Comparison of Fully Optimized α- and 310-Helices with Extended β-Strands. An ONIOM Density Functional Theory Study

Propensities of Some Amino Acid Pairings in α-Helices Vary with Length

The results of secondary structure prediction methods are widely used in applications in biotechnology and bioinformatics. However, the accuracy limit of these methods could be improved up to 92%. One approach to achieve this goal is to harvest information from the primary structure of the peptide. This study aims to contribute to this goal by investigating the variations in propensity of amino acid pairings to α-helices in globular proteins depending on helix length. (n):(n + 4) residue pairings were determined using a comprehensive peptide data set according to backbone hydrogen bond criterion which states that backbone hydrogen bond is the dominant driving force of protein folding. Helix length is limited to 13 to 26 residues. Findings of this study show that propensities of ALA:GLY and GLY:GLU pairings to α-helix in globular protein increase with increasing helix length but of ALA:ALA and ALA:VAL decrease. While the frequencies of ILE:ALA, LEU:ALA, LEU:GLN, LEU:GLU, LEU:LEU, MET:ILE and VAL:LEU pairings remain roughly constant with length, the 25 residue pairings have varying propensities in narrow helix lengths. The remaining pairings have no prominent propensity to α-helices.

Thermodynamics of Helix formation in small peptides of varying lengthin vacuo, implicit solvent and explicit solvent: Comparison between AMBER force fields

Helix formation is of great significance in protein folding. The helix-forming tendencies of amino acids are accumulated along the sequence to determine the helix-forming tendency of peptides. Computer simulation can be used to model this process in atomic details and give structural insights. In the current work, we employ equilibrate-state free energy simulation to systematically study the folding/unfolding thermodynamics of a series of mutated peptides. Two AMBER force fields including AMBER99SB and AMBER14SB are compared. The new 14SB force field uses refitted torsion parameters compared with 99SB and they share the same atomic charge scheme. We find that in vacuo the helix formation is mutation dependent, which reflects the different helix propensities of different amino acids. In general, there are helix formers, helix indifferent groups and helix breakers. The helical structure becomes more favored when the length of the sequence becomes longer, which arises from the formation of additional backbone hydrogen bonds in the lengthened sequence. Therefore, the helix indifferent groups and helix breakers will become helix formers in long sequences. Also, protonation-dependent helix formation is observed for ionizable groups. In 14SB, the helical structures are more stable than in 99SB and differences can be observed in their grouping schemes, especially in the helix indifferent group. In solvents, all mutations are helix indifferent due to protein–solvent interactions. The decrease in the number of backbone hydrogen bonds is the same with the increase in the number of protein–water hydrogen bonds. The 14SB in explicit solvent is able to capture the free energy minima in the helical state while 14SB in implicit solvent, 99SB in explicit solvent and 99SB in implicit solvent cannot. The helix propensities calculated under 14SB agree with the corresponding experimental values, while the 99SB results obviously deviate from the references. Hence, implicit solvent models are unable to correctly describe the thermodynamics even for the simple helix formation in isolated peptides. Well-developed force fields and explicit solvents are needed to correctly describe the protein dynamics. Aside from the free energy, differences in conformational ensemble under different force fields in different solvent models are observed. The numbers of hydrogen bonds formed under different force fields agree and they are mostly determined by the solvent model.

Experimental and theoretical investigation of intramolecular cooperativity in cyclic benzene trimer motif

A series of new symmetrical tripodal molecules 1a–4b with a central benzene scaffold substituted with methyl/ethyl groups and three benzimidazolyl units having a bithiophene/biphenyl/5-alkylthiophene motif at the 2-position via a –CH₂– unit were synthesized and characterized by elemental analysis, HR-MS, and NMR spectroscopy. NMR spectral data reveal that all molecules adopt a cyclic benzene trimer (CBT) using three benzimidazolyl units. Intramolecular cooperative edge-to-face C–H⋯π interactions stabilize the CBT motif in solution and are strong in ethyl substituted molecules (1b–4b) compared to methyl substituted (1a–4a) ones. However, the strength of the CBT unit in the tripodal molecule is independent of the length of the substituent at the 2-position of the benzimidazolyl unit. The relative ¹H NMR chemical shift calculated at the MPW1PW91/6-311+G(d,p) level of theory corroborates the experimental values, and the calculations predict the distribution of the structures into syn isomers. The relative change in the NMR chemical shift is justified by the relative change in the magnitude of the (3,+3) critical point (CP) in the molecular electrostatic potential (MESP) topography. Also, a linear correlation of the intramolecular C–H⋯π interactions evaluated at M062X/6-311+G(d,p) with the relative NMR chemical shift suggest the latter as a measure of intramolecular cooperativity.

