Cooperative Hydrogen-Bonding in Models of Antiparallel β-Sheets

Stabilization of the Protein Structure by the Many-Body Cooperative Effect in the NH/π Hydrogen-bonding Tryptophan Triad

The indole ring of tryptophan can form NH/π hydrogen bonds, acting both as a hydrogen donor at the NH group in the pyrrole subring and as a hydrogen acceptor at the benzene subring. In the structural core of the trimeric stable protein Pholiota squarrosa lectin (PhoSL), three indoles are symmetrically arranged and form NH/π hydrogen bonds among each other. Here, we conducted quantum chemical calculations on this indole triad by using various methods and basis sets. The analyses revealed cooperativity in triad formation, with the many-body effect contributing approximately -2 kcal mol-1, which significantly stabilizes this protein. Symmetry-adapted perturbation theory ascribed this effect to the induced polarization. The electrostatic potential and atomic charges indeed revealed a charge redistribution through the NH/π hydrogen bond, which was favorable for triad formation.

Detecting the Hydrogen Bond Cooperativity in a Protein β-Sheet by H/D Exchange

The hydrogen bond (H-bond) cooperativity in the β-sheet of GB3 is investigated by a NMR hydrogen/deuterium (H/D) exchange method. It is shown that the weakening of one backbone N-H…O=C H-bond between two β-strands, β1 and β2, due to the exchange of NH to ND of the H-bond donor in β1, perturbs the chemical shift of ¹³C_α, ¹³C_β, ¹H_α, ¹H_N, and ¹⁵N of the H-bond acceptor and its following residue in β2. Quantum mechanical calculations suggest that the -H-bond chemical shift isotope effect is caused by the structural reorganization in response to the H-bond weakening. This structural reorganization perturbs four neighboring H-bonds, with three being weaker and one being stronger, indicating that three H-bonds are cooperative and one is anticooperative with the perturbed H-bond. The sign of the cooperativity depends on the relative position of the H-bonds. This H-bond cooperativity, which contributes to β-sheet stability overall, can be important for conformational coupling across the β-sheet.

Accurate Backbone 13 C and 15 N Chemical Shift Tensors in Galectin-3 Determined by MAS NMR and QM/MM: Details of Structure and Environment Matter

Chemical shift tensors obtained from solid-state NMR spectroscopy are very sensitive reporters of structure and dynamics in proteins. While accurate 13 C and 15 N chemical shift tensors are accessible by magic angle spinning (MAS) NMR, their quantum mechanical calculations remain challenging, particularly for 15 N atoms. Here we compare experimentally determined backbone 13 Cα and 15 NH chemical shift tensors by MAS NMR with hybrid quantum mechanics/molecular mechanics/molecular dynamics (MD-QM/MM) calculations for the carbohydrate-binding domain of galectin-3. Excellent agreement between experimental and computed 15 NH chemical shift anisotropy values was obtained using the Amber ff15ipq force field when solvent dynamics was taken into account in the calculation. Our results establish important benchmark conditions for improving the accuracy of chemical shift calculations in proteins and may aid in the validation of protein structure models derived by MAS NMR.

