Solvent and Protein Effects on the Structure and Dynamics of the Rhodopsin Chromophore

Quantum Simulation of Molecules in Solution

Quantum chemical calculations on quantum computers have been focused mostly on simulating molecules in the gas phase. Molecules in liquid solution are, however, most relevant for chemistry. Continuum solvation models represent a good compromise between computational affordability and accuracy in describing solvation effects within a quantum chemical description of solute molecules. In this work, we extend the variational quantum eigensolver to simulate solvated systems using the polarizable continuum model. To account for the state dependent solute-solvent interaction we generalize the variational quantum eigensolver algorithm to treat non-linear molecular Hamiltonians. We show that including solvation effects does not impact the algorithmic efficiency. Numerical results of noiseless simulations for molecular systems with up to 12 spin-orbitals (qubits) are presented. Furthermore, calculations performed on a simulated noisy quantum hardware (IBM Q, Mumbai) yield computed solvation free energies in fair agreement with the classical calculations.

Dual QM and MM Approach for Computing Equilibrium Isotope Fractionation Factor of Organic Species in Solution

A dual QM and MM approach for computing equilibrium isotope effects has been described. In the first partition, the potential energy surface is represented by a combined quantum mechanical and molecular mechanical (QM/MM) method, in which a solute molecule is treated quantum mechanically, and the remaining solvent molecules are approximated classically by molecular mechanics. In the second QM/MM partition, differential nuclear quantum effects responsible for the isotope effect are determined by a statistical mechanical double-averaging formalism, in which the nuclear centroid distribution is sampled classically by Newtonian molecular dynamics and the quantum mechanical spread of quantized particles about the centroid positions is treated using the path integral (PI) method. These partitions allow the potential energy surface to be properly represented such that the solute part is free of nuclear quantum effects for nuclear quantum mechanical simulations, and the double-averaging approach has the advantage of sampling efficiency for solvent configuration and for path integral convergence. Importantly, computational precision is achieved through free energy perturbation (FEP) theory to alchemically mutate one isotope into another. The PI-FEP approach is applied to model systems for the 18O enrichment found in cellulose of trees to determine the isotope enrichment factor of carbonyl compounds in water. The present method may be useful as a general tool for studying isotope fractionation in biological and geochemical systems.

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.

Implications of short time scale dynamics on long time processes

This review provides a comprehensive overview of the structural dynamics in topical gas- and condensed-phase systems on multiple length and time scales. Starting from vibrationally induced dissociation of small molecules in the gas phase, the question of vibrational and internal energy redistribution through conformational dynamics is further developed by considering coupled electron/proton transfer in a model peptide over many orders of magnitude. The influence of the surrounding solvent is probed for electron transfer to the solvent in hydrated I-. Next, the dynamics of a modified PDZ domain over many time scales is analyzed following activation of a photoswitch. The hydration dynamics around halogenated amino acid side chains and their structural dynamics in proteins are relevant for iodinated TyrB26 insulin. Binding of nitric oxide to myoglobin is a process for which experimental and computational analyses have converged to a common view which connects rebinding time scales and the underlying dynamics. Finally, rhodopsin is a paradigmatic system for multiple length- and time-scale processes for which experimental and computational methods provide valuable insights into the functional dynamics. The systems discussed here highlight that for a comprehensive understanding of how structure, flexibility, energetics, and dynamics contribute to functional dynamics, experimental studies in multiple wavelength regions and computational studies including quantum, classical, and more coarse grained levels are required.