A family of biaryl/alkylthiophene (R–R) benzimidazolyl-based tripodal molecules with cyclic benzene trimer (CBT) motif was synthesized and studied by NMR spectroscopy and MPW1PW91/6-311+G(d,p) theory.

Vibrational infrared and Raman spectra of polypeptides: Fragments-in-fragments within molecular tailoring approach

The present work reports the calculation of vibrational infrared (IR) and Raman spectra of large molecular systems employing molecular tailoring approach (MTA). Further, it extends the grafting procedure for the accurate evaluation of IR and Raman spectra of large molecular systems, employing a new methodology termed as Fragments-in-Fragments (FIF), within MTA. Unlike the previous MTA-based studies, the accurate estimation of the requisite molecular properties is achieved without performing any full calculations (FC). The basic idea of the grafting procedure is implemented by invoking the nearly basis-set-independent nature of the MTA-based error vis-à-vis the respective FCs. FIF has been tested out for the estimation of the above molecular properties for three isomers, viz., β-strand, 310- and α-helix of acetyl(alanine)nNH2 (n = 10, 15) polypeptides, three conformers of doubly protonated gramicidin S decapeptide and trpzip2 protein (PDB id: 1LE1), respectively, employing BP86/TZVP, M06/6-311G**, and M05-2X/6-31G** levels of theory. For most of the cases, a maximum difference of 3 cm(-1) is achieved between the grafted-MTA frequencies and the corresponding FC values. Further, a comparison of the BP86/TZVP level IR and Raman spectra of α-helical (alanine)20 and its N-deuterated derivative shows an excellent agreement with the existing experimental spectra. In view of the requirement of only MTA-based calculations and the ability of FIF to work at any level of theory, the current methodology provides a cost-effective solution for obtaining accurate spectra of large molecular systems.

Structure and stability of clusters of β-alanine in the gas phase: importance of the nature of intermolecular interactions

We present a theoretical study of neutral clusters of β-alanine molecules in the gas phase, (β-ala)_nn ≤ 5.

Analysis of Different Fragmentation Strategies on a Variety of Large Peptides: Implementation of a Low Level of Theory in Fragment-Based Methods Can Be a Crucial Factor

We have investigated the performance of two classes of fragmentation methods developed in our group (Molecules-in-Molecules (MIM) and Many-Overlapping-Body (MOB) expansion), to reproduce the unfragmented MP2 energies on a test set composed of 10 small to large biomolecules. They have also been assessed to recover the relative energies of different motifs of the acetyl(ala)18NH2 system. Performance of different bond-cutting environments and the use of Hartree-Fock and different density functionals (as a low level of theory) in conjunction with the fragmentation strategies have been analyzed. Our investigation shows that while a low level of theory (for recovering long-range interactions) may not be necessary for small peptides, it provides a very effective strategy to accurately reproduce the total and relative energies of larger peptides such as the different motifs of the acetyl(ala)18NH2 system. Employing M06-2X as the low level of theory, the calculated mean total energy deviation (maximum deviation) in the total MP2 energies for the 10 molecules in the test set at MIM(d=3.5Å), MIM(η=9), and MOB(d=5Å) are 1.16 (2.31), 0.72 (1.87), and 0.43 (2.02) kcal/mol, respectively. The excellent performance suggests that such fragment-based methods should be of general use for the computation of accurate energies of large biomolecular systems.

The importance of cooperative interactions and a solid-state paradigm to proteins: what Peptide chemists can learn from molecular crystals

Proteins and peptides in solution or in vivo share properties with both liquids and solids. More often than not, they are studied using the liquid paradigm rather than that of a solid. Studies of molecular crystals illustrate how the use of a solid paradigm may change the way that we consider these important molecules. Cooperative interactions, particularly those involving H-bonding, play much more important roles in the solid than in the liquid paradigms, as molecular crystals clearly illustrate. Using the solid rather than the liquid paradigm for proteins and peptides includes these cooperative interactions while application of the liquid paradigm tends to ignore or minimize them. Use of the solid paradigm has important implications for basic principles that are often implied about peptide and protein chemistry, such as the importance of entropy in protein folding and the nature of the hydrophobic effect. Understanding the folded states of peptides and proteins (especially alpha-helices) often requires the solid paradigm, whereas understanding unfolded states does not. Both theoretical and experimental studies of the energetics of protein and peptide folding require comparison to a suitable standard. Our perspective on these energetics depends on the reasonable choice of reference. The use of multiple reference states, particularly that of component amino acids in the gas phase, is proposed.