Mechanical unfolding of alpha- and beta-helical protein motifs

Alpha-helices and beta-sheets are the two most common secondary structure motifs in proteins. Beta-helical structures merge features of the two motifs, containing two or three beta-sheet faces connected by loops or turns in a single protein. Beta-helical structures form the basis of proteins with diverse mechanical functions such as bacterial adhesins, phage cell-puncture devices, antifreeze proteins, and extracellular matrices. Alpha-helices are commonly found in cellular and extracellular matrix components, whereas beta-helices such as curli fibrils are more common as bacterial and biofilm matrix components. It is currently not known whether it may be advantageous to use one helical motif over the other for different structural and mechanical functions. To better understand the mechanical implications of using different helix motifs in networks, here we use Steered Molecular Dynamics (SMD) simulations to mechanically unfold multiple alpha- and beta-helical proteins at constant velocity at the single molecule scale. We focus on the energy dissipated during unfolding as a means of comparison between proteins and work normalized by protein characteristics (initial and final length, # H-bonds, # residues, etc.). We find that although alpha-helices such as keratin and beta-helices CsgA and CsgB can require similar amounts of work to unfold, the normalized work per hydrogen bond, initial end to end length, and number of residues is greater for beta-helices at the same pulling rate. To explain this, we analyze the orientation of the backbone alpha carbons and backbone hydrogen bonds during unfolding. We find that the larger width and shorter height of beta-helices results in smaller angles between the protein backbone and the pulling direction during unfolding. As subsequent strands are separated from the beta-helix core, the angle between the backbone and the pulling direction diminishes. This marks a transition where beta-sheet hydrogen bonds become loaded predominantly in a collective shearing mode, which requires a larger rupture force. This finding underlines the importance of geometry in optimizing resistance to mechanical unfolding in proteins. The helix radius is identified here as an important parameter that governs how much sacrificial energy dissipation capacity can be stored in protein networks, where beta-helices offer unique properties.

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.

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.

Observation of α-Helical Hydrogen-Bond Cooperativity in an Intact Protein

The presence and extent of hydrogen-bonding (H-bonding) cooperativity in proteins remains a fundamental question, which in the past has been studied extensively, mostly by infrared and fluorescence measurements on model peptides. We demonstrate that such cooperativity can be studied in an intact protein by hydrogen/deuterium exchange NMR spectroscopy. The method is based on the fact that substitution of NH by ND in a backbone amide group slightly weakens the N-H···O═C hydrogen bond. Our results show that such substitution at position i in an α-helix impacts the (1)H and (15)N chemical shifts of the amide sites of residues i - 3 to i + 3. Quantum mechanical calculations indicate that the upfield shifts of (1)H and (15)N resonances at site i, observed upon H/D exchanges at sites i - 3, i + 1, i + 2, and i + 3, correspond to a decrease of the ith backbone amide electric dipole moment, which weakens its H-bonding and long-range electrostatic interactions with other backbone amides in the α-helix. These results provide new quantitative insights into the cooperativity of H-bonding in protein α-helices.

Study on the cooperativity of hydrogen bonds between H2Y and HX (X = F, Cl, Br; Y = O, S, Se)

The structure characteristics, interaction energies, cooperative energies of the complexes between chalcogen hydrides ( H 2 Y ) and halogen hydrides (HX) have been studied theoretically at the MP2 level with aug-cc-pVTZ basis set in this paper. The conclusions show that there are strong interactions between H 2 Y and HX. The stability of the complex is decided by the electronegativity of the negatively charged atom. The cooperativity is observed in the two or three hydrogen bonds of each trimer structures in title system. The values of the cooperative energies and the cooperative contributions all illustrate that the cooperativity is of great importance in these complexes. The "atoms in molecules" (AIM) analyses show that the complexes in title system are mainly electrostatic interactions (closed-shell interactions) in character. For H ⋯ O bonds in H 2 O ⋯ HF ⋯ H 2 O , H 2 O ⋯ HBr ⋯ H 2 O and HF ⋯ H 2 O ⋯ HF , the 1 < |Vc|/Gc < 2 and -Gc < Hc < 0 indicate the interactions in these compounds are between closed-shell interaction and opened-shell interaction.

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.

Cooperativity in beryllium bonds

Positive cooperativity is found in beryllium bonded complexes similar to that described for hydrogen bonded systems.

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.

Unzipping a functional microbial amyloid

Bacterial and fungal species produce some of the best-characterized functional amyloids, that is, extracellular fibres that play key roles in mediating adhesion and biofilm formation. Yet, the molecular details underlying their mechanical strength remain poorly understood. Here, we use single-molecule atomic force microscopy to measure the mechanical properties of amyloids formed by Als cell adhesion proteins from the pathogen Candida albicans. We show that stretching Als proteins through their amyloid sequence yields characteristic force signatures corresponding to the mechanical unzipping of β-sheet interactions formed between surface-arrayed Als proteins. The unzipping probability increases with contact time, reflecting the time necessary for optimal inter β-strand associations. These results demonstrate that amyloid interactions provide cohesive strength to a major adhesion protein from a microbial pathogen, thereby strengthening cell adhesion. We suggest that such functional amyloids may represent a generic mechanism for providing mechanical strength to cell adhesion proteins. In nanotechnology, these single-molecule manipulation experiments provide new opportunities to understand the molecular mechanisms driving the cohesion of functional amyloid-based nanostructures.

