Conformational behaviour of the architectural units of peptides and proteins. Assessment of current understanding by ab initio quantum mechanical methods and refinement of the dipeptide energy surface.

The conformational energy surfaces of analogues of the dipeptide unit of polypeptides and proteins are calculated by ab initio methods using extended basis sets.The calculations are not particularly sensitive to the choice of (extended) basis set.The calculations are shown to support a particular empirical method parameterized with respect to crystal data. Non-hydrogen bonded conformations agree to within 3 kcal mol^?1, even for conformations in which quite considerable degrees of atomic overlap occur.Hydrogen bonded conformations, are, however, in less satisfactory agreement and it is the ab initio calculations which appear to be at fault.A simple correction is applied to the ab initio energy for hydrogen bonded conformations, and with the use of the empirical energy surface a full quantum mechanical conformational energy map is interpolated for the alanyl dipeptide.The effect of flexibility in the peptide backbone is taken into account, and supports recent empirical findings that distortions in valence angles must be considered in calculations of the conformational behaviour of peptides.     

Hydrogen Bonding and Stacking of DNA Bases: A Review of Quantum-chemical ab initio Studies

Abstract

Ab initio quantum-chemical calculations with inclusion of electron correlation made since 1994 (such reliable calculations were not feasible before) significantly modified our view on interactions of nucleic acid bases. These calculations allowed to perform the first reliable comparison of the strength of stacked and hydrogen bonded pairs of nucleic acid bases, and to characterize the nature of the base-base interactions. Although hydrogen-bonded complexes of nucleobases are primarily stabilized by the electrostatic interaction, the dispersion attraction is also important. The stacked pairs are stabilized by dispersion attraction, however, the mutual orientation of stacked bases is determined rather by the electrostatic energy. Some popular theories of stacking were ruled out: The theory based on attractive interactions of polar exocyclic groups of bases with delocalized electrons of the aromatic rings (Bugg et al., Biopolymers 10, 175 (1971).), and the II-II interactions model (C.A. Hunter, J. Mol. Biol. 230, 1025 (1993)). The calculations demonstrated that amino groups of nucleobases are very flexible and intrinsically nonplanar, allowing hydrogen-bond-like interactions which are oriented out of the plane of the nucleobase. Many H-bonded DNA base pairs are intrinsically nonplanar. Higher-level ab initio calculations provide a unique set of reliable and consistent data for parametrization and verification of empirical potentials. In this article, we present a short survey of the recent calculations, and discuss their significance and limitations. This summary is written for readers which are not experts in computational quantum chemistry.     

Peptides and Peptoids - A Systematic Structure Comparison

A systematic analysis of the conformational space of the basic structure unit of peptoids in comparison to the corresponding peptide unit was performed based on ab initio MO theory and complemented by molecular mechanics (MM) and molecular dynamics (MD) calculations both in the gas phase and in aqueous solution.The calculations show three minimum conformations denoted as C_7ß, a_D and a that do not correspond to conformers on the gas phase peptide potential energy hypersurface. The influence of aqueous solvation was estimated by means of continuum models. The MD simulations indicate the a_D form as the preferred conformation in solution both in cis and trans peptide bond orientations.     

A computational analysis of some diaryl ureas in relation to their observed crystalline hydrogen bonding patterns

We have carried out anab initio self-consistent-field molecular orbital analysis of the structures, atomic charges and electrostatic potentials of 1,3-bisphenylurea, 1,3-bis(m-nitrophenyl)urea and 1,3-bis(p-nitrophenyl)urea. Our results provide insight into the contrasting hydrogen bond patterns and preferences of these molecules in crystalline environments. The tendency for 1,3-bisphenylurea to form homomeric rather than heteromeric (i.e. host-guest) crystals is attributed to a relatively strong and extended homomeric attractive electrostatic interaction between two like molecules. Our calculated internuclear distances and atomic charges indicate that these molecules have some degree of H...O intramolecular hydrogen bonding between the carbonyl oxygen and the nearest aromatic hydrogens when the aromatic and the urea portions of the molecules are coplanar. This interaction is strongest for the meta nitro derivative, consistent with the latter remaining very nearly planar in its cocrystal structures. Our surface electrostatic potentials for the three diaryl ureas are used to interpret their differing crystallization properties and tendencies to form cocrystals with guest molecules.     

