Predictive First-Principles Modeling of a Photosynthetic Antenna Protein: The Fenna-Matthews-Olson Complex

Quantum Algorithms and Applications for Open Quantum Systems

Accurate models for open quantum systems─quantum states that have nontrivial interactions with their environment─may aid in the advancement of a diverse array of fields, including quantum computation, informatics, and the prediction of static and dynamic molecular properties. In recent years, quantum algorithms have been leveraged for the computation of open quantum systems as the predicted quantum advantage of quantum devices over classical ones may allow previously inaccessible applications. Accomplishing this goal will require input and expertise from different research perspectives, as well as the training of a diverse quantum workforce, making a compilation of current quantum methods for treating open quantum systems both useful and timely. In this Review, we first provide a succinct summary of the fundamental theory of open quantum systems and then delve into a discussion on recent quantum algorithms. We conclude with a discussion of pertinent applications, demonstrating the applicability of this field to realistic chemical, biological, and material systems.

Rationalizing protein-ligand interactions via the effective fragment potential method and structural data from classical molecular dynamics

The Effective Fragment Potential (EFP) method, a polarizable quantum mechanics-based force field for describing non-covalent interactions, is utilized to calculate protein-ligand interactions in seven inactive cyclin-dependent kinase 2-ligand complexes, employing structural data from molecular dynamics simulations to assess dynamic and solvent effects. Our results reveal high correlations between experimental binding affinities and EFP interaction energies across all the structural data considered. Using representative structures found by clustering analysis and excluding water molecules yields the highest correlation (R2 of 0.95). In addition, the EFP pairwise interaction energy decomposition analysis identifies critical interactions between the ligands and protein residues and provides insight into their nature. Overall, this study indicates the potential applications of the EFP method in structure-based drug design.

ANI/EFP: Modeling Long-Range Interactions in ANI Neural Network with Effective Fragment Potentials

Deep learning Neural Networks (NN) have been developed in the field of molecular modeling for the purpose of circumventing the high computational cost of quantum-mechanical calculations while rivaling their accuracies. Although these networks have found great success, they generally lack the ability to accurately describe long-range interactions, which makes them unusable for extended molecular systems. Herein, we provide a method for partially retraining the deep learning general-use neural network ANI, in which the long-range interactions are represented via atomic electrostatic potentials. The electrostatic potentials, generated with polarizable effective fragment potentials (EFP), are used as an additional input feature for the network. This new ANI/EFP network can predict solute-solvent interaction energies on a trained data set with a kcal/mol accuracy. It also shows promise in predicting the interaction energies of a solute in solvent environments that have not been included in a training data set. The proposed protocol can be taken as an example and further developed, leading to highly accurate and transferable neural network potentials capable of handling long-range interactions and extended molecular systems.

Impact of Peripheral Hydrogen Bond on Electronic Properties of the Primary Acceptor Chlorophyll in the Reaction Center of Photosystem I

Photosystem I (PS I) is a photosynthetic pigment-protein complex that absorbs light and uses the absorbed energy to initiate electron transfer. Electron transfer has been shown to occur concurrently along two (A- and B-) branches of reaction center (RC) cofactors. The electron transfer chain originates from a special pair of chlorophyll a molecules (P700), followed by two chlorophylls and one phylloquinone in each branch (denoted as A-1, A0, A1, respectively), converging in a single iron-sulfur complex Fx. While there is a consensus that the ultimate electron donor-acceptor pair is P700+A0-, the involvement of A-1 in electron transfer, as well as the mechanism of the very first step in the charge separation sequence, has been under debate. To resolve this question, multiple groups have targeted electron transfer cofactors by site-directed mutations. In this work, the peripheral hydrogen bonds to keto groups of A0 chlorophylls have been disrupted by mutagenesis. Four mutants were generated: PsaA-Y692F; PsaB-Y667F; PsaB-Y667A; and a double mutant PsaA-Y692F/PsaB-Y667F. Contrary to expectations, but in agreement with density functional theory modeling, the removal of the hydrogen bond by Tyr → Phe substitution was found to have a negligible effect on redox potentials and optical absorption spectra of respective chlorophylls. In contrast, Tyr → Ala substitution was shown to have a fatal effect on the PS I function. It is thus inferred that PsaA-Y692 and PsaB-Y667 residues have primarily structural significance, and their ability to coordinate respective chlorophylls in electron transfer via hydrogen bond plays a minor role.

