Spectral Tuning of Rhodopsin and Visual Cone Pigments

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.

Charge-Transfer Excitations within Density Functional Theory: How Accurate Are the Most Recommended Approaches?

The performance of the most recent density functionals is assessed for charge-transfer (CT) excitations using comprehensive intra- and intermolecular CT benchmark sets with high-quality reference values. For this comparison, the state-of-the-art range-separated (RS) and long-range-corrected (LC) double hybrid (DH) approaches are selected, and global DH and LC hybrid functionals are also inspected. The correct long-range behavior of the exchange-correlation (XC) energy is extensively studied, and various CT descriptors are compared as well. Our results show that the most robust performance is attained by RS-PBE-P86/SOS-ADC(2), as it is suitable to describe both types of CT excitations with outstanding accuracy. Furthermore, concerning the intramolecular transitions, unexpectedly excellent results are obtained for most of the global DHs, but their limitations are also demonstrated for bimolecular complexes. Despite the outstanding performance of the LC-DH methods for common intramolecular excitations, serious deficiencies are pointed out for intermolecular CT transitions, and the wrong long-range behavior of the XC energy is revealed. The application of LC hybrids to such transitions is not recommended in any respect.

The Seamless Connection of Local and Collective Excited States in Subsystem Time-Dependent Density Functional Theory

The theoretical understanding of photoinduced processes in multichromophoric systems requires, as an essential ingredient, the possibility of accurately describing their electronically excited states. However, the size of these systems often prohibits the usage of conventional electronic-structure methods, so that often multiscale approaches based on phenomenologically motivated models are employed. In contrast, subsystem time-dependent density functional theory (sTDDFT) allows for a subsystem-based ab initio description of multichromophoric systems and therefore allows for, in principle, an exact description of photoinduced processes. This Perspective aims to outline the theoretical foundations and commonly used practical realizations as well as to illustrate benefits of recent developments and open issues in the field of sTDDFT. Prospective, potential future applications and possible methodological developments are discussed.

Electrostatic profiling of photosynthetic pigments: implications for directed spectral tuning

Photosynthetic pigment-protein complexes harvest solar energy with a high quantum efficiency. Protein scaffolds are known to tune the spectral properties of embedded pigments principally through structured electrostatic environments. Although the physical nature of electrostatic tuning is straightforward, the precise spatial principles of electrostatic preorganization remain poorly explored for different protein matrices and incompletely characterized with respect to the intrinsic properties of different photosynthetic pigments. In this work, we study the electronic structure features associated with the lowest excited state of a series of eight naturally occurring (bacterio)chlorophylls and pheophytins to describe the precise topological differences in electrostatic potentials and hence determine intrinsic differences in the expected mode and impact of electrostatic tuning. The difference electrostatic potentials between the ground and first excited states are used as fingerprints. Both the spatial profile and the propensity for spectral tuning are found to be unique for each pigment, indicating spatially and directionally distinct modes of electrostatic tuning. The results define a specific partitioning of the protein matrix around each pigment as an aid to identify regions with a maximal impact on spectral tuning and have direct implications for dimensionality reduction in protein design and engineering. Thus, a quantum mechanical basis is provided for understanding, predicting, and ultimately designing sequence-modified or pigment-exchanged biological systems, as suggested for selected examples of pigment-reconstituted proteins.

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.

A Fock-operator complete active space self-consistent field (CAS-SCF) method combined with frozen-density embedding

We report the implementation of a Fock-operator complete-active space self-consistent field (CAS-SCF) method combined with frozen-density embedding (FDE) into the KOALA quantum-chemistry program. The implementation is based on configuration interaction from an unrestricted reference determinant and is able to treat electronic configurations such as singlet, triplet, or quintet states embedded in a molecular environment. In order to account for possible spin polarization effects, the FDE contribution is extended to the unrestricted case. We assess the convergence obtained with the implementation at the example of a stretched lithium dimer with significant multi-reference character. The efficiency of the implementation enables the orbital optimization for 25 states in a state-average SA[S₀-S₁₀,T₁-T₁₂,Q₁-Q₂]-CAS(10,10)-SCF calculation for the retinal molecule using a def2-TZVP basis. The FDE ansatz leads to orbitals localized by definition on the target system, thus facilitating the orbital selection required for CAS methods in complex environments.

