Acceleration of the Z to E photoisomerization of penta-2,4-dieniminium by hydrogen out-of-plane motion: theoretical study on a model system of retinal protonated Schiff base

Fluorescence of the Retinal Chromophore in Microbial and Animal Rhodopsins

Fluorescence of the vast majority of natural opsin-based photoactive proteins is extremely low, in accordance with their functions that depend on efficient transduction of absorbed light energy. However, several recently proposed classes of engineered rhodopsins with enhanced fluorescence, along with the discovery of a new natural highly fluorescent rhodopsin, NeoR, opened a way to exploit these transmembrane proteins as fluorescent sensors and draw more attention to studies on this untypical rhodopsin property. Here, we review the available data on the fluorescence of the retinal chromophore in microbial and animal rhodopsins and their photocycle intermediates, as well as different isomers of the protonated retinal Schiff base in various solvents and the gas phase.

QCforever: A Quantum Chemistry Wrapper for Everyone to Use in Black-Box Optimization

To obtain observable physical or molecular properties such as ionization potential and fluorescent wavelength with quantum chemical (QC) computation, multi-step computation manipulated by a human is required. Hence, automating the multi-step computational process and making it a black box that can be handled by anybody are important for effective database construction and fast realistic material design through the framework of black-box optimization where machine learning algorithms are introduced as a predictor. Here, we propose a Python library, QCforever, to automate the computation of some molecular properties and chemical phenomena induced by molecules. This tool just requires a molecule file for providing its observable properties, automating the computation process of molecular properties (for ionization potential, fluorescence, etc.) and output analysis for providing their multi-values for evaluating a molecule. Incorporating the tool in black-box optimization, we can explore molecules that have properties we desired within the limitation of QC computation.

Free Energy Computation for an Isomerizing Chromophore in a Molecular Cavity via the Average Solvent Electrostatic Configuration Model: Applications in Rhodopsin and Rhodopsin-Mimicking Systems

We present a novel technique for computing the free energy differences between two chromophore "isomers" hosted in a molecular environment (a generalized solvent). Such an environment may range from a relatively rigid protein cavity to a flexible solvent environment. The technique is characterized by the application of the previously reported "average electrostatic solvent configuration" method, and it is based on the idea of using the free energy perturbation theory along with a chromophore annihilation procedure in thermodynamic cycle calculations. The method is benchmarked by computing the ground-state room-temperature relative stabilities between (i) the cis and trans isomers of prototypal animal and microbial rhodopsins and (ii) the analogue isomers of a rhodopsin-like light-driven molecular switch in methanol. Furthermore, we show that the same technology can be used to estimate the activation free energy for the thermal isomerization of systems i-ii by replacing one isomer with a transition state. The results show that the computed relative stability and isomerization barrier magnitudes for the selected systems are in line with the available experimental observation in spite of their widely diverse complexity.

Simple Models to Study Spectral Properties of Microbial and Animal Rhodopsins: Evaluation of the Electrostatic Effect of Charged and Polar Residues on the First Absorption Band Maxima

A typical feature of proteins from the rhodopsin family is the sensitivity of their absorption band maximum to protein amino acid composition. For this reason, studies of these proteins often require methodologies that determine spectral shift caused by amino acid substitutions. Generally, quantum mechanics/molecular mechanics models allow for the calculation of a substitution-induced spectral shift with high accuracy, but their application is not always easy and requires special knowledge. In the present study, we propose simple models that allow us to estimate the direct effect of a charged or polar residue substitution without extensive calculations using only rhodopsin three-dimensional structure and plots or tables that are provided in this article. The models are based on absorption maximum values calculated at the SORCI+Q level of theory for cis- and trans-forms of retinal protonated Schiff base in an external electrostatic field of charges and dipoles. Each value corresponds to a certain position of a charged or polar residue relative to the retinal chromophore. The proposed approach was evaluated against an example set consisting of twelve bovine rhodopsin and sodium pumping rhodopsin mutants. The limits of the applicability of the models are also discussed. The results of our study can be useful for the interpretation of experimental data and for the rational design of rhodopsins with required spectral properties.

An assessment of water placement algorithms in quantum mechanics/molecular mechanics modeling: the case of rhodopsins' first spectral absorption band maxima

Quantum mechanics/molecular mechanics (QM/MM) models are a widely used tool to obtain detailed insight into the properties and functioning of proteins. The outcome of QM/MM studies heavily depends on the quality of the applied QM/MM model. Prediction and right placement of internal water molecules in protein cavities is one of the critical parts of any QM/MM model construction. Herein, we performed a systematic study of four protein hydration algorithms. We tested these algorithms for their ability to predict X-ray-resolved water molecules for a set of membrane photosensitive rhodopsin proteins, as well as the influence of the applied water placement algorithms on the QM/MM calculated absorption maxima (λ_max) of these proteins. We used 49 rhodopsins and their intermediates with available X-ray structures as the test set. We found that a proper choice of hydration algorithms and setups is needed to predict functionally important water molecules in the chromophore-binding cavity of rhodopsins, such as the water cluster in the N-H region of bacteriorhodopsin or two water molecules in the binding pocket of bovine visual rhodopsin. The QM/MM calculated λ_max of rhodopsins is also quite sensitive to the applied protein hydration protocols. The best methodology allows obtaining an 18.0 nm average value for the absolute deviation of the calculated λ_max from the experimental λ_max. Although the major effect of water molecules on λ_max originates from the water molecules located in the binding pocket, the water molecules outside the binding pocket also affect the calculated λ_max mainly by causing a reorganization of the protein structure. The results reported in this study can be used for the evaluation and further development of hydration methodologies, in general, and rhodopsin QM/MM models, in particular.

