Structure, initial excited-state relaxation, and energy storage of rhodopsin resolved at the multiconfigurational perturbation theory level

Understanding the Photoprocesses in Biological Systems: Need for Accurate Multireference Treatment

Light-matter interaction is crucial to life itself and revolves around many of the central processes in biology. The need for understanding these photochemical and photophysical processes cannot be overemphasized. Interaction of light with biological systems starts with the absorption of light and subsequent phenomena that occur in the excited states of the system. However, excited states are typically difficult to understand within the mean field approximation of quantum chemical methods. Therefore, suitable multireference methods and methodologies have been developed to understand these phenomena. In this Perspective, we will describe a few methods and methodologies suitable for these descriptions and discuss some persisting difficulties.

The development of the QM/MM interface and its application for the on-the-fly QM/MM nonadiabatic dynamics in JADE package: Theory, implementation, and applications

Understanding the nonadiabatic dynamics of complex systems is a challenging task in computational photochemistry. Herein, we present an efficient and user-friendly quantum mechanics/molecular mechanics (QM/MM) interface to run on-the-fly nonadiabatic dynamics. Currently, this interface consists of an independent set of codes designed for general-purpose use. Herein, we demonstrate the ability and feasibility of the QM/MM interface by integrating it with our long-term developed JADE package. Tailored to handle nonadiabatic processes in various complex systems, especially condensed phases and protein environments, we delve into the theories, implementations, and applications of on-the-fly QM/MM nonadiabatic dynamics. The QM/MM approach is established within the framework of the additive QM/MM scheme, employing electrostatic embedding, link-atom inclusion, and charge-redistribution schemes to treat the QM/MM boundary. Trajectory surface-hopping dynamics are facilitated using the fewest switches algorithm, encompassing classical and quantum treatments for nuclear and electronic motions, respectively. Finally, we report simulations of nonadiabatic dynamics for two typical systems: azomethane in water and the retinal chromophore PSB3 in a protein environment. Our results not only illustrate the power of the QM/MM program but also reveal the important roles of environmental factors in nonadiabatic processes.

Comparative quantum-classical dynamics of natural and synthetic molecular rotors show how vibrational synchronization modulates the photoisomerization quantum efficiency

We use quantum-classical trajectories to investigate the origin of the different photoisomerization quantum efficiency observed in the dim-light visual pigment Rhodopsin and in the light-driven biomimetic molecular rotor para-methoxy N-methyl indanylidene-pyrrolinium (MeO-NAIP) in methanol. Our results reveal that effective light-energy conversion requires, in general, an auxiliary molecular vibration (called promoter) that does not correspond to the rotary motion but synchronizes with it at specific times. They also reveal that Nature has designed Rhodopsin to exploit two mechanisms working in a vibrationally coherent regime. The first uses a wag promoter to ensure that ca. 75% of the absorbed photons lead to unidirectional rotations. The second mechanism ensures that the same process is fast enough to avoid directional randomization. It is found that MeO-NAIP in methanol is incapable of exploiting the above mechanisms resulting into a 50% quantum efficiency loss. However, when the solvent is removed, MeO-NAIP rotation is predicted to synchronize with a ring-inversion promoter leading to a 30% increase in quantum efficiency and, therefore, biomimetic behavior.

Recommendations for Velocity Adjustment in Surface Hopping

This study investigates velocity adjustment directions after hopping in surface hopping dynamics. Using fulvene and a protonated Schiff base (PSB4) as case studies, we investigate the population decay and reaction yields of different sets of dynamics with the velocity adjusted in either the nonadiabatic coupling, gradient difference, or momentum directions. For the latter, in addition to the conventional algorithm, we investigated the performance of a reduced kinetic energy reservoir approach recently proposed. Our evaluation also considered velocity adjustment in the directions of approximate nonadiabatic coupling vectors. While results for fulvene are susceptible to the adjustment approach, PSB4 is not. We correlated this dependence to the topography near the conical intersections. When nonadiabatic coupling vectors are unavailable, the gradient difference direction is the best adjustment option. If the gradient difference is also unavailable, a semiempirical vector direction or the momentum direction with a reduced kinetic energy reservoir becomes an excellent option to prevent an artificial excess of back hoppings. The precise velocity adjustment direction is less crucial for describing the nonadiabatic dynamics than the kinetic energy reservoir's size.

