NMR Chemical Shifts of the Rhodopsin Chromophore in the Dark State and in Bathorhodopsin: A Hybrid QM/MM Molecular Dynamics Study

Residue-Residue Mutual Work Analysis of Retinal-Opsin Interaction in Rhodopsin: Implications for Protein-Ligand Binding

Energetic contributions at the single-residue level for retinal-opsin interactions in rhodopsin were studied by combining molecular dynamics simulations, transition path sampling, and a newly developed energy decomposition approach. The virtual work at an infinitesimal time interval was decomposed into the work components on one residue due to its interaction with another residue, which were then averaged over the transition path ensemble along a proposed reaction coordinate. Such residue-residue mutual work analysis on 62 residues within the active center of rhodopsin resulted in a very sparse interaction matrix, which is generally not symmetric but antisymmetric to some extent. Fourteen residues were identified to be major players in retinal relaxation along a plausible pathway from bathorhodopsin to the blue-shifted intermediate, which is in good agreement with an existing NMR study. Based on the matrix of mutual work, a comprehensive network was constructed to provide detailed insights into the chromophore-protein interaction from a viewpoint of energy flow.

Temperature Dependence of NMR Parameters Calculated from Path Integral Molecular Dynamics Simulations

The influence of temperature on NMR chemical shifts and quadrupolar couplings in model molecular organic solids is explored using path integral molecular dynamics (PIMD) and density functional theory (DFT) calculations of shielding and electric field gradient (EFG) tensors. An approach based on convoluting calculated shielding or EFG tensor components with probability distributions of selected bond distances and valence angles obtained from DFT-PIMD simulations at several temperatures is used to calculate the temperature effects. The probability distributions obtained from the quantum PIMD simulations, which includes nuclear quantum effects, are significantly broader and less temperature dependent than those obtained with conventional DFT molecular dynamics or with 1D scans through the potential energy surface. Predicted NMR observables for the model systems were in excellent agreement with experimental data.

Opsin Effect on the Electronic Structure of the Retinylidene Chromophore in Rhodopsin

Direct examination of experimental NMR parameters combined with electronic structure analysis was used to provide a first-principle interpretation of NMR experiments and give a precise evaluation of how the electronic perturbation of the protein environment affects the electronic properties of the retinylidene chromophere in rhodopsin. To this end, we pursued a theoretical analysis using a combination of tools including quantum mechanics/molecular mechanics (QM/MM) at the Density Functional Theory (DFT) level, in conjunction with gauge independent atomic orbital (GIAO) calculations of (13)C NMR chemical shieldings and (1)J(CC) spin-spin coupling constants obtained with the Coupled Perturbed DFT (CPDFT) method. The opsin effect on the retinylidene chromophere is interpreted as an inductive effect of Glu-113 which readjusts the weighting factors of resonance substructures of the conjugated chain of the chromophere. These changes give a rationalization to the alternating effect of the (13)C chemical shifts magnitudes when comparing the retinylidene chromophere in the presence and absence of the protein environment. Conversely, perturbation of π orbitals has little to no effect over (1)J (13)C-(13)C spin-spin coupling constants, as they are mainly dominated by the Fermi contact term, and hence the counteraion effect is restricted to the vicinity of the perturbation. Thus, the apparent contradiction between experimental findings based on chemical shifts (deep penetration) and one-bond J-couplings (localized effects of the protonated Schiff base at the chain terminus) is in fact a consequence of different properties responding differently to the same external perturbation.

Phycocyanobilin in solution – a solvent triggered molecular switch

The chromophore phycocyanobilin changes its spectroscopic behaviour upon solvent change. Our calculations trace this effect back to conformational switching, induced by changes in the hydrogen bonding pattern.

Isotropic magnetic shielding constants of retinal derivatives in aprotic and protic solvents

We investigate the nuclear isotropic shielding constants σ((13)C) and σ((17)O) of isomers of retinoic acid and retinal in gas-phase and in chloroform, acetonitrile, methanol, and water solutions via Monte Carlo simulation and quantum mechanics calculations using the GIAO-B3LYP∕6-311++G(2d,2p) approach. Electronic solute polarization effects due to protic and aprotic solvents are included iteratively and play an important role in the quantitative determination of oxygen shielding constants. Our MP2∕6-31G+(d) results show substantial increases of the dipole moment of both retinal derivatives in solution as compared with the gas-phase results (between 22% and 26% in chloroform and between 55% and 99% in water). For the oxygen atoms the influence of the solute polarization is mild for σ((17)O) of hydroxyl group, even in protic solvents, but it is particularly important for σ((17)O) of carbonyl group. For the latter, there is a sizable increase in the magnitude with increasing solvent polarity. For the carbon atoms, the solvent effects on the σ((13)C) values are in general small, being more appreciable in carbon atoms of the polyene chain than in the carbon atoms of the β-ionone ring and methyl groups. The results also show that isomeric changes on the backbones of the polyene chains have marked influence on the (13)C chemical shifts of carbon atoms near to the structural distortions, in good agreement with the experimental results measured in solution.

