Semiempirical Quantum Mechanical Methods Research Articles

H-Bonding Cooperativity Effects in Amyloids: Quantum Mechanical and Molecular Mechanics Study

Abstract The cooperativity effects have been evaluated on three model systems, the formamide, (formylamino)acetamide and amyloidic-layer oligomers with an increasing size of the monomer units (6, 13 and 214 atoms). In the last model, each layer is a dimer of the amino-acid sequence GNNQQNY in one-letter amino-acid abbreviations. The series of oligomers for each model system of up to six monomers have been constructed. For the calculation of the strength of a particular H-bond formed between various sub-oligomers within an oligomer, different wave function, density functional and semi-empirical quantum mechanical methods as well as empirical force fields have been used. Semi-empirical methods are found to be a reasonable compromise between accuracy and computational cost. These methods are able to describe the cooperativity effects with an accuracy almost comparable to that of the ab initio methods. On the contrary, the empirical force-field methods for all of the model systems mostly failed to describe the H-bonding cooperativity effects properly. Based on the results obtained in this work, we recommend using semi-empirical methods. For the systems where this is impossible, we agree to use polarizable force fields with some reservations. Generally, the more flexible the oligomer chain is (the less steric the repulsion or rigid motifs are), the larger the cooperativity that can be achieved. With the increasing number of monomers in a sequence connected via H-bonds, the cooperativity effects appear to be growing, but relatively soon (at 3–4 monomer units) they tend to become saturated.

Transferable scoring function based on semiempirical quantum mechanical PM6-DH2 method: CDK2 with 15 structurally diverse inhibitors

A semiempirical quantum mechanical PM6-DH2 method accurately covering the dispersion interaction and H-bonding was used to score fifteen structurally diverse CDK2 inhibitors. The geometries of all the complexes were taken from the X-ray structures and were reoptimised by the PM6-DH2 method in continuum water. The total scoring function was constructed as an estimate of the binding free energy, i.e., as a sum of the interaction enthalpy, interaction entropy and the corrections for the inhibitor desolvation and deformation energies. The applied scoring function contains a clear thermodynamical terms and does not involve any adjustable empirical parameter. The best correlations with the experimental inhibition constants (ln K (i)) were found for bare interaction enthalpy (r (2)=0.87) and interaction enthalpy corrected for ligand desolvation and deformation energies (r (2)=0.77); when the entropic term was considered, however, the correlation becomes worse but still acceptable (r (2)=0.52). The resulting correlation based on the PM6-DH2 scoring function is better than previously published function based on various docking/scoring, SAR studies or advanced QM/MM approach, however, the robustness is limited by number of available experimental data used in the correlation. Since a very similar correlation between the experimental and theoretical results was found also for a different system of the HIV-1 protease, the suggested scoring function based on the PM6-DH2 method seems to be applicable in drug design, even if diverse protein-ligand complexes have to be ranked.

Use of Artificial Neural Network for a QSAR Study on Neurotrophic Activities of N-p-Tolyl/phenylsulfonyl L-Amino Acid Thiolester Derivatives

The objective of the present work was to use artificial neural network to study the quantitative structure-activity relationship (QSAR) of the protective effects of N-p-tolyl/phenylsulfonyl L-amino acid thiolester derivatives on anoxic damage of rat pheochromocytoma (PC12) cells. Five molecular parameters of these target compounds, including heat of formation, total energy, dipole moment, the energy of the highest occupied molecular orbital and the energy of the lowest unoccupied molecular orbital, were calculated with the PM6 semi-empirical quantum mechanical method. A multilayer feed-forward (MLFF) network with back-propagation (BP) learning was employed in the present work with the molecular parameters as inputs and neurotrophic activities as outputs. Results showed that the neural network can provide a good prediction of neurotrophic activity and may be useful for predicting the bioactivity of new compounds of similar class.

