QM/MM study of the absorption spectra of DsRed.M1 chromophores

We report geometries and vertical excitation energies for the red and green chromophores of the DsRed.M1 protein in the gas phase and in the solvated protein environment. Geometries are optimized using density functional theory (DFT, B3LYP functional) for the isolated chromophores and combined quantum mechanical/molecular mechanical (QM/MM) methods for the protein (B3LYP/MM). Vertical excitation energies are computed using DFT/MRCI, OM2/MRCI, and TDDFT as QM methods. In the case of the red chromophore, there is a general blue shift in the excitation energies when going from the isolated chromophore to the protein, which is caused both by structural changes and by electrostatic interactions with the environment. For the lowest ππ* transition, these two factors contribute to a similar extent to the overall DFT/MRCI shift of 0.4 eV. An enlargement of the QM region to include active‐site residues does not change the DFT/MRCI excitation energies much. The DFT/MRCI results are closest to experiment for both chromophores. OM2/MRCI and TDDFT overestimate the first vertical excitation energy by 0.3–0.5 and 0.2–0.4 eV, respectively, relative to the experimental or DFT/MRCI values. The experimental gap of 0.35 eV between the lowest ππ* excitation energies of the red (cis‐acylimine) and green (trans‐peptide) forms is well reproduced by DFT/MRCI and TDDFT (0.32 and 0.37 eV, respectively). A histogram spectrum for an equal mixture of the two forms, generated by OM2/MRCI calculations on 450 snapshots along molecular dynamics trajectories, matches the experimental spectrum quite well, with a gap of 0.23 eV and an overall blue shift of about 0.3 eV. DFT/MRCI appears as an attractive choice for calculating excitation energies in fluorescent proteins, without the shortcomings of TDDFT and computationally more affordable than CASSCF‐based approaches. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

QM/MM calculation of solvent effects on absorption spectra of guanine

Electronic spectra of guanine in the gas phase and in water were studied by quantum mechanical/molecular mechanical (QM/MM) methods. Geometries for the excited‐state calculations were extracted from ground‐state molecular dynamics (MD) simulations using the self‐consistent‐charge density functional tight binding (SCC‐DFTB) method for the QM region and the TIP3P force field for the water environment. Theoretical absorption spectra were generated from excitation energies and oscillator strengths calculated for 50 to 500 MD snapshots of guanine in the gas phase (QM) and in solution (QM/MM). The excited‐state calculations used time‐dependent density functional theory (TDDFT) and the DFT‐based multireference configuration interaction (DFT/MRCI) method of Grimme and Waletzke, in combination with two basis sets. Our investigation covered keto‐N7H and keto‐N9H guanine, with particular focus on solvent effects in the low‐energy spectrum of the keto‐N9H tautomer. When compared with the vertical excitation energies of gas‐phase guanine at the optimized DFT (B3LYP/TZVP) geometry, the maxima in the computed solution spectra are shifted by several tenths of an eV. Three effects contribute: the use of SCC‐DFTB‐based rather than B3LYP‐based geometries in the MD snapshots (red shift of ca. 0.1 eV), explicit inclusion of nuclear motion through the MD snapshots (red shift of ca. 0.1 eV), and intrinsic solvent effects (differences in the absorption maxima in the computed gas‐phase and solution spectra, typically ca. 0.1–0.3 eV). A detailed analysis of the results indicates that the intrinsic solvent effects arise both from solvent‐induced structural changes and from electrostatic solute–solvent interactions, the latter being dominant. © 2009 Wiley Periodicals, Inc. J Comput Chem 2010     

Accurate evaluation of the absorption maxima of retinal proteins based on a hybrid QM/MM method

Here we improved our hybrid QM/MM methodology (Houjou et al. J Phys Chem B 2001, 105, 867) for evaluating the absorption maxima of photoreceptor proteins. The renewed method was applied to evaluation of the absorption maxima of several retinal proteins and photoactive yellow protein. The calculated absorption maxima were in good agreement with the corresponding experimental data with a computational error of <10 nm. In addition, our calculations reproduced the experimental gas-phase absorption maxima of model chromophores (protonated all-trans retinal Schiff base and deprotonated thiophenyl-p-coumarate) with the same accuracy. It is expected that our methodology allows for definitive interpretation of the spectral tuning mechanism of retinal proteins.     

