occurs on a 10 ps time scale, whereas intramonomer exciton equilibration is roughly two orders of magnitude faster. At cryogenic temperatures, intermonomer transfer limits the lifetimes of the lowest exciton band. The lifetimes are found to increase between 20 ps in the center of this band up to 100 ps toward lower energies, which is in very good agreement with the estimates from hole burning data. Interestingly, exciton delocalization in the FMO monomers is found to slow down intermonomer energy transfer, at both physiological and cryogenic temperatures.

Protein Matrix Control of Reaction Center Excitation in Photosystem II

Photosystem II (PSII) is a multisubunit pigment-protein complex that uses light-induced charge separation to power oxygenic photosynthesis. Its reaction center chromophores, where the charge transfer cascade is initiated, are arranged symmetrically along the D1 and D2 core polypeptides and comprise four chlorophyll (PD1, PD2, ChlD1, ChlD2) and two pheophytin molecules (PheoD1 and PheoD2). Evolution favored productive electron transfer only via the D1 branch, with the precise nature of primary excitation and the factors that control asymmetric charge transfer remaining under investigation. Here we present a detailed atomistic description for both. We combine large-scale simulations of membrane-embedded PSII with high-level quantum-mechanics/molecular-mechanics (QM/MM) calculations of individual and coupled reaction center chromophores to describe reaction center excited states. We employ both range-separated time-dependent density functional theory and the recently developed domain based local pair natural orbital (DLPNO) implementation of the similarity transformed equation of motion coupled cluster theory with single and double excitations (STEOM-CCSD), the first coupled cluster QM/MM calculations of the reaction center. We find that the protein matrix is exclusively responsible for both transverse (chlorophylls versus pheophytins) and lateral (D1 versus D2 branch) excitation asymmetry, making ChlD1 the chromophore with the lowest site energy. Multipigment calculations show that the protein matrix renders the ChlD1 → PheoD1 charge-transfer the lowest energy excitation globally within the reaction center, lower than any pigment-centered local excitation. Remarkably, no low-energy charge transfer states are located within the "special pair" PD1-PD2, which is therefore excluded as the site of initial charge separation in PSII. Finally, molecular dynamics simulations suggest that modulation of the electrostatic environment due to protein conformational flexibility enables direct excitation of low-lying charge transfer states by far-red light.

DFTB/MM Molecular Dynamics Simulations of the FMO Light-Harvesting Complex

Because of the size of light-harvesting complexes and the involvement of electronic degrees of freedom, computationally these systems need to be treated with a combined quantum-classical description. To this end, Born-Oppenheimer molecular dynamics simulations have been employed in a quantum mechanics/molecular mechanics (QM/MM) fashion for the ground state followed by excitation energy calculations again in a QM/MM scheme for the Fenna-Matthews-Olson (FMO) complex. The self-consistent-charge density functional tight-binding (DFTB) method electrostatically coupled to a classical description of the environment was applied to perform the ground-state dynamics. Subsequently, long-range-corrected time-dependent DFTB calculations were performed to determine the excitation energy fluctuations of the individual bacteriochlorophyll a molecules. The spectral densities obtained using this approach show an excellent agreement with experimental findings. In addition, the fluctuating site energies and couplings were used to estimate the exciton transfer dynamics.

Molecular dynamics simulations in photosynthesis

Photosynthesis is regulated by a dynamic interplay between proteins, enzymes, pigments, lipids, and cofactors that takes place on a large spatio-temporal scale. Molecular dynamics (MD) simulations provide a powerful toolkit to investigate dynamical processes in (bio)molecular ensembles from the (sub)picosecond to the (sub)millisecond regime and from the Å to hundreds of nm length scale. Therefore, MD is well suited to address a variety of questions arising in the field of photosynthesis research. In this review, we provide an introduction to the basic concepts of MD simulations, at atomistic and coarse-grained level of resolution. Furthermore, we discuss applications of MD simulations to model photosynthetic systems of different sizes and complexity and their connection to experimental observables. Finally, we provide a brief glance on which methods provide opportunities to capture phenomena beyond the applicability of classical MD.

