Chromophore–Protein Coupling beyond Nonpolarizable Models: Understanding Absorption in Green Fluorescent Protein

Theoretical and Numerical Comparison of Quantum- and Classical Embedding Models for Optical Spectra

Quantum-mechanical (QM) and classical embedding models approximate a supermolecular quantum-chemical calculation. This is particularly useful when the supermolecular calculation has a size that is out of reach for present QM models. Although QM and classical embedding methods share the same goal, they approach this goal from different starting points. In this study, we compare the polarizable embedding (PE) and frozen-density embedding (FDE) models. The former is a classical embedding model, whereas the latter is a density-based QM embedding model. Our comparison focuses on solvent effects on optical spectra of solutes. This is a typical scenario where super-system calculations including the solvent environment become prohibitively large. We formulate a common theoretical framework for PE and FDE models and systematically investigate how PE and FDE approximate solvent effects. Generally, differences are found to be small, except in cases where electron spill-out becomes problematic in the classical frameworks. In these cases, however, atomic pseudopotentials can reduce the electron-spill-out issue.

Quantum chemistry study of the multiphoton absorption in enhanced green fluorescent protein at the single amino acid residue level

The chromophore (CRO) of fluorescent proteins (FPs) is embedded in a complex environment that is a source of specific interactions with the CRO. Understanding how these interactions influence FPs spectral properties is important for a directed design of novel markers with desired characteristics. In this work, we apply computational chemistry methods to gain insight into one-, two- and three-photon absorption (1PA, 2PA, 3PA) tuning in enhanced green fluorescent protein (EGFP). To achieve this goal, we built EGFP models differing in: i) number and position of hydrogen-bonds (h-bonds) donors to the CRO and ii) the electric field, as approximated by polarizable force  field, acting on the CRO. We  find that h-bonding to the CRO's phenolate oxygen results in stronger one- and multiphoton absorption. The brighter absorption can be also achieved by creating more positive electric field near the CRO's phenolate moiety. Interestingly, while individual CRO-environment h-bonds usually enhance 1PA and 2PA, it takes a few h-bond donors to enhance 3PA. Clearly, response of the absorption intensity to many-body effects depends on the excitation mechanism.  We further employ symmetry-adapted perturbation theory (SAPT) to reveal excellent (2PA) and good (3PA) correlation of multiphoton intensity with electrostatic and induction interaction energies. This points to importance of accounting for mutual CRO-environment polarization in quantitative calculations of absorption spectra in FPs.

The role of hydrogen bonds and electrostatic interactions in enhancing two-photon absorption in green and yellow fluorescent proteins

The spectral properties of fluorescent proteins (FPs) depend on the protein environment of the chromophore (CRO). A deeper understanding of the CRO - environment interactions in terms of FPs spectral characteristics will allow for a rational design of novel markers with desired properties. Here, we are taking a step towards achieving this important goal. With the time-dependent density functional theory (TDDFT), we calculate one- and two-photon absorption (OPA and TPA) spectra for 5 green FPs (GFPs) and 3 yellow FPs (YFPs) differing in amino acid sequence. The goal is to reveal a role of: (i) electrostatic interactions, (ii) hydrogen-bonds (h-bonds), and (iii) h-bonds together with distant electrostatic field in absorption spectra tuning. Our results point to design hypothesis towards FPs optimised for TPA-based applications. Both h-bonds and electrostatic interactions co-operate in enhancing TPA cross-section (σ TPA ) for the S 0 ->S 1   transition in GFPs. Furthermore, it seems that details of h-bonds network in the CRO's vicinity influences σ TPA   response to CRO - environment electrostatic interactions in YFPs. We postulate that engineering FPs with more hydrophilic CRO's environment can lead to greater σ TPA . We also find that removing h-bonds formed with the CRO's phenolate leads to TPA enhancement for transition to higher excited states than S 1 . Particularly Y145 and T203 residues are important in this regard.

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.