Quantum Mechanical and Molecular Mechanics Modeling of Membrane-Embedded Rhodopsins

Computational chemistry provides versatile methods for studying the properties and functioning of biological systems at different levels of precision and at different time scales. The aim of this article is to review the computational methodologies that are applicable to rhodopsins as archetypes for photoactive membrane proteins that are of great importance both in nature and in modern technologies. For each class of computational techniques, from methods that use quantum mechanics for simulating rhodopsin photophysics to less-accurate coarse-grained methodologies used for long-scale protein dynamics, we consider possible applications and the main directions for improvement.

A Comparative Study of Modern Homology Modeling Algorithms for Rhodopsin Structure Prediction

Rhodopsins are seven α-helical membrane proteins that are of great importance in chemistry, biology, and modern biotechnology. Any in silico study on rhodopsin properties and functioning requires a high-quality three-dimensional structure. Due to particular difficulties with obtaining membrane protein structures from the experiment, in silico prediction of the three-dimensional rhodopsin structure based only on its primary sequence is an especially important task. For the last few years, significant progress was made in the field of protein structure prediction, especially for methods based on comparative modeling. However, the majority of this progress was made for soluble proteins and further investigations are needed to achieve similar progress for membrane proteins. In this paper, we evaluate the performance of modern protein structure prediction methodologies (implemented in the Medeller, I-TASSER, and Rosetta packages) for their ability to predict rhodopsin structures. Three widely used methodologies were considered: two general methodologies that are commonly applied to soluble proteins and a methodology that uses constraints that are specific for membrane proteins. The test pool consisted of 36 target-template pairs with different sequence similarities that was constructed on the basis of 24 experimental rhodopsin structures taken from the RCSB database. As a result, we showed that all three considered methodologies allow obtaining rhodopsin structures with the quality that is close to the crystallographic one (root mean square deviation (RMSD) of the predicted structure from the corresponding X-ray structure up to 1.5 Å) if the target-template sequence identity is higher than 40%. Moreover, all considered methodologies provided structures of average quality (RMSD < 4.0 Å) if the target-template sequence identity is higher than 20%. Such structures can be subsequently used for further investigation of molecular mechanisms of protein functioning and for the development of modern protein-based biotechnologies.

A voltage-dependent fluorescent indicator for optogenetic applications, archaerhodopsin-3: Structure and optical properties from in silico modeling

It was demonstrated in recent studies that some rhodopsins can be used in optogenetics as fluorescent indicators of membrane voltage. One of the promising candidates for these applications is archaerhodopsin-3. While it has already shown encouraging results, there is still a large room for improvement. One of possible directions is increasing the intensity of the protein's fluorescent signal. Rational design of mutants with an improved signal is an important task, which requires both experimental and theoretical studies. Herein, we used a homology-based computational approach to predict the three-dimensional structure of archaerhodopsin-3, and a Quantum Mechanics/Molecular Mechanics (QM/MM) hybrid approach with high-level multireference ab initio methodology (SORCI+Q/AMBER) to model optical properties of this protein. We demonstrated that this methodology allows for reliable prediction of structure and spectral properties of archaerhodopsin-3. The results of this study can be utilized for computational molecular design of efficient fluorescent indicators of membrane voltage for modern optogenetics on the basis of archaerhodopsin-3.

Assessment of Approximate Coupled-Cluster and Algebraic-Diagrammatic-Construction Methods for Ground- and Excited-State Reaction Paths and the Conical-Intersection Seam of a Retinal-Chromophore Model

As a minimal model of the chromophore of rhodopsin proteins, the penta-2,4-dieniminium cation (PSB3) poses a challenging test system for the assessment of electronic-structure methods for the exploration of ground- and excited-state potential-energy surfaces, the topography of conical intersections, and the dimensionality (topology) of the branching space. Herein, we report on the performance of the approximate linear-response coupled-cluster method of second order (CC2) and the algebraic-diagrammatic-construction scheme of the polarization propagator of second and third orders (ADC(2) and ADC(3)). For the ADC(2) method, we considered both the strict and extended variants (ADC(2)-s and ADC(2)-x). For both CC2 and ADC methods, we also tested the spin-component-scaled (SCS) and spin-opposite-scaled (SOS) variants. We have explored several ground- and excited-state reaction paths, a circular path centered around the S1/S0 surface crossing, and a 2D scan of the potential-energy surfaces along the branching space. We find that the CC2 and ADC methods yield a different dimensionality of the intersection space. While the ADC methods yield a linear intersection topology, we find a conical intersection topology for the CC2 method. We present computational evidence showing that the linear-response CC2 method yields a surface crossing between the reference state and the first response state featuring characteristics that are expected for a true conical intersection. Finally, we test the performance of these methods for the approximate geometry optimization of the S1/S0 minimum-energy conical intersection and compare the geometries with available data from multireference methods. The present study provides new insight into the performance of linear-response CC2 and polarization-propagator ADC methods for molecular electronic spectroscopy and applications in computational photochemistry.