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.

Artificial-Intelligence-Based Surrogate Solution of Dissipative Quantum Dynamics: Physics-Informed Reconstruction of the Universal Propagator

The accurate (or even approximate) solution of the equations that govern the dynamics of dissipative quantum systems remains a challenging task in quantum science. While several algorithms have been designed to solve those equations with different degrees of flexibility, they rely mainly on highly expensive iterative schemes. Most recently, deep neural networks have been used for quantum dynamics, but current architectures are highly dependent on the physics of the particular system and usually limited to population dynamics. Here we introduce an artificial-intelligence-based surrogate model that solves dissipative quantum dynamics by parametrizing quantum propagators as Fourier neural operators, which we train using both data set and physics-informed loss functions. Compared with conventional algorithms, our quantum neural propagator avoids time-consuming iterations and provides a universal superoperator that can be used to evolve any initial quantum state for arbitrarily long times. To illustrate the wide applicability of the approach, we employ our quantum neural propagator to compute the population dynamics and time-correlation functions of the Fenna-Matthews-Olson complex.

High-Resolution Frequency-Domain Spectroscopic and Modeling Studies of Photosystem I (PSI), PSI Mutants and PSI Supercomplexes

Photosystem I (PSI) is one of the two main pigment-protein complexes where the primary steps of oxygenic photosynthesis take place. This review describes low-temperature frequency-domain experiments (absorption, emission, circular dichroism, resonant and non-resonant hole-burned spectra) and modeling efforts reported for PSI in recent years. In particular, we focus on the spectral hole-burning studies, which are not as common in photosynthesis research as the time-domain spectroscopies. Experimental and modeling data obtained for trimeric cyanobacterial Photosystem I (PSI3), PSI3 mutants, and PSI3-IsiA18 supercomplexes are analyzed to provide a more comprehensive understanding of their excitonic structure and excitation energy transfer (EET) processes. Detailed information on the excitonic structure of photosynthetic complexes is essential to determine the structure-function relationship. We will focus on the so-called "red antenna states" of cyanobacterial PSI, as these states play an important role in photochemical processes and EET pathways. The high-resolution data and modeling studies presented here provide additional information on the energetics of the lowest energy states and their chlorophyll (Chl) compositions, as well as the EET pathways and how they are altered by mutations. We present evidence that the low-energy traps observed in PSI are excitonically coupled states with significant charge-transfer (CT) character. The analysis presented for various optical spectra of PSI3 and PSI3-IsiA18 supercomplexes allowed us to make inferences about EET from the IsiA18 ring to the PSI3 core and demonstrate that the number of entry points varies between sample preparations studied by different groups. In our most recent samples, there most likely are three entry points for EET from the IsiA18 ring per the PSI core monomer, with two of these entry points likely being located next to each other. Therefore, there are nine entry points from the IsiA18 ring to the PSI3 trimer. We anticipate that the data discussed below will stimulate further research in this area, providing even more insight into the structure-based models of these important cyanobacterial photosystems.

Detangling Solvatochromic Effects by the Effective Fragment Potential Method

Understanding molecular interactions in complex systems opens avenues for the efficient design of new materials with target properties. Energy decomposition methods provide a means to obtain a detailed picture of intermolecular interactions. This work introduces a molecular modeling approach for decomposing the solvatochromic shifts of the electronic excited states into the contributions of the individual molecular fragments of the environment surrounding the chromophore. The developed approach is implemented for the QM/EFP (quantum mechanics/effective fragment potential) model that provides a rigorous first-principles-based description of the electronic states of the chromophores in complex polarizable environments. On the example of two model systems, water pentamer and hydrated uracil, we show how the decomposition of the solvatochromic shifts into the contributions of individual solvent water molecules provides a detailed picture of the intermolecular interactions in the ground and excited states of these systems. The analysis also demonstrates the nonadditivity of solute-solvent interactions and the significant contribution of solute polarization to the total values of solvatochromic shifts.