A Modified Version of the Cornell et al. Force Field with Improved Sugar Pucker Phases and Helical Repeat

Abstract

We have examined some subtle parameter modifications to the Cornell et al. force field, which has proven quite successful in reproducing nucleic acid properties, but whose C2′-endo sugar pucker phase and helical repeat for B DNA appear to be somewhat underestimated. Encouragingly, the addition of a single V₂ term involving the atoms C(sp³)-O-(sp³)-C(sp³)- N(sp²), which can be nicely rationalized because of the anomeric effect (lone pairs on oxygen are preferentially oriented relative to the electron withdrawing N), brings the sugar pucker phase of C2′-endo sugars to near perfect agreement with ab initio calculations (W near 162°). Secondly, the use of high level ab initio calculations on entire nucleosides (in contrast to smaller model systems necessitated in 1994–95 by computer limitations) lets one improve the % torsional potential for nucleic acids. Finally, the O(sp³)-C(sp³)- C(sp³)-O(sp³) V₂ torsional potential has been empirically adjusted to reproduce the ab initio calculated relative energy of C2′- endo and C3′-endo nucleosides. These modifications are tested in molecular dynamics simulations of mononucleosides (to assess sugar pucker percentages) and double helices of DNA and RNA (to assess helical and sequence specific structural properties). In both areas, the modified force field leads to improved agreement with experimental data.     

Introducing a novel method based on the imperialistic competitive algorithm to determine fluorine intermolecular potential from ab initio calculations and calculation of some properties via MD simulations

In this work, the possibility of obtaining an accurate site-site potential model suitable for use in molecular dynamics (MD) simulations of fluorine from ab initio calculations has been explored. The exploration was made on ab initio calculations. To reduce the ab initio pair potentials into a site-site potential, a higher significance was assigned to the configuration which is more stable. For this purpose, the imperialistic competitive algorithm (ICA) was implemented as a powerful optimisation tool. The calculated second virial coefficients were compared to the experimental values to test the quality of the presented intermolecular potential. The relative error for the calculated second virial coefficient ranged from 0.1 to 5.6%. MD simulations were used to evaluate the ability of the proposed intermolecular potential function. The relative error for the MD simulations ranged from 0.5 to 5.2%. The results are in good agreement with experimental data.     

Electrostatic interactions in proteins: Calculations of the electrostatic term of free energy and the electrostatic potential field

The pH-dependence of the electrostatic energy of interactions between titratable groups is calculated for some well studied globular proteins: basic pancreatic trypsin inhibitor, sperm whale myoglobin and tuna cytochrome c. The calculations are carried out using a semi-empirical appraach in terms of the macroscopic model based on the Kirkwood-Tanford theory. The results are discussed in the light of their physicochemical and biological properties. It was found that the pH-dependence of the electrostatic energy correlates with the III–IV transition of cytochrome c. The electrostatic field of the cysteine proteinase inhibitor, cystatin, was calculated in two ways. In the first one, the electrostatic field created by the pH dependent charges of the ionizable groups and peptide dipoles was calculated using the approach proposed. In the second one, the finite-difference method was used. The results obtained by the two methods are in overall agreement. The calculated field was discussed in terms of the binding of cystatin to papain.     

Comparison of Different Three-site Interaction Potentials for Liquid Acetonitrile

Abstract

Computer simulations of liquid acetonitrile at normal room conditions are reported. Both static and dynamic properties are analysed. Special attention is paid to the dielectric properties. A three-site interaction potential has been derived from ab initio calculations on the gas phase dimer and a comparison with different three-site interaction potentials available in the literature is presented. The suitability of three-site models to reproduce the properties of the real liquid is discussed by comparing computer simulation results with experimental data.     

Peptide Free Energy Landscapes Calibrated by Molecular Orbital Calculations

Free energy landscapes of peptide conformations werecalibrated by ab initiomolecular orbital calculations, after enhancedconformational sampling using the multicanonical molecular dynamicssimulations. Three different potentials of mean force for an isolateddipeptide were individually obtained using the conventional force fields,AMBER parm94, AMBER parm96, and CHARMm22. Each potential ofmean force was calibrated based on the umbrella sampling algorithm fromthe adiabatic energy map that was calculated separately by the abinitiomolecular orbital method. All the calibrated potentials of mean forcecoincided well. The calibration was applied to a peptide in explicit water,and the calibrated free energy landscapes did not depend on the force fieldused in conformational sampling, as far as the conformational space waswell sampled.     