Frontiers in Multiscale Modeling of Photoreceptor Proteins

This perspective article highlights the challenges in the theoretical description of photoreceptor proteins using multiscale modeling, as discussed at the CECAM workshop in Tel Aviv, Israel. The participants have identified grand challenges and discussed the development of new tools to address them. Recent progress in understanding representative proteins such as green fluorescent protein, photoactive yellow protein, phytochrome, and rhodopsin is presented, along with methodological developments.

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.

Benchmarking the Performance of Time-Dependent Density Functional Theory Methods on Biochromophores

Quantum chemical calculations are important for elucidating light-capturing mechanisms in photobiological systems. The time-dependent density functional theory (TDDFT) has become a popular methodology because of its balance between accuracy and computational scaling, despite its problems in describing, for example, charge transfer states. As a step toward systematically understanding the performance of TDDFT calculations on biomolecular systems, we study here 17 commonly used density functionals, including seven long-range separated functionals, and compare the obtained results with excitation energies calculated at the approximate second order coupled-cluster theory level (CC2). The benchmarking set includes the first five singlet excited states of 11 chemical analogues of biochromophores from the green fluorescent protein, rhodopsin/bacteriorhodopsin (Rh/bR), and the photoactive yellow protein. We find that commonly used pure density functionals such as BP86, PBE, M11-L, and hybrid functionals with 20-25% of Hartree-Fock (HF) exchange (B3LYP, PBE0) have a tendency to consistently underestimate vertical excitation energies (VEEs) relative to the CC2 values, whereas hybrid density functionals with around 50% HF exchange such as BHLYP, PBE50, and M06-2X and long-range corrected functionals such as CAM-B3LYP, ωPBE, ωPBEh, ωB97X, ωB97XD, BNL, and M11 overestimate the VEEs. We observe that calculations using the CAM-B3LYP and ωPBEh functionals with 65% and 100% long-range HF exchange, respectively, lead to an overestimation of the VEEs by 0.2-0.3 eV for the benchmarking set. To reduce the systematic error, we introduce here two new empirical functionals, CAMh-B3LYP and ωhPBE0, for which we adjusted the long-range HF exchange to 50%. The introduced parameterization reduces the mean signed average (MSA) deviation to 0.07 eV and the root mean square (rms) deviation to 0.17 eV as compared to the CC2 values. In the present study, TDDFT calculations using the aug-def2-TZVP basis sets, the best performing functionals relative to CC2 are ωhPBE0 (rms = 0.17, MSA = 0.06 eV); CAMh-B3LYP (rms = 0.16, MSA = 0.07 eV); and PBE0 (rms = 0.23, MSA = -0.14 eV). For the popular range-separated CAM-B3LYP functional, we obtain an rms value of 0.31 eV and an MSA value of 0.25 eV, which can be compared with the rms and MSA values of 0.37 and -0.31 eV, respectively, as obtained at the B3LYP level.

Tuning the optical properties of N-aryl benzothiadiazole via Cu(ii)-catalyzed intramolecular C–H amination: the impact of the molecular structure on aggregation and solid state luminescence

The optical performance of 1–3 was influenced by the subtle change of the molecular structure as expected.

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.

Analytical Nuclear Excited-State Gradients for the Second-Order Approximate Coupled-Cluster Singles and Doubles (CC2) Method Employing Uncoupled Frozen-Density Embedding

We report the derivation and implementation of analytical orbital-relaxed properties and nuclear gradients for excited states using the second-order approximate coupled-cluster singles and doubles (CC2) model combined with uncoupled frozen-density embedding (FDEu). An implementation of the algebraic diagrammatic construction through second-order ADC(2), which arises from simplification of RICC2 FDEu, is also presented. In order to ensure a RICC2 FDEu Lagrange functional that is linear in the Lagrange multipliers, the Hartree-Fock density is employed for the target subsystem in the embedding contributions. The accuracy of the new scheme is assessed using the carbon monoxide molecule, 4-aminophthalimide, and a benzonitrile dimer, revealing that the obtained errors are below the method error of RICC2. Using density functional theory for the environment, the efficiency of the new method is illustrated by computing the perturbed excited-state dipole moment of a chromophore in a biological environment. For this system, comprising 32 molecules consisting of 366 atoms in total, the computation requires only a couple of days on a standard compute node. RICC2 FDEu thus enables large-scale calculations of ab initio wave functions for molecules in complex environments as routine applications.