Predicting Mutation-Induced Changes in the Electronic Properties of Photosynthetic Proteins from First Principles: The Fenna-Matthews-Olson Complex Example

Multiscale molecular modeling is utilized to predict optical absorption and circular dichroism spectra of two single-point mutants of the Fenna-Matthews-Olson photosynthetic pigment-protein complex. The modeling approach combines classical molecular dynamics simulations with structural refinement of photosynthetic pigments and calculations of their excited states in a polarizable protein environment. The only experimental input to the modeling protocol is the X-ray structure of the wild-type protein. The first-principles modeling reproduces changes in the experimental optical spectra of the considered mutants, Y16F and Q198V. Interestingly, the Q198V mutation has a negligible effect on the electronic properties of the targeted bacteriochlorophyll a pigment. Instead, the electronic properties of several other pigments respond to this mutation. The molecular modeling demonstrates that a single-point mutation can induce long-range effects on the protein structure, while extensive structural changes near a pigment do not necessarily lead to significant changes in the electronic properties of that pigment.

Bioexcitons by Design: How Do We Get There?

Biological pigment-protein complexes (PPCs) exhibit a remarkable ability to tune the optical properties of biological excitons (bioexcitons) through specific pigment-protein interactions. While such fine-tuning allows natural systems (e.g., photosynthetic proteins) to carry out their native functions with near-optimal performance, native function itself is often suboptimal for applications such as biofuel production or quantum technology development. This perspective offers a look at near-term prospects for the rational reoptimization of PPC bioexcitons for new functions using site-directed mutagenesis. The primary focus is on the "structure-spectrum" challenge of understanding the relationships between structural features and spectroscopic properties. While recent examples demonstrate that site-directed mutagenesis can be used to tune nearly all key bioexciton parameters (e.g., site energies, interpigment couplings, and electronic-vibrational interactions), critical challenges remain before we achieve truly rational design of bioexciton properties.

Towards a quantitative description of excitonic couplings in photosynthetic pigment-protein complexes: quantum chemistry driven multiscale approaches

A structure-based quantitative calculation of excitonic couplings between photosynthetic pigments has to describe the dynamical polarization of the protein/solvent environment of the pigments, giving rise to reaction field and screening effects. Here, this challenging problem is approached by combining the fragment molecular orbital (FMO) method with the polarizable continuum model (PCM). The method is applied to compute excitonic couplings between chlorophyll a (Chl a) pigments of the water-soluble chlorophyll-binding protein (WSCP). By calibrating the vacuum dipole strength of the 0-0 transition of the Chl a chromophores according to experimental data, an excellent agreement between calculated and experimental linear absorption and circular dichroism spectra of WSCP is obtained. The effect of the mutual polarization of the pigment ground states is calculated to be very small. The simple Poisson-Transition-charge-from-Electrostatic-potential (Poisson-TrEsp) method is found to accurately describe the screening part of the excitonic coupling, obtained with FMO/PCM. Taking into account that the reaction field effects of the latter method can be described by a scalar constant leads to an improvement of Poisson-TrEsp that is expected to provide the basis for simple and realistic calculations of optical spectra and energy transfer in photosynthetic light-harvesting complexes. In addition, we present an expression for the estimation of Huang-Rhys factors of high-frequency pigment vibrations from experimental fluorescence line-narrowing spectra that takes into account the redistribution of oscillator strength by the interpigment excitonic coupling. Application to WSCP results in corrected Huang-Rhys factors that are less than one third of the original values obtained by the standard electronic two-state analysis that neglects the above redistribution. These factors are important for the estimation of the dipole strength of the 0-0 transition of the chromophores and for the development of calculation schemes for the spectral density of the exciton-vibrational coupling.