Spectroscopic and computational investigations of organometallic complexation of group 12 transition metals by methanobactins from Methylocystis sp. SB2

Methanotrophic bacteria catalyze the aerobic oxidation of methane to methanol using Cu-containing enzymes, thereby exerting a modulating influence on the global methane cycle. To facilitate the acquisition of Cu ions, some methanotrophic bacteria secrete small modified peptides known as "methanobactins," which strongly bind Cu and function as an extracellular Cu recruitment relay, analogous to siderophores and Fe. In addition to Cu, methanobactins form complexes with other late transition metals, including the Group 12 transition metals Zn, Cd, and Hg, although the interplay among solution-phase configurations, metal interactions, and the spectroscopic signatures of methanobactin-metal complexes remains ambiguous. In this study, the complexation of Zn, Cd, and Hg by methanobactin from Methylocystis sp. strain SB2 was studied using a combination of absorbance, fluorescence, extended x-ray absorption fine structure (EXAFS) spectroscopy, and time-dependent density functional theory (TD-DFT) calculations. We report changes in sample absorbance and fluorescence spectral dynamics, which occur on a wide range of experimental timescales and characterize a clear stoichiometric complexation dependence. Mercury L3-edge EXAFS and TD-DFT calculations suggest a linear model for HgS coordination, and TD-DFT suggests a tetrahedral model for Zn2+ and Cd2+. We observed an enhancement in the fluorescence of methanobactin upon interaction with transition metals and propose a mechanism of complexation-hindered isomerization drawing inspiration from the wild-type Green Fluorescent Protein active site. Collectively, our results represent the first combined computational and experimental spectroscopy study of methanobactins and shed new light on molecular interactions and dynamics that characterize complexes of methanobactins with Group 12 transition metals.

Energy, Structures, and Response Properties with a Fully Coupled QM/AMOEBA/ddCOSMO Implementation

We present the implementation of a fully coupled polarizable QM/MM/continuum model based on the AMOEBA polarizable force field and the domain decomposition implementation of the conductor-like screening model. Energies, response properties, and analytical gradients with respect to both QM and MM nuclear positions are available, and a generic, atomistic cavity can be employed. The model is linear scaling in memory requirements and computational cost with respect to the number of classical atoms and is therefore suited to model large, complex systems. Using three variants of the green-fluorescent protein, we investigate the overall computational cost of such calculations and the effect of the continuum model on the convergence of the computed properties with respect to the size of the embedding. We also demonstrate the fundamental role of polarization effects by comparing polarizable and nonpolarizable embeddings to fully QM ones.

Removing artifacts in polarizable embedding calculations of one- and two-photon absorption spectra of fluorescent proteins

The multiscale calculations involving excited states may suffer from the electron spill-out (ESO) problem. This seems to be especially the case when the environment of the core region, described with the electronic structure method, is approximated by a polarizable force field. The ESO effect often leads to incorrect physical character of electronic excitations, spreading outside the quantum region, which, in turn, results in erroneous absorption spectra. In this work, we investigate means to remove the artifacts in one-photon absorption (OPA) and two-photon absorption (TPA) spectra of green and yellow fluorescent protein representatives. This includes (i) using different basis sets, (ii) extending the core subsystem beyond the chromophore, (iii) modification of polarization interaction between the core region and its environment, and (iv) including the Pauli repulsion through effective core potentials (ECPs). Our results clearly show that ESO is observed when diffuse functions are used to assemble the multielectron wave function regardless of the exchange-correlation functional used. Furthermore, extending the core region, thus accounting for exchange interactions between the chromophore and its environment, leads to even more spurious excited states. Also, damping the interactions between the core subsystem and the polarizable force field is hardly helpful. In contrast, placing ECPs in the position of sites creating the embedding potential leads to the removal of artificious excited states that presumably should not be observed in the OPA and TPA spectra. We prove that it is a reliable and cost-effective approach for systems where the covalent bond(s) between the core region and its environment must be cut.