Ultrafast structural changes direct the first molecular events of vision

Vision is initiated by the rhodopsin family of light-sensitive G protein-coupled receptors (GPCRs)1. A photon is absorbed by the 11-cis retinal chromophore of rhodopsin, which isomerizes within 200 femtoseconds to the all-trans conformation2, thereby initiating the cellular signal transduction processes that ultimately lead to vision. However, the intramolecular mechanism by which the photoactivated retinal induces the activation events inside rhodopsin remains experimentally unclear. Here we use ultrafast time-resolved crystallography at room temperature3 to determine how an isomerized twisted all-trans retinal stores the photon energy that is required to initiate the protein conformational changes associated with the formation of the G protein-binding signalling state. The distorted retinal at a 1-ps time delay after photoactivation has pulled away from half of its numerous interactions with its binding pocket, and the excess of the photon energy is released through an anisotropic protein breathing motion in the direction of the extracellular space. Notably, the very early structural motions in the protein side chains of rhodopsin appear in regions that are involved in later stages of the conserved class A GPCR activation mechanism. Our study sheds light on the earliest stages of vision in vertebrates and points to fundamental aspects of the molecular mechanisms of agonist-mediated GPCR activation.

Molecular Mechanism of Spectral Tuning by Chloride Binding in Monkey Green Sensitive Visual Pigment

The visual pigments of the cones perceive red, green, and blue colors. The monkey green (MG) pigment possesses a unique Cl^- binding site; however, its relationship to the spectral tuning in green pigments remains elusive. Recently, FTIR spectroscopy revealed the characteristic structural modifications of the retinal binding site by Cl^- binding. Herein, we report the computational structural modeling of MG pigments and quantum-chemical simulation to investigate its spectral redshift and physicochemical relevance when Cl^- is present. Our protein structures reflect the previously suggested structural changes. AlphaFold2 failed to predict these structural changes. Excited-state calculations successfully reproduced the experimental red-shifted absorption energies, corroborating our protein structures. Electrostatic energy decomposition revealed that the redshift results from the His197 protonation state and conformations of Glu129, Ser202, and Ala308; however, Cl^- itself contributes to the blueshift. Site-directed mutagenesis supported our analysis. These modeled structures may provide a valuable foundation for studying cone pigments.

Alternative Strategy for Spectral Tuning of Flavin-Binding Fluorescent Proteins

iLOV is an engineered flavin-binding fluorescent protein (FbFP) with applications for in vivo cellular imaging. To expand the range of applications of FbFPs for multicolor imaging and FRET-based biosensing, it is desirable to understand how to modify their absorption and emission wavelengths (i.e., through spectral tuning). There is particular interest in developing FbFPs that absorb and emit light at longer wavelengths, which has proven challenging thus far. Existing spectral tuning strategies that do not involve chemical modification of the flavin cofactor have focused on placing positively charged amino acids near flavin's C4a and N5 atoms. Guided by previously reported electrostatic spectral tunning maps (ESTMs) of the flavin cofactor and by quantum mechanical/molecular mechanical (QM/MM) calculations reported in this work, we suggest an alternative strategy: placing a negatively charged amino acid near flavin's N1 atom. We predict that a single-point mutant, iLOV-Q430E, has a slightly red-shifted absorption and fluorescence maximum wavelength relative to iLOV. To validate our theoretical prediction, we experimentally expressed and purified iLOV-Q430E and measured its spectral properties. We found that the Q430E mutation results in a slight change in absorption and a 4-8 nm red shift in the fluorescence relative to iLOV, in good agreement with the computational predictions. Molecular dynamics simulations showed that the carboxylate side chain of the glutamate in iLOV-Q430E points away from the flavin cofactor, which leads to a future expectation that further red shifting may be achieved by bringing the side chain closer to the cofactor.

Additive and epistatic effects influence spectral tuning in molluscan retinochrome opsin

The relationship between genotype and phenotype is nontrivial due to often complex molecular pathways that make it difficult to unambiguously relate phenotypes to specific genotypes. Photopigments, an opsin apoprotein bound to a light-absorbing chromophore, present an opportunity to directly relate the amino acid sequence to an absorbance peak phenotype (λmax). We examined this relationship by conducting a series of site-directed mutagenesis experiments of retinochrome, a non-visual opsin, from two closely related species: the common bay scallop, Argopecten irradians, and the king scallop, Pecten maximus. Using protein folding models, we identified three amino acid sites of likely functional importance and expressed mutated retinochrome proteins in vitro. Our results show that the mutation of amino acids lining the opsin binding pocket are responsible for fine spectral tuning, or small changes in the λmax of these light sensitive proteins Mutations resulted in a blue or red shift as predicted, but with dissimilar magnitudes. Shifts ranged from a 16 nm blue shift to a 12 nm red shift from the wild-type λmax. These mutations do not show an additive effect, but rather suggests the presence of epistatic interactions. This work highlights the importance of binding pocket shape in the evolution of spectral tuning and builds on our ability to relate genotypic changes to phenotypes in an emerging model for opsin functional analysis.