Computational elucidations on the role of vibrations in energy transfer processes of photosynthetic complexes

Coupling between pigment excitations and nuclear movements in photosynthetic complexes is known to modulate the excitation energy transfer (EET) efficiencies. Toward providing microscopic information, researchers often apply simulation techniques and investigate how vibrations are involved in EET processes. Here, reports on such roles of nuclear movements are discussed from a theory perspective. While vibrations naturally present random thermal fluctuations that can affect energy transferring characteristics, they can also be intertwined with exciton structures and create more specific non-adiabatic energy transfer pathways. For reliable simulations, a bath model that accurately mimics a given molecular system is required. Methods for obtaining such a model in combination with quantum chemical electronic structure calculations and molecular dynamics trajectory simulations are discussed. Various quantum dynamics simulation tools that can handle pigment-to-pigment energy transfers together with their vibrational characters are also touched on. Behaviors of molecular vibrations often deviate from ideality, especially when all-atom details are included, which practically forces us to treat them classically. We conclude this perspective by considering some recent reports that suggest that classical descriptions of bath effects with all-atom details may still produce valuable information for analyzing sophisticated contributions by vibrations to EET processes.

Accurate prediction of mutation-induced frequency shifts in chlorophyll proteins with a simple electrostatic model

Photosynthetic pigment-protein complexes control local chlorophyll (Chl) transition frequencies through a variety of electrostatic and steric forces. Site-directed mutations can modify this local spectroscopic tuning, providing critical insight into native photosynthetic functions and offering the tantalizing prospect of creating rationally designed Chl proteins with customized optical properties. Unfortunately, at present, no proven methods exist for reliably predicting mutation-induced frequency shifts in advance, limiting the method's utility for quantitative applications. Here, we address this challenge by constructing a series of point mutants in the water-soluble chlorophyll protein of Lepidium virginicum and using them to test the reliability of a simple computational protocol for mutation-induced site energy shifts. The protocol uses molecular dynamics to prepare mutant protein structures and the charge density coupling model of Adolphs et al. [Photosynth. Res. 95, 197-209 (2008)] for site energy prediction; a graphical interface that implements the protocol automatically is published online at http://nanohub.org/tools/pigmenthunter. With the exception of a single outlier (presumably due to unexpected structural changes), we find that the calculated frequency shifts match the experiment remarkably well, with an average error of 1.6 nm over a 9 nm spread in wavelengths. We anticipate that the accuracy of the method can be improved in the future with more advanced sampling of mutant protein structures.

Exciton Lifetime Distributions and Population Dynamics in the FMO Protein Complex from Prosthecochloris aestuarii

Significant protein rearrangement upon excitation and energy transfer in Fenna-Matthews-Olson protein of Prosthecochloris aestuarii results in a modified energy landscape, which induces more changes in pigment site energies than predicted by the "standard" hole-burning theory. The energy changes are elucidated by simulations while investigating the effects of site-dependent disorder, both static (site-energy distribution widths) and dynamic (spectral density shapes). The resulting optimized site energies and their fluctuations are consistent with relative differences observed in inhomogeneous widths calculated by recent molecular dynamic simulations. Two sets of different spectral densities reveal how their shapes affect the population dynamics and distribution of exciton lifetimes. Calculations revealed the wavelength-dependent distributions of exciton lifetimes (T ₁) in the femtosecond to picosecond time frame. We suggest that the calculated multimodal and asymmetric wavelength-dependent T ₁ distributions offer more insight into the interpretation of resonant hole-burned (HB) spectra, kinetic traces in two-dimensional (2D) electronic spectroscopy experiments, and widely used global analyses in fitting data from transient absorption experiments.

Artificial Photosynthesis: Is Computation Ready for the Challenge Ahead?

A tremendous effort is currently devoted to the generation of novel hybrid materials with enhanced electronic properties for the creation of artificial photosynthetic systems. This compelling and challenging problem is well-defined from an experimental point of view, as the design of such materials relies on combining organic materials or metals with biological systems like light harvesting and redox-active proteins. Such hybrid systems can be used, e.g., as bio-sensors, bio-fuel cells, biohybrid photoelectrochemical cells, and nanostructured photoelectronic devices. Despite these efforts, the main bottleneck is the formation of efficient interfaces between the biological and the organic/metal counterparts for efficient electron transfer (ET). It is within this aspect that computation can make the difference and improve the current understanding of the mechanisms underneath the interface formation and the charge transfer efficiency. Yet, the systems considered (i.e., light harvesting protein, self-assembly monolayer and surface assembly) are more and more complex, reaching (and often passing) the limit of current computation power. In this review, recent developments in computational methods for studying complex interfaces for artificial photosynthesis will be provided and selected cases discussed, to assess the inherent ability of computation to leave a mark in this field of research.