How Rhodopsin Tunes the Equilibrium between Protonated and Deprotonated Forms of the Retinal Chromophore

Rhodopsin is a photoactive G-protein-coupled receptor (GPCR) that converts dim light into a signal for the brain, leading to eyesight. Full activation of this GPCR is achieved after passing through several steps of the protein's photoactivation pathway. Key events of rhodopsin activation are the initial cis-trans photoisomerization of the covalently bound retinal moiety followed by conformational rearrangements and deprotonation of the chromophore's protonated Schiff base (PSB), which ultimately lead to full activation in the meta II state. PSB deprotonation is crucial for achieving full activation of rhodopsin; however, the specific structural rearrangements that have to take place to induce this pK_a shift are not well understood. Classical molecular dynamics (MD) simulations were employed to identify intermediate states after the cis-trans isomerization of rhodopsin's retinal moiety. In order to select the intermediate state in which PSB deprotonation is experimentally known to occur, the validity of the intermediate configurations was checked through an evaluation of the optical properties in comparison with experiment. Subsequently, the selected state was used to investigate the molecular factors that enable PSB deprotonation at body temperature to obtain a better understanding of the difference between the protonated and the deprotonated state of the chromophore. To this end, the deprotonation reaction has been investigated by applying QM/MM MD simulations in combination with thermodynamic integration. The study shows that, compared to the inactive 11-cis-retinal case, trans-retinal rhodopsin is able to undergo PSB deprotonation due to a change in the conformation of the retinal and a consequent alteration in the hydrogen-bond (HB) network in which PSB and the counterion Glu113 are embedded. Besides the retinal moiety and Glu113, also two water molecules as well as Thr94 and Gly90 that are related to congenital night blindness are part of this essential HB network.

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.

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.

Enzymatic Kinetic Isotope Effects from Path-Integral Free Energy Perturbation Theory

Path-integral free energy perturbation (PI-FEP) theory is presented to directly determine the ratio of quantum mechanical partition functions of different isotopologs in a single simulation. Furthermore, a double averaging strategy is used to carry out the practical simulation, separating the quantum mechanical path integral exactly into two separate calculations, one corresponding to a classical molecular dynamics simulation of the centroid coordinates, and another involving free-particle path-integral sampling over the classical, centroid positions. An integrated centroid path-integral free energy perturbation and umbrella sampling (PI-FEP/UM, or simply, PI-FEP) method along with bisection sampling was summarized, which provides an accurate and fast convergent method for computing kinetic isotope effects for chemical reactions in solution and in enzymes. The PI-FEP method is illustrated by a number of applications, to highlight the computational precision and accuracy, the rule of geometrical mean in kinetic isotope effects, enhanced nuclear quantum effects in enzyme catalysis, and protein dynamics on temperature dependence of kinetic isotope effects.

Excited States and Photochemistry of Chromophores in the Photoactive Proteins Explored by the Combined Quantum Mechanical and Molecular Mechanical Calculations

A photoactive protein usually contains a unique chromophore that is responsible for the initial photoresponse and functions of the photoactive protein are determined by the interaction between the chromophore and its protein surroundings. The combined quantum mechanical and molecular mechanical (QM/MM) approach is demonstrated to be a very useful tool for exploring structures and functions of a photoactive protein with the chromophore and its protein surroundings treated by the QM and MM methods, respectively. In this review, we summarize the basic formulas of the QM/MM approach and emphasize its applications to excited states and photoreactions of chromophores in rhodopsin protein, photoactive yellow protein, and green fluorescent protein.

Rhodopsin Absorption from First Principles: Bypassing Common Pitfalls

Bovine rhodopsin is the most extensively studied retinal protein and is considered the prototype of this important class of photosensitive biosystems involved in the process of vision. Many theoretical investigations have attempted to elucidate the role of the protein matrix in modulating the absorption of retinal chromophore in rhodopsin, but, while generally agreeing in predicting the correct location of the absorption maximum, they often reached contradicting conclusions on how the environment tunes the spectrum. To address this controversial issue, we combine here a thorough structural and dynamical characterization of rhodopsin with a careful validation of its excited-state properties via the use of a wide range of state-of-the-art quantum chemical approaches including various flavors of time-dependent density functional theory (TDDFT), different multireference perturbative schemes (CASPT2 and NEVPT2), and quantum Monte Carlo (QMC) methods. Through extensive quantum mechanical/molecular mechanical (QM/MM) molecular dynamics simulations, we obtain a comprehensive structural description of the chromophore-protein system and sample a wide range of thermally accessible configurations. We show that, in order to obtain reliable excitation properties, it is crucial to employ a sufficient number of representative configurations of the system. In fact, the common use of a single, ad hoc structure can easily lead to an incorrect model and an agreement with experimental absorption spectra due to cancelation of errors. Finally, we show that, to properly account for polarization effects on the chromophore and to quench the large blue-shift induced by the counterion on the excitation energies, it is necessary to adopt an enhanced description of the protein environment as given by a large quantum region including as many as 250 atoms.

