Computational photochemistry of retinal proteins

High spectral tunability and quantum yield are the striking features of rhodopsin photochemistry. They rely on a strong and complex interaction of their chromophore, the protonated Schiff base of retinal, with its protein environment. In this article, we review the progress in the computational modeling of these systems, focusing on the optical properties and the excited state dynamics. While the earlier success of atomistic theoretical models was based on the breakthrough in X-ray crystallography and combined quantum mechanical molecular mechanical (QM/MM) methodology, recent advances point out the importance of high-level QM methods and the incorporation of effects that are neglected in conventional QM/MM or ONIOM schemes, like polarization and charge transfer.     

Spectral tuning in visual pigments: an ONIOM(QM:MM) study on bovine rhodopsin and its mutants

We have investigated geometries and excitation energies of bovine rhodopsin and some of its mutants by hybrid quantum mechanical/molecular mechanical (QM/MM) calculations in ONIOM scheme, employing B3LYP and BLYP density functionals as well as DFTB method for the QM part and AMBER force field for the MM part. QM/MM geometries of the protonated Schiff-base 11- cis-retinal with B3LYP and DFTB are very similar to each other. TD-B3LYP/MM excitation energy calculations reproduce the experimental absorption maximum of 500 nm in the presence of native rhodopsin environment and predict spectral shifts due to mutations within 10 nm, whereas TD-BLYP/MM excitation energies have red-shift error of at least 50 nm. In the wild-type rhodopsin, Glu113 shifts the first excitation energy to blue and accounts for most of the shift found. Other amino acids individually contribute to the first excitation energy but their net effect is small. The electronic polarization effect is essential for reproducing experimental bond length alternation along the polyene chain in protonated Schiff-base retinal, which correlates with the computed first excitation energy. It also corrects the excitation energies and spectral shifts in mutants, more effectively for deprotonated Schiff-base retinal than for the protonated form. The protonation state and conformation of mutated residues affect electronic spectrum significantly. The present QM/MM calculations estimate not only the experimental excitation energies but also the source of spectral shifts in mutants.     

Effect of polarization on the opsin shift in rhodopsins. 1. A combined QM/QM/MM model for bacteriorhodopsin and pharaonis sensory rhodopsin II

The optical and IR-spectroscopic properties of the protonated Schiff base of retinal are highly sensitive to the electrostatic environment. This feature makes retinal a useful probe to study structural differences and changes in rhodopsins. It also raises an interest to theoretically predict the spectroscopic response to mutation and structural evolution. Computational models appropriate for this purpose usually combine sophisticated quantum mechanical (QM) methods with molecular mechanics (MM) force fields. In an effort to test and improve the accuracy of these QM/MM models, we consider in this article the effects of polarization and inter-residual charge transfer within the binding pocket of bacteriorhodopsin (bR) and pharaonis sensory rhodopsin II (psRII, also called pharaonis phoborhodopsin, ppR) on the excitation energy using an ab initio QM/QM/MM approach. The results will serve as reference for assessing empirical polarization models in a consecutive article.     

Effect of polarization on the opsin shift in rhodopsins. 2. Empirical polarization models for proteins

The explicit treatment of polarization as a many-body interaction in condensed-phase systems represents a current problem in empirical force-field development. Although a variety of efficient models for molecular polarization have been suggested, polarizable force fields are still far from common use nowadays. In this work, we consider interactive polarization models employing Thole's short-range damping scheme and assess them for application on polypeptides. Despite the simplicity of the model, we find mean polarizabilities and anisotropies of amino acid side chains in excellent agreement with MP2/cc-pVQZ benchmark calculations. Combined with restrained electrostatic potential (RESP) derived atomic charges, the models are applied in a quantum-mechanical/molecular-mechanical (QM/MM) approach. An iterative scheme is used to establish a self-consistent mutual polarization between the QM and MM moieties. This ansatz is employed to study the influence of the protein polarizability on calculated optical properties of the protonated Schiff base of retinal in rhodopsin (Rh), bacterio-rhodopsin (bR), and pharaonis sensory rhodopsin II (psRII). The shifts of the excitation energy due to the instantaneous polarization response of the protein to the charge transfer on the retinal chromophore are quantified using the high level ab initio multireference spectroscopy-oriented configuration interaction (SORCI) method. The results are compared with those of previously published QM1/QM2/MM models for bR and psRII.     

