NMR chemical shifts of the rhodopsin chromophore in the dark state and in bathorhodopsin: a hybrid QM/MM molecular dynamics study

We investigate nuclear magnetic resonance (NMR) parameters of the rhodopsin chromophore in the dark state of the protein and in the early photointermediate bathorhodopsin via first-principles molecular dynamics simulations and NMR chemical shift calculations in a hybrid quantum/classical (QM/MM) framework. NMR parameters are particularly sensitive to structural properties and to the chemical environment, which allows us to address different questions about the retinal chromophore in situ. Our calculations show that both the 13C and the 1H NMR chemical shifts are rather insensitive to the protonation state of Glu181, an ionizable amino acid side chain located in the vicinity of the isomerizing 11-cis bond. Thus, other techniques should be better suited to establish its protonation state. The calculated chemical shifts for bathorhodopsin further support our previously published theoretical structure, which is in very good agreement with more recent X-ray data.     

Quantum mechanics/molecular mechanics electrostatic embedding with continuous and discrete functions

A quantum mechanics/molecular mechanics (QM/MM) implementation that uses the Gaussian electrostatic model (GEM) as the MM force field is presented. GEM relies on the reproduction of electronic density by using auxiliary basis sets to calculate each component of the intermolecular interaction. This hybrid method has been used, along with a conventional QM/MM (point charges) method, to determine the polarization on the QM subsystem by the MM environment in QM/MM calculations on 10 individual H(2)O dimers and a Mg(2+)-H(2)O dimer. We observe that GEM gives the correct polarization response in cases when the MM fragment has a small charge, while the point charges produce significant over-polarization of the QM subsystem and in several cases present an opposite sign for the polarization contribution. In the case when a large charge is located in the MM subsystem, for example, the Mg(2+) ion, the opposite is observed at small distances. However, this is overcome by the use of a damped Hermite charge, which provides the correct polarization response.     

Structure of the enzyme-substrate complex for guanosine triphosphate hydrolysis by elongation factor EF-Tu: Comparison of quantum mechanics/molecular mechanics and molecular dynamics results

The equilibrium geometric configurations of the enzyme-substrate complex for guanosine triphosphate hydrolysis by elongation factor EF-Tu calculated using two theoretical approaches, a combined quantum mechanics/molecular mechanics (QM/MM) method and a molecular dynamics method, are compared. The reaction complex geometry determined by the QM/MM method is consistent with the accepted reaction mechanism, whereas, in the enzyme-substrate structure predicted by the molecular dynamics method with the CHARMM force field, the relative positions of the nucleophilic reagent (water molecules) and the base (a histidine side chain) do not correspond to the optimal reagent arrangement.     

Ground-state structures and vertical excitations for the kindling fluorescent protein asFP595

Geometry configurations of a large fraction of the kindling fluorescent protein asFP595 around the chromophore region were optimized by using the effective fragment potential quantum mechanical-molecular mechanical (QM/MM) method. The initial coordinates of heavy atoms were taken from the structure from the Protein Data Bank archive corresponding to the dark-adapted state of the Ala143 --> Gly mutant of asFP595. Optimization of geometry parameters was performed for all internal coordinates in the QM part composed of the chromophore unit and the side chains of His197, Glu215, and Arg92 as well as for positions of effective fragments constituting the MMpart. The structures corresponding to the anion trans, anion cis, and zwitterion trans moieties were considered among various alternatives for the chromophore unit inside the protein matrix. The QM/MM simulations show that the protein environment provides stabilization for the trans-zwitterion isomer compared to the gas-phase conditions. By using the multiconfigurational CASSCF and the time-dependent density functional theory calculations, we estimated positions of spectral bands corresponding to vertical S(0)-S(1) transitions. The results of simulations support the assumption that the dark state of asFP595 corresponds to the anionic or zwitterionic trans-conformation, while the kindled state corresponds to the anionic cis-conformation.     

Protein/ligand binding free energies calculated with quantum mechanics/molecular mechanics

The calculation of binding affinities for flexible ligands has hitherto required the availability of reliable molecular mechanics parameters for the ligands, a restriction that can in principle be lifted by using a mixed quantum mechanics/molecular mechanics (QM/MM) representation in which the ligand is treated quantum mechanically. The feasibility of this approach is evaluated here, combining QM/MM with the Poisson-Boltzmann/surface area model of continuum solvation and testing the method on a set of 47 benzamidine derivatives binding to trypsin. The experimental range of the absolute binding energy (DeltaG = -3.9 to -7.6 kcal/mol) is reproduced well, with a root-mean-square (RMS) error of 1.2 kcal/mol. When QM/MM is applied without reoptimization to the very different ligands of FK506 binding protein the RMS error is only 0.7 kcal/mol. The results show that QM/MM is a promising new avenue for automated docking and scoring of flexible ligands. Suggestions are made for further improvements in accuracy.     