The unusual metal ion binding ability of histidyl tags and their mutated derivatives

Peptides that consist of repeated sequences of alternating histidines and alanines strongly bind Cu(ii) and form α-helical structures.

African Viper Poly-His Tag Peptide Fragment Efficiently Binds Metal Ions and Is Folded into an α-Helical Structure

Snake venoms are complex mixtures of toxic and often spectacularly biologically active components. Some African vipers contain polyhistidine and polyglycine peptides, which play a crucial role in the interaction with metal ions during the inhibition of snake metalloproteases. Polyhistidine peptide fragments, known as poly-His tags, play many important functions, e.g., in metal ion transport in bacterial chaperon proteins. In this paper, we report a detailed characterization of Cu(2+), Ni(2+), and Zn(2+) complexes with the EDDHHHHHHHHHG peptide fragment (pHG) derived from the venom of the rough scale bush viper (Atheris squamigera). In order to determine the thermodynamic properties, stoichiometry, binding sites, and structures of the metal-pHG complexes, we used a combination of experimental techniques (potentiometric titrations, electrospray ionization mass spectrometry, UV-vis spectroscopy, circular dichroism spectroscopy, and electron paramagnetic resonance spectroscopy) and extensive computational tools (molecular dynamics simulations and density functional theory calculations). The results showed that pHG has a high affinity toward metal ions. The numerous histidine residues located along this sequence are efficient metal ion chelators with high affinities toward Cu(2+), Ni(2+), and Zn(2+) ions. The formation of an α-helical structure induced by metal ion coordination and the occurrence of polymorphic binding states were observed. It is proposed that metal ions can "move along" the poly-His tag, which serves as a metal ion transport pathway. The coordination of Cu(2+), Ni(2+), and Zn(2+) ions to the histidine tag is very effective in comparison with other histidine-rich peptides. The stabilities of the metal-pHG complexes increase in the order Zn(2+) < Ni(2+)≪ Cu(2+).

High-resolution crystal structures of protein helices reconciled with three-centered hydrogen bonds and multipole electrostatics

Theoretical and experimental evidence for non-linear hydrogen bonds in protein helices is ubiquitous. In particular, amide three-centered hydrogen bonds are common features of helices in high-resolution crystal structures of proteins. These high-resolution structures (1.0 to 1.5 Å nominal crystallographic resolution) position backbone atoms without significant bias from modeling constraints and identify Φ = -62°, ψ = -43 as the consensus backbone torsional angles of protein helices. These torsional angles preserve the atomic positions of α-β carbons of the classic Pauling α-helix while allowing the amide carbonyls to form bifurcated hydrogen bonds as first suggested by Némethy et al. in 1967. Molecular dynamics simulations of a capped 12-residue oligoalanine in water with AMOEBA (Atomic Multipole Optimized Energetics for Biomolecular Applications), a second-generation force field that includes multipole electrostatics and polarizability, reproduces the experimentally observed high-resolution helical conformation and correctly reorients the amide-bond carbonyls into bifurcated hydrogen bonds. This simple modification of backbone torsional angles reconciles experimental and theoretical views to provide a unified view of amide three-centered hydrogen bonds as crucial components of protein helices. The reason why they have been overlooked by structural biologists depends on the small crankshaft-like changes in orientation of the amide bond that allows maintenance of the overall helical parameters (helix pitch (p) and residues per turn (n)). The Pauling 3.6₁₃ α-helix fits the high-resolution experimental data with the minor exception of the amide-carbonyl electron density, but the previously associated backbone torsional angles (Φ, Ψ) needed slight modification to be reconciled with three-atom centered H-bonds and multipole electrostatics. Thus, a new standard helix, the 3.6_13/10-, Némethy- or N-helix, is proposed. Due to the use of constraints from monopole force fields and assumed secondary structures used in low-resolution refinement of electron density of proteins, such structures in the PDB often show linear hydrogen bonding.