Human Blue Cone Opsin Regeneration Involves Secondary Retinal Binding with Analog Specificity

Human color vision is mediated by the red, green, and blue cone visual pigments. Cone opsins are G-protein-coupled receptors consisting of an opsin apoprotein covalently linked to the 11-cis-retinal chromophore. All visual pigments share a common evolutionary origin, and red and green cone opsins exhibit a higher homology, whereas blue cone opsin shows more resemblance to the dim light receptor rhodopsin. Here we show that chromophore regeneration in photoactivated blue cone opsin exhibits intermediate transient conformations and a secondary retinoid binding event with slower binding kinetics. We also detected a fine-tuning of the conformational change in the photoactivated blue cone opsin binding site that alters the retinal isomer binding specificity. Furthermore, the molecular models of active and inactive blue cone opsins show specific molecular interactions in the retinal binding site that are not present in other opsins. These findings highlight the differential conformational versatility of human cone opsin pigments in the chromophore regeneration process, particularly compared to rhodopsin, and point to relevant functional, unexpected roles other than spectral tuning for the cone visual pigments.

Excitation spectra of retinal by multiconfiguration pair-density functional theory

Retinal is the chromophore in proteins responsible for vision. The absorption maximum of retinal is sensitive to mutations of the protein. However, it is not easy to predict the absorption spectrum of retinal accurately, and questions remain even after intensive investigation. Retinal poses a challenge for Kohn-Sham density functional theory (KS-DFT) because of the charge transfer character in its excitations, and it poses a challenge for wave function theory because the large size of the molecule makes multiconfigurational perturbation theory methods expensive. In this study, we demonstrate that multiconfiguration pair-density functional theory (MC-PDFT) provides an efficient way to predict the vertical excitation energies of 11-Z retinal, and it reproduces the experimentally determined absorption band widths and peak positions better than complete active space second-order perturbation theory (CASPT2). The consistency between complete active space self-consistent field (CASSCF) and KS-DFT dipole moments is demonstrated to be a useful criterion in selecting the active space. We also found that the nature of the terminal groups and the conformations of retinal play a significant role in the absorption spectrum. By considering a thermal distribution of conformations, we predict an absorption spectrum of retinal that is consistent with the experimental gas-phase spectrum. The location of the absorption peak and the spectral broadening based on MC-PDFT calculations agree better with experiments than those of CASPT2.

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.

Electrostatic versus Resonance Interactions in Photoreceptor Proteins: The Case of Rhodopsin

Light sensing in photoreceptor proteins is subtly modulated by the multiple interactions between the chromophoric unit and its binding pocket. Many theoretical and experimental studies have tried to uncover the fundamental origin of these interactions but reached contradictory conclusions as to whether electrostatics, polarization, or intrinsically quantum effects prevail. Here, we select rhodopsin as a prototypical photoreceptor system to reveal the molecular mechanism underlying these interactions and regulating the spectral tuning. Combining a multireference perturbation method and density functional theory with a classical but atomistic and polarizable embedding scheme, we show that accounting for electrostatics only leads to a qualitatively wrong picture, while a responsive environment can successfully capture both the classical and quantum dominant effects. Several residues are found to tune the excitation by both differentially stabilizing ground and excited states and through nonclassical "inductive resonance" interactions. The results obtained with such a quantum-in-classical model are validated against both experimental data and fully quantum calculations.

Role of the Molecular Environment in Flavoprotein Color and Redox Tuning: QM Cluster versus QM/MM Modeling