Third-Generation Hydrogen-Bonding Corrections for Semiempirical QM Methods and Force Fields

Computational modeling of biological systems is a rapidly evolving field that calls for methods that are able to allow for extensive sampling with systems consisting of thousands of atoms. Semiempirical quantum chemical (SE) methods are a promising tool to aid with this, but the rather bad performance of standard SE methods for noncovalent interactions is clearly a limiting factor. Enhancing SE methods with empirical corrections for dispersion and hydrogen-bonding interactions was found to be a big improvement, but for the hydrogen-bonding corrections the drawback of breaking down in the case of substantial changes to the hydrogen bond, e.g., proton transfer, posed a serious limitation for its general applicability. This work presents a further improved hydrogen-bonding correction that can be generally included in parameter fitting procedures, as it does not suffer from the conceptual flaws of previous approaches: hydrogen bonds are now treated as an interaction term between electronegative acceptor and donor atoms, “weighted” by a function of the position of H atoms between them, and multiplied with a damping function to correct the short- and long-range behavior. The performance of the new approach is evaluated for PM6, AM1, OM3, and SCC-DFTB as well as several force-field (FF) methods for a number of standard benchmark sets with hydrogen-bonded systems. The new approach is found to reach the same accuracy as the second-generation hydrogen-bonding correction with less parameters, while it avoids among other issues the conceptual problem with electronic structure changes. SE methods augmented this way reach the accuracy of DFT-D approaches for a large number of cases investigated, while still being about 3 orders of magnitude faster. Moreover, the new correction scheme is transferable also to FF methods that were shown to have serious problems with hydrogen-bonding interactions.

A Reliable Docking/Scoring Scheme Based on the Semiempirical Quantum Mechanical PM6-DH2 Method Accurately Covering Dispersion and H-Bonding: HIV-1 Protease with 22 Ligands

In this study, we introduce a fast and reliable rescoring scheme for docked complexes based on a semiempirical quantum mechanical PM6-DH2 method. The method utilizes a PM6-based Hamiltonian with corrections for dispersion energy and hydrogen bonds. The total score is constructed as the sum of the PM6-DH2 interaction enthalpy, the empirical force field (AMBER) interaction entropy, and the sum of the deformation (PM6-DH2, SMD) and the desolvation (SMD) energies of the ligand. The main advantage of the procedure is the fact that we do not add any empirical parameter for either an individual component of the total score or an individual protein-ligand complex. This rescoring method is applied to a very challenging system, namely, the HIV-1 protease with a set of ligands. As opposed to the conventional DOCK procedure, the PM6-DH2 rescoring based on all of the terms distinguishes between binders and nonbinders and provides a reliable correlation of the theoretical and experimental binding free energies. Such a dramatic improvement, resulting from the PM6-DH2 rescoring of all the complexes, provides a valuable yet inexpensive tool for rational drug discovery and de novo ligand design.

A density functional theory study of the atomic structure, formation energy, and vibrational properties of nitrogen-vacancy-oxygen defects in silicon

The atomic structure, energy, stability, vibrational spectra, and infrared absorption intensities of major intrinsic nitrogen-related defects in nitrogen doped silicon crystals have been investigated using ab initio density functional theory and semi-empirical quantum mechanics methods. The defects that are of interest are nitrogen-vacancy-oxygen complexes which are believed to affect oxygen precipitation and void formation as well as nitrogen concentration measurement in nitrogen-doped silicon. Several chemical reactions involving nitrogen, Si vacancies and oxygen interstitial have been studied. After relaxation, the local vibrational modes of each complex are calculated within the harmonic oscillator approximation and the infrared absorption intensities are evaluated from the dipole moment derivatives. By cross correlating the stability and the infrared active lines of the defect, and taking into consideration the symmetry group of each complex, we were able to emphasize which nitrogen related complexes are likely to control the oxygen precipitation and voids formation and to assert a new calibration relationship for nitrogen concentration measurement in nitrogen doped Czochralski and float zone silicon wafers.