Computational characterization of reaction intermediates in the photocycle of the sensory domain of the AppA blue light photoreceptor

The AppA protein with the BLUF (blue light using flavin adenine dinucleotide) domain is a blue light photoreceptor that cycle between dark-adapted and light-induced functional states. We characterized possible reaction intermediates in the photocycle of AppA BLUF. Molecular dynamics (MD), quantum chemical and quantum mechanical-molecular mechanical (QM/MM) calculations were carried out to describe several stable structures of a molecular system modeling the protein. The coordinates of heavy atoms from the crystal structure (PDB code 2IYG) of the protein in the dark state served as starting point for 10 ns MD simulations. Representative MD frames were used in QM(B3LYP/cc-pVDZ)/MM(AMBER) calculations to locate minimum energy configurations of the model system. Vertical electronic excitation energies were estimated for the molecular clusters comprising the quantum subsystems of the QM/MM optimized structures using the SOS-CIS(D) quantum chemistry method. Computational results support the occurrence of photoreaction intermediates that are characterized by spectral absorption bands between those of the dark and light states. They agree with crystal structures of reaction intermediates (PDB code 2IYI) observed in the AppA BLUF domain. Transformations of the Gln63 side chain stimulated by photo-excitation and performed with the assistance of the chromophore and the Met106 side chain are responsible for these intermediates.     

Exploring the molecular mechanism for color distinction in humans

We examine here the role of the red, green, and blue human opsin structures in modulating the absorption properties of 11-cis-retinal bonded to the protein via a protonated Schiff base (PSB). We built the three-dimensional structures of the human red, green, and blue opsins using homology modeling techniques with the crystal structure of bovine rhodopsin as the template. We then used quantum mechanics (QM) combined with molecular mechanics (MM) (denoted as QM/MM) techniques in conjunction with molecular dynamics to determine how the room temperature molecular structures of the three human color opsin proteins modulate the absorption frequency of the same bound 11-cis-retinal chromophore to account for the differences in the observed absorption spectra. We find that the conformational twisting of the 11-cis-retinal PSB plays an important role in the green to blue opsin shift, whereas the dipolar side chains in the binding pocket play a surprising role of red-shifting the blue opsin with respect to the green opsin, as a fine adjustment to the opsin shift. The dipolar side chains play a large role in the opsin shift from red to green.     

Quantum mechanics/molecular mechanics minimum free-energy path for accurate reaction energetics in solution and enzymes: sequential sampling and optimization on the potential of mean force surface

To accurately determine the reaction path and its energetics for enzymatic and solution-phase reactions, we present a sequential sampling and optimization approach that greatly enhances the efficiency of the ab initio quantum mechanics/molecular mechanics minimum free-energy path (QM/MM-MFEP) method. In the QM/MM-MFEP method, the thermodynamics of a complex reaction system is described by the potential of mean force (PMF) surface of the quantum mechanical (QM) subsystem with a small number of degrees of freedom, somewhat like describing a reaction process in the gas phase. The main computational cost of the QM/MM-MFEP method comes from the statistical sampling of conformations of the molecular mechanical (MM) subsystem required for the calculation of the QM PMF and its gradient. In our new sequential sampling and optimization approach, we aim to reduce the amount of MM sampling while still retaining the accuracy of the results by first carrying out MM phase-space sampling and then optimizing the QM subsystem in the fixed-size ensemble of MM conformations. The resulting QM optimized structures are then used to obtain more accurate sampling of the MM subsystem. This process of sequential MM sampling and QM optimization is iterated until convergence. The use of a fixed-size, finite MM conformational ensemble enables the precise evaluation of the QM potential of mean force and its gradient within the ensemble, thus circumventing the challenges associated with statistical averaging and significantly speeding up the convergence of the optimization process. To further improve the accuracy of the QM/MM-MFEP method, the reaction path potential method developed by Lu and Yang [Z. Lu and W. Yang, J. Chem. Phys. 121, 89 (2004)] is employed to describe the QM/MM electrostatic interactions in an approximate yet accurate way with a computational cost that is comparable to classical MM simulations. The new method was successfully applied to two example reaction processes, the classical SN2 reaction of Cl-+CH3Cl in solution and the second proton transfer step of the reaction catalyzed by the enzyme 4-oxalocrotonate tautomerase. The activation free energies calculated with this new sequential sampling and optimization approach to the QM/MM-MFEP method agree well with results from other simulation approaches such as the umbrella sampling technique with direct QM/MM dynamics sampling, demonstrating the accuracy of the iterative QM/MM-MFEP method.     