Tetramer model of leukoemeraldine-emeraldine electrochemistry in the presence of trihalogenoacetic acids. DFT approach

First results of the application of the DFT computational approach to the reversible electrochemistry of polyaniline are presented. A tetrameric chain was used as the simplest model of the polyaniline polymer species. The system under theoretical investigation involved six tetramer species, two electrons, and two protons, taking part in 14 elementary reactions. Moreover, the tetramer species were interacting with two trihalogenoacetic acid molecules. Trifluoroacetic, trichloroacetic, and tribromoacetic acids were found to impact the redox transformation of polyaniline as shown by cyclic voltammetry. The theoretical approach was considered as a powerful tool for investigating the main factors of importance for the experimental behavior. The DFT method provided molecular structures, interaction energies, and equilibrium energies of all of the tetramer-acid complexes. Differences between the energies of the isolated tetramer species and their complexes with acids are discussed in terms of the elementary reactions, that is, ionization potentials and electron affinities, equilibrium constants, electrode potentials, and reorganization energies. The DFT results indicate a high impact of the acid on the reorganization energy of a particular elementary electron-transfer reaction. The ECEC oxidation path was predicted by the calculations. The model of the reacting system must be extended to octamer species and/or dimeric oligomer species to better approximate the real polymer situation.

Insight into the coordination and the binding sites of Cu(2+) by the histidyl-6-tag using experimental and computational tools

His-tags are specific sequences containing six to nine subsequent histydyl residues, and they are used for purification of recombinant proteins by use of IMAC chromatography. Such polyhistydyl tags, often used in molecular biology, can be also found in nature. Proteins containing histidine-rich domains play a critical role in many life functions in both prokaryote and eukaryote organisms. Binding mode and the thermodynamic properties of the system depend on the specific metal ion and the histidine sequence. Despite the wide application of the His-tag for purification of proteins, little is known about the properties of metal-binding to such tag domains. This inspired us to undertake detailed studies on the coordination of Cu(2+) ion to hexa-His-tag. Experiments were performed using the potentiometric, UV-visible, CD, and EPR techniques. In addition, molecular dynamics (MD) simulations and density functional theory (DFT) calculations were applied. The experimental studies have shown that the Cu(2+) ion binds most likely to two imidazoles and one, two, or three amide nitrogens, depending on the pH. The structures and stabilities of the complexes for the Cu(2+)-Ac-(His)6-NH2 system using experimental and computational tools were established. Polymorphic binding states are suggested, with a possibility of the formation of α-helix structure induced by metal ion coordination. Metal ion is bound to various pairs of imidazole moieties derived from the tag with different efficiencies. The coordination sphere around the metal ion is completed by molecules of water. Finally, the Cu(2+) binding by Ac-(His)6-NH2 is much more efficient compared to other multihistidine protein domains.

Capping amyloid β-sheets of the tau-amyloid structure VQIVYK with hexapeptides designed to arrest growth. An ONIOM and density functional theory study

We present ONIOM calculations using density functional theory (DFT) as the high and AM1 as the medium level that explore the abilities of different hexapeptide sequences to terminate the growth of a model for the tau-amyloid implicated in Alzheimer’s disease. We delineate and explore several design principles (H-bonding in the side chains, using antiparallel interactions on the growing edge of a parallel sheet, using all-d residues to form rippled interactions at the edge of the sheet, and replacing the H-bond donor N–H’s that inhibit further growth) that can be used individually and in combination to design such peptides that will have a greater affinity for binding to the parallel β-sheet of acetyl-VQIVYK-NHCH₃ than the natural sequence and will prevent another strand from binding to the sheet, thus providing a cap to the growing sheet that arrests further growth. We found peptides in which the Q is replaced by an acetyllysine (aK) residue to be particularly promising candidates, particularly if the reverse sequence (KYVIaKV) is used to form an antiparallel interaction with the sheet.