Less is more when simulating unsulfated glycosaminoglycan 3D‐structure: Comparison of GLYCAM06/TIP3P, PM3‐CARB1/TIP3P, and SCC‐DFTB‐D/TIP3P predictions with experiment

The 3D-structure of extracellular matrix glycosaminoglycans is central to function, but is currently poorly understood. Resolving this will provide insight into their heterogeneous biological roles and help to realize their significant therapeutic potential. Glycosaminoglycan chemical isoforms are too numerous to study experimentally and simulation provides a tractable alternative. However, best practice for accurate calculation of glycosaminoglycan 3D-structure within biologically relevant nanosecond timescales is uncertain. Here, we evaluate the ability of three potentials to reproduce experimentally observed glycosaminoglycan monosaccharide puckering, disaccharide 3D-conformation, and characteristic solvent interactions. Temporal dynamics of unsulfated chondroitin, chondroitin-4-sulfate, and hyaluronan β(1→3) disaccharides were simulated within TIP3P explicit solvent unrestrained for 20 ns using the GLYCAM06 force-field and two semi-empirical quantum mechanics methods, PM3-CARB1 and SCC-DFTB-D (both within a hybrid QM/MM formalism). Comparison of calculated and experimental properties (vicinal couplings, nuclear Overhauser enhancements, and glycosidic linkage geometries) showed that the carbohydrate-specific parameterization of PM3-CARB1 imparted quantifiable benefits on monosaccharide puckering and that the SCC-DFTB-D method (including an empirical correction for dispersion) best modeled the effects of hexosamine 4-sulfation. However, paradoxically, the most approximate approach (GLYCAM06/TIP3P) was the best at predicting monosaccharide puckering, 3D-conformation, and solvent interactions. Our data contribute to the debate and emerging consensus on the relative performance of these levels of theory for biological molecules.

Computational alanine scanning with linear scaling semiempirical quantum mechanical methods

Alanine scanning is a powerful experimental tool for understanding the key interactions in protein-protein interfaces. Linear scaling semiempirical quantum mechanical calculations are now sufficiently fast and robust to allow meaningful calculations on large systems such as proteins, RNA and DNA. In particular, they have proven useful in understanding protein-ligand interactions. Here we ask the question: can these linear scaling quantum mechanical methods developed for protein-ligand scoring be useful for computational alanine scanning? To answer this question, we assembled 15 protein-protein complexes with available crystal structures and sufficient alanine scanning data. In all, the data set contains Delta Delta Gs for 400 single point alanine mutations of these 15 complexes. We show that with only one adjusted parameter the quantum mechanics-based methods outperform both buried accessible surface area and a potential of mean force and compare favorably to a variety of published empirical methods. Finally, we closely examined the outliers in the data set and discuss some of the challenges that arise from this examination.

Quantitative structure-activity relationship (QSAR) analysis of cationic complexes of heart perfusion imaging agents and subsequent proposition of two different uptake mechanisms.

Some physicochemical and quantum-chemical discriptors of two series of cationic complexes of heart perfusion imaging agents ([(99m)Tc(I)(NO)Cl(PL)(2)](+) and [(99m)Tc-Mine](+) series) have been obtained using a semi-empirical quantum mechanics method - ZINDO/1. Quantitative structure-activity relationships (QSARs) between these descriptors and heart uptake were investigated by multiple linear regression analysis method, as the result of which, several equations were obtained. Fairly complete new heart uptake mechanisms, redox mechanism for [(99m)Tc(I)(NO)Cl(PL)(2)](+) series and passively transport mechanism for [(99m)Tc-Mine](+) series are proposed based on the results shown in the equations.

Determination of side‐chain‐rotamer and side‐chain and backbone virtual‐bond‐stretching potentials of mean force from AM1 energy surfaces of terminally‐blocked amino‐acid residues, for coarse‐grained simulations of protein structure and folding. I. The method

In this and the accompanying article, we report the development of new physics-based side-chain-rotamer and virtual-bond-deformation potentials which now replace the respective statistical potentials used so far in our physics-based united-reside UNRES force field for large-scale simulations of protein structure and dynamics. In this article, we describe the methodology for determining the corresponding potentials of mean force (PMF's) from the energy surfaces of terminally-blocked amino-acid residues calculated with the AM1 quantum-mechanical semiempirical method. The approach is based on minimization of the AM1 energy for fixed values of the angles lambda for rotation of the peptide groups about the C(alpha)...C(alpha) virtual bonds, and for fixed values of the side-chain dihedral angles chi, which formed a multidimensional grid. A harmonic-approximation approach was developed to extrapolate from the energy at a given grid point to other points of the conformational space to compute the respective contributions to the PMF. To test the applicability of the harmonic approximation, the rotamer PMF's of alanine and valine obtained with this approach have been compared with those obtained by using a Metropolis Monte Carlo method. The PMF surfaces computed with the harmonic approximation are more rugged and have more pronounced minima than the MC-calculated surfaces but the harmonic-approximation- and MC-calculated PMF values are linearly correlated. The potentials derived with the harmonic approximation are, therefore, appropriate for UNRES for which the weights (scaling factors) of the energy terms are determined by force-field optimization for foldability.