Evolution of the Automatic Rhodopsin Modeling (ARM) Protocol

In recent years, photoactive proteins such as rhodopsins have become a common target for cutting-edge research in the field of optogenetics. Alongside wet-lab research, computational methods are also developing rapidly to provide the necessary tools to analyze and rationalize experimental results and, most of all, drive the design of novel systems. The Automatic Rhodopsin Modeling (ARM) protocol is focused on providing exactly the necessary computational tools to study rhodopsins, those being either natural or resulting from mutations. The code has evolved along the years to finally provide results that are reproducible by any user, accurate and reliable so as to replicate experimental trends. Furthermore, the code is efficient in terms of necessary computing resources and time, and scalable in terms of both number of concurrent calculations as well as features. In this review, we will show how the code underlying ARM achieved each of these properties.

Protein Response Effects on Cofactor Excitation Energies from First Principles: Augmenting Subsystem Time-Dependent Density-Functional Theory with Many-Body Expansion Techniques

We investigate the possibility of describing protein response effects on a chromophore excitation by means of subsystem time-dependent density-functional theory (sTDDFT) in combination with a many-body expansion (MBE) approach. While sTDDFT is in principle intrinsically able to include such contributions, addressing cofactor excitations in protein models or entire proteins with full environment-response treatments is currently out of reach. Taking different model structures of the green fluorescent protein (GFP) and bovine rhodopsin as examples, we demonstrate that an embedded-MBE approach based on sTDDFT in its simplest version leads to a good agreement of the predicted protein response effect already at second order. To reproduce reference response effects from nonsubsystem TDDFT calculations quantitatively (error ≤ 5%), however, a third- or even fourth-order MBE may be required. For the latter case, we explore a selective inclusion of fourth-order terms that drastically reduces the computational burden. In addition, we demonstrate how this sTDDFT-MBE treatment can be utilized as an analysis tool to identify residues with dominant response contributions. This, in turn, can be employed to arrive at smaller structural models for light-absorbing proteins, which still feature all of the main characteristics in terms of photoresponse properties.

Electronic Couplings and Electrostatic Interactions Behind the Light Absorption of Retinal Proteins

The photo-functional chromophore retinal exhibits a wide variety of optical absorption properties depending on its intermolecular interactions with surrounding proteins and other chromophores. By utilizing these properties, microbial and animal rhodopsins express biological functions such as ion-transport and signal transduction. In this review, we present the molecular mechanisms underlying light absorption in rhodopsins, as revealed by quantum chemical calculations. Here, symmetry-adapted cluster-configuration interaction (SAC-CI), combined quantum mechanical and molecular mechanical (QM/MM), and transition-density-fragment interaction (TDFI) methods are used to describe the electronic structure of the retinal, the surrounding protein environment, and the electronic coupling between chromophores, respectively. These computational approaches provide successful reproductions of experimentally observed absorption and circular dichroism (CD) spectra, as well as insights into the mechanisms of unique optical properties in terms of chromophore-protein electrostatic interactions and chromophore-chromophore electronic couplings. On the basis of the molecular mechanisms revealed in these studies, we also discuss strategies for artificial design of the optical absorption properties of rhodopsins.

The integrative biology of pigment organelles, a quantum chemical approach

Coloration is a complex phenotypic trait involving both physical and chemical processes at a multiscale level, from molecules to tissues. Pigments, whose main property is to absorb specific wavelengths of visible light, are usually deposited in specialized organelles or complex matrices comprising proteins, metals, ions and redox compounds, among others. By modulating electronic properties and stability, interactions between pigments and these molecular actors can lead to color tuning. Furthermore, pigments are not only important for visual effects but also provide other critical functions, such as detoxification and antiradical activity. Hence, integrative studies of pigment organelles are required to understand how pigments interact with their cellular environment. In this review, we show how quantum chemistry, a computational method that models the molecular and optical properties of pigments, has provided key insights into the mechanisms by which pigment properties, from color to reactivity, are modulated by their organellar environment. These results allow to rationalize and to predict the way pigments behave in supramolecular complexes, up to the complete modelling of pigment organelles. We also discuss the main limitations of quantum chemistry, emphasizing the need for carrying experimental work with identical vigor. We finally suggest that taking into account the ecology of pigments (i.e. how they interact with these various other cellular components and at higher organizational levels) will lead to a greater understanding of how and why animals are vividly and variably colored, two fundamental questions in organismal biology.

Towards practical applications in quantum computational biology

Fascinating progress in understanding our world at the smallest scales moves us to the border of a new technological revolution governed by quantum physics. By taking advantage of quantum phenomena, quantum computing devices allow a speedup in solving diverse tasks. In this Perspective, we discuss the potential impact of quantum computing on computational biology. Bearing in mind the limitations of existing quantum computing devices, we attempt to indicate promising directions for further research in the emerging area of quantum computational biology.

