Multiobjective evolutionary algorithm with many tables for purely ab initio protein structure prediction

This article focuses on the development of an approach for ab initio protein structure prediction (PSP) without using any earlier knowledge from similar protein structures, as fragment‐based statistics or inference of secondary structures. Such an approach is called purely ab initio prediction. The article shows that well‐designed multiobjective evolutionary algorithms can predict relevant protein structures in a purely ab initio way. One challenge for purely ab initio PSP is the prediction of structures with β‐sheets. To work with such proteins, this research has also developed procedures to efficiently estimate hydrogen bond and solvation contribution energies. Considering van der Waals, electrostatic, hydrogen bond, and solvation contribution energies, the PSP is a problem with four energetic terms to be minimized. Each interaction energy term can be considered an objective of an optimization method. Combinatorial problems with four objectives have been considered too complex for the available multiobjective optimization (MOO) methods. The proposed approach, called “Multiobjective evolutionary algorithms with many tables” (MEAMT), can efficiently deal with four objectives through the combination thereof, performing a more adequate sampling of the objective space. Therefore, this method can better map the promising regions in this space, predicting structures in a purely ab initio way. In other words, MEAMT is an efficient optimization method for MOO, which explores simultaneously the search space as well as the objective space. MEAMT can predict structures with one or two domains with RMSDs comparable to values obtained by recently developed ab initio methods (GAPF_CG, I‐PAES, and Quark) that use different levels of earlier knowledge. © 2013 Wiley Periodicals, Inc.     

Electronic structure of testosterone: A semiempirical and ab initio assessment

Testosterone (17β-hydroxy-4-androsten-3-one) was studied by the semiempirical AM1 and PM3 and ab initio STO-3G^*, 3–21G^*, and 6–31G^* methods. The goals were to compare those methods and to know the electronic structure of the hormone. Full geometry optimization was performed, and two crystal conformers (T1 and T2), and experimental dipole moment in solution were used for comparison. One conformer with a dipole moment similar to the solvated conditions was generated. Total energy, entalphies, dipole moments, charges, electrostatic potentials, and highest occupied molecular orbitals (HOMO) and lowest unoccupied molecular orbital (LUMO) were calculated. Root-mean-square (RMS) index of the theoretical molecules against T1 and T2 showed best results with the 3–21G^* and 6–31G^* methods, while AM1 gave better energies than PM3. Dipole moments were directed toward the OH group and the botton face of the A ring. The frontier orbitals were located along the C4–C5 π bond, particularly the LUMO was split between C4 and C5, predicting the action of enzymes at C5 yielding to 5α and 5β-reduced androgens. Electrostatic potentials might be also of biological importance since they are coincidental with the dipole-moment orientation. Finally, it is interesting that the solvatedlike conformer, its properties, and the OH group laid between the same group of T1 and T2 and with a total energy between the crystals and the gas phase or in vacuo conditions. This results might also explain the biology of testosterone and use them to model the hormone-receptor interaction. © 1997 John Wiley & Sons, Inc.     

Ab initio polypeptide structure prediction

The biological activity of a polypeptide strongly depends on its 3D structure. Ab initio prediction of the native structure from the sequence of amino acids has long motivated the development of an optimum energy model such that interactions present in the native conformation are stronger than those present in nonnative conformations and of algorithms capable of finding the basin of lowest free energy among an astronomically large number of possible conformations. Despite recent progress in our understanding of the factors responsible for both polypeptide stability and formation, computer simulations of polypeptide models are still far from being practical software tools for biologists. In this work, state-of-the-art computer simulations aimed at ab initio structure prediction in aqueous solution are reviewed and their strengths and weaknesses are highlighted. Received: 23 June 1999 / Accepted: 20 September 1999 / Published online: 15 December 1999     

Crystal structure prediction using the minima hopping method

A structure prediction method is presented based on the minima hopping method. To escape local minima, moves on the configurational enthalpy surface are performed by variable cell shape molecular dynamics. To optimize the escape steps the initial atomic and cell velocities are aligned to low curvature directions of the current local minimum. The method is applied to both silicon crystals and well-studied binary Lennard-Jones mixtures. For the latter new putative ground state structures are presented. It is shown that a high success rate is achieved and a reliable prediction of unknown ground state structures is possible.     