Performance assessment of semiempirical molecular orbital methods in describing halogen bonding: quantum mechanical and quantum mechanical/molecular mechanical-molecular dynamics study

The performance of semiempirical molecular-orbital methods--MNDO, MNDO-d, AM1, RM1, PM3 and PM6--in describing halogen bonding was evaluated, and the results were compared with molecular mechanical (MM) and quantum mechanical (QM) data. Three types of performance were assessed: (1) geometrical optimizations and binding energy calculations for 27 halogen-containing molecules complexed with various Lewis bases (Two of the tested methods, AM1 and RM1, gave results that agree with the QM data.); (2) charge distribution calculations for halobenzene molecules, determined by calculating the solvation free energies of the molecules relative to benzene in explicit and implicit generalized Born (GB) solvents (None of the methods gave results that agree with the experimental data.); and (3) appropriateness of the semiempirical methods in the hybrid quantum-mechanical/molecular-mechanical (QM/MM) scheme, investigated by studying the molecular inhibition of CK2 protein by eight halobenzimidazole and -benzotriazole derivatives using hybrid QM/MM molecular-dynamics (MD) simulations with the inhibitor described at the QM level by the AM1 method and the rest of the system described at the MM level. The pure MM approach with inclusion of an extra point of positive charge on the halogen atom approach gave better results than the hybrid QM/MM approach involving the AM1 method. Also, in comparison with the pure MM-GBSA (generalized Born surface area) binding energies and experimental data, the calculated QM/MM-GBSA binding energies of the inhibitors were improved by replacing the G(GB,QM/MM) solvation term with the corresponding G(GB,MM) term.     

Dynamic structures of phosphodiesterase-5 active site by combined molecular dynamics simulations and hybrid quantum mechanical/molecular mechanical calculations

Various quantum mechanical/molecular mechanical (QM/MM) geometry optimizations starting from an x-ray crystal structure and from the snapshot structures of constrained molecular dynamics (MD) simulations have been performed to characterize two dynamically stable active site structures of phosphodiesterase-5 (PDE5) in solution. The only difference between the two PDE5 structures exists in the catalytic, second bridging ligand (BL2) which is HO- or H2O. It has been shown that, whereas BL2 (i.e. HO-) in the PDE5(BL2 = HO-) structure can really bridge the two positively charged metal ions (Zn2+ and Mg2+), BL2 (i.e. H2O) in the PDE5(BL2 = H2O) structure can only coordinate Mg2+. It has been demonstrated that the results of the QM/MM geometry optimizations are remarkably affected by the solvent water molecules, the dynamics of the protein environment, and the electronic embedding charges of the MM region in the QM part of the QMM/MM calculation. The PDE5(BL2 = H2O) geometries optimized by using the QM/MM method in different ways show strong couplings between these important factors. It is interesting to note that the PDE5(BL2 = HO-) and PDE5(BL2 = H2O) geometries determined by the QM/MM calculations neglecting these three factors are all consistent with the corresponding geometries determined by the QM/MM calculations that account for all of these three factors. These results suggest the overall effects of these three important factors on the optimized geometries can roughly cancel out. However, the QM/MM calculations that only account for some of these factors could lead to considerably different geometries. These results might be useful also in guiding future QM/MM geometry optimizations on other enzymes.     

Quantum mechanical/molecular mechanical study on the mechanism of the enzymatic Baeyer-Villiger reaction

We report a combined quantum mechanical/molecular mechanical (QM/MM) study on the mechanism of the enzymatic Baeyer-Villiger reaction catalyzed by cyclohexanone monooxygenase (CHMO). In QM/MM geometry optimizations and reaction path calculations, density functional theory (B3LYP/TZVP) is used to describe the QM region consisting of the substrate (cyclohexanone), the isoalloxazine ring of C4a-peroxyflavin, the side chain of Arg-329, and the nicotinamide ring and the adjacent ribose of NADP(+), while the remainder of the enzyme is represented by the CHARMM force field. QM/MM molecular dynamics simulations and free energy calculations at the semiempirical OM3/CHARMM level employ the same QM/MM partitioning. According to the QM/MM calculations, the enzyme-reactant complex contains an anionic deprotonated C4a-peroxyflavin that is stabilized by strong hydrogen bonds with the Arg-329 residue and the NADP(+) cofactor. The CHMO-catalyzed reaction proceeds via a Criegee intermediate having pronounced anionic character. The initial addition reaction has to overcome an energy barrier of about 9 kcal/mol. The formed Criegee intermediate occupies a shallow minimum on the QM/MM potential energy surface and can undergo fragmentation to the lactone product by surmounting a second energy barrier of about 7 kcal/mol. The transition state for the latter migration step is the highest point on the QM/MM energy profile. Gas-phase reoptimizations of the QM region lead to higher barriers and confirm the crucial role of the Arg-329 residue and the NADP(+) cofactor for the catalytic efficiency of CHMO. QM/MM calculations for the CHMO-catalyzed oxidation of 4-methylcyclohexanone reproduce and rationalize the experimentally observed (S)-enantioselectivity for this substrate, which is governed by the conformational preferences of the corresponding Criegee intermediate and the subsequent transition state for the migration step.     