Systematic Partitioning of Proteins for Quantum-Chemical Fragmentation Methods Using Graph Algorithms

Quantum-chemical fragmentation methods offer an efficient approach for the treatment of large proteins, in particular if local target quantities such as protein-ligand interaction energies, enzymatic reaction energies, or spectroscopic properties of embedded chromophores are sought. However, the accuracy that is achievable for such local target quantities intricately depends on how the protein is partitioned into smaller fragments. While the commonly employed naı̈ve approach of using fragments with a fixed size is widely used, it can result in large and unpredictable errors when varying the fragment size. Here, we present a systematic partitioning scheme that aims at minimizing the fragmentation error of a local target quantity for a given maximum fragment size. To this end, we construct a weighted graph representation of the protein, in which the amino acids constitute the nodes. These nodes are connected by edges weighted with an estimate for the fragmentation error that is expected when cutting this edge. This allows us to employ graph partitioning algorithms provided by computer science to determine near-optimal partitions of the protein. We apply this scheme to a test set of six proteins representing various prototypical applications of quantum-chemical fragmentation methods using a simplified molecular fractionation with conjugate caps (MFCC) approach with hydrogen caps. We show that our graph-based scheme consistently improves upon the naı̈ve approach.

A Not Obvious Correlation Between the Structure of Green Fluorescent Protein Chromophore Pocket and Hydrogen Bond Dynamics: A Choreography From ab initio Molecular Dynamics

The Green Fluorescent Protein (GFP) is a widely studied chemical system both for its large amount of applications and the complexity of the excited state proton transfer responsible of the change in the protonation state of the chromophore. A detailed investigation on the structure of the chromophore environment and the influence of chromophore form (either neutral or anionic) on it is of crucial importance to understand how these factors could potentially influence the protein function. In this study, we perform a detailed computational investigation based on the analysis of ab-initio molecular dynamics simulations, to disentangle the main structural quantities determining the fine balance in the chromophore environment. We found that specific hydrogen bonds interactions directly involving the chromophore (or not), are correlated to quantities, such as the volume of the cavity in which the chromophore is embedded and that it is importantly affected by the chromophore protonation state. The cross-correlation analysis performed on some of these hydrogen bonds and the cavity volume, demonstrates a direct correlation among them and we also identified the ones specifically involved in this correlation. We also found that specific interactions among residues far in the space are correlated, demonstrating the complexity of the chromophore environment and that many structural quantities have to be taken into account to properly describe and understand the main factors tuning the active site of the protein. From an overall evaluation of the results obtained in this work, it is shown that the residues which a priori are perceived to be spectators play instead an important role in both influencing the chromophore environment (cavity volume) and its dynamics (cross-correlations among spatially distant residues).

What is the Optimal Size of the Quantum Region in Embedding Calculations of Two-Photon Absorption Spectra of Fluorescent Proteins?

We systematically investigate an impact of the size and content of a quantum (QM) region, treated at the density functional theory level, in embedding calculations on one- (OPA) and two-photon absorption (TPA) spectra of the following fluorescent proteins (FPs) models: Aequorea victoria green FP (avGFP) with neutral (avGFP-n) and anionic (avGFP-a) chromophore as well as Citrine FP. We find that amino acid (a.a.) residues as well as water molecules hydrogen-bonded (h-bonded) to the chromophore usually boost both OPA and TPA processes intensity. The presence of hydrophobic a.a. residues in the quantum region also non-negligibly affects both absorption spectra but decreases absorption intensity. We conclude that to reach a quantitative description of OPA and TPA spectra in multiscale modeling of FPs, the quantum region should consist of a chromophore and most of a.a. residues and water molecules in a radius of 0.30–0.35 nm (ca. 200–230 atoms) when the remaining part of the system is approximated by the electrostatic point-charges. The optimal size of the QM region can be reduced to 80–100 atoms by utilizing a more advanced polarizable embedding model. We also find components of the QM region that are specific to a FP under study. We propose that the F165 a.a. residue is important in tuning the TPA spectrum of avGFP-n but not other investigated FPs. In the case of Citrine, Y203 and M69 a.a. residues must definitely be part of the QM subsystem. Furthermore, we find that long-range electrostatic interactions between the QM region and the rest of the protein cannot be neglected even for the most extensive QM regions (ca. 350 atoms).