Finite-temperature effects in enzymatic reactions — Insights from QM/MM free-energy simulations

We report potential-energy and free-energy data for three enzymatic reactions: carbon–halogen bond formation in fluorinase, hydrogen abstraction from camphor in cytochrome P450cam, and chorismate-to-prephenate Claisen rearrangement in chorismate mutase. The results were obtained by combined quantum mechanics/molecular mechanics (QM/MM) optimizations and two types of QM/MM free-energy simulations (free-energy perturbation and umbrella sampling) using semi-empirical or density-functional QM methods. Based on these results and our previously published free-energy data on electrophilic substitution in para-hydroxybenzoate hydroxylase, we discuss the importance of finite-temperature effects in the chemical step of enzyme reactions. We find that the entropic contribution to the activation barrier is generally rather small, usually of the order of 5 kJ mol–1 or less, consistent with the notion that enzymes bind and pre-organize the reactants in the active site. A somewhat larger entropic contribution is encountered in the case of chorismate mutase where the pericyclic transition state is intrinsically more rigid than the chorismate reactant (also in the enzyme). The present results suggest that barriers from QM/MM geometry optimization may often be close to free-energy barriers for the chemical step in enzymatic reactions.

Application of the PM6 semi-empirical method to modeling proteins enhances docking accuracy of AutoDock.

BackgroundMolecular docking methods are commonly used for predicting binding modes and energies of ligands to proteins. For accurate complex geometry and binding energy estimation, an appropriate method for calculating partial charges is essential. AutoDockTools software, the interface for preparing input files for one of the most widely used docking programs AutoDock 4, utilizes the Gasteiger partial charge calculation method for both protein and ligand charge calculation. However, it has already been shown that more accurate partial charge calculation - and as a consequence, more accurate docking- can be achieved by using quantum chemical methods. For docking calculations quantum chemical partial charge calculation as a routine was only used for ligands so far. The newly developed Mozyme function of MOPAC2009 allows fast partial charge calculation of proteins by quantum mechanical semi-empirical methods. Thus, in the current study, the effect of semi-empirical quantum-mechanical partial charge calculation on docking accuracy could be investigated.ResultsThe docking accuracy of AutoDock 4 using the original AutoDock scoring function was investigated on a set of 53 protein ligand complexes using Gasteiger and PM6 partial charge calculation methods. This has enabled us to compare the effect of the partial charge calculation method on docking accuracy utilizing AutoDock 4 software. Our results showed that the docking accuracy in regard to complex geometry (docking result defined as accurate when the RMSD of the first rank docking result complex is within 2 Å of the experimentally determined X-ray structure) significantly increased when partial charges of the ligands and proteins were calculated with the semi-empirical PM6 method.Out of the 53 complexes analyzed in the course of our study, the geometry of 42 complexes were accurately calculated using PM6 partial charges, while the use of Gasteiger charges resulted in only 28 accurate geometries. The binding affinity estimation was not influenced by the partial charge calculation method - for more accurate binding affinity prediction development of a new scoring function for AutoDock is needed.ConclusionOur results demonstrate that the accuracy of determination of complex geometry using AutoDock 4 for docking calculation greatly increases with the use of quantum chemical partial charge calculation on both the ligands and proteins.

Kinetics and mechanism of elimination of ethyl acetate in the gas phase: A theoretical study

Using the PM3 semi-empirical quantum mechanical molecular orbital method, a procedure was devised to study the gas phase pyrolytic reaction of ethyl acetate in order to gain a deeper insight into both its kinetics and mechanism. By considering the involvement of formal charges and geometrical changes in the activation, a mechanism was proposed in which a pre-equilibrium of acidic proton transfer is followed by the rate limiting bond polarization of C-O bond in a cyclic transition state. The reactions involve a non-synchronous break in the b-carbon-hydrogen and the a-ether oxygen bonds through a six-centred transition state. The results obtained showed that the rate constant and the computed Arrhenius parameters compare well with the experimental values in the literature. Key words: Kinetics, unimolecular elimination, semi-empirical calculation, MOPAC, transition state structure.

