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

Probing the Effect of Mutations on Light Harvesting in CP29 by Transient Absorption and First-Principles Simulations

Natural light harvesting is exceptionally efficient thanks to the local energy funnel created within light-harvesting complexes (LHCs). To understand the design principles underlying energy transport in LHCs, ultrafast spectroscopy is often complemented by mutational studies that introduce perturbations into the excitonic structure of the natural complexes. However, such studies may fall short of identifying all excitation energy transfer (EET) pathways and their changes upon mutation. Here, we show that a synergistic combination of first-principles calculations and ultrafast spectroscopy can give unprecedented insight into the EET pathways occurring within LHCs. We measured the transient absorption spectra of the minor CP29 complex of plants and of two mutants, systematically mapping the kinetic components seen in experiments to the simulated exciton dynamics. With our combined strategy, we show that EET in CP29 is surprisingly robust to the changes in the exciton states induced by mutations, explaining the versatility of plant LHCs.

Insights into Energy Transfer in Light-Harvesting Complex II Through Machine-Learning Assisted Simulations

Light-harvesting complex II (LHCII) is the major antenna of higher plants. Energy transfer processes taking place inside its aggregate of chlorophylls have been experimentally investigated with time-resolved techniques, but a complete understanding of the most relevant energy transfer pathways and relative characteristic times remains elusive. Theoretical models to disentangle experimental data in LHCII have long been challenged by the large size and complex nature of the system. Here, we show that a fully first-principles approach combining molecular dynamics and machine learning can be successfully used to reproduce transient absorption spectra and characterize the EET pathways and the involved times.

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.

Environmentally Driven Symmetry Breaking Quenches Dual Fluorescence in Proflavine

Nonadiabatic couplings between several electronic excited states are ubiquitous in many organic chromophores and can significantly influence optical properties. A recent experimental study demonstrated that the proflavine molecule exhibits surprising dual fluorescence in the gas phase, which is suppressed in polar solvent environments. Here, we uncover the origin of this phenomenon by parametrizing a linear-vibronic coupling Hamiltonian from spectral densities of system-bath coupling constructed along molecular dynamics trajectories, fully accounting for interactions with the condensed-phase environment. The finite-temperature absorption, steady-state emission, and time-resolved emission spectra are then computed using powerful, numerically exact tensor network approaches. We find that the dual fluorescence in vacuum is driven by a single well-defined coupling mode but is quenched in solution due to dynamic solvent-driven symmetry breaking that mixes the two low-lying electronic states. We expect the computational framework developed here to be widely applicable to the study of non-Condon effects in complex condensed-phase environments.

Observation of Dark States in Two-Dimensional Electronic Spectra of Chlorosomes

Observations of low-lying dark states in several photosynthetic complexes challenge our understanding of the mechanisms behind their efficient energy transfer processes. Computational models are necessary for providing novel insights into the nature and function of dark states, especially since these are not directly accessible in spectroscopy experiments. Here, we will focus on signatures of dark-type states in chlorosomes, a light-harvesting complex from green sulfur bacteria well-known for uniting a broad absorption band with very efficient energy transfer. In agreement with experiments, our simulations of two-dimensional electronic spectra capture the ultrafast exciton transfer occurring in 100s of femtoseconds within a single chlorosome cylinder. The sub-100 fs process corresponds to relaxation within the single-excitation manifold in a single chlorosome tube, where all initially created populations in the bright exciton states are quickly transferred to dark-type exciton states. Structural inhomogeneities on the local scale cause a redistribution of the oscillator strength, leading to the emergence of these dark-type exciton states, which dominate ultrafast energy transfer. The presence of the dark-type exciton states suppresses energy loss from an isolated chlorosome via fluorescence quenching, as observed experimentally. Our results further question whether relaxation to dark-exciton states is a leading process or merely competes with transfer to the baseplate within the photosynthetic apparatus of green sulfur bacteria.