pKa calculations in solution and proteins with QM/MM free energy perturbation simulations: a quantitative test of QM/MM protocols

The accuracy of biological simulations depends, in large part, on the treatment of electrostatics. Due to the availability of accurate experimental values, calculation of pKa provides stringent evaluation of computational methods. The generalized solvent boundary potential (GSBP) and Ewald summation electrostatic treatments were recently implemented for combined quantum mechanical and molecular mechanics (QM/MM) simulations by our group. These approaches were tested by calculating pKa shifts due to differences in electronic structure and electrostatic environment; the shifts were determined for a series of small molecules in solution, using various electrostatic treatments, and two residues (His 31, Lys 102) in the M102K T4-lysozyme mutant with large pKa shifts, using the GSBP approach. The calculations utilized a free energy perturbation scheme with the QM/MM potential function involving the self-consistent charge density functional tight binding (SCC-DFTB) and CHARMM as the QM and MM methods, respectively. The study of small molecules demonstrated that inconsistent electrostatic models produced results that were difficult to correct in a robust manner; by contrast, extended electrostatics, GSBP, and Ewald simulations produced consistent results once a bulk solvation contribution was carefully chosen. In addition to the electrostatic treatment, the pKa shifts were also sensitive to the level of the QM method and the scheme of treating QM/MM Coulombic interactions; however, simple perturbative corrections based on SCC-DFTB/CHARMM trajectories and higher level single point energy calculations were found to give satisfactory results. Combining all factors gave a root-mean-square difference of 0.7 pKa units for the relative pKa values of the small molecules compared to experiment. For the residues in the lysozyme, an accurate pKa shift was obtained for His 31 with multiple nanosecond simulations. For Lys 102, however, the pKa shift was estimated to be too large, even after more than 10 nanosecond simulations for each lambda window; the difficulty was due to the significant, but slow, reorganization of the protein and water structure when Lys 102 was protonated. The simulations support that Lys 102 is deprotonated in the X-ray structure and the protein is highly destabilized when this residue is protonated.     

Monitoring biological membrane-potential changes: a CI QM/MM study

In recent decades, new less-invasive, nonlinear optical methods have been proposed and optimized for monitoring fast physiological processes in biological cells. One of these methods allows the action potential (AP) in cardiomyocytes or neurons to be monitored by means of second-harmonic generation (SHG). We now present the first, to our knowledge, simulations of the dependency of the intensity of the second harmonic (I(SHG)) on variations of the transmembrane potential (TMP) in a cardiomyocyte during an action potential (AP). For this, an amphiphilic potential-sensitive styryl dye molecule with nonlinear optical properties was embedded in a dipalmitoylphosphatidylcholine (DPPC) bilayer, replacing one of the phospholipid molecules. External electrical fields with different strengths were applied across the membrane to simulate the AP of a heart-muscle cell. We used a combined classical/quantum mechanical approach to model the structure and the spectroscopic properties of the embedded chromophore. Two 10 ns molecular dynamics (MD) simulations provided input geometries for semiempirical molecular orbital (QM/MM) single-point configuration interaction (CI) calculations, which were used to calculate the wavelengths and oscillator strengths of electronic transitions in the di-8-ANEPPS dye molecule. The results were then used in a sum-over-states treatment to calculate the second-order hyperpolarizability. The square of the hyperpolarizability scales with the intensity of the second harmonic, which is used to monitor the action potentials of cardiomyocytes experimentally. Thus, we computed changes in the intensity of the second harmonic (DeltaI(SHG)) as function of TMP changes. Our results agree well with experimental measurements.     