Color-tuning of natural variants of heliorhodopsin

Microbial rhodopsins are distributed through many microorganisms. Heliorhodopsins are newly discovered but have an unclear function. They have seven transmembrane helices similar to type-I and type-II rhodopsins, but they are different in that the N-terminal region of heliorhodopsin is cytoplasmic. We chose 13 representative heliorhodopsins from various microorganisms, expressed and purified with an N-terminal His tag, and measured the absorption spectra. The 13 natural variants had an absorption maximum (λmax) in the range 530–556 nm similar to proteorhodopsin (λmax = 490–525 nm). We selected several candidate residues that influence rhodopsin color-tuning based on sequence alignment and constructed mutants via site-directed mutagenesis to confirm the spectral changes. We found two important residues located near retinal chromophore that influence λmax. We also predict the 3D structure via homology-modeling of Thermoplasmatales heliorhodopsin. The results indicate that the color-tuning mechanism of type-I rhodopsin can be applied to understand the color-tuning of heliorhodopsin.

Quantum and Quantum-Classical Studies of the Photoisomerization of a Retinal Chromophore Model

We report an in-depth analysis of the photo-induced isomerization of the 2-cis-penta-2,4-dieniminium cation: a minimal model of the 11-cis retinal protonated Schiff base chromophore of the dim-light photoreceptor rhodopsin. Based on recently developed three-dimensional potentials parametrized on ab initio multi-state multi-configurational second-order perturbation theory data, we perform quantum-dynamical studies. In addition, simulations based on various quantum-classical methods, among which Tully surface hopping and the coupled-trajectory approach derived from the exact factorization, allow us to validate their performance against vibronic wavepacket propagation and, therefore, a purely quantum treatment. Quantum-dynamics results uncover qualitative differences with respect to the two-dimensional Hahn-Stock potentials, widely used as model potentials for the isomerization of the same chromophore, due to the increased dimensionality and three-mode correlation. Quantum-classical simulations show, instead, that three-dimensional model potentials are capable of capturing a number of features revealed by atomistic simulations and experimental observations. In particular, a recently reported vibrational phase relationship between double-bond torsion and hydrogen-out-of-plane modes critical for rhodopsin isomerization efficiency is correctly reproduced.

Modern quantum chemistry with [Open]Molcas

MOLCAS/OpenMolcas is an ab initio electronic structure program providing a large set of computational methods from Hartree-Fock and density functional theory to various implementations of multiconfigurational theory. This article provides a comprehensive overview of the main features of the code, specifically reviewing the use of the code in previously reported chemical applications as well as more recent applications including the calculation of magnetic properties from optimized density matrix renormalization group wave functions.

Quantum Chemical and QM/MM Models in Biochemistry

Quantum chemical (QC) calculations provide a basis for deriving a microscopic understanding of enzymes and photobiological systems. Here we describe how QC models can be used to explore the electronic structure, dynamics, and energetics of biomolecules. We introduce the hybrid quantum mechanics/classical mechanics (QM/MM) approach, where a quantum mechanically described system of interest is embedded in a classically described force field representation of the biochemical surroundings. We also discuss the QM cluster model approach, as well as embedding theories, that provide complementary methodologies to model quantum mechanical effects in biomolecules. The chapter also provides some practical guides for building quantum biochemical models using the quinone reduction catalysis in respiratory complex I and a model reaction in solution as examples.

Robust field-dressed spectra of diatomics in an optical lattice

The absorption spectra of the cold Na₂ molecule dressed by a linearly polarized standing laser wave is investigated with a theoretical model incorporating translational, electronic, vibrational as well as rotational degrees of freedom. In such a situation a light-induced conical intersection (LICI) can be formed (J. Phys. B: At. Mol. Opt. Phys., 2008, 41, 221001). To measure the spectra a weak field is used whose propagation direction is perpendicular to the direction of the dressing field but has identical polarization direction. Although LICIs are present in our model, the simulations demonstrate a very robust absorption spectrum, which is insensitive to the intensity and the wavelength of the dressing field and which does not reflect clear signatures of light-induced nonadiabatic phenomena related to the strong mixing between the electronic, vibrational, rotational and translational motions. However, by widening artificially the very narrow translational energy level gaps, the fingerprint of the LICI appears to some extent in the spectrum.

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.