Protein Field Effect on the Dark State of 11-cis Retinal in Rhodopsin by Quantum Monte Carlo/Molecular Mechanics

The accurate determination of the geometrical details of the dark state of 11-cis retinal in rhodopsin represents a fundamental step for the rationalization of the protein role in the optical spectral tuning in the vision mechanism. We have calculated geometries of the full retinal protonated Schiff base chromophore in the gas phase and in the protein environment using the correlated variational Monte Carlo method. The bond length alternation of the conjugated carbon chain of the chromophore in the gas phase shows a significant reduction when moving from the β-ionone ring to the nitrogen, whereas, as expected, the protein environment reduces the electronic conjugation. The proposed dark state structure is fully compatible with solid-state NMR data reported by Carravetta et al. [J. Am. Chem. Soc. 2004, 126, 3948-3953]. TDDFT/B3LYP calculations on such geometries show a blue opsin shift of 0.28 and 0.24 eV induced by the protein for S1 and S2 states, consistently with literature spectroscopic data. The effect of the geometrical distortion alone is a red shift of 0.21 and 0.16 eV with respect to the optimized gas phase chromophore. Our results open new perspectives for the study of the properties of chromophores in their biological environment using correlated methods.

Gas-Phase Retinal Spectroscopy: Temperature Effects Are But a Mirage

We employ state-of-the-art first-principle approaches to investigate whether temperature effects are responsible for the unusually broad and flat spectrum of protonated Schiff base retinal observed in photodissociation spectroscopy, as has recently been proposed. We first carefully calibrate how to construct a realistic geometrical model of retinal and show that the exchange-correlation M06-2X functional yields an accurate description while the commonly used complete active space self-consistent field method (CASSCF) is not adequate. Using modern multiconfigurational perturbative methods (NEVPT2) to compute the excitations, we then demonstrate that conformations with different orientations of the β-ionone ring are characterized by similar excitations. Moreover, other degrees of freedom identified as active in room-temperature molecular dynamics simulations do not yield the shift required to explain the anomalous spectral shape. Our findings indicate that photodissociation experiments are not representative of the optical spectrum of retinal in the gas phase and call for further experimental characterization of the dissociation spectra.

Steric and electronic influences on the torsional energy landscape of retinal

We have performed quantum mechanical calculations for retinal model compounds to establish the rotational energy barriers for the C5-, C9-, and C13-methyl groups known to play an essential role in rhodopsin activation. Intraretinal steric interactions as well as electronic effects lower the rotational barriers of both the C9- and C13-methyl groups, consistent with experimental (2)H NMR data. Each retinal methyl group has a unique rotational behavior which must be treated individually. These results are highly relevant for the parameterization of molecular mechanics force fields which form the basis of molecular dynamics simulations of retinal proteins such as rhodopsin.

Studies of the ground and excited-state surfaces of the retinal chromophore using CAM-B3LYP

The isomerization of the 11-cis isomer (PSB11) of the retinal chromophore to its all-trans isomer (PSBT) is examined. Optimized structures on both the ground state and the excited state are calculated, and the dependence on torsional angles in the carbon chain is investigated. Time-dependent density functional theory is used to produce excitation energies and the excited-state surface. To avoid problems with the description of excited states that can arise with standard DFT methods, the CAM-B3LYP functional was used. Comparing CAM-B3LYP with B3LYP results indicates that the former is significantly more accurate, as a consequence of which detailed cross sections of the retinal excited-state surface are obtained.