QM/MM study of dehydro and dihydro β-ionone retinal analogues in squid and bovine rhodopsins: implications for vision in salamander rhodopsin

Visual pigment rhodopsin provides a decisive crossing point for interaction between organisms and environment. Naturally occurring visual pigments contain only PSB11 and 3,4-dehydro-PSB11 as chromophores. Therefore, the ability of visual opsin to discriminate between the retinal geometries is investigated by means of QM/MM incorporation of PSB11, 6-s-cis and 6-s-trans forms of 3,4-dehydro-PSB11, and 3,4-dehydro-5,6-dihydro-PSB11 and 5,6-dihydro-PSB11 analogues into squid and bovine rhodopsin environments. The analogue-protein interaction reveals the binding site of squid rhodopsin to be malleable and ductile, while that of bovine rhodopsin is rigid and stiff. On the basis of these studies, a tentative model of the salamander rhodopsin binding site is also proposed.     

Role of hydrogen-bond network in energy storage of bacteriorhodopsin's light-driven proton pump revealed by ab initio normal-mode analysis

Vibrational modes of the hydrogen-bond network in the binding site of bacteriorhodopsin (bR), a protein in halobacteria functioning as a light-driven proton pump, were investigated by an ab initio quantum mechanical/molecular mechanical (QM/MM) method. Normal-mode analysis calculations for O-D and N-D stretching modes of internal water molecules and the Schiff base of the retinal chromophore in the early intermediate state, K, reproduced well experimentally observed vibrational spectra. Supported by agreement with observed spectra, the QM/MM calculation suggests that weakened hydrogen bonds upon photoisomerization of the chromophore are an important means of energy storage in bR.     

Combined quantum mechanical/molecular mechanical study on the pentacoordinated ferric and ferrous cytochrome P450cam complexes

The pentacoordinated ferric and ferrous cytochrome P450(cam) complexes have been investigated by combined quantum mechanical/molecular mechanical (QM/MM) calculations in the presence of a protein/solvent environment and by QM calculations on the isolated QM regions with use of density functional theory. The B3LYP functional has been found more reliable than the BLYP and BHLYP functionals for estimating the relative state energies. The B3LYP/CHARMM calculations with an all-electron basis set for iron give high-spin ground states for the title complexes, in agreement with experiment. The comparison of the B3LYP/CHARMM results of the entire protein system with the B3LYP calculations on the naked QM regions shows that the amount of stabilization by the protein environment is largest for the intermediate-spin states, followed by the high-spin states of the complexes. The calculation of M?ssbauer parameters in the presence of the enzyme environment confirms the double occupation of the d(xz) orbital in the quintet spin state of the ferrous complex, consistent with the computed QM/MM energies in the enzyme environment, while the d(x)2(-)(y)2 orbital is doubly occupied in the gas-phase quintet state.     

YinYang atom: a simple combined ab initio quantum mechanical molecular mechanical model

A simple interface is proposed for combined quantum mechanical (QM) molecular mechanical (MM) calculations for the systems where the QM and MM regions are connected through covalent bonds. Within this model, the atom that connects the two regions, called YinYang atom here, serves as an ordinary MM atom to other MM atoms and as a hydrogen-like atom to other QM atoms. Only one new empirical parameter is introduced to adjust the length of the connecting bond and is calibrated with the molecule propanol. This model is tested with the computation of equilibrium geometries and protonation energies for dozens of molecules. Special attention is paid on the influence of MM point charges on optimized geometry and protonation energy, and it is found that it is important to maintain local charge-neutrality in the MM region in order for the accurate calculation of the protonation and deprotonation energies. Overall the simple YinYang atom model yields comparable results to some other QM/MM models.     