Capping parallel β-sheets of acetyl(Ala)6NH2 with an acetyl(Ala)5ProNH2 can arrest the growth of the sheet, suggesting a potential for curtailing amyloid growth. An ONIOM and density functional theory study

We present ONIOM calculations using B3LYP/d95(d,p) as the high level and AM1 as the medium level on parallel β-sheets containing four strands of Ac-AAAAAA-NH2 capped with either Ac-AAPAAA-NH2 or Ac-AAAPAA-NH2. Because Pro can form H-bonds from only one side of the peptide linkage (that containing the C═O H-bond acceptor), only one of the two Pro-containing strands can favorably add to the sheet on each side. Surprisingly, when the sheet is capped with AAPAAA-NH2 at one edge, the interaction between the cap and sheet is slightly more stabilizing than that of another all Ala strand. Breaking down the interaction enthalpies into H-bonding and distortion energies shows the favorable interaction to be due to lower distortion energies in both the strand and the four-stranded sheet. Because another strand would be inhibited for attachment to the other side of the capping (Pro-containing) strand, we suggest the possible use of Pro residues in peptides designed to arrest the growth of many amyloids.

Contribution of the empirical dispersion correction on the conformation of short alanine peptides obtained by gas-phase QM calculations

In this work we analyze the effect of the inclusion of an empirical dispersion term to standard DFT (DFT-D) in the prediction of the conformational energy of the alanine dipeptide (Ala2) and in assessing the relative stabilities of short polyala-nine peptides in helical conformations, i.e., α and 310 helices, from Ala4 to Ala16. The Ala2 conformational energies obtained with the dispersion-corrected GGA functional B97-D are compared to previously published high level MP2 data. Meanwhile, the B97-D performance on larger polyalanine peptides is compared to MP2, B3LYP and RHF calculations obtained at a lower level of theory. Our results show that electron correlation affects the conformational energies of short peptides with a weight that increases with the peptide length. Indeed, while the contribution of vdW forces is significant for larger peptides, in the case of Ala2 it is negligible when compared to solvent effects. Even for short peptides, the inclusion of an empirical dispersion term greatly improves accuracy of DFT methods, providing results that correlate very well with the MP2 reference at no additional computational cost.

Comparison of some dispersion-corrected and traditional functionals as applied to peptides and conformations of cyclohexane derivatives

We compare the energetic and structural properties of fully optimized α-helical and antiparallel β-sheet polyalanines and the energetic differences between axial and equatorial conformations of three cyclohexane derivatives (methyl, fluoro, and chloro) as calculated using several functionals designed to treat dispersion (B97-D, ωB97x-D, M06, M06L, and M06-2X) with other traditional functionals not specifically parametrized to treat dispersion (B3LYP, X3LYP, and PBE1PBE) and with experimental results. Those functionals developed to treat dispersion significantly overestimate interaction enthalpies of folding for the α-helix and predict unreasonable structures that contain Ramachandran φ and ψ and C = O...N H-bonding angles that are out of the bounds of databases compiled the β-sheets. These structures are consistent with overestimation of the interaction energies. For the cyclohexanes, these functionals overestimate the stabilities of the axial conformation, especially when used with smaller basis sets. Their performance improves when the basis set is improved from D95∗∗ to aug-cc-pVTZ (which would not be possible with systems as large as the peptides).

The folding of acetyl(Ala)28NH2 and acetyl(Ala)40NH2 extended strand peptides into antiparallel β-sheets. A density functional theory study of β-sheets with β-turns

We report ONIOM calculations using B3LYP/D95** and AM1 on β-sheet formation from acetyl(Ala)(N)NH(2) (N = 28 or 40). The sheets contain from one to four β-turns for N = 28 and up to six for N = 40. We have obtained four types of geometrically optimized structures. All contain only β-turns. They differ from each other in the types of β-turns formed. The unsolvated sheets containing two turns are most stable. Aqueous solvation (using the SM5.2 and CPCM methods) reduces the stabilities of the folded structures compared to the extended strands.

Density functional theory study of β-hairpins in antiparallel β-sheets, a new classification based upon H-bond topology

We present a new classification of β-turns specific to antiparallel β-sheets based upon the topology of H-bond formation. This classification results from ONIOM calculations using B3LYP/D95** density functional theory and AM1 semiempirical calculations as the high and low levels, respectively. We chose acetyl(Ala)(6)NH(2) as a model system as it is the simplest all-alanine system that can form all the H-bonds required for a β-turn in a sheet. Of the 10 different conformations we have found, the most stable structures have C(7) cyclic H-bonds in place of the C(10) interactions specified in the classic definition. Also, the chiralities specified for residues i + 1 and i + 2 in the classic definition disappear when the structures are optimized using our techniques, as the energetic differences among the four diastereomers of each structure are not substantial for 8 of the 10 conformations.