Quality Threshold Clustering of Molecular Dynamics: A Word of Caution

Clustering Molecular Dynamics trajectories is a common analysis that allows grouping together similar conformations. Several algorithms have been designed and optimized to perform this routine task, and among them, Quality Threshold stands as a very attractive option. This algorithm guarantees that in retrieved clusters no pair of frames will have a similarity value greater than a specified threshold, and hence, a set of strongly correlated frames are obtained for each cluster. In this work, it is shown that various commonly used software implementations are flawed by confusing Quality Threshold with another simplistic well-known clustering algorithm published by Daura et al. (Daura, X.; van Gunsteren, W. F.; Jaun, B.; Mark, A. E.; Gademann, K.; Seebach, D. Peptide Folding: When Simulation Meets Experiment. Angew. Chemie Int. Ed. 1999, 38 (1/2), 236-240). Daura's algorithm does not impose any quality threshold for the frames contained in retrieved clusters, bringing unrelated structural configurations altogether. The advantages of using Quality Threshold whenever possible to explore Molecular Dynamic trajectories is exemplified. An in-house implementation of the original Quality Threshold algorithm has been developed in order to illustrate our comments, and its code is freely available for further use by the scientific community.

The key to the yellow-to-cyan tuning in the green fluorescent protein family is polarisation

Computational approaches have to date failed to fully capture the large (about 0.4 eV) excitation energy tuning displayed by the nearly identical anionic chromophore in different green fluorescent protein (GFP) variants. Here, we present a thorough comparative study of a set of proteins in this sub-family, including the most red- (phiYFP) and blue-shifted (mTFP0.7) ones. We employ a classical polarisable embedding through induced dipoles and combine it with time-dependent density functional theory and multireference perturbation theory in order to capture both state-specific induction contributions and the coupling of the polarisation of the protein to the chromophore transition density. The obtained results show that only upon inclusion of both these two effects generated by the mutual polarisation between the chromophore and the protein can the full spectral tuning be replicated. We finally discuss how this mutual polarisation affects the correlation between excitation energies, dipole moment variation, and molecular electrostatic field.

Subatomic resolution X-ray structures of green fluorescent protein

Green fluorescent protein (GFP) is a light-emitting protein that does not require a prosthetic group for its fluorescent activity. As such, GFP has become indispensable as a molecular tool in molecular biology. Nonetheless, there has been no subatomic elucidation of the GFP structure owing to the structural polymorphism around the chromophore. Here, subatomic resolution X-ray structures of GFP without the structural polymorphism are reported. The positions of H atoms, hydrogen-bonding network patterns and accurate geometric parameters were determined for the two protonated forms. Compared with previously determined crystal structures and theoretically optimized structures, the anionic chromophores of the structures represent the authentic resonance state of GFP. In addition, charge-density analysis based on atoms-in-molecules theory and noncovalent interaction analysis highlight weak but substantial interactions between the chromophore and the protein environment. Considered with the derived chemical indicators, the lone pair-π interactions between the chromophore and Thr62 should play a sufficient role in maintaining the electronic state of the chromophore. These results not only reveal the fine structural features that are critical to understanding the properties of GFP, but also highlight the limitations of current quantum-chemical calculations.

Macrocycle ring deformation as the secondary design principle for light-harvesting complexes

Natural light-harvesting is performed by pigment-protein complexes, which collect and funnel the solar energy at the start of photosynthesis. The identity and arrangement of pigments largely define the absorption spectrum of the antenna complex, which is further regulated by a palette of structural factors. Small alterations are induced by pigment-protein interactions. In light-harvesting systems 2 and 3 from Rhodoblastus acidophilus, the pigments are arranged identically, yet the former has an absorption peak at 850 nm that is blue-shifted to 820 nm in the latter. While the shift has previously been attributed to the removal of hydrogen bonds, which brings changes in the acetyl moiety of the bacteriochlorophyll, recent work has shown that other mechanisms are also present. Using computational and modeling tools on the corresponding crystal structures, we reach a different conclusion: The most critical factor for the shift is the curvature of the macrocycle ring. The bending of the planar part of the pigment is identified as the second-most important design principle for the function of pigment-protein complexes-a finding that can inspire the design of novel artificial systems.