Conformational Sampling by Ab Initio Molecular Dynamics Simulations Improves NMR Chemical Shift Predictions

Car-Parrinello molecular dynamics simulations were performed for N-methyl acetamide as a small test system for amide groups in protein backbones, and NMR chemical shifts were calculated based on the generated ensemble. If conformational sampling and explicit solvent molecules are taken into account, excellent agreement between the calculated and experimental chemical shifts is obtained. These results represent a landmark improvement over calculations based on classical molecular dynamics (MD) simulations especially for amide protons, which are predicted too high-field shifted based on the latter ensembles. We were able to show that the better results are caused by the solute-solvents interactions forming shorter hydrogen bonds as well as by the internal degrees of freedom of the solute. Inspired by these results, we propose our approach as a new tool for the validation of force fields due to its power of identifying the structural reasons for discrepancies between the experimental and calculated data.

Vibrational averaging of the chemical shift in crystalline α-glycine

Averaging of the chemical shift over the molecular motion improves the simulated data and provides additional information about the temperature dependence and system dynamics. However, crystal modeling is difficult due to the limited precision of the plane-wave density functional theory (DFT) methods and approximate vibrational schemes. On the glycine example, we investigate how the averaging can be achieved within the periodic boundary conditions at the DFT level. The nuclear motion is modeled with the vibrational configuration interaction, with other simplified quantum anharmonic schemes, and the classical Born-Oppenheimer molecular dynamics (BOMD). The results confirm a large vibrational contribution to the isotropic shielding values. Both the first and second derivatives of the shielding were found important for the quantum averaging. The first derivatives influence the shielding mostly due to the anharmonic character of the CH and NH stretching modes, whereas second derivatives produce most vibrational corrections associated with the lower-frequency vibrational modes. Temperature excitations of the lowest-frequency vibrational states and the expansion of the crystal cell both determine the temperature dependence of nuclear magnetic resonance parameters. The vibrational quantum approach as well as classical BOMD schemes provided temperature dependencies of the chemical shifts that are consistent with the previous experimental data.

The effect of protein environment on photoexcitation properties of retinal

Retinal is the photon absorbing chromophore of rhodopsin and other visual pigments, enabling the vertebrate vision process. The effects of the protein environment on the primary photoexcitation process of retinal were studied by time-dependent density functional theory (TDDFT) and the algebraic diagrammatic construction through second order (ADC(2)) combined with our recently introduced reduction of virtual space (RVS) approximation method. The calculations were performed on large full quantum chemical cluster models of the bluecone (BC) and rhodopsin (Rh) pigments with 165-171 atoms. Absorption wavelengths of 441 and 491 nm were obtained at the B3LYP level of theory for the respective models, which agree well with the experimental values of 414 and 498 nm. Electrostatic rather than structural strain effects were shown to dominate the spectral tuning properties of the surrounding protein. The Schiff base retinal and a neighboring Glu-113 residue were found to have comparable proton affinities in the ground state of the BC model, whereas in the excited state, the proton affinity of the Schiff base is 5.9 kcal/mol (0.26 eV) higher. For the ground and excited states of the Rh model, the proton affinity of the Schiff base is 3.2 kcal/mol (0.14 eV) and 7.9 kcal/mol (0.34 eV) higher than for Glu-113, respectively. The protein environment was found to enhance the bond length alternation (BLA) of the retinyl chain and blueshift the first absorption maxima of the protonated Schiff base in the BC and Rh models relative to the chromophore in the gas phase. The protein environment was also found to decrease the intensity of the second excited state, thus improving the quantum yield of the photoexcitation process. Relaxation of the BC model on the excited state potential energy surface led to a vanishing BLA around the isomerization center of the conjugated retinyl chain, rendering the retinal accessible for cis-trans isomerization. The energy of the relaxed excited state was found to be 30 kcal/mol (1.3 eV) above the minimum ground state energy, and might be related to the transition state of the thermal activation process.