FMOxFMO: Elucidating Excitonic Interactions in the Fenna-Matthews-Olson Complex with the Fragment Molecular Orbital Method

In order to study Förster resonance energy transfer (FRET), the fragment molecular orbital (FMO) method is extended to compute electronic couplings between local excitations via the excited state transition density model, enabling efficient calculations of nonlocal excitations in a large molecular system and overcoming the previous limitation of being able to compute only local excitations. The results of these simple but accurate models are validated against full quantum calculations without fragmentation. The developed method is applied to a very important photosynthetic pigment-protein complex, the Fenna-Matthews-Olson complex (FMOc), that is responsible for the energy transfer from a chlorosome to the reaction center in the green sulfur bacteria. Absorption and circular dichroism spectra of FMOc are simulated, and the role of the molecular environment on the excitations is revealed.

Local and Global Electric Field Asymmetry in Photosynthetic Reaction Centers

The origin of unidirectional electron transfer in photosynthetic reaction centers (RCs) has been widely discussed. Despite the high level of structural similarity between the two branches of pigments that participate in the initial electron transfer steps of photosynthesis, electron transfer only occurs along one branch. One possible explanation for this functional asymmetry is the differences in the electrostatic environment between the active and the inactive branches arising from the charges and dipoles of the organized protein structure. We present an analysis of electric fields in the RC of the purple bacterium Rhodobacter sphaeroides using the intrinsic carbonyl groups of the pigments as vibrational reporters whose vibrational frequency shifts can be converted into electric fields based on the vibrational Stark effect and also provide Stark effect data for plant pigments that can be used in future studies. The carbonyl stretches of the isolated pigments show pronounced Stark effects. We use these data, solvatochromism, molecular dynamics simulations, and data in the literature from IR and Raman spectra to evaluate differences in fields at symmetry-related positions, in particular at the 9-keto and 2-acetyl positions of the pigments involved in primary charge separation.

The role of charge-transfer states in the spectral tuning of antenna complexes of purple bacteria

The LH2 antenna complexes of purple bacteria occur, depending on light conditions, in various different spectroscopic forms, with a similar structure but different absorption spectra. The differences are related to point changes in the primary amino acid sequence, but the molecular-level relationship between these changes and the resulting spectrum is still not well understood. We undertook a systematic quantum chemical analysis of all the main factors that contribute to the exciton structure, looking at how the environment modulates site energies and couplings in the B800-850 and B800-820 spectroscopic forms of LH2. A multiscale approach combining quantum chemistry and an atomistic classical embedding has been used where mutual polarization effects between the two parts are taken into account. We find that the loss of hydrogen bonds following amino acid changes can only explain a part of the observed blue-shift in the B850 band. The coupling of excitonic states to charge-transfer states, which is different in the two forms, contributes with a similar amount to the overall blue-shift.

Development of CHARMM-Compatible Force-Field Parameters for Cobalamin and Related Cofactors from Quantum Mechanical Calculations

Corrinoid cofactors such as cobalamin are used by many enzymes and are essential for most living organisms. Therefore, there is broad interest in investigating cobalamin-protein interactions with molecular dynamics simulations. Previously developed parameters for cobalamins are based mainly on crystal structure data. Here, we report CHARMM-compatible force field parameters for several corrinoids developed from quantum mechanical calculations. We provide parameters for corrinoids in three oxidation states, Co³⁺, Co²⁺, and Co¹⁺, and with various axial ligands. Lennard-Jones parameters for the cobalt center in the Co(II) and Co(I) states were optimized using a helium atom probe, and partial atomic charges were obtained with a combination of natural population analysis (NPA) and restrained electrostatic potential (RESP) fitting approaches. The Force Field Toolkit was used to optimize all bonded terms. The resulting parameters, determined solely from calculations of cobalamin alone or in water, were then validated by assessing their agreement with density functional theory geometries and by analyzing molecular dynamics simulation trajectories of several corrinoid proteins for which X-ray crystal structures are available. In each case, we obtained excellent agreement with the reference data. In comparison to previous CHARMM-compatible parameters for cobalamin, we observe a better agreement for the fold angle and lower RMSD in the cobalamin binding site. The approach described here is readily adaptable for developing CHARMM-compatible force-field parameters for other corrinoids or large biomolecules.