The Dynamic Origin of Color Tuning in Proteins Revealed by a Carotenoid Pigment

Understanding the microscopic origin of the color tuning in pigment-protein complexes is a challenging yet fundamental issue in photoactive biological systems. Here, we propose a possible interpretation by using a state-of-the-art multiscale strategy based on the integration of quantum chemistry and polarizable atomistic embeddings into a dynamic description. By means of such a strategy we are able to resolve the long-standing dispute over the coloration mechanism in the crustacyanin protein. It is shown that the combination of the dynamical flexibility of the carotenoid pigments (astaxanthin) with the responsive protein environment is essential to obtain quantitative predictions of the spectral tuning. The strong linear correlation between the excitation energies and the bond length alternation in the long-chain carotenoids modulated by the dynamical protein environment is a novel finding explaining the high color tunability in crustacyanin.

Polarizable Embedding for Excited-State Reactions: Dynamically Weighted Polarizable QM/MM

Recent interest in polarizable embedding methods for electronic excited states has so far been focused on optical absorption and emission spectra calculations. To explore the suitability of these methods for excited-state reactions, we constructed a simple molecular system with an electronic crossing coupled to a polarizable species: the triatomic LiFBe. We found that current polarizable QM/MM methods inadequately describe the potential energy surfaces in this system, particularly close to the electronic crossing, so we developed a new polarizable embedding method called dynamically weighted polarizable QM/MM. The new method reproduces the potential energy surfaces of LiFBe from full-system multireference configuration interaction singles and doubles calculations with near-quantitative accuracy.

The mechanism of a green fluorescent protein proton shuttle unveiled in the time-resolved frequency domain by excited state ab initio dynamics

We simulated an excited state proton transfer in green fluorescent protein by excited state ab initio dynamics, and examined the reaction mechanism in both the time and the frequency domain through a multi resolution wavelet analysis. This original approach allowed us, for the first time, to directly compare the trends of photoactivated vibrations to femtosecond stimulated Raman spectroscopy results, and to give an unequivocal interpretation of the role played by low frequency modes in promoting the reaction. We could attribute the main driving force of the reaction to an important photoinduced softening of the ring-ring orientational motion of the chromophore, thus permitting the tightening of the hydrogen bond network and the opening of the reaction pathway. We also found that both the chromophore (in terms of its inter-ring dihedral angle and phenolic C-O and imidazolinone C-N bond distances) and its pocket (in terms of the inter-molecular oxygen's dihedral angle of the chromophore pocket) relaxations are modulated by low frequency (about 120 cm-1) modes involving the oxygen atoms of the network. This is in agreement with the femtosecond Raman spectroscopy findings in the time-frequency domain. Moreover, the rate in proximity to the Franck Condon region involves a picosecond time scale, with a significant influence from fluctuations of nearby hydrogen bonded residues such as His148. This approach opens a new scenario with ab initio simulations as routinely used tools to understand photoreactivity and the results of advanced time resolved spectroscopy techniques.

QM/MM methods for free energies and photochemistry

Hybrid computational methods describing a small region of a biomolecular system with quantum mechanics and the bulk with molecular mechanics, referred to as QM/MM methods, are now a central part of computational biochemistry. This review considers developments in the QM/MM approach that make it easier to calculate free energies using accurate QM-based potential energy expressions. We also describe techniques to treat electronic coupling between the core region and the MM environment. Polarizability of the protein matrix is important but so is electronic coupling. Applications of these new methods, especially to photochemistry, are discussed.