QM/MM study of the taxadiene synthase mechanism

Combined quantum mechanics/molecular mechanics (QM/MM) calculations were used to investigate the reaction mechanism of taxadiene synthase (TXS). TXS catalyzes the cyclization of geranylgeranyl diphosphate (GGPP) to taxadiene (T) and four minor cyclic products. All these products originate from the deprotonation of carbocation intermediates. The reaction profiles for the conversion of GGPP to T as well as to minor products were calculated for different configurations of relevant TXS carbocation complexes. The QM region was treated at the M06-2X/TZVP level, while the CHARMM27 force field was used to describe the MM region. The QM/MM calculations suggest a reaction pathway for the conversion of GGPP to T, which slightly differs from previous proposals regarding the number of reaction steps and the conformation of the carbocations. The QM/MM results also indicate that the formation of minor products via water-assisted deprotonation of the carbocations is highly exothermic, by about −7 to −23 kcal/mol. Curiously, however, the computed barriers and reaction energies indicate that the formation of some of the minor products is more facile than the formation of T. Thus, the present QM/MM calculations provide detailed insights into possible reaction pathways and into the origin of the promiscuity of TXS, but they do not reproduce the product distribution observed experimentally. © 2019 Wiley Periodicals, Inc.     

The reaction mechanism of hydroxyethylphosphonate dioxygenase: a QM/MM study

By employing ab initio quantum mechanical/molecular mechanical (QM/MM) and molecular dynamics (MD) simulations, we have provided further evidence against the previously proposed hydroperoxylation or hydroxylation mechanism of hydroxyethylphosphonate dioxygenase (HEPD). HEPD employs an interesting catalytic cycle based on concatenated bifurcations. The first bifurcation is based on the abstraction of hydrogen atoms from the substrate, which leads to a distal or proximal hydroperoxo species (Fe-OOH or Fe-(OH)O). The second and the third bifurcations refer to the carbon-carbon bond cleavage reaction. And this is achieved through a tridentate intermediate, or employing a proton-shuttle assisted mechanism, in which the residue Glu(176) or the Fe(IV)=O group serves as a general base. The reaction directions seem to be tunable and show significant environment dependence. This mechanism can provide a comprehensive interpretation for the seemingly contradicting experimental evidences and provide insight into the development of biochemistry and material sciences.     

Electronic absorption spectra of pyridine and nicotine in aqueous solution with a combined molecular dynamics and polarizable QM/MM approach

The electronic absorption spectra of pyridine and nicotine in aqueous solution have been computed using a multistep approach. The computational protocol consists in studying the solute solvation with accurate molecular dynamics simulations, characterizing the hydrogen bond interactions, and calculating electronic transitions for a series of configurations extracted from the molecular dynamics trajectories with a polarizable QM/MM scheme based on the fluctuating charge model. Molecular dynamics simulations and electronic transition calculations have been performed on both pyridine and nicotine. Furthermore, the contributions of solute vibrational effect on electronic absorption spectra have been taken into account in the so called vertical gradient approximation. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

Compound I in heme thiolate enzymes: a comparative QM/MM study

This study directly compares the active species of heme enzymes, so-called Compound I (Cpd I), across the heme-thiolate enzyme family. Thus, sixty-four different Cpd I structures are calculated by hybrid quantum mechanical/molecular mechanical (QM/MM) methods using four different cysteine-ligated heme enzymes (P450(cam), the mutant P450(cam)-L358P, CPO and NOS) with varying QM region sizes in two multiplicities each. The overall result is that these Cpd I species are similar to each other with regard to many characteristic features. Hence, using the more stable CPO Cpd I as a model for P450 Cpd I in experiments should be a reasonable approach. However, systematic differences were also observed, and it is shown that NOS stands out in most comparisons. By analyzing the electrical field generated by the enzyme on the QM region, one can see that (a) the protein exerts a large influence and modifies all the Cpd I species compared with the gas-phase situation and (b) in NOS this field is approximately planar to the heme plane, whereas it is approximately perpendicular in the other enzymes, explaining the deviating results on NOS. The calculations on the P450(cam) mutant L358P show that the effects of removing the hydrogen bond between the heme sulfur and L358 are small at the Cpd I stage. Finally, Mossbauer parameters are calculated for the different Cpd I species, enabling future comparisons with experiments. These results are discussed in the broader context of recent findings of Cpd I species that exhibit large variations in the electronic structure due to the presence of the substrate.     