Concerted Asynchronous Hula‐Twist Photoisomerization in the S65T/H148D Mutant of Green Fluorescent Protein

Fluorescence emission of wild‐type green fluorescent protein (GFP) is lost in the S65T mutant, but partly recovered in the S65T/H148D double mutant. These experimental findings are rationalized by a combined quantum mechanics/molecular mechanics (QM/MM) study at the QM(CASPT2//CASSCF)/AMBER level. A barrierless excited‐state proton transfer, which is exclusively driven by the Asp148 residue introduced in the double mutant, is responsible for the ultrafast formation of the anionic fluorescent state, which can be deactivated through a concerted asynchronous hula‐twist photoisomerization. This causes the lower fluorescence quantum yield in S65T/H148D compared to wild‐type GFP. Hydrogen out‐of‐plane motion plays an important role in the deactivation of the S65T/H148D fluorescent state.     

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.     

Calculation of wave‐functions with frozen orbitals in mixed quantum mechanics/molecular mechanics methods. II. Application of the local basis equation

The application of the local basis equation (Ferenczy and Adams, J. Chem. Phys. 2009 , 130, 134108) in mixed quantum mechanics/molecular mechanics (QM/MM) and quantum mechanics/quantum mechanics (QM/QM) methods is investigated. This equation is suitable to derive local basis nonorthogonal orbitals that minimize the energy of the system and it exhibits good convergence properties in a self‐consistent field solution. These features make the equation appropriate to be used in mixed QM/MM and QM/QM methods to optimize orbitals in the field of frozen localized orbitals connecting the subsystems. Calculations performed for several properties in divers systems show that the method is robust with various choices of the frozen orbitals and frontier atom properties. With appropriate basis set assignment, it gives results equivalent with those of a related approach [G. G. Ferenczy previous paper in this issue] using the Huzinaga equation. Thus, the local basis equation can be used in mixed QM/MM methods with small size quantum subsystems to calculate properties in good agreement with reference Hartree–Fock–Roothaan results. It is shown that bond charges are not necessary when the local basis equation is applied, although they are required for the self‐consistent field solution of the Huzinaga equation based method. Conversely, the deformation of the wave‐function near to the boundary is observed without bond charges and this has a significant effect on deprotonation energies but a less pronounced effect when the total charge of the system is conserved. The local basis equation can also be used to define a two layer quantum system with nonorthogonal localized orbitals surrounding the central delocalized quantum subsystem. © 2013 Wiley Periodicals, Inc.     

Mechanistic aspects of proton chain transfer: a computational study for the green fluorescent protein chromophore

We explore several models for the ground-state proton chain transfer pathway between the green fluorescent protein chromophore and its surrounding protein matrix, with a view to elucidating mechanistic aspects of this process. We have computed quantum chemically the minimum energy pathways (MEPs) in the ground electronic state for one-, two-, and three-proton models of the chain transfer. There are no stable intermediates for our models, indicating that the proton chain transfer is likely to be a single, concerted kinetic step. However, despite the concerted nature of the overall energy profile, a more detailed analysis of the MEPs reveals clear evidence of sequential movement of protons in the chain. The ground-state proton chain transfer does not appear to be driven by the movement of the phenolic proton off the chromophore onto the neutral water bridge. Rather, this proton is the last of the three protons in the chain to move. We find that the first proton movement is from the bridging Ser205 moiety to the accepting Glu222 group. This is followed by the second proton moving from the bridging water to the Ser205--for our model this is where the barrier occurs. The phenolic proton on the chromophore is hence the last in the chain to move, transferring to a bridging "water" that already has substantial negative charge.     