Electronic structure of NH+: An ab initio study

We report ab initio self‐consistent field MRSD‐CI electronic structure calculations of the NH⁺ cation. A basis set of DZ + POL quality augmented with Rydberg and bond functions was employed together with an extensive treatment of electron correlation. More than 50 electronic states of NH⁺ are reported, including doublets, quartets, and sextets. Leading configurations, vertical ionization energies of NH, vertical excitation energies of NH⁺, and potential energy curves are reported. Spectroscopic properties calculated for the known bound electronic states of NH⁺ are found in good agreement with experiment. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Organic carbonates: experiment and ab initio calculations for prediction of thermochemical properties

This work has been undertaken in order to obtain data on thermodynamic properties of organic carbonates and to revise the group-additivity values necessary for predicting their standard enthalpies of formation and enthalpies of vaporization. The standard molar enthalpies of formation of dibenzyl carbonate, tert-butyl phenyl carbonate, and diphenyl carbonate were measured using combustion calorimetry. Molar enthalpies of vaporization of these compounds were obtained from the temperature dependence of the vapor pressure measured by the transpiration method. Molar enthalpy of sublimation of diphenyl carbonate was measured in the same way. Ab initio calculations of molar enthalpies of formation of organic carbonates have been performed using the G3MP2 method, and results are in excellent agreement with the available experiment. Then the group-contribution method has been developed to predict values of the enthalpies of formation and enthalpies of vaporization of organic carbonates.     

Ab initio protein fold prediction using evolutionary algorithms: influence of design and control parameters on performance

True ab initio prediction of protein 3D structure requires only the protein primary structure, a physicochemical free energy model, and a search method for identifying the free energy global minimum. Various characteristics of evolutionary algorithms (EAs) mean they are in principle well suited to the latter. Studies to date have been less than encouraging, however. This is because of the limited consideration given to EA design and control parameter issues. A comprehensive study of these issues was, therefore, undertaken for ab initio protein fold prediction using a full atomistic protein model. The performance and optimal control parameter settings of twelve EA designs where first established using a 15-residue polyalanine molecule-design aspects varied include the encoding alphabet, crossover operator, and replacement strategy. It can be concluded that real encoding and multipoint crossover are superior, while both generational and steady-state replacement strategies have merits. The scaling between the optimal control parameter settings and polyalanine size was also identified for both generational and steady-state designs based on real encoding and multipoint crossover. Application of the steady-state design to met-enkephalin indicated that these scalings are potentially transferable to real proteins. Comparison of the performance of the steady state design for met-enkephalin with other ab initio methods indicates that EAs can be competitive provided the correct design and control parameter values are used.     

The structure of nitrosoacetylene by ab initio methods

The geometrical structure of HCCNO has been calculated using ab initio SCF and GVB methods. Since it has not yet been prepared, attempts are made to predict spectroscopic constants related to its microwave, infrared and visible absorption spectra.     

De novo prediction of the ground state structure of transition metal complexes using semiempirical and ab initio quantum mechanics. Coordination isomerism

The ground state coordination isomers for 30 different trigonal bipyramidal transition metal complexes have been predicted using different levels of quantum mechanics: semiempirical (PM3(tm)), ab initio (MP2//HF), pure (BPW91) and hybrid (B3PW91) density functional theory (DFT) methods. For species where these methods failed to reproduce crystallographic data, hybrid quantum mechanics/molecular mechanics (QM/MM) methods were used to study more exact experimental models. Literature deficiencies regarding ground state multiplicity of these species were supplemented by spin predictions using previously tested PM3(tm) methods. Geometry optimization calculations were performed for each possible coordination isomer. The predicted ground state minima provided by the different methods are compared to each other and with crystallographic data. Pure DFT functionals outperformed hybrid functionals and MP2//HF. The very rapid PM3(tm) parameterization method provided accurate predictions in comparison to other levels of theory. An integrated MM/PM3(tm)/DFT de novo scheme accurately reproduced crystallographic data for species where the individual methods failed.     