New Multicentre Point Charge Models for Molecular Electrostatic Potentials from Semiempirical M0-Calculations

Two quasi-multipole electrostatic models for molecular charge distributions are presented. They assign arrays of point charges to nonhydrogen atoms on the basis of hybrid orbitals or localised molecular orbitals. When used with common semiempirical MO-techniques, they reproduce natural atomic orbital derived point charge (NAO-PC) and ab initio molecular potentials well. The localised orbital technique (LMO-PC) is intuitively more attractive than the hybrid orbital-point charge (HO-PC) method, although the former is more CPU-intensive.Electronic Supplementary Material available.     

A Detailed Study of VESPA Electrostatic Potential-Derived Atomic Charges

VESPA, an improved semiempirical method for the calculation of electrostatic potential-derived atomic charges has been tested. It is shown that this approach is even less dependent upon molecular orientation than "high density" CHELPG ab initio ESP-derived charges. The conformational dependence of VESPA charges has been investigated for rotation around the C-N bond in formamide and 11 different conformers of glycerolphosphorylcholine. The results obtained are also compared to the corresponding ab initio values. Finally, VESPA is used to calculate electrostatic potential-derived charges for bioorganic molecules. We discuss the abilities and the limitations of ESP charges in this area.     

Towards the Understanding of the Folding of Methylene Units in the Glutamine Residue

The conformational preferences of the methylenic sequence in the side chain of the glutamine residue were investigated by ab initio and semi-empirical quantum mechanical calculations and examination of both the Brookhaven Protein Databank and Cambridge Structural Data Base. The results were analysed on the basis of our previous findings about the folding of methylene groups in aliphatic segments. Both energy calculations and the crystallographic structure of small peptides indicate that methylene units of the glutamine residue tend to fold in a gauche conformation. In contrast, such groups usually adopt an all-trans conformation in proteins due basically to the entropic and solvent contributions. These results have been demonstrated by computing the entropic correction to the free energy and evaluating the solvent effects through SCRF calculations     

Modelling of Structural and Vibrational Properties of Poly(p-Phenylene) and Polypyrrole Using Molecular Orbital Methods

Abstract

This paper concentrates on two very important conducting polymers poly(p-phenylene) and polypyrrole. Detailed atomistic molecular models have been developed with the help of ab initio and semi-empirical quantum mechanical calculations using the Cerius² and WinMOPAC (version 6.0) programs.

Their optimised geometry had been calculated and compared with experimental X-ray diffraction data. The simulated and experimental vibrational spectra of biphenyl as well as isolated pyrrole monomers and oligomers from n = 1 and 2, where n is the number of structural repeat units used, have been computed using the ab initio 3–21G basis set. The results obtained are compared with experimental data for the case of biphenyl and for oligomers with n = 2 to 5 for both neutral benzenoid and quinonoid oligopyrroles, from semi-empirical predictions obtained by AM1 and PM3. The trends in the computed harmonic force fields, vibrational frequencies and intensities are monitored as a function of the chain length. The data are analyzed in conjunction with the trends in computed equilibrium geometries.     

On the accuracy of analytical potentials: comment on ‘Accurate ab initio calculation of the Ar–CF4 intermolecular potential energy surface’

In a recent study of the Ar–CF₄ intermolecular interaction potential [Shen C-C, Chang R-Y. Accurate ab initio calculation of the Ar–CF₄ intermolecular potential energy surface. Mol Sim. 2010;36:1111–1122], Shen and Chang (SC) illustrated how the use of bond functions can improve the accuracy and basis-set saturation of electronic structure calculations employing perturbation and coupled-cluster theory. SC then used these ab initio data to derive analytic potential energy functions for use in chemical dynamics simulations. We critically examine these analytic potentials and comment on their usage in such simulations. Our analysis highlights the need for care and global validation when deriving analytic potential energy functions.     

A force field for naproxen

A united-atom potential model for naproxen suitable for molecular dynamics (MD) simulation has been developed. The charge distribution is approximated by point charges obtained from ab initio calculations using the CHELPG method. Also the intramolecular interactions such as bond and angle vibration, and the torsion potential are obtained from ab initio calculations. The dispersive interaction contribution is taken from the literature. By MD simulation using a naproxen film in slap geometry, the temperature dependence of the density, surface tension and self-diffusion coefficient as well as the melting temperature for the developed potential model are obtained.     