Molecular simulations and solid-state NMR investigate dynamical structure in rhodopsin activation

Rhodopsin has served as the primary model for studying G protein-coupled receptors (GPCRs)-the largest group in the human genome, and consequently a primary target for pharmaceutical development. Understanding the functions and activation mechanisms of GPCRs has proven to be extraordinarily difficult, as they are part of a complex signaling cascade and reside within the cell membrane. Although X-ray crystallography has recently solved several GPCR structures that may resemble the activated conformation, the dynamics and mechanism of rhodopsin activation continue to remain elusive. Notably solid-state ((2))H NMR spectroscopy provides key information pertinent to how local dynamics of the retinal ligand change during rhodopsin activation. When combined with molecular mechanics simulations of proteolipid membranes, a new paradigm for the rhodopsin activation process emerges. Experiment and simulation both suggest that retinal isomerization initiates the rhodopsin photocascade to yield not a single activated structure, but rather an ensemble of activated conformational states. This article is part of a Special Issue entitled: Membrane protein structure and function.

Approaches to the solvation of the molecular probe N-methyl-6-quinolone in its excited state

The molecular probe N-methyl-6-quinolone (MQ) gives experimental access to its local chemical environment, e.g. inside a biomolecule. Using ab initio molecular dynamics (MD), it is possible to simulate the time evolution of the Stokes shift as a function of the actual atomistic coupling to the surrounding hydrogen bond network and thus obtain a comprehensive view of the local environment. In contrast to ground state ab initio MD simulations, the choice of a method for excited state MD is nontrivial. Here, we develop a simple and accurate model for the solvation dynamics of MQ in its first excited state.

The protonation state of Glu181 in rhodopsin revisited: interpretation of experimental data on the basis of QM/MM calculations

The structure and spectroscopy of rhodopsin have been intensely studied in the past decade both experimentally and theoretically; however, important issues still remain unresolved. Of central interest is the protonation state of Glu181, where controversial and contradictory experimental evidence has appeared. While FTIR measurements indicate this residue to be unprotonated, preresonance Raman and UV-vis spectra have been interpreted in favor of a protonated Glu181. Previous computational approaches were not able to resolve this issue, providing contradicting data as well. Here, we perform hybrid QM/MM calculations using DFT methods for the electronic ground state, MRCI methods for the electronically excited states, and a polarization model for the MM part in order to investigate this issue systematically. We constructed various active-site models for protonated as well as unprotonated Glu181, which were evaluated by computing NMR, IR, Raman, and UV-vis spectroscopic data. The resulting differences in the UV-vis and Raman spectra between protonated and unprotonated models are very subtle, which has two major consequences. First, the common interpretation of prior Raman and UV-vis experiments in favor of a neutral Glu181 appears questionable, as it is based on the assumption that a charge at the Glu181 location would have a sizable impact. Second, also theoretical results should be interpreted with care. Spectroscopic differences between the structural models must be related to modeling uncertainties and intrinsic methodological errors. Despite a detailed comparison of various rhodopsins and mutants and consistently favorite results with charged Glu181 models, we find merely weak evidence from UV-vis and Raman calculations. On the contrary, difference FTIR and NMR chemical shift measurements on Rh mutants are indicative of the protonation state of Glu181. Supported by our results, they provide strong and independent evidence for a charged Glu181.

Dynamical effects in ab initio NMR calculations: classical force fields fitted to quantum forces

NMR chemical shifts for an L-alanine molecular crystal are calculated using ab initio plane wave density functional theory. Dynamical effects including anharmonicity may be included by averaging chemical shifts over an ensemble of structural configurations generated using molecular dynamics (MD). The time scales required mean that ab initio MD is prohibitively expensive. Yet the sensitivity of chemical shifts to structural details requires that the methodologies for performing MD and calculating NMR shifts be consistent. This work resolves these previously competing requirements by fitting classical force fields to reproduce ab initio forces. This methodology is first validated by reproducing the averaged chemical shifts found using ab initio molecular dynamics. Study of a supercell of L-alanine demonstrates that finite size effects can be significant when accounting for dynamics.