Some recent applications of ab initio electronic structure methods to metal,semimetal, and molecular clusters

Recent experimental and theoretical cluster studies are reviewed. Areas of current and developing interest in theoretical and computational chemistry are identified. Some promising methods applied to metal clusters, main group clusters, molecular clusters, spectroscopy, and models of cluster-molecule reactions are indicated. Results of calculations on small hydrogenated lithium clusters and hydrated sodium clusters are discussed in some detail.     

Communication: Thermodynamics of water modeled using ab initio simulations

We regularize the potential distribution framework to calculate the excess free energy of liquid water simulated with the BLYP-D density functional. Assuming classical statistical mechanical simulations at 350 K model the liquid at 298 K, the calculated free energy is found in fair agreement with experiments, but the excess internal energy and hence also the excess entropy are not. The utility of thermodynamic characterization in understanding the role of high temperatures to mimic nuclear quantum effects and in evaluating ab initio simulations is noted.     

Electronic structure and excitations in oligoacenes from ab initio calculations

Oligoacenes C(4n+2)H(2n+4) (n=2,...,6) are studied using a variety of ab initio methods. Density functional theory (DFT) optimized geometries were in good agreement with experiment. Vertical and adiabatic ionization potentials and electron affinities were computed with DFT and it was found that standard exchange-correlation (xc) functionals underestimate ionization potentials in oligoacenes. Possible reasons for this underestimation are discussed. Low lying electronic excitations were computed using time-dependent density functional theory, configuration interaction singles, and configuration interaction singles with approximate treatment of doubles. In agreement with earlier work, time-dependent DFT in conjunction with standard xc-energy functionals substantially underestimates the lowest (p) singlet-singlet electronic transition.     

Simple ab initio calculations using a floating basis

Calculations are described on three rotamers of hydrogen disulphide (transgauche- and cis-HSSH) using an ab initio Floating Gaussian Orbital model. The optimised geometrical and electronic structures of each rotamer are discussed in terms of several electronic properties, a population and orbital analysis and an extensive partitioning of the electronic energy amongst the orbitals. The so-called Gauche Effect in HSSH is discussed in connexion with the various models proposed to account for this particular structural feature.     

pKa prediction from an ab initio bond length: part 3--benzoic acids and anilines

The prediction of pK(a) from a single ab initio bond length has been extended to provide equations for benzoic acids and anilines. The HF/6-31G(d) level of theory is used for all geometry optimisations. Similarly to phenols (Part 2 of this series of publications), the meta-/para-substituted benzoic acids can be predicted from a single model constructed from one bond length. This model had an impressive RMSEP of 0.13 pK(a) units. The prediction of ortho-substituted benzoic acids required the identification of high-correlation subsets, where the compounds in the same subset have at least one of the same (e.g. halogens, hydroxy) ortho substituent. Two pK(a) equations are provided for o-halogen benzoic acids and o-hydroxybenzoic acids, where the RMSEP values are 0.19 and 0.15 pK(a) units, respectively. Interestingly, the bond length that provided the best model differed between these two high-correlation subsets. This demonstrates the importance of investigating the most predictive bond length, which is not necessarily the bond involving the acid hydrogen. Three high-correlation subsets were identified for the ortho-substituted anilines. These were o-halogen, o-nitro and o-alkyl-substituted aniline high-correlation subsets, where the RMSEP ranged from 0.23 to 0.44 pK(a) units. The RMSEP for the meta-/para-substituted aniline model was 0.54 pK(a) units. This value exceeded our threshold of 0.50 pK(a) units and was higher than both the m-/p-benzoic acids in this work and the m-/p-phenols (RMSEP = 0.43) of Part 2. Constructing two separate models for the meta- and para- substituted anilines, where RMSEP values of 0.63 and 0.33 pK(a) units were obtained respectively, revealed it was the meta-substituted anilines that caused the large RMSEP value. For unknown reasons the RMSEP value increased with the addition of a further twenty meta-substituted anilines to this model. The C-N bond always produced the best correlations with pK(a) for all the high-correlation subsets. A higher level of theory and an ammonia probe improved the statistics only marginally for the hydroxybenzoic acid high-correlation subsets.     