A QM/MM study on the catalytic mechanism of pyruvate decarboxylase

Pyruvate decarboxylase (PDC) is a typical thiamin diphosphate (ThDP)-dependent enzyme with widespread applications in industry. Though studies regarding the reaction mechanism of PDC have been reported, they are mainly focused on the formation of ThDP ylide and some elementary steps in the catalytic cycle, studies about the whole catalytic cycle of PDC are still not completed. In these previous studies, a major controversy is whether the key active residues (Glu473, Glu50′, Asp27′, His113′, His114′) are protonated or ionized during the reaction. To explore the catalytic mechanism and the role of key residues in the active site, three whole-enzyme models were considered, and the combined QM/MM calculations on the nonoxidative decarboxylation of pyruvate to acetaldehyde catalyzed by PDC were performed. According to our computational results, the fundamental reaction pathways, the complete energy profiles of the whole catalytic cycle, and the specific role of key residues in the common steps were obtained. It is also found that the same residue with different protonation states will lead to different reaction pathways and energy profiles. The mechanism derived from the model in which the residues (Glu473, Glu50′, Asp27′, His113′, His114′) are in their protonated states is most consistent with experimental observations. Therefore, extreme care must be taken when assigning the protonation states in the mechanism study. Because the experimental determination of protonation state is currently difficult, the combined QM/MM method provides an indirect means for determining the active-site protonation state.     

Intermediates in dioxygen activation by methane monooxygenase: a QM/MM study

Protein effects in the activation of dioxygen by methane monooxygenase (MMO) were investigated by using combined QM/MM and broken-symmetry Density Functional Theory (DFT) methods. The effects of a novel empirical scheme recently developed by our group on the relative DFT energies of the various intermediates in the catalytic cycle are investigated. Inclusion of the protein leads to much better agreement between the experimental and computed geometric structures for the reduced form (MMOH(red)). Analysis of the electronic structure of MMOH(red) reveals that the two iron atoms have distinct environments. Different coordination geometries tested for the MMOH(peroxo) intermediate reveal that, in the protein environment, the mu-eta2,eta2 structure is more stable than the others. Our analysis also shows that the protein helps to drive reactants toward products along the reaction path. Furthermore, these results demonstrate the importance of including the protein environment in our models and the usefulness of the QM/MM approach for accurate modeling of enzymatic reactions. A discrepancy remains in our calculation of the Fe-Fe distance in our model of HQ as compared to EXAFS data obtained several years ago, for which we currently do not have an explanation.     

Solvents effects on the mechanism of cellulose hydrolysis: A QM/MM study

This article reports a combined quantum mechanics/molecular mechanics (QM/MM) investigation on the acid hydrolysis of cellulose in water using two different models, cellobiose and a 40‐unit cellulose chain. The explicitly treated solvent molecules strongly influence the conformations, intramolecular hydrogen bonds, and exoanomeric effects in these models. As these features are largely responsible for the barrier to cellulose hydrolysis, the present QM/MM results for the pathways and reaction intermediates in water are expected to be more realistic than those from a former density functional theory (DFT) study with implicit solvent (CPCM). However, in a qualitative sense, there is reasonable agreement between the DFT/CPCM and QM/MM predictions for the reaction mechanism. Differences arise mainly from specific solute–solvent hydrogen bonds that are only captured by QM/MM and not by DFT/CPCM. © 2015 Wiley Periodicals, Inc.     