Fine control of chlorophyll-carotenoid interactions defines the functionality of light-harvesting proteins in plants

Photosynthetic antenna proteins can be thought of as "programmed solvents", which bind pigments at specific mutual orientations, thus tuning the overall energetic landscape and ensuring highly efficient light-harvesting. While positioning of chlorophyll cofactors is well understood and rationalized by the principle of an "energy funnel", the carotenoids still pose many open questions. Particularly, their short excited state lifetime (<25 ps) renders them potential energy sinks able to compete with the reaction centers and drastically undermine light-harvesting efficiency. Exploration of the orientational phase-space revealed that the placement of central carotenoids minimizes their interaction with the nearest chlorophylls in the plant antenna complexes LHCII, CP26, CP29 and LHCI. At the same time we show that this interaction is highly sensitive to structural perturbations, which has a profound effect on the overall lifetime of the complex. This links the protein dynamics to the light-harvesting regulation in plants by the carotenoids.

Relation between Vibrational Dephasing Time and Energy Gap Fluctuations

Dephasing processes are present in basically all applications in which quantum mechanics plays a role. These applications certainly include excitation energy and charge transfer in biological systems. In a previous study, we have analyzed the vibrational dephasing time as a function of energy gap fluctuation for a large set of molecular simulations. In that investigation, individual molecular subunits were the focus of the calculations. The set of studied molecules included bacteriochlorophylls in Fenna-Matthews-Olson and light-harvesting system 2 complexes as well as bilins in PE545 aggregates. The present work extends this study to entire complexes, including the respective intermolecular couplings. Again, it can be concluded that a universal and inverse proportionality exists between dephasing time and variance of the excitonic energy gap fluctuations, whereas the respective proportionality constants can be rationalized using the energy gap autocorrelation functions. Furthermore, these findings can be extended to the gaps between higher-lying neighboring excitonic states.

Atomistic non-adiabatic dynamics of the LH2 complex with a GPU-accelerated ab initio exciton model

We present GPU-accelerated ab initio molecular dynamics simulations of nonadiabatic dynamics in the LH2 complex in full atomistic detail.

Constructing an Interpolated Potential Energy Surface of a Large Molecule: A Case Study with Bacteriochlorophyll a Model in the Fenna-Matthews-Olson Complex

Constructing a reliable potential energy surface (PES) is a key step toward computationally studying the chemical dynamics of any molecular system. The interpolation scheme is a useful tool that can closely follow the accuracy of quantum chemical means at a dramatically reduced computational cost. However, applying interpolation to building a PES of a large molecule is not a straightforward black-box approach, as it frequently encounters practical difficulties associated with its large dimensionality. Here, we present detailed courses of applying interpolation toward building a PES of a large chromophore molecule. We take the example of S₀ and S₁ electronic states of bacteriochlorophyll a (BChla) molecules in the Fenna-Matthews-Olson light harvesting complex. With a reduced model molecule that bears BChla's main π-conjugated ring, various practical approaches are designed for improving the PES quality in a stable manner and for fine-tuning the final surface such that the surface can be adopted for long time molecular dynamics simulations. Combined with parallel implementation, we show that interpolated mechanics/molecular mechanics (IM/MM) simulations of the entire complex in the nanosecond time scale can be conducted readily without any practical issues. With 1500 interpolation data points for each chromophore unit, the PES error relative to the reference quantum chemical calculation is found to be ∼0.15 eV in the thermally accessible region of the conformational space, together with ∼0.01 eV error in S₀ - S₁ transition energies. The performance issue related to the use of a large interpolation database within the framework of our parallel routines is also discussed.