Molecular mechanism for thermal denaturation of thermophilic rhodopsin

Understanding the factors affecting the stability and function of proteins at the molecular level is of fundamental importance. In spite of their use in bioelectronics and optogenetics, factors influencing thermal stability of microbial rhodopsins, a class of photoreceptor protein ubiquitous in nature are not yet well-understood. Here we report on the molecular mechanism for thermal denaturation of microbial retinal proteins, including, a highly thermostable protein, thermophilic rhodopsin (TR). External stimuli-dependent thermal denaturation of TR, the proton pumping rhodopsin of Thermus thermophilus bacterium, and other microbial rhodopsins are spectroscopically studied to decipher the common factors guiding their thermal stability. The thermal denaturation process of the studied proteins is light-catalyzed and the apo-protein is thermally less stable than the corresponding retinal-covalently bound opsin. In addition, changes in structure of the retinal chromophore affect the thermal stability of TR. Our results indicate that the hydrolysis of the retinal protonated Schiff base (PSB) is the rate-determining step for denaturation of the TR as well as other retinal proteins. Unusually high thermal stability of TR multilayers, in which PSB hydrolysis is restricted due to lack of bulk water, strongly supports this proposal. Our results also show that the protonation state of the PSB counter-ion does not affect the thermal stability of the studied proteins. Thermal photo-bleaching of an artificial TR pigment derived from non-isomerizable trans-locked retinal suggests, rather counterintuitively, that the photoinduced retinal trans-cis isomerization is not a pre-requisite for light catalyzed thermal denaturation of TR. Protein conformation alteration triggered by light-induced retinal excited state formation is likely to facilitate the PSB hydrolysis.

Effect of point mutations on the ultrafast photo-isomerization of Anabaena sensory rhodopsin

Anabaena sensory rhodopsin (ASR) is a particular microbial retinal protein for which light-adaptation leads to the ability to bind both the all-trans, 15-anti (AT) and the 13-cis, 15-syn (13C) isomers of the protonated Schiff base of retinal (PSBR). In the context of obtaining insight into the mechanisms by which retinal proteins catalyse the PSBR photo-isomerization reaction, ASR is a model system allowing to study, within the same protein, the protein-PSBR interactions for two different PSBR conformers at the same time. A detailed analysis of the vibrational spectra of AT and 13C, and their photo-products in wild-type ASR obtained through femtosecond (pump-) four-wave-mixing is reported for the first time, and compared to bacterio- and channelrhodopsin. As part of an extensive study of ASR mutants with blue-shifted absorption spectra, we present here a detailed computational analysis of the origin of the mutation-induced blue-shift of the absorption spectra, and identify electrostatic interactions as dominating steric effects that would entail a red-shift. The excited state lifetimes and isomerization reaction times (IRT) for the three mutants V112N, W76F, and L83Q are studied experimentally by femtosecond broadband transient absorption spectroscopy. Interestingly, in all three mutants, isomerization is accelerated for AT with respect to wild-type ASR, and this the more, the shorter the wavelength of maximum absorption. On the contrary, the 13C photo-reaction is slightly slowed down, leading to an inversion of the ESLs of AT and 13C, with respect to wt-ASR, in the blue-most absorbing mutant L83Q. Possible mechanisms for these mutation effects, and their steric and electrostatic origins are discussed.

a-ARM: Automatic Rhodopsin Modeling with Chromophore Cavity Generation, Ionization State Selection, and External Counterion Placement

The Automatic Rhodopsin Modeling (ARM) protocol has recently been proposed as a tool for the fast and parallel generation of basic hybrid quantum mechanics/molecular mechanics (QM/MM) models of wild type and mutant rhodopsins. However, in its present version, input preparation requires a few hours long user's manipulation of the template protein structure, which also impairs the reproducibility of the generated models. This limitation, which makes model building semiautomatic rather than fully automatic, comprises four tasks: definition of the retinal chromophore cavity, assignment of protonation states of the ionizable residues, neutralization of the protein with external counterions, and finally congruous generation of single or multiple mutations. In this work, we show that the automation of the original ARM protocol can be extended to a level suitable for performing the above tasks without user's manipulation and with an input preparation time of minutes. The new protocol, called a-ARM, delivers fully reproducible (i.e., user independent) rhodopsin QM/MM models as well as an improved model quality. More specifically, we show that the trend in vertical excitation energies observed for a set of 25 wild type and 14 mutant rhodopsins is predicted by the new protocol better than when using the original. Such an agreement is reflected by an estimated (relative to the probed set) trend deviation of 0.7 ± 0.5 kcal mol-1 (0.03 ± 0.02 eV) and mean absolute error of 1.0 kcal mol-1 (0.04 eV).