Propionaldehyde: ab initio and semi-empirical calculations

The internal rotation of propionaldehyde about the 1–2 bond has been studied by means of ab initio calculations. The most stable conformer has methyl and carbonyl eclipsed. Increasing the 1–2 dihedral angle to 60°, 120°, and 180° gives energies of 1.7, 0.4, and 0.7 Kcal/mol, respectively. The agreement with force field calculations and with experiment is reasonable.     

Structural Properties of Nitromethane Molecular Crystal under High Pressure： An ab initio Investigation

The pressure-dependent structural properties under hydrostatic pressure up to 120 GPa and the decomposition under uniaxial compression along the b lattice vector up to 40 GPa of nitromethane molecular crystal using ab initio method are presented. The internal molecular bond lengths and bond angles were calculated for different pressures. All bond lengths decrease as the pressures are increased under hydrostatic compression. The obvious rotation of methyl group is 33.89° under hydrostatic pressure at 120 GPa. In addition, we observe the change of C-H bonds, which have been stretched under uniaxial compression along b lattice vector in the range of 0-40 GPa of nitromethane.     

Crystal structure, Raman spectroscopy, and ab initio calculations of a new bialkali alanate K2LiAlH6

A new bialkali alanate K2LiAlH6 was synthesized at 320-330 degrees C and 100-700 bar. It was structurally characterized by powder X-ray diffraction. It crystallizes in space group R3m (No. 166) with unit cell parameters a = 5.62068(8) and c = 27.3986(6) A. The Li and K cation sites are mutually exclusive, and Rietveld refinement finds no cation mixing. First-principles total energy calculations were performed for nine competing database structures of the stoichiometry A2BCX6, taken from fluoride and oxide compounds in the Inorganic Crystal Structure Database (ICSD). The relaxed structures were compared via their total energies and their agreement with experimental diffraction spectra. Two database structures K2LiAlF6 (R3m) and Cs2NaAlF6 (C2/m) were found to have the lowest total energies, but with the Rietveld method the K2LiAlF6 structure type was shown to be the most favorable. Ab initio total energy calculations support the validity of the structure determination. First-principles calculations also indicate that cation mixing is energetically unfavorable. Hydride properties such as plateau pressure are therefore more difficult to manipulate through alloying in this class of compounds.     

Local-orbital-based correlated ab initio band structure calculations in insulating solids: LiF

 A local-orbital-based ab initio approach to calculate correlation effects on quasi-particle energies in insulating solids is presented. The use of localized Wannier-type Hartree–Fock orbitals allows correlation effects to be efficiently assessed. First a Green's function approach based on exact diagonalization is introduced and this is combined with an incremental scheme, while subsequently different levels of perturbative approximations are derived from the general procedure. With these methods the band structure of LiF is calculated and good agreement with experiment is found. By comparing the different approximations proposed, including the exact diagonalization procedure, their relative quality is established. Received: 25 June 2001 / Accepted: 31 August 2001 / Published online: 19 December 2001     

A theoretical study of malonate and formate calcium binding by ab initio techniques

Ab initio calculations at the STO—3G level have been performed on the binding of CA(II) ion to malonate and formate with and without d orbitals in the basis set for the CA(II) ion. The malonate and formate binding results with CA(II) are similar. The addition of d orbitals to CA(II) has little effect on the conformational minimum. The results are qualitatively similar to those from our previous calculations on the Mg²⁺—malonate interaction: a single carboxyl interaction with the metal ion appears to be preferred over a conformation in which two carboxyl groups bind to Ca(II). Moreover, the single carboxyl group interaction with CA(II) appears to be favored over the binding of CA(II) to a single oxygen of a carboxyl group.