Coupling Real-Time Time-Dependent Density Functional Theory with Polarizable Force Field

Real-time time-dependent density functional theory (RT-TDDFT) is a powerful tool for obtaining spectroscopic observables and understanding complex, time-dependent properties. Currently, performing RT-TDDFT calculations on large, fully quantum mechanical systems is not computationally feasible. Previously, polarizable mixed quantum mechanical and molecular mechanical (QM/MMPol) models have been successful in providing accurate, yet efficient, approximations to a fully quantum mechanical system. Here we develop a coupling scheme between induced dipole based QM/MMPol and RT-TDDFT. Our approach is validated by comparing calculated spectra with both real-time and linear-response TDDFT calculations. The model developed within provides an accurate method for performing RT-TDDFT calculations on extended systems while accounting for mutual polarization between the quantum mechanical and molecular mechanical regions.

Combined quantum-mechanical molecular mechanics calculations with NWChem and AMBER: Excited state properties of green fluorescent protein chromophore analogue in aqueous solution

Combined quantum mechanical molecular mechanics (QM/MM) calculations have become a popular methodology for efficient and accurate description of large molecular systems. In this work we introduce our development of a QM/MM framework based on two well-known codes-NWChem and AMBER. As an initial application area we are focused on excited state properties of small molecules in an aqueous phase using an analogue of the green fluorescent protein (GFP) chromophore as a particular test case. Our approach incorporates high level coupled cluster theory for the analysis of excited states providing a reliable theoretical analysis of effects of an aqueous solvation environment on the photochemical properties of the GFP chromophore. Using a systematic approach, which involves comparison of gas phase and aqueous phase results for different protonation states and conformations, we resolve existing uncertainties regarding the theoretical interpretation of experimental data. We observe that the impact of aqueous environment on charged states generally results in blue shifts of the absorption spectra, but the magnitude of the effect is sensitive to both protonation state and conformation and can be rationalized based on charge movement into the area of higher/lower external electrostatic potentials. At neutral pH levels the experimentally observed absorption signal is most likely coming from the phenol protonated form. Our results also show that the high level electron correlated method is essential for a proper description of excited states of GFP. © 2017 Wiley Periodicals, Inc.

Intermolecular Modes between LH2 Bacteriochlorophylls and Protein Residues: The Effect on the Excitation Energies

Light-harvesting system 2 (LH2) executes the primary processes of photosynthesis in purple bacteria; photon absorption, and energy transportation to the reaction center. A detailed mechanistic insight into these operations is obscured by the complexity of the light-harvesting systems, particularly by the chromophore-environment interaction. In this work, we focus on the effects of the protein residues that are ligated to the bacteriochlorophylls (BChls) and construct potential energy surfaces of the ground and first optically excited state for the various BChl-residue systems where we in each case consider two degrees of freedom in the intermolecular region. We find that the excitation energies are only slightly affected by the considered modes. In addition, we see that axial ligands and hydrogen-bonded residues have opposite effects on both excitation energies and oscillator strengths by comparing to the isolated BChls. Our results indicate that only a small part of the chromophore-environment interaction can be associated with the intermolecular region between a BChl and an adjacent residue, but that it may be possible to selectively raise or lower the excitation energy at the axial and planar residue positions, respectively.

QM/MM Study of Substituent and Solvent Effects on the Excited State Dynamics of the Photoactive Yellow Protein Chromophore

Substituent and solvent effects on the excited state dynamics of the Photoactive Yellow Protein chromophore are studied using the average solvent electrostatic potential from molecular dynamics (ASEP/MD) method. Four molecular models were considered: the ester and thioester derivatives of the p-coumaric acid anion and their methylated derivatives. We found that the solvent produces dramatic modifications on the free energy profile of the S1 state: 1) Two twisted structures that are minima in the gas phase could not be located in aqueous solution. 2) Conical intersections (CIs) associated with the rotation of the single bond adjacent to the phenyl group are found for the four derivatives in water solution but only for thio derivatives in the gas phase. 3) The relative stability of minima and CIs is reverted with respect to the gas phase values, affecting the prevalent de-excitation paths. As a consequence of these changes, three competitive de-excitation channels are open in aqueous solution: the fluorescence emission from a planar minimum on S1, the trans-cis photoisomerization through a CI that involves the rotation of the vinyl double bond, and the nonradiative, nonreactive, de-excitation through the CI associated with the rotation of the single bond adjacent to the phenyl group. In the gas phase, the minima are the structures with the lower energy, while in solution these are the conical intersections. In solution, the de-excitation prevalent path seems to be the photoisomerization for oxo compounds, while thio compounds return to the initial trans ground state without emission.