Conical intersections in solution: formulation, algorithm, and implementation with combined quantum mechanics/molecular mechanics method

The significance of conical intersections in photophysics, photochemistry, and photodissociation of polyatomic molecules in gas phase has been demonstrated by numerous experimental and theoretical studies. Optimization of conical intersections of small- and medium-size molecules in gas phase has currently become a routine optimization process, as it has been implemented in many electronic structure packages. However, optimization of conical intersections of small- and medium-size molecules in solution or macromolecules remains inefficient, even poorly defined, due to large number of degrees of freedom and costly evaluations of gradient difference and nonadiabatic coupling vectors. In this work, based on the sequential quantum mechanics and molecular mechanics (QM/MM) and QM/MM-minimum free energy path methods, we have designed two conical intersection optimization methods for small- and medium-size molecules in solution or macromolecules. The first one is sequential QM conical intersection optimization and MM minimization for potential energy surfaces; the second one is sequential QM conical intersection optimization and MM sampling for potential of mean force surfaces, i.e., free energy surfaces. In such methods, the region where electronic structures change remarkably is placed into the QM subsystem, while the rest of the system is placed into the MM subsystem; thus, dimensionalities of gradient difference and nonadiabatic coupling vectors are decreased due to the relatively small QM subsystem. Furthermore, in comparison with the concurrent optimization scheme, sequential QM conical intersection optimization and MM minimization or sampling reduce the number of evaluations of gradient difference and nonadiabatic coupling vectors because these vectors need to be calculated only when the QM subsystem moves, independent of the MM minimization or sampling. Taken together, costly evaluations of gradient difference and nonadiabatic coupling vectors in solution or macromolecules can be reduced significantly. Test optimizations of conical intersections of cyclopropanone and acetaldehyde in aqueous solution have been carried out successfully.     

Proton storage site in bacteriorhodopsin: new insights from quantum mechanics/molecular mechanics simulations of microscopic pK(a) and infrared spectra

Identifying the group that acts as the proton storage/loading site is a challenging but important problem for understanding the mechanism of proton pumping in biomolecular proton pumps, such as bacteriorhodopsin (bR) and cytochrome c oxidase. Recent experimental studies of bR propelled the idea that the proton storage/release group (PRG) in bR is not an amino acid but a water cluster embedded in the protein. We argue that this idea is at odds with our knowledge of protein electrostatics, since invoking the water cluster as the PRG would require the protein to raise the pK(a) of a hydronium by almost 11 pK(a) units, which is difficult considering known cases of pK(a) shifts in proteins. Our recent quantum mechanics/molecular mechanics (QM/MM) simulations suggested an alternative "intermolecular proton bond" model in which the stored proton is shared between two conserved Glu residues (194 and 204). Here we show that this model leads to microscopic pK(a) values consistent with available experimental data and the functional requirement of a PRG. Extensive QM/MM simulations also show that, independent of a number of technical issues, such as the influence of QM region size, starting X-ray structure, and nuclear quantum effects, the "intermolecular proton bond" model is qualitatively consistent with available spectroscopic data. Potential of mean force calculations show explicitly that the stored proton strongly prefers the pair of Glu residues over the water cluster. The results and analyses help highlight the importance of considering protein electrostatics and provide arguments for why the "intermolecular proton bond" model is likely applicable to the PRG in biomolecular proton pumps in general.     

Computational methods for the study of enzymic reaction mechanisms III: a perturbation plus QM/MM approach for calculating relative free energies of protonation

We describe a coupling parameter, that is, perturbation, approach to effectively create and annihilate atoms in the quantum mechanical Hamiltonian within the closed shell restricted Hartree-Fock formalism. This perturbed quantum mechanical atom (PQA) method is combined with molecular mechanics (MM) methods (PQA/MM) within a molecular dynamics simulation, to model the protein environment (MM region) effects that also make a contribution to the overall free energy change. Using the semiempirical PM3 method to model the QM region, the application of this PQA/MM method is illustrated by calculation of the relative protonation free energy of the conserved OD2 (Asp27) and the N5 (dihydrofolate) proton acceptor sites in the active site of Escherichia coli dihydrofolate reductase (DHFR) with the bound nicotinamide adenine dinucleotide phosphate (NADPH) cofactor. For a number of choices for the QM region, the relative protonation free energy was calculated as the sum of contributions from the QM region and the interaction between the QM and MM regions via the thermodynamic integration (TI) method. The results demonstrate the importance of including the whole substrate molecule in the QM region, and the overall protein (MM) environment in determining the relative stabilities of protonation sites in the enzyme active site. The PQA/MM free energies obtained by TI were also compared with those estimated by a less computationally demanding nonperturbative method based on the linear response approximation (LRA). For some choices of QM region, the total free energies calculated using the LRA method were in very close agreement with the PQA/MM values. However, the QM and QM/MM component free energies were found to differ significantly between the two methods.