Drawing the Retinal Out of Its Comfort Zone: An ONIOM(QM/MM) Study of Mutant Squid Rhodopsin

Engineering squid rhodopsin with modified retinal analogues is essential for understanding the conserved steric and electrostatic interaction networks that govern the architecture of the Schiff base binding site. Depriving the retinal of its steric and electrostatic contacts affects the positioning of the Schiff-base relative to the key residues Asn87, Tyr111, and Glu180. Displacement of the W1 and W2 positions and the impact on the structural rearrangements near the Schiff base binding region reiterates the need for the presence of internal water molecules and the accessibility of binding sites to them. Also, the dominant role of the Glu180 counterion in inducing the S(1)/S(2) state reversal for SBR is shown for the first time in squid rhodopsin.

Hybrid quantum and classical methods for computing kinetic isotope effects of chemical reactions in solutions and in enzymes

A method for incorporating quantum mechanics into enzyme kinetics modeling is presented. Three aspects are emphasized: 1) combined quantum mechanical and molecular mechanical methods are used to represent the potential energy surface for modeling bond forming and breaking processes, 2) instantaneous normal mode analyses are used to incorporate quantum vibrational free energies to the classical potential of mean force, and 3) multidimensional tunneling methods are used to estimate quantum effects on the reaction coordinate motion. Centroid path integral simulations are described to make quantum corrections to the classical potential of mean force. In this method, the nuclear quantum vibrational and tunneling contributions are not separable. An integrated centroid path integral-free energy perturbation and umbrella sampling (PI-FEP/UM) method along with a bisection sampling procedure was summarized, which provides an accurate, easily convergent method for computing kinetic isotope effects for chemical reactions in solution and in enzymes. In the ensemble-averaged variational transition state theory with multidimensional tunneling (EA-VTST/MT), these three aspects of quantum mechanical effects can be individually treated, providing useful insights into the mechanism of enzymatic reactions. These methods are illustrated by applications to a model process in the gas phase, the decarboxylation reaction of N-methyl picolinate in water, and the proton abstraction and reprotonation process catalyzed by alanine racemase. These examples show that the incorporation of quantum mechanical effects is essential for enzyme kinetics simulations.

Glycine in an Electronically Excited State: Ab Initio Electronic Structure and Dynamical Calculations

The goal of this study is to explore the photochemical processes following optical excitation of the glycine molecule into its two low-lying excited states. We employed electronic structure methods at various levels to map the PES of the ground state and the two low-lying excited states of glycine. It follows from our calculations that the photochemistry of glycine can be regarded as a combination of photochemical behavior of amines and carboxylic acid. The first channel (connected to the presence of amino group) results in ultrafast decay, while the channels characteristic for the carboxylic group occur on a longer time scale. Dynamical calculations provided the branching ratio for these channels. We also addressed the question whether conformationally dependent photochemistry can be observed for glycine. While electronic structure calculations favor this possibility, the ab initio multiple spawning (AIMS) calculations showed only minor relevance of the reaction path resulting in conformationally dependent dynamics.

Probing the Sub-microsecond Photodissociation Dynamics in Gas-Phase Retinal Chromophores

The photoinduced fragmentation of a retinal model chromophore (all-trans-n-butyl protonated Schiff-base retinal) was studied in vacuo using a new experimental technique. The apparatus is able to record the photodissociation yield of gas-phase biomolecular ions in the first microseconds after absorption. Together with the existing ion storage ring ELISA, which operates on the millisecond to second time scale, the complete decay dynamics of such molecules can now be followed. In the case of retinal, the time-dependent fragmentation yield observed after irradiation with a 410 nm laser pulse exhibits contributions from one- and two-photon absorption, which decay non-exponentially with lifetimes on the order of 1 ms and 1 micros, respectively. The decay can be simulated using a statistical model, yielding good agreement with the experimental findings on both the millisecond and the microsecond time scales. No indication for nonstatistical processes is found for this molecule, the upper limit for a possible direct rate being a factor of 10(4) below the observed statistical dissociation rate.