Static Disorder in Excitation Energies of the Fenna-Matthews-Olson Protein: Structure-Based Theory Meets Experiment

Inhomogeneous broadening of optical lines of the Fenna-Matthews-Olson (FMO) light-harvesting protein is investigated by combining a Monte Carlo sampling of low-energy conformational substates of the protein with a quantum chemical/electrostatic calculation of local transition energies (site energies) of the pigments. The good agreement between the optical spectra calculated for the inhomogeneous ensemble and the experimental data demonstrates that electrostatics is the dominant contributor to static disorder in site energies. Rotamers of polar amino acid side chains are found to cause bimodal distribution functions of site energy shifts, which can be probed by hole burning and single-molecule spectroscopy. When summing over the large number of contributions, the resulting distribution functions of the site energies become Gaussians, and the correlations in site energy fluctuations at different sites practically average to zero. These results demonstrate that static disorder in the FMO protein is in the realm of the central limit theorem of statistics.

Effective Fragment Potentials for Flexible Molecules: Transferability of Parameters and Amino Acid Database

An accurate but efficient description of noncovalent interactions is a key to predictive modeling of biological and materials systems. The effective fragment potential (EFP) is an ab initio-based force field that provides a physically meaningful decomposition of noncovalent interactions of a molecular system into Coulomb, polarization, dispersion, and exchange-repulsion components. An EFP simulation protocol consists of two steps, preparing parameters for molecular fragments by a series of ab initio calculations on each individual fragment, and calculation of interaction energy and properties of a total molecular system based on the prepared parameters. As the fragment parameters (distributed multipoles, polarizabilities, localized wave function, etc.) depend on a fragment geometry, straightforward application of the EFP method requires recomputing parameters of each fragment if its geometry changes, for example, during thermal fluctuations of a molecular system. Thus, recomputing fragment parameters can easily become both computational and human bottlenecks and lead to a loss of efficiency of a simulation protocol. An alternative approach, in which fragment parameters are adjusted to different fragment geometries, referred to as "flexible EFP", is explored here. The parameter adjustment is based on translations and rotations of local coordinate frames associated with fragment atoms. The protocol is validated on extensive benchmark of amino acid dimers extracted from molecular dynamics snapshots of a cryptochrome protein. A parameter database for standard amino acids is developed to automate flexible EFP simulations in proteins. To demonstrate applicability of flexible EFP in large-scale protein simulations, binding energies and vertical electron ionization and electron attachment energies of a lumiflavin chromophore of the cryptochrome protein are computed. The results obtained with flexible EFP are in a close agreement with the standard EFP procedure but provide a significant reduction in computational cost.

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.

Analysis of Photosynthetic Systems and Their Applications with Mathematical and Computational Models

In biological and life science applications, photosynthesis is an important process that involves the absorption and transformation of sunlight into chemical energy. During the photosynthesis process, the light photons are captured by the green chlorophyll pigments in their photosynthetic antennae and further funneled to the reaction center. One of the most important light harvesting complexes that are highly important in the study of photosynthesis is the membrane-attached Fenna–Matthews–Olson (FMO) complex found in the green sulfur bacteria. In this review, we discuss the mathematical formulations and computational modeling of some of the light harvesting complexes including FMO. The most recent research developments in the photosynthetic light harvesting complexes are thoroughly discussed. The theoretical background related to the spectral density, quantum coherence and density functional theory has been elaborated. Furthermore, details about the transfer and excitation of energy in different sites of the FMO complex along with other vital photosynthetic light harvesting complexes have also been provided. Finally, we conclude this review by providing the current and potential applications in environmental science, energy, health and medicine, where such mathematical and computational studies of the photosynthesis and the light harvesting complexes can be readily integrated.