We investigate the origin of the excitation energy shifts induced by the apoprotein in the active site of the bacterial photoreceptor BLUF (Blue Light sensor Using Flavin adenine dinucleotide). In order to compute the vertical excitation energies of three low-lying electronic states, including two π-π* states of flavin (S1 and S2) and a π-π* tyrosine-flavin electron-transfer state (ET), with respect to the energy of the closed-shell ground state (S0), we prepared alternative quantum mechanical (QM) cluster and quantum mechanics/molecular mechanics (QM/MM) models. We found that the excitation energies computed with both types of models correlate with the magnitude of the charge transfer character of the excitation. Accordingly, we conclude that the small charge transfer character of the light absorbing S0-S1 transition and the substantial charge transfer character of the nonabsorbing but redox active S0-ET transition explain the small color changes but substantial redox tuning in BLUF and also in other flavoproteins. Further analysis showed that redox tuning is governed by the electrostatic interaction in the QM/MM model and transfer of charge between the active site and its environment in the QM cluster. Moreover, the wave function polarization of the QM subsystem by the MM subsystem influences the magnitude of the charge transfer, resulting in the QM/MM and QM excitation energies that are not entirely consistent.

Conversion of light-energy into molecular strain in the photocycle of the photoactive yellow protein

The Photoactive Yellow Protein (PYP) converts light energy into molecular strain, stored in the early pR₀-photocycle intermediate.

Recent advances in engineering microbial rhodopsins for optogenetics

Protein engineering of microbial rhodopsins has been successful in generating variants with improved properties for applications in optogenetics. Members of this membrane protein family can act as both actuators and sensors of neuronal activity. Chimeragenesis, structure-guided mutagenesis, and directed evolution have proven effective strategies for tuning absorption wavelength, altering ion specificity and increasing fluorescence. These approaches facilitate the development of useful optogenetic tools and, in some cases, have yielded insights into rhodopsin structure-function relationships.

Protein-Induced Color Shift of Carotenoids in β-Crustacyanin

β-Crustacyanin (β-CR) is a pigment protein responsible for the blue color of lobsters. We show using correlated ab initio calculations how the protein environment tunes the chromophores of β-CR through electrostatic and steric effects.

Advances in understanding the molecular basis of the first steps in color vision

Serving as one of our primary environmental inputs, vision is the most sophisticated sensory system in humans. Here, we present recent findings derived from energetics, genetics and physiology that provide a more advanced understanding of color perception in mammals. Energetics of cis-trans isomerization of 11-cis-retinal accounts for color perception in the narrow region of the electromagnetic spectrum and how human eyes can absorb light in the near infrared (IR) range. Structural homology models of visual pigments reveal complex interactions of the protein moieties with the light sensitive chromophore 11-cis-retinal and that certain color blinding mutations impair secondary structural elements of these G protein-coupled receptors (GPCRs). Finally, we identify unsolved critical aspects of color tuning that require future investigation.

Mechanosensitive membrane probes

This article assembles pertinent insights behind the concept of planarizable push-pull probes. As a response to the planarization of their polarized ground state, a red shift of their excitation maximum is expected to report on either the disorder, the tension, or the potential of biomembranes. The combination of chromophore planarization and polarization contributes to various, usually more complex processes in nature. Examples include the color change of crabs or lobsters during cooking or the chemistry of vision, particularly color vision. The summary of lessons from nature is followed by an overview of mechanosensitive organic materials. Although often twisted and sometimes also polarized, their change of color under pressure usually originates from changes in their crystal packing. Intriguing exceptions include the planarization of several elegantly twisted phenylethynyl oligomers and polymers. Also mechanosensitive probes in plastics usually respond to stretching by disassembly. True ground-state planarization in response to molecular recognition is best exemplified with the binding of thoughtfully twisted cationic polythiophenes to single- and double-stranded oligonucleotides. Molecular rotors, en vogue as viscosity sensors in cells, operate by deplanarization of the first excited state. Pertinent recent examples are described, focusing on λ-ratiometry and intracellular targeting. Complementary to planarization of the ground state with twisted push-pull probes, molecular rotors report on environmental changes with quenching or shifts in emission rather than absorption. The labeling of mechanosensitive channels is discussed as a bioengineering approach to bypass the challenge to create molecular mechanosensitivity and use biological systems instead to sense membrane tension. With planarizable push-pull probes, this challenge is met not with twistome screening, but with "fluorescent flippers," a new concept to insert large and bright monomers into oligomeric probes to really feel the environment and also shine when twisted out of conjugation.

Planarizable push–pull oligothiophenes: in search of the perfect twist

The “twistome” of push–pull oligothiophenes is covered comprehensively. Particular emphasis is on the development of conceptually innovative fluorescent membrane probes.