Red-shifting mutation of light-driven sodium-pump rhodopsin

Microbial rhodopsins are photoreceptive membrane proteins that transport various ions using light energy. While they are widely used in optogenetics to optically control neuronal activity, rhodopsins that function with longer-wavelength light are highly demanded because of their low phototoxicity and high tissue penetration. Here, we achieve a 40-nm red-shift in the absorption wavelength of a sodium-pump rhodopsin (KR2) by altering dipole moment of residues around the retinal chromophore (KR2 P219T/S254A) without impairing its ion-transport activity. Structural differences in the chromophore of the red-shifted protein from that of the wildtype are observed by Fourier transform infrared spectroscopy. QM/MM models generated with an automated protocol show that the changes in the electrostatic interaction between protein and chromophore induced by the amino-acid replacements, lowered the energy gap between the ground and the first electronically excited state. Based on these insights, a natural sodium pump with red-shifted absorption is identified from Jannaschia seosinensis.

Microbial rhodopsins are photoreceptive and widely used in optogenetics for which they should preferable function with longer-wavelength light. Here, authors achieve a 40-nm red-shift in the absorption wavelength of a sodium-pump rhodopsin (KR2) by altering the distribution of the retinal chromophore.

Photoreactivity Control Mediated by Molecular Force Probes in Stilbene

We report theoretical and experimental evidence showing that photochemical reactivity of a chromophore can be modified by applying mechanical forces via molecular force probes. This mechanical action permits us to modulate main photochemical properties, such as fluorescence yield, excited-state lifetime, or photoisomerization quantum yield. The effect of molecular force probes can be rationalized in terms of simple mechanochemical models, establishing a qualitative framework for understanding the mechanical control of photoreactivity in stilbenes.

Initial excited-state relaxation of locked retinal protonated schiff base chromophore. An insight from coupled cluster and multireference perturbation theory calculations

The initial S₁ excited-state relaxation of retinal protonated Schiff base (RPSB) analog with central C11C12 double bond locked by eight-membered ring (locked-11.8) was investigated by means of multireference perturbation theory methods (XMCQDPT2, XMS-CASPT2, MS-CASPT2) as well as single-reference coupled-cluster CC2 method. The analysis of XMCQDPT2-based geometries reveals rather weak coupling between in-plane and out-of-plane structural evolution and minor energetical relaxation of three locked-11.8 conformers. Therefore, a strong coupling between bonds length inversion and backbone out-of-plane deformation resulting in a very steep S₁ energy profile predicted by CASSCF/CASPT2 calculations is in clear contradiction with the reference XMCQDPT2 results. Even though CC2 method predicts good quality ground-state structures, the excited-state structures display more advanced torsional deformation leading to ca. 0.2 eV exaggerated energy relaxation and significantly red shifted (0.4-0.7 eV) emission maxima. According to our findings, the initial photoisomerization process in locked-11.8, and possibly in other RPSB analogs, studied fully (both geometries and energies) by multireference perturbation theory may be somewhat slower than predicted by CASSCF/CASPT2 or CC2 methods. © 2018 Wiley Periodicals, Inc.

How Methylation Modifies the Photophysics of the Native All- trans-Retinal Protonated Schiff Base: A CASPT2/MD Study in Gas Phase and in Methanol

A comparison between the free-energy surfaces of the all- trans-retinal protonated Schiff base (RPSB) and its 10-methylated derivative in gas phase and methanol solution is performed at CASSCF//CASSCF and CASPT2//CASSCF levels. Solvent effects were included using the average solvent electrostatic potential from molecular dynamics method. This is a QM/MM (quantum mechanics/molecular mechanics) method that makes use of the mean field approximation. It is found that the methyl group bonded to C10 produces noticeable changes in the solution free-energy profile of the S₁ excited state, mainly in the relative stability of the minimum energy conical intersections (MECIs) with respect to the Franck-Condon (FC) point. The conical intersections yielding the 9- cis and 11- cis isomers are stabilized while that yielding the 13- cis isomer is destabilized; in fact, it becomes inaccessible by excitation to S₁. Furthermore, the planar S₁ minimum is not present in the methylated compound. The solvent notably stabilizes the S₂ excited state at the FC geometry. Therefore, if the S₂ state has an effect on the photoisomerization dynamics, it must be because it permits the RPSB population to branch around the FC point. All these changes combine to speed up the photoisomerization in the 10-methylated compound with respect to the native compound.

Different hydrogen bonding environments of the retinal protonated Schiff base control the photoisomerization in channelrhodopsin-2

The first event of the channelrhodopsin-2 (ChR2) photocycle, i.e. trans-to-cis photoisomerization, is studied by means of quantum mechanics/molecular mechanics, taking into account the flexible retinal environment in the ground state.

The origin of absorptive features in the two-dimensional electronic spectra of rhodopsin

A three-state three-mode model Hamiltonian reveals the origin of the absorptive features in the two-dimensional electronic spectra of rhodopsin.