Aqueous solvation of polyalanine α-helices with specific water molecules and with the CPCM and SM5.2 aqueous continuum models using density functional theory

We present density functional theory (DFT) calculations at the X3LYP/D95(d,p) level on the solvation of polyalanine α-helices in water. The study includes the effects of discrete water molecules and the CPCM and AMSOL SM5.2 solvent continuum model both separately and in combination. We find that individual water molecules cooperatively hydrogen-bond to both the C- and N-termini of the helix, which results in increases in the dipole moment of the helix/water complex to more than the vector sum of their individual dipole moments. These waters are found to be more stable than in bulk solvent. On the other hand, individual water molecules that interact with the backbone lower the dipole moment of the helix/water complex to below that of the helix itself. Small clusters of waters at the termini increase the dipole moments of the helix/water aggregates, but the effect diminishes as more waters are added. We discuss the somewhat complex behavior of the helix with the discrete waters in the continuum models.

Comparison of β-sheets of capped polyalanine with those of the tau-amyloid structures VQIVYK and VQIINK. A density functional theory study

We present ONIOM calculations using B3LYP/d95(d,p) as the high and AM1 as the low level on parallel β-sheets containing from two to ten strands of Ac-VQIVYK-NHMe and Ac-VQIINK-NHMe, as well as both parallel and antiparallel Ac-AAAAAA-NHMe. We find that the first two sequences form more stable sheets due to the additional H-bonding between the Q's in the side chains of both and the N's in the side chain of Ac-VQIINK-NHMe. However, the H-bonds in the amyloid chains are significantly weakened by attractive strain, which prevents all the interstrand H-bonds from achieving their optimal geometries simultaneously and requires high distortion energies for the individual strands in the sheets. The antiparallel Ac-AAAAAA-NHMe's are generally more stable and more cooperative than the parallel sheets, principally due to the higher distortion energies of the latter.

The Effects of Regularly Spaced Glutamine Substitutions on Alpha-Helical Peptide Structures. A DFT/ONIOM Study

The side-chains of the residues of glutamine (Q) and asparagine (N) contain amide groups. These can H-bond to each other in patterns similar to those of the backbone amides in α-helices. We show that mutating multiple Q's for alanines (A's) in a polyalanine helix stabilizes the helical structure, while similar mutations with multiple N's do not. We suggest that modification of peptides by incorporating Q's in such positions can make more robust helices that can be used to test the effects of secondary structures in biochemical experiments linked to proteins with variable structures such as tau and α-synuclein.

The effect of polarization on multiple hydrogen-bond formation in models of self-assembling materials

We report density functional theory calculations at the B3LYP/D95(d,p) level on several different cyclic H-bonding dimers, where the monomers of each are connected by a pair of N-H···O=C H-bonding interactions, and the H-bonding donors and acceptors on each monomer are separated by polarizable spacers. Depending on the structures, the individual H-bonds vary in strength (enthalpy) by over a factor of four, from 2.41 to 10.99 kcal/mol. We attribute most of the variation in interaction energies to differences in the extent of polarization due to each of the H-bonds, which can either combine constructively or destructively. The dipole-dipole interactions between the pair of H-bonds also contribute somewhat to the relative stabilities. The relevance of these results to the design of self-assembling materials is discussed.

A comparison of the behavior of functional/basis set combinations for hydrogen-bonding in the water dimer with emphasis on basis set superposition error

We evaluate the performance of ten functionals (B3LYP, M05, M05-2X, M06, M06-2X, B2PLYP, B2PLYPD, X3LYP, B97D, and MPWB1K) in combination with 16 basis sets ranging in complexity from 6-31G(d) to aug-cc-pV5Z for the calculation of the H-bonded water dimer with the goal of defining which combinations of functionals and basis sets provide a combination of economy and accuracy for H-bonded systems. We have compared the results to the best non-density functional theory (non-DFT) molecular orbital (MO) calculations and to experimental results. Several of the smaller basis sets lead to qualitatively incorrect geometries when optimized on a normal potential energy surface (PES). This problem disappears when the optimization is performed on a counterpoise (CP) corrected PES. The calculated interaction energies (ΔEs) with the largest basis sets vary from -4.42 (B97D) to -5.19 (B2PLYPD) kcal/mol for the different functionals. Small basis sets generally predict stronger interactions than the large ones. We found that, because of error compensation, the smaller basis sets gave the best results (in comparison to experimental and high-level non-DFT MO calculations) when combined with a functional that predicts a weak interaction with the largest basis set. As many applications are complex systems and require economical calculations, we suggest the following functional/basis set combinations in order of increasing complexity and cost: (1) D95(d,p) with B3LYP, B97D, M06, or MPWB1k; (2) 6-311G(d,p) with B3LYP; (3) D95++(d,p) with B3LYP, B97D, or MPWB1K; (4) 6-311++G(d,p) with B3LYP or B97D; and (5) aug-cc-pVDZ with M05-2X, M06-2X, or X3LYP.