Perspective on Integrative Simulations of Bioenergetic Domains

Bioenergetic processes in cells, such as photosynthesis or respiration, integrate many time and length scales, which makes the simulation of energy conversion with a mere single level of theory impossible. Just like the myriad of experimental techniques required to examine each level of organization, an array of overlapping computational techniques is necessary to model energy conversion. Here, a perspective is presented on recent efforts for modeling bioenergetic phenomena with a focus on molecular dynamics simulations and its variants as a primary method. An overview of the various classical, quantum mechanical, enhanced sampling, coarse-grained, Brownian dynamics, and Monte Carlo methods is presented. Example applications discussed include multiscale simulations of membrane-wide electron transport, rate kinetics of ATP turnover from electrochemical gradients, and finally, integrative modeling of the chromatophore, a photosynthetic pseudo-organelle.

Electric Field Susceptibility of Chlorophyll c Leads to Unexpected Excitation Dynamics in the Major Light-Harvesting Complex of Diatoms

Diatoms are one of the most abundant photosynthetic organisms on earth and contribute largely to atmospheric oxygen production. They contain fucoxanthin and chlorophyll-a/c binding proteins (FCPs) as light-harvesting complexes with a remarkable adaptation to the fluctuating light on ocean surfaces. To understand the basis of the photosynthetic process in diatoms, the excitation energy funneling within FCPs must be probed. A state-of-the-art multiscale analysis within a quantum mechanics/molecular mechanics framework has been employed. To this end, the chlorophyll (Chl) excitation energies within the FCP complex from the diatom Phaeodactylum tricornutum have been determined. The Chl-c excitation energies were found to be 5-fold more susceptible to electric fields than those of Chl-a pigments and thus are significantly lower in FCP than in organic solvents. This finding challenges the general belief that the excitation energy of Chl-c is always higher than that of Chl-a in FCP proteins and reveals that Chl-c molecules are much more sensitive to electric fields within protein scaffolds than in Chl-a pigments. The analysis of the linear absorption spectrum and the two-dimensional electronic spectra of the FCP complex strongly supports these findings and allows us to study the excitation transfer within the FCP complex.

Taming the third order cumulant approximation to linear optical spectroscopy

The second order cumulant method offers a promising pathway to predicting optical properties in condensed phase systems. It allows for the computation of linear absorption spectra from excitation energy fluctuations sampled along molecular dynamics (MD) trajectories, fully accounting for vibronic effects, direct solute-solvent interactions, and environmental polarization effects. However, the second order cumulant approximation only guarantees accurate line shapes for energy gap fluctuations obeying Gaussian statistics. A third order correction has recently been derived but often yields unphysical spectra or divergent line shapes for moderately non-Gaussian fluctuations due to the neglect of higher order terms in the cumulant expansion. In this work, we develop a corrected cumulant approach, where the collective effect of neglected higher order contributions is approximately accounted for through a dampening factor applied to the third order cumulant term. We show that this dampening factor can be expressed as a function of the skewness and kurtosis of energy gap fluctuations and can be parameterized from a large set of randomly sampled model Hamiltonians for which exact spectral line shapes are known. This approach is shown to systematically remove unphysical contributions in the form of negative absorbances from cumulant spectra in both model Hamiltonians and condensed phase systems sampled from MD and dramatically improves over the second order cumulant method in describing systems exhibiting Duschinsky mode mixing effects. We successfully apply the approach to the coumarin-153 dye in toluene, obtaining excellent agreement with experiment.

Energy transfer from two luteins to chlorophylls in light-harvesting complex II study by using exciton models with phase correction

In light-harvesting complex II of plants, the two lutein pigments (LUT1 and LUT2) are always paired and an energy transfer pathway between them is believed to exist. However, it remains unclear whether this pathway is essential for the energy transfer between carotenoids and chlorophylls. In this work, we performed hybrid quantum mechanics/molecular mechanics simulations with Frenkel exciton models to investigate this energy transfer. The results show that the energy transfer pathways between the S2 state of LUT1 and CLAs are not affected by LUT2 S2. The energy transfer between LUT and chlorophyll-a (CLA) also follows a resonance mechanism. The two LUTs have different energy transfer pathways according to their energy gaps and coupling strengths with each CLA. The present work sheds light on the energy transfer pathways involved in the two LUTs.