Excited-state minima and emission energies of retinal chromophore analogues: Performance of CASSCF and CC2 methods as compared with CASPT2

This study provides gas-phase S₁ excited-state geometries along with emission and adiabatic energies for methylated/demethylated and ring-locked analogues of protonated Schiff base retinal models comprising system of five conjugated double bonds (PSB5), using second order multiconfiguration perturbation theory (CASPT2). CASPT2 results serve as reference data to assess the performance of CC2 (second-order approximate coupled cluster singles and doubles) and a commonly used CASSCF/CASPT2 protocol, that is, complete active space self-consistent field (CASSCF) geometry optimization followed by CASPT2 energy calculation. We find that the CASSCF methodology fails to locate planar S₁ minimum energy structures for four out of five investigated planar models in contrast to CC2 and CASPT2 methods. However, for those which were found: one planar and two twisted minima, there is an excellent agreement between CASSCF and CASPT2 results in terms of geometrical parameters, one-electron properties, as well as emission and adiabatic energies. CC2 performs well for in-plane S₁ minima and their spectroscopic and electronic properties. However, this picture deteriorates for twisted minima. As expected, the CC2 description of the S₂ electronic state, with strong multireference and significant double excitation character, is very poor, exhibiting errors in transition energies exceeding 1 eV. They may be substantially diminished by recalculating transition energies with CASPT2 method. Our work shows that CASSCF/CASPT2 and CC2 shortcomings may influence gas-phase retinal analogues' excited state description in a dramatic way. © 2017 Wiley Periodicals, Inc.

Photoactivation Intermediates of a G-Protein Coupled Receptor Rhodopsin Investigated by a Hybrid Molecular Simulation

Rhodopsin is a G-protein coupled receptor functioning as a photoreceptor for vision through photoactivation of a covalently bound ligand of a retinal protonated Schiff base chromophore. Despite the availability of structural information on the inactivated and activated forms of the receptor, the transition processes initiated by the photoabsorption have not been well understood. Here we theoretically examined the photoactivation processes by means of molecular dynamics (MD) simulations and ab initio quantum mechanical/molecular mechanical (QM/MM) free energy geometry optimizations which enabled accurate geometry determination of the ligand molecule in ample statistical conformational samples of the protein. Structures of the intermediate states of the activation process, blue-shifted intermediate and Lumi, as well as the dark state first generated by MD simulations and then refined by the QM/MM free energy geometry optimizations were characterized by large displacement of the β-ionone ring of retinal along with change in the hydrogen bond of the protonated Schiff base. The ab initio calculations of vibrational and electronic spectroscopic properties of those states well reproduced the experimental observations and successfully identified the molecular origins underlying the spectroscopic features. The structural evolution in the formation of the intermediates provides a molecular insight into the efficient activation processes of the receptor.

pH-dependent absorption spectra of rhodopsin mutant E113Q: On the role of counterions and protein

The absorption spectra of bovine rhodopsin mutant E113Q in solutions were investigated at the molecular level by using a hybrid quantum mechanics/molecular mechanics (QM/MM) method. The calculations suggest the mechanism of the absorption variations of E113Q at different pH values. The results indicate that the polarizations of the counterions in the vicinity of Schiff base under protonation and unprotonation states of the mutant E113Q would be a crucial factor to change the energy gap of the retinal to tune the absorption spectra. Glu-181 residue, which is close to the chromophore, cannot serve as the counterion of the protonated Schiff base of E113Q in dark state. Moreover, the results of the absorption maximum in mutant E113Q with the various anions (Cl^-, Br^-, I^- and NO₃^-) manifested that the mutant E113Q could have the potential for use as a template of anion biosensors at visible wavelength.

Theoretical description of protein field effects on electronic excitations of biological chromophores

Photoinitiated phenomena play a crucial role in many living organisms. Plants, algae, and bacteria absorb sunlight to perform photosynthesis, and convert water and carbon dioxide into molecular oxygen and carbohydrates, thus forming the basis for life on Earth. The vision of vertebrates is accomplished in the eye by a protein called rhodopsin, which upon photon absorption performs an ultrafast isomerisation of the retinal chromophore, triggering the signal cascade. Many other biological functions start with the photoexcitation of a protein-embedded pigment, followed by complex processes comprising, for example, electron or excitation energy transfer in photosynthetic complexes. The optical properties of chromophores in living systems are strongly dependent on the interaction with the surrounding environment (nearby protein residues, membrane, water), and the complexity of such interplay is, in most cases, at the origin of the functional diversity of the photoactive proteins. The specific interactions with the environment often lead to a significant shift of the chromophore excitation energies, compared with their absorption in solution or gas phase. The investigation of the optical response of chromophores is generally not straightforward, from both experimental and theoretical standpoints; this is due to the difficulty in understanding diverse behaviours and effects, occurring at different scales, with a single technique. In particular, the role played by ab initio calculations in assisting and guiding experiments, as well as in understanding the physics of photoactive proteins, is fundamental. At the same time, owing to the large size of the systems, more approximate strategies which take into account the environmental effects on the absorption spectra are also of paramount importance. Here we review the recent advances in the first-principle description of electronic and optical properties of biological chromophores embedded in a protein environment. We show their applications on paradigmatic systems, such as the light-harvesting complexes, rhodopsin and green fluorescent protein, emphasising the theoretical frameworks which are of common use in solid state physics, and emerging as promising tools for biomolecular systems.