Modeling reaction routes from rhodopsin to bathorhodopsin

The quantum mechanical-molecular mechanical (QM/MM) theory was applied to calculate accurate structural parameters, vibrational and optical spectra of bathorhodopsin (BATHO), one of the primary photoproducts of the functional cycle of the visual pigment rhodopsin (RHO), and to characterize reaction routes from RHO to BATHO. The recently resolved crystal structure of BATHO (PDBID: 2G87) served as an initial source of coordinates of heavy atoms. Protein structures in the ground electronic state and vibrational frequencies were determined by using the density functional theory in the PBE0/cc-pVDZ approximation for the QM part and the AMBER force field parameters in the MM part. Calculated and assigned vibrational spectra of both model protein systems, BATHO and RHO, cover three main regions referring to the hydrogen-out-of-plan (HOOP) motion, the C==C ethylenic stretches, and the C--C single-bond stretches. The S(0)-S(1) electronic excitation energies of the QM part, including the chromophore group in the field of the protein matrix, were estimated by using the advanced quantum chemistry methods. The computed structural parameters as well as the spectral bands match perfectly the experimental findings. A structure of the transition state on the S(0) potential energy surface for the ground electronic state rearrangement from RHO to BATHO was located proving a possible route of the thermal protein activation to the primary photoproduct.

Molecular mechanism of long-range synergetic color tuning between multiple amino acid residues in conger rhodopsin

The synergetic effects of multiple rhodopsin mutations on color tuning need to be completely elucidated. Systematic genetic studies and spectroscopy have demonstrated an interesting example of synergetic color tuning between two amino acid residues in conger rhodopsin's ancestral pigment (p501): -a double mutation at one nearby and one distant residue led to a significant λ(max) blue shift of 13 nm, whereas neither of the single mutations at these two sites led to meaningful shifts.To analyze the molecular mechanisms of this synergetic color tuning, we performed homology modeling, molecular simulations, and electronic state calculations. For the double mutant, N195A/A292S, in silico mutation analysis demonstrated conspicuous structural changes in the retinal chromophore, whereas that of the single mutant, A292S, was almost unchanged. Using statistical ensembles of QM/MM optimized structures, the excitation energy of retinal chromophore was evaluated for the three visual pigments. As a result, the λ(max) shift of double mutant (DM) from p501 was -8 nm, while that of single mutant (SM) from p501 was +1 nm. Molecular dynamics simulation for DM demonstrated frequent isomerization between 6-s-cis and 6-s-trans conformers. Unexpectedly, however, the two conformers exhibited almost identical excitation energy, whereas principal component analysis (PCA) identified the retinal-counterion cooperative change of BLA (bond length alternation) and retinal-counterion interaction lead to the shift.

Calculation of NMR chemical shifts in organic solids: accounting for motional effects

NMR chemical shifts were calculated from first principles for well defined crystalline organic solids. These density functional theory calculations were carried out within the plane-wave pseudopotential framework, in which truly extended systems are implicitly considered. The influence of motional effects was assessed by averaging over vibrational modes or over snapshots taken from ab initio molecular dynamics simulations. It is observed that the zero-point correction to chemical shifts can be significant, and that thermal effects are particularly noticeable for shielding anisotropies and for a temperature-dependent chemical shift. This study provides insight into the development of highly accurate first principles calculations of chemical shifts in solids, highlighting the role of motional effects on well defined systems.

Towards an interpretation of 13C chemical shifts in bathorhodopsin, a functional intermediate of a G-protein coupled receptor

Photoisomerization of the membrane-bound light receptor protein rhodopsin leads to an energy-rich photostate called bathorhodopsin, which may be trapped at temperatures of 120 K or lower. We recently studied bathorhodopsin by low-temperature solid-state NMR, using in situ illumination of the sample in a purpose-built NMR probe. In this way we acquired (13)C chemical shifts along the retinylidene chain of the chromophore. Here we compare these results with the chemical shifts of the dark state chromophore in rhodopsin, as well as with the chemical shifts of retinylidene model compounds in solution. An earlier solid-state NMR study of bathorhodopsin found only small changes in the (13)C chemical shifts upon isomerization, suggesting only minor perturbations of the electronic structure in the isomerized retinylidene chain. This is at variance with our recent measurements which show much larger perturbations of the (13)C chemical shifts. Here we present a tentative interpretation of our NMR results involving an increased charge delocalization inside the polyene chain of the bathorhodopsin chromophore. Our results suggest that the bathochromic shift of bathorhodopsin is due to modified electrostatic interactions between the chromophore and the binding pocket, whereas both electrostatic interactions and torsional strain are involved in the energy storage mechanism of bathorhodopsin.