Quantifying Electronic Effects in QM and QM/MM Biomolecular Modeling with the Fukui Function

Multi-scale quantum-mechanical/molecular-mechanical(QM/MM) and large-scale QM simulation provide valuable insight into enzyme mechanism and structure-property relationships. Analysis of the electron density afforded through these methods can enhance our understanding of how the enzyme environment modulates reactivity at the enzyme active site. From this perspective, tools from conceptual density functional theory to interrogate electron densities can provide added insight into enzyme function. We recently introduced the highly parallelizable Fukui shift analysis(FSA) method, which identifies how frontier states of an active site are altered by the presence of an additional QM residue to identify when QM treatment of a residue is essential as a result of quantum-mechanically affecting the behavior of the active site. We now demonstrate and analyze distance and residue dependence of Fukui function shifts in pairs of residues representing different non-covalent interactions. We also show how the interpretation of the Fukui function as a measure of relative nucleophilicity provides insight into enzymes that carry out S_N2 methyl transfer. The FSA method represents a promising approach for the systematic, unbiased determination of quantum mechanical effects in enzymes and for other complex systems that necessitate multi-scale modeling.     

QM/MM Studies on Cyclodextrin-Alcohol Interaction

The main objective of this study is to provide an insight into the interactions involved during adsorption of the alcohols on β-CD composite nanostructured membrane. Interactions between β-cyclodextrin (β-CD) and alcohols (methanol, ethanol and butanol) are studied using the QM/MM method. Magnitude of interaction energies show that the alcohols are adsorbed on the membrane. In addition, the thermochemical analysis suggests that the formation of these host-guest complexes is enthalpy driven.     

Theoretical insights into the aggregation-induced emission by hydrogen bonding: a QM/MM study

We investigate the excited-state decay processes for the 3-(2-cyano-2- phenylethenyl-Z)-NH-indole (CPEI) in the solid phase through combined quantum mechanics and molecular mechanics (QM/MM) and vibration correlation formalisms for radiative and nonradiative decay rates, coupled with time-dependent density functional theory (TDDFT). By comparing the isolated CPEI molecule and the molecule-in-cluster, we show that the molecular packing through intermolecular hydrogen-bonding interactions can hinder the excited-state nonradiative decay and thus enhance the fluorescence efficiency in the solid phase. Aggregation effect is shown to block the nonradiative decay process through hindering the low-frequency vibration motions. The fluorescence quantum yields for both isolated molecule and aggregation are predicted to be insensitive to temperature due to the hydrogen-bonding nature, and their values at room temperature are consistent with the experiment.     

Chaperoned alchemical free energy simulations: a general method for QM, MM, and QM/MM potentials

A general method for alchemical free energy simulations using QM, MM, and QM/MM potential is developed by introducing "chaperones" to restrain the structures, particularly near the end points. A calculation of the free energy difference between two triazole tautomers in aqueous solution is used to illustrate the method.     

Flexible-boundary QM/MM calculations: II. Partial charge transfer across the QM/MM boundary that passes through a covalent bond

Recently, based on the principle of electronic chemical potential equalization and the principle of charge conservation, we proposed a flexible-boundary scheme that allows both partial charge transfer and self-consistent polarization between the quantum mechanical (QM) and molecular mechanical (MM) subsystems in QM/MM calculations; the scheme was applied to study the atomic charges in selected ion–solvent complexes. In the present contribution, we further extend the flexible-boundary treatment to handle the QM/MM boundary passing through covalent bonds. We find that the flexible-boundary redistributed charge and dipole schemes yield reasonable agreement with full-QM calculations for a number of molecular ions and amino acids with charged side chains. Using the full-QM results as reference, the mean unsigned deviations are computed to be 0.06 e for atomic partial charges of the QM atoms, 0.11 e for the amounts of charge transfer between the QM and MM subsystems, and 0.016 Å for the lengths of the covalent bonds that directly connect the QM and MM subsystems. The results indicate the importance of accounting for partial charge transfer across the QM/MM boundary when the QM subsystems are charged.     