Mapping electronic decoherence pathways in molecules

Establishing the fundamental chemical principles that govern molecular electronic quantum decoherence has remained an outstanding challenge. Fundamental questions such as how solvent and intramolecular vibrations or chemical functionalization contribute to the decoherence remain unanswered and are beyond the reach of state-of-the-art theoretical and experimental approaches. Here we address this challenge by developing a strategy to isolate electronic decoherence pathways for molecular chromophores immersed in condensed phase environments that enables elucidating how electronic quantum coherence is lost. For this, we first identify resonance Raman spectroscopy as a general experimental method to reconstruct molecular spectral densities with full chemical complexity at room temperature, in solvent, and for fluorescent and non-fluorescent molecules. We then show how to quantitatively capture the decoherence dynamics from the spectral density and identify decoherence pathways by decomposing the overall coherence loss into contributions due to individual molecular vibrations and solvent modes. We illustrate the utility of the strategy by analyzing the electronic decoherence pathways of the DNA base thymine in water. Its electronic coherences decay in [Formula: see text]30 fs. The early-time decoherence is determined by intramolecular vibrations while the overall decay by solvent. Chemical substitution of thymine modulates the decoherence with hydrogen-bond interactions of the thymine ring with water leading to the fastest decoherence. Increasing temperature leads to faster decoherence as it enhances the importance of solvent contributions but leaves the early-time decoherence dynamics intact. The developed strategy opens key opportunities to establish the connection between molecular structure and quantum decoherence as needed to develop chemical strategies to rationally modulate it.

Multifidelity Machine Learning for Molecular Excitation Energies

The accurate but fast calculation of molecular excited states is still a very challenging topic. For many applications, detailed knowledge of the energy funnel in larger molecular aggregates is of key importance, requiring highly accurate excitation energies. To this end, machine learning techniques can be a very useful tool, though the cost of generating highly accurate training data sets still remains a severe challenge. To overcome this hurdle, this work proposes the use of multifidelity machine learning where very little training data from high accuracies is combined with cheaper and less accurate data to achieve the accuracy of the costlier level. In the present study, the approach is employed to predict vertical excitation energies to the first excited state for three molecules of increasing size, namely, benzene, naphthalene, and anthracene. The energies are trained and tested for conformations stemming from classical molecular dynamics and density functional based tight-binding simulations. It can be shown that the multifidelity machine learning model can achieve the same accuracy as a machine learning model built only on high-cost training data while expending a much lower computational effort to generate the data. The numerical gain observed in these benchmark test calculations was over a factor of 30 but certainly can be much higher for high-accuracy data.

First-principles simulation of excitation energy transfer and transient absorption spectroscopy in the CP29 light-harvesting complex

The dynamics of delocalized excitons in light-harvesting complexes (LHCs) can be investigated using different experimental techniques, and transient absorption (TA) spectroscopy is one of the most valuable methods for this purpose. A careful interpretation of TA spectra is essential for the clarification of excitation energy transfer (EET) processes occurring during light-harvesting. However, even in the simplest LHCs, a physical model is needed to interpret transient spectra as the number of EET processes occurring at the same time is very large to be disentangled from measurements alone. Physical EET models are commonly built by fittings of the microscopic exciton Hamiltonians and exciton-vibrational parameters, an approach that can lead to biases. Here, we present a first-principles strategy to simulate EET and transient absorption spectra in LHCs, combining molecular dynamics and accurate multiscale quantum chemical calculations to obtain an independent estimate of the excitonic structure of the complex. The microscopic parameters thus obtained are then used in EET simulations to obtain the population dynamics and the related spectroscopic signature. We apply this approach to the CP29 minor antenna complex of plants for which we follow the EET dynamics and transient spectra after excitation in the chlorophyll b region. Our calculations reproduce all the main features observed in the transient absorption spectra and provide independent insight on the excited-state dynamics of CP29. The approach presented here lays the groundwork for the accurate simulation of EET and unbiased interpretation of transient spectra in multichromophoric systems.