Prediction of the mechanisms of enzyme-catalysed reactions using hybrid quantum mechanical/molecular mechanical methods

The use of hybrid methods, involving both quantum mechanics and molecular mechanics, to model the mechanism of enzyme-catalysed reactions, is discussed. Two alternative approaches to treating the electrostatic interactions between the quantum mechanical and molecular mechanical regions are studied, involving either the inclusion of this term in the electronic Hamiltonian (QM/MM), or evaluating it purely classically (MO + MM). In the latter scheme, possible problems of using force fields that are standard for macromolecular modelling are identified. The use of QM/MM schemes to investigate the mechanism of the enzymes thymidine phosphorylase (ThdPase) and protein tyrosine phosphatase (PTP) is described. For both systems, transition states have been identified using a PM3 Hamiltonian. For ThdPase, concerted motion of the enzyme during the course of the reaction is suggested and, for PTP, a two-step dephosphorylation reaction is indicated, both with quite low barriers.     

A combined quantum mechanical and molecular mechanical method using modified generalized hybrid orbitals: implementation for electronic excited states

The generalized hybrid orbital (GHO) method is implemented at the second-order approximate coupled cluster singles and doubles (CC2) level for quantum mechanical (QM)/molecular mechanical (MM) electronic excited state calculations. The linear response function of CC2 in the GHO scheme is derived and implemented. The new implementation is applied to the first singlet excited states of three aromatic amino acids, phenylalanine, tyrosine, and tryptophan, and also bacteriorhodopsin for assessment. The results obtained for aromatic amino acids agreed well with the full QM CC2 calculations, while the calculated excitation energies of bacteriorhodopsin and its chromophore, all-trans retinal, reproduced the environmental shift of the experimental data. For the bacteriorhodopsin case, the environmental shift of GHO also showed good agreements with the experimental data. The contribution of the quantum effect of certain moieties in the excited states is elucidated by changing the partitioning of QM and MM regions.     

Reaction path potential for complex systems derived from combined ab initio quantum mechanical and molecular mechanical calculations

Combined ab initio quantum mechanical and molecular mechanical calculations have been widely used for modeling chemical reactions in complex systems such as enzymes, with most applications being based on the determination of a minimum energy path connecting the reactant through the transition state to the product in the enzyme environment. However, statistical mechanics sampling and reaction dynamics calculations with a combined ab initio quantum mechanical (QM) and molecular mechanical (MM) potential are still not feasible because of the computational costs associated mainly with the ab initio quantum mechanical calculations for the QM subsystem. To address this issue, a reaction path potential energy surface is developed here for statistical mechanics and dynamics simulation of chemical reactions in enzymes and other complex systems. The reaction path potential follows the ideas from the reaction path Hamiltonian of Miller, Handy and Adams for gas phase chemical reactions but is designed specifically for large systems that are described with combined ab initio quantum mechanical and molecular mechanical methods. The reaction path potential is an analytical energy expression of the combined quantum mechanical and molecular mechanical potential energy along the minimum energy path. An expansion around the minimum energy path is made in both the nuclear and the electronic degrees of freedom for the QM subsystem internal energy, while the energy of the subsystem described with MM remains unchanged from that in the combined quantum mechanical and molecular mechanical expression and the electrostatic interaction between the QM and MM subsystems is described as the interaction of the MM charges with the QM charges. The QM charges are polarizable in response to the changes in both the MM and the QM degrees of freedom through a new response kernel developed in the present work. The input data for constructing the reaction path potential are energies, vibrational frequencies, and electron density response properties of the QM subsystem along the minimum energy path, all of which can be obtained from the combined quantum mechanical and molecular mechanical calculations. Once constructed, it costs much less for its evaluation. Thus, the reaction path potential provides a potential energy surface for rigorous statistical mechanics and reaction dynamics calculations of complex systems. As an example, the method is applied to the statistical mechanical calculations for the potential of mean force of the chemical reaction in triosephosphate isomerase.     

Importance of accurate charges in molecular docking: quantum mechanical/molecular mechanical (QM/MM) approach

The extent to which accuracy of electric charges plays a role in protein-ligand docking is investigated through development of a docking algorithm, which incorporates quantum mechanical/molecular mechanical (QM/MM) calculations. In this algorithm, fixed charges of ligands obtained from force field parameterization are replaced by QM/MM calculations in the protein environment, treating only the ligands as the quantum region. The algorithm is tested on a set of 40 cocrystallized structures taken from the Protein Data Bank (PDB) and provides strong evidence that use of nonfixed charges is important. An algorithm, dubbed "Survival of the Fittest" (SOF) algorithm, is implemented to incorporate QM/MM charge calculations without any prior knowledge of native structures of the complexes. Using an iterative protocol, this algorithm is able in many cases to converge to a nativelike structure in systems where redocking of the ligand using a standard fixed charge force field exhibits nontrivial errors. The results demonstrate that polarization effects can play a significant role in determining the structures of protein-ligand complexes, and provide a promising start towards the development of more accurate docking methods for lead optimization applications.