How a small change in retinal leads to G-protein activation: initial events suggested by molecular dynamics calculations

Rhodopsin is the prototypical G-protein coupled receptor, coupling light activation with high efficiency to signaling molecules. The dark-state X-ray structures of the protein provide a starting point for consideration of the relaxation from initial light activation to conformational changes that may lead to signaling. In this study we create an energetically unstable retinal in the light activated state and then use molecular dynamics simulations to examine the types of compensation, relaxation, and conformational changes that occur following the cis-trans light activation. The results suggest that changes occur throughout the protein, with changes in the orientation of Helices 5 and 6, a closer interaction between Ala 169 on Helix 4 and retinal, and a shift in the Schiff base counterion that also reflects changes in sidechain interactions with the retinal. Taken together, the simulation is suggestive of the types of changes that lead from local conformational change to light-activated signaling in this prototypical system.

Photochemistry of a Retinal Protonated Schiff-Base Analogue Mimicking the Opsin Shift of Bacteriorhodopsin

A retinal Schiff base analogue which artificially mimics the protein-induced red shifting of absorption in bacteriorhodopsin (BR) has been investigated with femtosecond multichannel pump probe spectroscopy. The objective is to determine if the catalysis of retinal internal conversion in the native protein BR, which absorbs at 570 nm, is directly correlated with the protein-induced Stokes shifting of this absorption band otherwise known as the "opsin shift". Results demonstrate that the red shift afforded in the model system does not hasten internal conversion relative to that taking place in a free retinal-protonated Schiff base (RPSB) in methanol solution, and stimulated emission takes place with biexponential kinetics and characteristic timescales of approximately 2 and 10.5 ps. This shows that interactions between the prosthetic group and the protein that lead to the opsin shift in BR are not directly involved in reducing the excited-state lifetime by nearly an order of magnitude. A sub-picosecond phase of spectral evolution, analogues of which are detected in photoexcited retinal proteins and RPSBs in solution, is observed after excitation anywhere within the intense visible absorption band. It consists of a large and discontinuous spectral shift in excited-state absorption and is assigned to electronic relaxation between excited states, a scenario which might also be relevant to those systems as well. Finally, a transient excess bleach component that tunes with the excitation wavelength is detected in the data and tentatively assigned to inhomogeneous broadening in the ground state absorption band. Possible sources of such inhomogeneity and its relevance to native RPSB photochemistry are discussed.

Excited-State Properties and Environmental Effects for Protonated Schiff Bases: A Theoretical Study

Complete active space self-consistent field (CASSCF), multireference configuration interaction (MRCI), density functional theory (DFT), time dependent DFT (TDDFT) and the singles and doubles coupled-cluster (CC2) methodologies have been used to study the ground state and excited states of protonated and neutral Schiff bases (PSB and SB) as models for the retinal chromophore. Systems with two to four conjugated double bonds are investigated. Geometry relaxation effects are studied in the excited pipi* state using the aforementioned methods. Taking the MRCI results as reference we find that CASSCF results are quite reliable even though overshooting of geometry changes is observed. TDDFT does not reproduce bond alternation well in the pipi* state. CC2 takes an intermediate position. Environmental effects due to solvent or protein surroundings have been studied in the excited states of the PSBs and SBs using a water molecule and solvated formate as model cases. Particular emphasis is given to the proton transfer process from the PSB to its solvent partner in the excited state. It is found that its feasibility is significantly enhanced in the excited state as compared to the ground state, which means that a proton transfer could be initiated already at an early step in the photodynamics of PSBs.

Solvent Effects on the Low-Lying Excited States of a Model of Retinal

The low-lying excited states of a solution in alcohol of a five-double-bond model of the rhodopsin protein chromophore, the protonated 11-cis-retinal Schiff base (PSB11), are studied theoretically. We combine a multireference perturbational treatment in the description of the solute molecule with molecular dynamics calculations in the description of the solvent. The geometry, charge distribution, and electronic spectra are strongly influenced by the solvent. The solvent shift values show a marked dependence on the use of relaxed geometries in solution and on the nature of the states involved in the excitation process. The dynamic correlation has a strong effect on the order of the excited states. In solution, the first two excited states almost become degenerate.