An Ab Initio Description of the Excitonic Properties of LH2 and Their Temperature Dependence

The spectroscopic properties of light-harvesting (LH) antennae in photosyntehtic organisms represent a fingerprint that is unique for each specific pigment-protein complex. Because of that, spectroscopic observations are generally combined with structural data from X-ray crystallography to obtain an indirect representation of the excitonic properties of the system. Here, an alternative strategy is presented which goes beyond this empirical approach and introduces an ab initio computational description of both structural and electronic properties and their dependence on the temperature. The strategy is applied to the peripheral light-harvesting antenna complex (LH2) present in purple bacteria. By comparing this model with the one based on the crystal structure, a detailed, molecular level explanation of the absorption and circular dichroism (CD) spectra and their temperature dependence is achieved. The agreement obtained with the experiments at both low and room temperature lays the groundwork for an atomistic understanding of the excitation dynamics in the LH2 system.

Machine learning exciton dynamics

Obtaining the exciton dynamics of large photosynthetic complexes by using mixed quantum mechanics/molecular mechanics (QM/MM) is computationally demanding. We propose a machine learning technique, multi-layer perceptrons, as a tool to reduce the time required to compute excited state energies. With this approach we predict time-dependent density functional theory (TDDFT) excited state energies of bacteriochlorophylls in the Fenna-Matthews-Olson (FMO) complex. Additionally we compute spectral densities and exciton populations from the predictions. Different methods to determine multi-layer perceptron training sets are introduced, leading to several initial data selections. In addition, we compute spectral densities and exciton populations. Once multi-layer perceptrons are trained, predicting excited state energies was found to be significantly faster than the corresponding QM/MM calculations. We showed that multi-layer perceptrons can successfully reproduce the energies of QM/MM calculations to a high degree of accuracy with prediction errors contained within 0.01 eV (0.5%). Spectral densities and exciton dynamics are also in agreement with the TDDFT results. The acceleration and accurate prediction of dynamics strongly encourage the combination of machine learning techniques with ab initio methods.

Relation between Dephasing Time and Energy Gap Fluctuations in Biomolecular Systems

Excitation energy and charge transfer are fundamental processes in biological systems. Because of their quantum nature, the effect of dephasing on these processes is of interest especially when trying to understand their efficiency. Moreover, recent experiments have shown quantum coherences in such systems. As a first step toward a better understanding, we studied the relationship between dephasing time and energy gap fluctuations of the individual molecular subunits. A larger set of molecular simulations has been investigated to shed light on this dependence. This set includes bacterio-chlorophylls in Fenna-Matthews-Olson complexes, the PE545 aggregate, the LH2 complexes, DNA, photolyase, and cryptochromes. For the individual molecular subunits of these aggregates it has been confirmed quantitatively that an inverse proportionality exists between dephasing time and average gap energy fluctuation. However, for entire complexes including the respective intermolecular couplings, such a relation still needs to be verified.

Towards an ab initio description of the optical spectra of light-harvesting antennae: application to the CP29 complex of photosystem II

Light-harvesting pigment-protein complexes (PPC) represent the fundamental units through which the photosynthetic organisms absorb sunlight and funnel the energy to the reaction centre for carrying out the primary energy conversion reactions of photosynthesis. Here we apply a multiscale computational strategy to a specific PPC present in the photosystem II of plants and algae (CP29) to investigate in what detail should the environment effects due to protein and membrane/solvent be included for an accurate description of optical spectra. We find that a refinement of the crystal structure is needed before any meaningful quantum chemical calculations of pigment transition energies can be performed. For this purpose we apply classical molecular dynamics simulations of the PPC within its natural environment and we perform ab initio computations of the exciton Hamiltonian of the complex, including the environment either implicitly by the polarizable continuum model (PCM) or explicitly using the polarizable QM/MM methodology (MMPol). However, PCM essentially leads to an unspecific redshift of all transition energies, and MMPol is able to reveal site-specific changes in the optical properties of the pigments. Based on the latter and the excitonic couplings obtained within a polarizable QM/MM methodology, optical spectra are calculated, which are in good qualitative agreement with experimental data. A weakness of the approach is however found in the overestimation of the fluctuations of the excitonic parameters of the pigments along the MD trajectory. An explanation for such a finding in terms of the limits of the force fields commonly used for protein cofactors is presented and discussed.