On the Structural Analysis and Electronic Properties of Chitosan/Hydroxyapatite Interaction

The interaction between chitosan and hydroxyapatite is discussed in terms the electronic properties using semiempirical PM5 quantum mechanical method. Furthermore, B3LYP/3-21G ∗∗ model shows comparable vibrational frequencies as compared with FTIR frequencies. Chitosan interacts physically through its hydrogen bonding with OH − ,C a 2+ and PO 3− 4 of hydroxyapatite. Electronic properties indicate that no charge transfer and no ionization as a result of the proposed interactions. However a decrease in HOMO/LUMO took place corresponding to chitosan/hydroxyapatite interactions. The present modeling work postulate that stable blends are obtained in terms the calculated thermodynamic parameters. The increased total dipole moment and decreased band gap energies dedicate these blends for many biological applications; where their interaction with the surrounding biological system is needed with minimal change in the chemical and/or electrical properties to ensure biocomptability.

Theoretical investigation of a proposed [HIS 175-ASP 235-TRP 191] proton transfer system in cytochrome c peroxidase

Peroxidases are oxidative metabolizing heme proteins, whereas myoglobin (Mb) with the same heme active site, a protoporphyrin IX with a proximal histidine and a water as axial ligands, belongs to the “globin” heme protein family that functions as reversible oxygen transfer agents. Thus, differences in function of these two heme proteins seems to be modulated by the amino acids surrounding the heme unit, specifically the presence of key polar residues on both the proximal and distal side in CCP that are absent in Mb. In the study presented here, we have investigated the plausibility of a key postulated transformation of the proximal imidazole ligand (His 175) to an imidazolate by proton transfer to a nearby aspartate (Asp 235) absent in Mb. The proton relay system studied included not only models for the His 175 and Asp 235 residues but also for a nearby Trp 191 residue that could also interact with Asp 235 through hydrogen bonding and polarization. Two semiempirical quantum mechanical methods, AM 1 and MNDO/H, with improved capabilities of describing H-bonded systems, were used to calculate the enthalpies of the three tautomeric forms of the proton relay system corresponding to the proton on the His, Asp, and Trp, respectively. These calculations were made for several models of the effect of the iron. Relative tautomeric enthalpies were calculated both with H-atom only optimization, keeping the heavy atoms fixed in their X-ray positions, and additional optimization that allowed the model Asp residue to relax. Transition-state enthalpies for the proton transfer from His to Asp were also calculated. The results of these studies suggest that the crucial postulated proton transfer from His to Asp is energetically favored, but only in the presence of the interaction of the iron with the imidazole ligand. Another stable form of the cluster, with competing proton transfer from the Trp to the Asp, was found only when the Asp position was allowed to optimize. Although no attempt was made in these studies to emulate the protein environment, the results obtained strongly support the hypothesis that an imidazolate could be the predominant species of the peroxidase heme unit.

Conformational analysis and vibrational spectroscopic investigation of 3-phenylpropylamine

The possible stable forms of 3-phenylpropylamine (3-PPA) molecule were experimentally and theoretically studied by infrared and Raman spectroscopy. FT-IR and Raman spectra of 3-PPA were recorded in the regions of 4000–400 cm −1 and 3700–60 cm −1, respectively. The potential energy surface corresponding to the internal rotations of the molecule was investigated by semi-empirical quantum mechanical methods, and appropriate conformers defined with B3LYP hybrid density functional theory method along with the basis sets of different size and type. Results from experimental and theoretical data showed the trans– trans– gauche (TTG) to be the most stable form of a 3-PPA molecule.