Bethe-Salpeter study of cationic dyes: Comparisons with ADC(2) and TD-DFT

We present a theoretical investigation of the excited-state properties of a large series of structurally diverse arylcarbonium derivatives that are known to be challenging for theoretical models. More specifically, we compare the pros and cons of TD-DFT (TD-M06-2X), ADC(2), and BSE/GW approaches for a large panel of compounds, using two different solvent models. Both 0-0 and vertical transition energies are considered and compared to the experimental values. All approaches reasonably reproduce the auxochromic and acidochromic shifts, although in most cases both TD-DFT and BSE/GW return larger correlation with experimental values than ADC(2) for these shifts. In contrast, the absolute transition energies obtained with ADC(2) tend to be closer to the measurements, TD-DFT using the M06-2X functional largely overestimating the experimental references (by ca. 0.5 eV), and BSE/GW providing intermediate values. In addition, we show that the selected solvent model has a significant impact on the results, the corrected linear-response approach providing larger transition energies than its linear-response counterpart.

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.

Multiscale Simulations on Spectral Tuning and the Photoisomerization Mechanism in Fluorescent RNA Spinach

Fluorescent RNA aptamer Spinach can bind and activate a green fluorescent protein (GFP)-like chromophore (an anionic DFHBDI chromophore) displaying green fluorescence. Spectroscopic properties, spectral tuning, and the photoisomerization mechanism in the Spinach-DFHBDI complex have been investigated by high-level QM and hybrid ONIOM(QM:AMBER) methods (QM method: (TD)DFT, SF-BHHLYP, SAC-CI, LT-DF-LCC2, CASSCF, or MS-CASPT2), as well as classical molecular dynamics (MD) simulations. First, our benchmark calculations have shown that TD-DFT and spin-flip (SF) TD-DFT (SF-BHHLYP) failed to give a satisfactory description of absorption and emission of the anionic DFHBDI chromophore. Comparatively, SAC-CI, LT-DF-LCC2, and MS-CASPT2 can give more reliable transition energies and are mainly used to further study the spectra of the anionic DFHBDI chromophore in Spinach. The RNA environmental effects on the spectral tuning and the photoisomerization mechanism have been elucidated. Our simulations show that interactions of the anionic cis-DFHBDI chromophore with two G-quadruplexes as well as a UAU base triple suppress photoisomerization of DFHBDI. In addition, strong hydrogen bonds between the anionic cis-DFHBDI chromophore and nearby nucleotides facilitate its binding to Spinach and further inhibit the cis-trans photoisomerization of DFHBDI. Solvent molecules, ions, and loss of key hydrogen bonds with nearby nucleotides could induce dissociation of the anionic trans-DFHBDI chromophore from the binding site. These results provide new insights into fluorescent RNA Spinach and may help rational design of other fluorescent RNAs.

Efficient determination of accurate atomic polarizabilities for polarizeable embedding calculations

We evaluate embedding potentials, obtained via various methods, used for polarizable embedding computations of excitation energies of para-nitroaniline in water and organic solvents as well as of the green fluorescent protein. We found that isotropic polarizabilities derived from DFTD3 dispersion coefficients correlate well with those obtained via the LoProp method. We show that these polarizabilities in conjunction with appropriately derived point charges are in good agreement with calculations employing static multipole moments up to quadrupoles and anisotropic polarizabilities for both computed systems. The (partial) use of these easily-accessible parameters drastically reduces the computational effort to obtain accurate embedding potentials especially for proteins. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.