Combining classical molecular dynamics and quantum mechanical methods for the description of electronic excitations: The case of carotenoids

Carotenoids are important actors both in light-harvesting (LH) and in photoprotection functions of photosynthetic pigment-protein complexes. A deep theoretical investigation of this multiple role is still missing owing to the difficulty of describing the delicate interplay between electronic and nuclear degrees of freedom. A possible strategy is to combine accurate quantum mechanical (QM) methods with classical molecular dynamics. To do this, however, accurate force-fields (FF) are necessary. This article presents a new FF for the different carotenoids present in LH complexes of plants. The results show that all the important structural properties described by the new FF are in very good agreement with QM reference values. This increased accuracy in the simulation of the structural fluctuations is also reflected in the description of excited states. Both the energy order and the different nature of the lowest singlet states are preserved during the dynamics when the new FF is used, whereas an unphysical mixing is found when a standard FF is used.

Elastic Vibrations in the Photosynthetic Bacterial Reaction Center Coupled to the Primary Charge Separation: Implications from Molecular Dynamics Simulations and Stochastic Langevin Approach

Primary electron transfer reactions in the bacterial reaction center are difficult for theoretical explication: the reaction kinetics, almost unalterable over a wide range of temperature and free energy changes, revealed oscillatory features observed initially by Shuvalov and coauthors (1997, 2002). Here the reaction mechanism was studied by molecular dynamics and analyzed within a phenomenological Langevin approach. The spectral function of polarization around the bacteriochlorophyll special pair PLPM and the dielectric response upon the formation of PL(+)PM(-) dipole within the special pair were calculated. The system response was approximated by Langevin oscillators; the respective frequencies, friction, and energy coupling coefficients were determined. The protein dynamics around PL and PM were distinctly asymmetric. The polarization around PL included slow modes with the frequency 30-80 cm(-1) and the total amplitude of 130 mV. Two main low-frequency modes of protein response around PM had frequencies of 95 and 155 cm(-1) and the total amplitude of 30 mV. In addition, a slowly damping mode with the frequency of 118 cm(-1) and the damping time >1.1 ps was coupled to the formation of PL(+)PM(-) dipole. It was attributed to elastic vibrations of α-helices in the vicinity of PLPM. The proposed trapping of P excitation energy in the form of the elastic vibrations can rationalize the observed properties of the primary electron transfer reactions, namely, the unusual temperature and ΔG dependences, the oscillating phenomena in kinetics, and the asymmetry of the charge separation reactions.

Atomistic and Coarse Grain Topologies for the Cofactors Associated with the Photosystem II Core Complex

Electron transfers within and between protein complexes are core processes of the electron transport chains occurring in thylakoid (chloroplast), mitochondrial, and bacterial membranes. These electron transfers involve a number of cofactors. Here we describe the derivation of molecular mechanics parameters for the cofactors associated with the function of the photosystem II core complex: plastoquinone, plastoquinol, heme b, chlorophyll A, pheophytin, and β-carotene. Parameters were also obtained for ubiquinol and ubiquinone, related cofactors involved in the respiratory chain. Parameters were derived at both atomistic and coarse grain (CG) resolutions, compatible with the building blocks of the GROMOS united-atom and Martini CG force fields, respectively. Structural and thermodynamic properties of the cofactors were compared to experimental values when available. The topologies were further tested in molecular dynamics simulations of the cofactors in their physiological environment, e.g., either in a lipid membrane environment or in complex with the heme binding protein bacterioferritin.