New potential model for molecular dynamic simulation of liquid HF. I—Parameter optimization for charge equilibration method

In order to build a complete potential model to perform classical molecular dynamic simulations of liquid HF, a new optimization method is proposed to obtain transferable parameters for charge equilibration method on the basis of ab initio reference data. The optimized parameters (the electronegativity χ and the Slater orbital exponent ζ for H and F atoms) appear to be able to reproduce the variations of the electrostatic potential calculated from an ab initio method in a liquid phase of HF molecules for different thermodynamic conditions. It is concluded that the proposed method is general, precise and efficient to obtain transferable and realistic parameters.     

Ab initio Investigation of the Molecular Structure of Methyl Methoxymethyl Phosphonate,a Promising Nuclease-resistant Alternative of the Phosphodiester Linkage

Abstract

Conformational flexibility of the methyl methoxymethyl phosphonate anion (CH₃-O-PO₂- CH₂-O-CH₃)^?, a nuclease resistant alternative to the phosphodiester linkage in DNA, have been investigated by ab initio quantum mechanical calculations. The potential of backbone torsional degrees of freedom of methyl methoxymethyl phosphonate anion (MMP) was determined at the Hartree-Fock (HF) 3–21G* level using the adiabatic mapping technique. Energies, geometries, and effective atomic charges of different conformers were calculated at HF/6–31G* and MP2/6–31G* levels of theory. These were compared to the results obtained for dimethyl phosphate calculated at the same level. The impact on DNA structure from inserting a methylene group between phosphorus and oxygen of the nucleoside sugar moiety was examined via distance- and angle-constrained geometry optimizations. Due to its high flexibility, MMP has been shown to be compatible with both A and B forms of DNA.     

Molecular Dynamics of the Ha-ras Protein: Nucleotide Atom-Centred Charges within the AMBER Force Field

Molecular dynamics simulations have become an essential tool for the study of biological systems. The Ha-ras protein, is a system suitable for such studies. Despite much recent progress, it is still not known exactly how the protein functions in the cell growth cycle. In this work atom-centred point charges for the guanosine nucleotide ligands are calculated and tested. To be compatible with the other AMBER force field parameters these are fitted to a molecular electrostatic potential derived from an ab initio wavefunction. The smallest basis set able to produce a stable wavefunction for the negatively charged GDP and GTP molecule ions was 3-21G* with diffuse functions added on the phosphate groups. To maintain force field integrity these charges were scaled to be equivalent to STO-3G derived values. This procedure is seen to produce a good magnesium-phosphate interaction potential when compared to 6-31++G* ab initio calculations. With the nucleotides fixed in the binding site conformation, it was found essential to include the electrostatics of the binding site in the calculation of the charges. It was also found to be inappropriate to divide the nucleotide into constituent parts for the calculations. From the calculated charges and experimental data, the nucleotide protonation states in the protein are deduced. It is unlikely that GDP is protonated, GTP probably binds one proton. The charges were tested in MD simulations of a protein modelled on the crystal structure of Tong et al., during which the dynamics of the nucleotide and binding site residues were in good agreement with the crystal structure data. The model is seen to be sensitive, not only to the inclusion of explicit solvent, but to the number of waters ligating the magnesium ion and the conformation of the loop between residues 60 and 66; both pieces of information are lacking in the crystal structure data.     

Neural networks as a tool for compact representation of ab initio molecular potential energy surfaces

Ab initio quantum chemical calculations of molecular properties such as, e.g., torsional potential energies, require massive computational effort even for moderately sized molecules, if basis sets with a reasonable quality are employed. Using ab initio data on conformational properties of the cofactor (6R,1′R,2′S)-5,6,7,8-tetrahydrobiopterin, we demonstrate that error backpropagation networks can be established that efficiently approximate complicated functional relationships such as torsional potential energy surfaces of a flexible molecule. Our pilot simulations suggest that properly trained neural networks might provide an extremely compact storage medium for quantum chemically obtained information. Moreover, they are outstandingly comfortable tools when it comes to making use of the stored information. One possible application is demonstrated, namely, computation of relaxed torsional energy surfaces.