Rapid evaluation of the binding energies in hydrogen-bonded amide-thymine and amide-uracil dimers in gas phase

The binding energies and the equilibrium hydrogen bond distances as well as the potential energy curves of 48 hydrogen-bonded amide-thymine and amide-uracil dimers are evaluated from the analytic potential energy function established in our lab recently. The calculation results show that the potential energy curves obtained from the analytic potential energy function are in good agreement with those obtained from MP2/6-311+G** calculations by including the BSSE correction. For all the 48 dimers, the analytic potential energy function yields the binding energies of the MP2/6-311+G** with BSSE correction within the error limits of 0.50 kcal/mol for 46 dimers, only two differences are larger than 0.50 kcal/mol and the largest one is only 0.60 kcal/mol. The analytic potential energy function produces the equilibrium hydrogen bond distances of the MP2/6-311+G** with BSSE correction within the error limits of 0.050 Å for all the 48 dimers. The analytic potential energy function is further applied to four more complicated hydrogen-bonded amide-base systems involving amino acid side chain and β-sheet. The values of the binding energies and equilibrium hydrogen bond distances obtained from the analytic potential energy function are also in good agreement with those obtained from MP2 calculations with the BSSE correction. These results demonstrate that the analytic potential energy function can be used to evaluate the binding energies in hydrogen-bonded amide-base dimers quickly and accurately.

Aggregation of capped hexaglycine strands into hydrogen-bonding motifs representative of pleated and rippled β-sheets, collagen, and polyglycine I and II crystal structures. A density functional theory study

We compare the energies and enthalpies of inter-action of three- and seven-stranded capped polyglycine aggregates in both the pleated and rippled antiparallel and parallel β-sheet structures as well as the collagenic (three-strand) or polyglycine II-like (seven-strand) forms using density functional theory at the B3LYP/D95(d,p) level. We present the overall interaction energies as broken down into pure H-bonding between the strands at the geometries they assume in the aggregates and the distortion energies required to achieve those geometries starting from the fully relaxed single strands. While the antiparallel sheets represent the most stable structures for both the three- and seven-strand structures, the pure H-bonding interactions are the smallest for these structures. The overall interaction energies are dominated by the energy required to distort the relaxed polyglycine strands rather than the H-bonding energies. The antiparallel β-sheet constrained to C(s) symmetry has a lower enthalpy, but higher energy, of interaction than the fully optimized structure.

A scheme for rapid prediction of cooperativity in hydrogen bond chains of formamides, acetamides, and N-methylformamides

A scheme is proposed in this article to predict the cooperativity in hydrogen bond chains of formamides, acetamides, and N-methylformamides. The parameters needed in the scheme are derived from fitting to the hydrogen bonding energies of MP2/6-31+G** with basis set superposition error (BSSE) correction of the hydrogen bond chains of formamides containing from two to eight monomeric units. The scheme is then used to calculate the individual hydrogen bonding energies in the chains of formamides containing 9 and 12 monomeric units, in the chains of acetamides containing from two to seven monomeric units, in the chains of N-methylformamides containing from two to seven monomeric units. The calculation results show that the cooperativity predicted by the scheme proposed in this paper is in good agreement with those obtained from MP2/6-31+G** calculations by including the BSSE correction, demonstrating that the scheme proposed in this article is reasonable. Based on our scheme, a cooperativity effect of almost 240% of the dimer hydrogen bonding energy in long hydrogen bond formamide chains, a cooperativity effect of almost 190% of the dimer hydrogen bonding energy in long hydrogen bond acetamide chains, and a cooperativity effect of almost 210% of the dimer hydrogen bonding energy in long hydrogen bond N-methylformamide chains are predicted. The scheme is further applied to some heterogeneous chains containing formamide, acetamide, and N-methylformamide. The individual hydrogen bonding energies in these heterogeneous chains predicted by our scheme are also in good agreement with those obtained from Møller-Plesset calculations including BSSE correction.