Combined QM/MM study of the opsin shift in bacteriorhodopsin

Combined quantum mechanical and molecular mechanical (QM/MM) calculations and molecular dynamics simulations of bacteriorhodopsin (bR) in the membrane matrix have been carried out to determine the factors that make significant contributions to the opsin shift. We found that both solvation and interactions with the protein significantly shifts the absorption maximum of the retinal protonated Schiff base, but the effects are much more pronounced in polar solvents such as methanol, acetonitrile, and water than in the protein environment. The differential solvatochromic shifts of PSB in methanol and in bR leads to a bathochromic shift of about 1800 cm(-1). Because the combined QM/MM configuration interaction calculation is essentially a point charge model, this contribution is attributed to the extended point-charge model of Honig and Nakanishi. The incorporation of retinal in bR is accompanied by a change in retinal conformation from the 6-s-cis form in solution to the 6-s-trans configuration in bR. The extension of the pi-conjugated system further increases the red-shift by 2400 cm(-1). The remaining factors are due to the change in dispersion interactions. Using an estimate of about 1000 cm(-1) in the dispersion contribution by Houjou et al., we obtained a theoretical opsin shift of 5200 cm(-1) in bR, which is in excellent agreement with the experimental value of 5100 cm(-1). Structural analysis of the PSB binding site revealed the specific interactions that make contributions to the observed opsin shift. The combined QM/MM method used in the present study provides an opportunity to accurately model the photoisomerization and proton transfer reactions in bR.     

Transition structure selectivity in enzyme catalysis: a QM/MM study of chorismate mutase

Two different transition structures (TSs) have been located and characterized for the chorismate conversion to prephenate in Bacillus subtilis chorismate mutase by means of hybrid quantum-mechanical/molecular-mechanical (QM/MM) calculations. GRACE software, combined with an AM1/CHARMM24/TIP3P potential, has been used involving full gradient relaxation of the position of ca. 3300 atoms. These TSs have been connected with their respective reactants and products by the intrinsic reaction coordinate (IRC) procedure carried out in the presence of the protein environment, thus obtaining for the first time a realistic enzymatic reaction path for this reaction. Similar QM/MM computational schemes have been applied to study the chemical reaction solvated by ca. 500 water molecules. Comparison of these results together with gas phase calculations has allowed understanding of the catalytic efficiency of the protein. The enzyme stabilizes one of the TSs (TS_OHout) by means of specific hydrogen bond interactions, while the other TS (TS_OHin) is the preferred one in vacuum and in water. The enzyme TS is effectively more polarized but less dissociative than the corresponding solvent and gas phase TSs. Electrostatic stabilization and an intramolecular charge-transfer process can explain this enzymatically induced change. Our theoretical results provide new information on an important enzymatic transformation and the key factors responsible for efficient selectivity are clarified. Received: 25 March 2000 / Accepted: 7 August 2000 / Published online: 23 November 2000     

Role of structural water molecule in HIV protease-inhibitor complexes: a QM/MM study

Structural water molecule 301 found at the interface of HIV protease-inhibitor complexes function as a hydrogen bond (H-bond) donor to carbonyl groups of the inhibitor as well as H-bond acceptor to amide/amine groups of the flap region of the protease. In this study, six systems of HIV protease-inhibitor complexes were analyzed, which have the presence of this "conserved" structural water molecule using a two-layer QM/MM ONIOM method. The combination of QM/MM and QM method enabled the calculation of strain energies of the bound ligands as well as the determination of their binding energies in the ligand-water and ligand-water-protease complexes. Although the ligand experiences considerable strain in the protein bound structure, the H-bond interactions through the structural water overcomes this strain effect to give a net stability in the range of 16-24 kcal/mol. For instance, in 1HIV system, the strain energy of the ligand was 12.2 kcal/mol, whereas the binding energy associated with the structural water molecule was 20.8 kcal/mol. In most of the cases, the calculated binding energy of structural water molecule showed the same trend as that of the experimental binding free energy values. Further, the classical MD simulations carried out on 1HVL system with and without structural water 301 showed that this conserved water molecule enhances the H-bond dynamics occurring at the Asp-bound active site region of the protease-inhibitor system, and therefore it will have a direct influence on the mechanism of drug action.