Dominant role of excitons in photosynthetic color-tuning and light-harvesting

Photosynthesis is a vital process that converts sunlight into energy for the Earth's ecosystems. Color adaptation is crucial for different photosynthetic organisms to thrive in their ecological niches. Although the presence of collective excitons in light-harvesting complexes is well known, the role of delocalized excited states in color tuning and excitation energy transfer remains unclear. This study evaluates the characteristics of photosynthetic excitons in sulfur and non-sulfur purple bacteria using advanced optical spectroscopic techniques at reduced temperatures. The exciton effects in these bacteriochlorophyll a-containing species are generally much stronger than in plant systems that rely on chlorophylls. Their exciton bandwidth varies based on multiple factors such as chromoprotein structure, surroundings of the pigments, carotenoid content, hydrogen bonding, and metal ion inclusion. The study nevertheless establishes a linear relationship between the exciton bandwidth and Qy singlet exciton absorption peak, which in case of LH1 core complexes from different species covers almost 130 nm. These findings provide important insights into bacterial color tuning and light-harvesting, which can inspire sustainable energy strategies and devices.

Impact of Spatial Inhomogeneity on Excitation Energy Transport in the Fenna-Matthews-Olson Complex

The dynamics of the excitation energy transfer (EET) in photosynthetic complexes is an interesting question both from the perspective of fundamental understanding and the research in artificial photosynthesis. Over the past decade, very accurate spectral densities have been developed to capture spatial inhomogeneities in the Fenna-Matthews-Olson (FMO) complex. However, challenges persist in numerically simulating these systems, both in terms of parameterizing them and following their dynamics over long periods of time because of long non-Markovian memories. We investigate the dynamics of FMO with the exact treatment of various theoretical spectral densities using the new tensor network path integral-based methods, which are uniquely capable of addressing the difficulty of long memory length and incoherent Förster theory. It is also important to be able to analyze the pathway of EET flow, which can be difficult to identify given the non-trivial structure of connections between bacteriochlorophyll molecules in FMO. We use the recently introduced ideas of relating coherence to population derivatives to analyze the transport process and reveal some new routes of transport. The combination of exact and approximate methods sheds light on the role of coherences in affecting the fine details of the transport and promises to be a powerful toolbox for future exploration of other open systems with quantum transport.

Understanding Primary Charge Separation in the Heliobacterial Reaction Center

The homodimeric reaction center of heliobacteria retains features of the ancestral reaction center and can thus provide insights into the evolution of photosynthesis. Primary charge separation is expected to proceed in a two-step mechanism along either of the two reaction center branches. We reveal the first charge-separation step from first-principles calculations based on time-dependent density functional theory with an optimally tuned range-separated hybrid and ab initio Born-Oppenheimer molecular dynamics: the electron is most likely localized on the electron transfer cofactor 3 (EC3, OH-chlorophyll a), and the hole on the adjacent EC2. Including substantial parts of the surrounding protein environment into the calculations shows that a distinct structural mechanism is decisive for the relative energetic positioning of the electronic excitations: specific charged amino acids in the vicinity of EC3 lower the energy of charge-transfer excitations and thus facilitate efficient charge separation. These results are discussed considering recent experimental insights.

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.