Photodynamics in Complex Environments: Ab Initio Multiple Spawning Quantum Mechanical/Molecular Mechanical Dynamics

Our picture of reactions on electronically excited states has evolved considerably in recent years, due to advances in our understanding of points of degeneracy between different electronic states, termed "conical intersections" (CIs). CIs serve as funnels for population transfer between different electronic states, and play a central role in ultrafast photochemistry. Because most practical photochemistry occurs in solution and protein environments, it is important to understand the role complex environments play in directing excited-state dynamics generally, as well as specific environmental effects on CI geometries and energies. In order to model such effects, we employ the full multiple spawning (FMS) method for multistate quantum dynamics, together with hybrid quantum mechanical/molecular mechanical (QM/MM) potential energy surfaces using both semiempirical and ab initio QM methods. In this article, we present an overview of these methods, and a comparison of the excited-state dynamics of several biological chromophores in solvent and protein environments. Aqueous solvation increases the rate of quenching to the ground state for both the photoactive yellow protein (PYP) and green fluorescent protein (GFP) chromophores, apparently by energetic stabilization of their respective CIs. In contrast, solvation in methanol retards the quenching process of the retinal protonated Schiff base (RPSB), the rhodopsin chromophore. Protein environments serve to direct the excited-state dynamics, leading to higher quantum yields and enhanced reaction selectivity.

Direct and Indirect Quantum Mechanical QSPR Hildebrand Solubility Parameter Models

AbstractThe objectives of this study were to develop Quantitative Structure–Property Relationship (QSPR) models to predict Hildebrand solubility parameters (δt). The study investigated direct δt prediction by QSPR and indirect δt calculation from QSPR‐predicted enthalpy of vaporization values. Molecular ground‐state minimum energy conformations were identified and optimized using the AM1 semiempirical Quantum Mechanical (QM) method. Predictive multiple linear regression models were derived correlating training set experimental solubility parameters or enthalpies of vaporization with descriptors obtained from the QM calculations. A four‐descriptor Hildebrand total solubility parameter regression equation was developed where R2=0.97, R$\rm{ {_{adj}^{2}}}$=0.97, F=461.5, s2=0.53, and Root Mean Square Error (RMSE)=0.69. A four‐descriptor QSPR model to predict enthalpies of vaporization (ΔHvap−kJ/mol) was constructed where R2=0.96, R$\rm{ {_{adj}^{2}}}$=0.96, F=230.3, s2=4.75, and RMSE=2.04. δt calculations from ΔHvap correlated well with literature δt , where R2=0.96. Both of these models are statistically significant as well as predictive. The direct and indirect δt models developed here compare favorably with liquid solubility parameter estimation accuracies (10%) reported by Hoftyzer–Van Krevelen and Hoy. These methods are useful for determining the miscibility of small organic molecules, an important consideration when formulating polymer blends.

Development of quantitative structure–property relationships for predictive modeling and design of energetic materials

A quantitative structure–property relationship (QSPR) based on the AM1 semiempirical quantum mechanical method was derived using the program, CODESSA, to describe published drop height impact sensitivities for 227 nitroorganic compounds. An eight-descriptor correlation equation having R 2 = 0.8141 was obtained through a robust least median squares regression. The resulting model is the most comprehensive and systematic quantum mechanically derived QSPR for energetic materials of those that have been published. The predictive capability of the model is also presented and discussed.

QM–MM interactions in simulations of liquid water using combined semi-empirical/classical Hamiltonians

Well-established semi-empirical quantum-mechanical methods such as AM1, PM3 and MNDO poorly describe hydrogen-bonding interactions. The recently developed OM1, OM2 and OM3 methods, which include explicit corrections in the one-electron terms of the Hamiltonian to counteract for the neglect of orthogonalization effects, show an improved description of hydrogen bonding. In the current work we compare the performance of the OMx models on the one hand and the AM1, PM3 and MNDO methods (as well as the SCC-DFTB method) on the other when used in combination with a classical force field in QM/MM calculations on a water dimer in the gas phase, and in QM/MM simulations of a QM water 'solute' in liquid MM water. It is found that when using the OMx methods to describe the QM water molecule, values for QM-MM interaction energies and the molecular dipole moment of the QM solute are significantly closer to experiment than when using the other semi-empirical methods. In addition, the compatibility of OM3 with the classical Hamiltonian improves upon explicitly including electronic polarization in the MM subsystem.