Redox potential tuning through differential quinone binding in the photosynthetic reaction center of Rhodobacter sphaeroides

Ubiquinone forms an integral part of the electron transport chain in cellular respiration and photosynthesis across a vast number of organisms. Prior experimental results have shown that the photosynthetic reaction center (RC) from Rhodobacter sphaeroides is only fully functional with a limited set of methoxy-bearing quinones, suggesting that specific interactions with this substituent are required to drive electron transport and the formation of quinol. The nature of these interactions has yet to be determined. Through parameterization of a CHARMM-compatible quinone force field and subsequent molecular dynamics simulations of the quinone-bound RC, we have investigated and characterized the interactions of the protein with the quinones in the Q(A) and Q(B) sites using both equilibrium simulation and thermodynamic integration. In particular, we identify a specific interaction between the 2-methoxy group of ubiquinone in the Q(B) site and the amide nitrogen of GlyL225 that we implicate in locking the orientation of the 2-methoxy group, thereby tuning the redox potential difference between the quinones occupying the Q(A) and Q(B) sites. Disruption of this interaction leads to weaker binding in a ubiquinone analogue that lacks a 2-methoxy group, a finding supported by reverse electron transfer electron paramagnetic resonance experiments of the Q(A)⁻Q(B)⁻ biradical and competitive binding assays.

Open quantum system parameters for light harvesting complexes from molecular dynamics

We elucidate the difference between various parameter extraction methods and demonstrate sensitivity to molecular dynamics equilibration.

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.

Theoretical study on excited states of bacteriochlorophyll a in solutions with density functional assessment

The excited-state properties of bacteriochlorophyll (BChl) a in triethylamine, 1-propanol, and methanol are investigated with the time-dependent density functional theory by using the quantum mechanical and molecular mechanical reweighting free energy self-consistant field method. It is found that no prevalent density functionals can reproduce the experimental excited-state properties, i.e., the absorption and reorganization energies, of BChl a in the solutions. The parameter μ in the range-separated hybrid functional is therefore optimized to reproduce the differences of the absorption energies in the solutions. We examine the origin of the differences of the absorption energies in the solutions and find that sensitive balance between contributions of structural changes and solute-solvent interactions determines the differences. The accurate description of the excitation with the density functional with the adjusted parameter is therefore essential to the understanding of the excited-state properties of BChl a in proteins and also the mechanism of the photosynthetic systems.

Visualizing a protein quake with time-resolved X-ray scattering at a free-electron laser

We describe a method to measure ultrafast protein structural changes using time-resolved wide-angle X-ray scattering at an X-ray free-electron laser. We demonstrated this approach using multiphoton excitation of the Blastochloris viridis photosynthetic reaction center, observing an ultrafast global conformational change that arises within picoseconds and precedes the propagation of heat through the protein. This provides direct structural evidence for a 'protein quake': the hypothesis that proteins rapidly dissipate energy through quake-like structural motions.

The Fenna-Matthews-Olson protein revisited: a fully polarizable (TD)DFT/MM description

We report a combined molecular dynamics and quantum mechanics (QM)/molecular mechanics (MM) analysis of the excitonic properties of the Fenna-Matthews-Olson (FMO) protein by using a polarizable MM model combined with a time-dependent density functional theory description. Overall, our results indicate that structural fluctuations, electrostatic interactions, and short-range quantum effects can significantly modulate the model Hamiltonian parameters (site energies and couplings). We find that the specific interactions with the axial ligand and the hydrogen-bonded residues are responsible for the energy ladder, with their effects being mainly due to electrostatic interactions, but with short-range quantum contributions that are not negligible. In addition, a striking modulation of the screening effects experienced by the BChl pairs, due to the heterogeneous polarizability of the FMO and solvent environment, is observed. Finally, we find that the exciton model gives a reliable description of the delocalized excited states in the complex.