Recent progress in atomistic modeling of light-harvesting complexes: a mini review

In this mini review, we focus on recent advances in the atomistic modeling of biological light-harvesting (LH) complexes. Because of their size and sophisticated electronic structures, multiscale methods are required to investigate the dynamical and spectroscopic properties of such complexes. The excitation energies, in this context also known as site energies, excitonic couplings, and spectral densities are key quantities which usually need to be extracted to be able to determine the exciton dynamics and spectroscopic properties. The recently developed multiscale approach based on the numerically efficient density functional tight-binding framework followed by excited state calculations has been shown to be superior to the scheme based on pure classical molecular dynamics simulations. The enhanced approach, which improves the description of the internal vibrational dynamics of the pigment molecules, yields spectral densities in good agreement with the experimental counterparts for various bacterial and plant LH systems. Here, we provide a brief overview of those results and described the theoretical foundation of the multiscale protocol.

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.

Machine Learning Exciton Hamiltonians in Light-Harvesting Complexes

We propose a machine learning (ML)-based strategy for an inexpensive calculation of excitonic properties of light-harvesting complexes (LHCs). The strategy uses classical molecular dynamics simulations of LHCs in their natural environment in combination with ML prediction of the excitonic Hamiltonian of the embedded aggregate of pigments. The proposed ML model can reproduce the effects of geometrical fluctuations together with those due to electrostatic and polarization interactions between the pigments and the protein. The training is performed on the chlorophylls of the major LHC of plants, but we demonstrate that the model is able to extrapolate well beyond the initial training set. Moreover, the accuracy in predicting the effects of the environment is tested on the simulation of the small changes observed in the absorption spectra of the wild-type and a mutant of a minor LHC.

Structure-based model of fucoxanthin-chlorophyll protein complex: Calculations of chlorophyll electronic couplings

Diatoms are a group of marine algae that are responsible for a significant part of global oxygen production. Adapted to life in an aqueous environment dominated by the blue-green light, their major light-harvesting antennae-fucoxanthin-chlorophyll protein complexes (FCPs)-exhibit different pigment compositions than of plants. Despite extensive experimental studies, until recently the theoretical description of excitation energy dynamics in these complexes was limited by the lack of high-resolution structural data. In this work, we use the recently resolved crystallographic information of the FCP complex from Phaeodactylum tricornutum diatom [Wang et al., Science 363, 6427 (2019)] and quantum chemistry-based calculations to evaluate the chlorophyll transition dipole moments, atomic transition charges from electrostatic potential, and the inter-chlorophyll couplings in this complex. The obtained structure-based excitonic couplings form the foundation for any modeling of stationary or time-resolved spectroscopic data. We also calculate the inter-pigment Förster energy transfer rates and identify two quickly equilibrating chlorophyll clusters.

Spectral densities and absorption spectra of the core antenna complex CP43 from photosystem II

Besides absorbing light, the core antenna complex CP43 of photosystem II is of great importance in transferring excitation energy from the antenna complexes to the reaction center. Excitation energies, spectral densities, and linear absorption spectra of the complex have been evaluated by a multiscale approach. In this scheme, quantum mechanics/molecular mechanics molecular dynamics simulations are performed employing the parameterized density functional tight binding (DFTB) while the time-dependent long-range-corrected DFTB scheme is applied for the excited state calculations. The obtained average spectral density of the CP43 complex shows a very good agreement with experimental results. Moreover, the excitonic Hamiltonian of the system along with the computed site-dependent spectral densities was used to determine the linear absorption. While a Redfield-like approximation has severe shortcomings in dealing with the CP43 complex due to quasi-degenerate states, the non-Markovian full second-order cumulant expansion formalism is able to overcome the drawbacks. Linear absorption spectra were obtained, which show a good agreement with the experimental counterparts at different temperatures. This study once more emphasizes that by combining diverse techniques from the areas of molecular dynamics simulations, quantum chemistry, and open quantum systems, it is possible to obtain first-principle results for photosynthetic complexes, which are in accord with experimental findings.

Theoretical Study of Macrocyclic Host Molecules: From Supramolecular Recognition to Self-Assembly

Supramolecular chemistry focuses on molecular recognition and self-assembly of various building blocks through weak non-covalent interactions, including anion-π, hydrogen bond (HB), hydrophobic interactions, van der Waals (vdW) interactions, etc, which...