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

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

pH-Dependent absorption spectrum of a protein: a minimal electrostatic model of Anabaena sensory rhodopsin

A minimal electrostatic model is introduced which aims at reproducing and analyzing the visible-light absorption energy shift of a protein with pH.

Polarizable Embedding Density Matrix Renormalization Group

The polarizable embedding (PE) approach is a flexible embedding model where a preselected region out of a larger system is described quantum mechanically, while the interaction with the surrounding environment is modeled through an effective operator. This effective operator represents the environment by atom-centered multipoles and polarizabilities derived from quantum mechanical calculations on (fragments of) the environment. Thereby, the polarization of the environment is explicitly accounted for. Here, we present the coupling of the PE approach with the density matrix renormalization group (DMRG). This PE-DMRG method is particularly suitable for embedded subsystems that feature a dense manifold of frontier orbitals which requires large active spaces. Recovering such static electron-correlation effects in multiconfigurational electronic structure problems, while accounting for both electrostatics and polarization of a surrounding environment, allows us to describe strongly correlated electronic structures in complex molecular environments. We investigate various embedding potentials for the well-studied first excited state of water with active spaces that correspond to a full configuration-interaction treatment. Moreover, we study the environment effect on the first excited state of a retinylidene Schiff base within a channelrhodopsin protein. For this system, we also investigate the effect of dynamical correlation included through short-range density functional theory.

Probing the Interstate Coupling near a Conical Intersection by Optical Spectroscopy

Conical intersections are points where adiabatic potential energy surfaces cross. The interstate coupling between the potential energy surfaces plays a crucial role in many processes associated with conical intersections. Still no method exists to measure this coupling driving the chemical reactions between the potential energy surfaces involved. In this Letter, using a generic model for photoisomerization, we propose a novel experimental approach to estimate the coupling that mixes the electronic states near a conical intersection. The approach is based on analyzing the vibrational wavepacket of the reactant in the adiabatic ground and excited electronic states. The nuclear wavepacket dynamics are extracted from linear absorption and two-dimensional electronic spectroscopy. Comparing the frequencies of the coupling mode in the adiabatic ground and excited states from models with and without coupling between the potential energy surfaces suggests an experimental tool to determine the interstate coupling.

Quantum Monte Carlo Treatment of the Charge Transfer and Diradical Electronic Character in a Retinal Chromophore Minimal Model

The penta-2,4-dieniminium cation (PSB3) displays similar ground state and first excited state potential energy features as those of the retinal protonated Schiff base (RPSB) chromophore in rhodopsin. Recently, PSB3 has been used to benchmark several electronic structure methods, including highly correlated multireference wave function approaches, highlighting the necessity to accurately describe the electronic correlation in order to obtain reliable properties even along the ground state (thermal) isomerization paths. In this work, we apply two quantum Monte Carlo approaches, the variational Monte Carlo and the lattice regularized diffusion Monte Carlo, to study the energetics and electronic properties of PSB3 along representative minimum energy paths and scans related to its thermal cis–trans isomerization. Quantum Monte Carlo is used in combination with the Jastrow antisymmetrized geminal power ansatz, which guarantees an accurate and balanced description of the static electronic correlation thanks to the multiconfigurational nature of the antisymmetrized geminal power term, and of the dynamical correlation, due to the presence of the Jastrow factor explicitly depending on electron–electron distances. Along the two ground state isomerization minimum energy paths of PSB3, CASSCF calculations yield wave functions having either charge transfer or diradical character in proximity of the two transition state configurations. Here, we observe that at the quantum Monte Carlo level of theory, only the transition state with charge transfer character can be located. The conical intersection, which becomes highly sloped, is observed only if the path connecting the two original CASSCF transition states is extended beyond the diradical one, namely by increasing the bond-length-alternation (BLA). These findings are in good agreement with the results obtained by MRCISD+Q calculations, and they demonstrate the importance of having an accurate description of the static and dynamical correlation when studying isomerization and transition states of conjugated systems.