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.

Modulating the Strength of Hydrogen Bonds through Beryllium Bonds

The mutual influence between beryllium bonds and inter- or intramolecular hydrogen bonds (HBs) has been investigated at the B3LYP/6-311++G(3df,2p) level of theory, using the complexes between imidazole dimer and malonaldehyde with BeH2 and BeF2 as suitable model systems. Imidazole and its dimer form very strong beryllium bonds with both BeH2 and BeF2, accompanied by a significant geometry distortion of the Lewis acid. More importantly, we have found a clear cooperativity between these two noncovalent interactions, since the intermolecular HB between the two imidazole molecules in the dimer-BeX2 complex becomes much stronger than in the isolated dimer, whereas the beryllium bond becomes also stronger in the dimer-BeX2 complex, with respect to that found in the imidazole-BeX2 complex. The effects of beryllium bonds are also dramatic on the strength of intramolecular HBs. Depending on to which center the BeX2 is attached, the intramolecular HB becomes much stronger or much weaker. The first situation is found when the beryllium derivative is attached to the HB donor, whereas the second occurs if it is attached to the HB acceptor. The first effect can be so strong as to produce a spontaneous proton transfer, as it is actually the case of the malonaldehyde-BeF2 complex.

"Additive" cooperativity of hydrogen bonds in complexes of catechol with proton acceptors in the gas phase: FTIR spectroscopy and quantum chemical calculations

Experimental study of hydrogen bond cooperativity in hetero-complexes in the gas phase was carried out by IR-spectroscopy method. Stretching vibration frequencies of O-H groups in phenol and catechol molecules as well as of their complexes with nitriles and ethers were determined in the gas phase using a specially designed cell. O-H groups experimental frequency shifts in the complexes of catechol induced by the formation of intermolecular hydrogen bonds are significantly higher than in the complexes of phenol due to the hydrogen bond cooperativity. It was shown that the cooperativity factors of hydrogen bonds in the complexes of catechol with nitriles and ethers in the gas phase are approximately the same. Quantum chemical calculations of the studied systems have been performed using density functional theory (DFT) methods. It was shown, that theoretically obtained cooperativity factors of hydrogen bonds in the complexes of catechol with proton acceptors are in good agreement with experimental values. Cooperative effects lead to a strengthening of intermolecular hydrogen bonds in the complexes of catechol on about 30%, despite the significant difference in the proton acceptor ability of the bases. The analysis within quantum theory of atoms in molecules was carried out for the explanation of this fact.

The NHF Interactions in the X-Pyridazine Complexes: Substituent Effects and Energy Components

The effects of substituents on the N⋯HF interactions in the X-pyridazine (X = N(CH3)2, NHCH3, NH2, C2H5, CH3, OCH3, OH, CN, OF, NO2, F, Br, Cl, and ) complexes have been studied at the B3LYP/6-311++G(d,p) level of theory. In all complexes, the binding energies increase for the electron-donating substituents and decrease for the electron-withdrawing substituents. A negative cooperativity is observed for two hydrogen bond interactions. There are meaningful relationships between the Hammett constants and the energy data and the results of population analysis in the binary and ternary complexes. Symmetryadapted perturbation theory (SAPT) analysis was also carried out to unveil the nature of hydrogen bond in the complexes 2 and 3. The electron-donating substituents increase the magnitude of the SAPT interaction energy components and the electron-withdrawing substituents decrease those components. The highest/lowest change is observed for the component. The effect of C2H5 (or CH3) on different components is higher than OCH3 in the complex 2 while the trend is reversed in the complex 3. It is demonstrated that the electrostatic interaction plays a main role in the interaction, although induction and dispersion interactions are also important.

Direct evaluation of individual hydrogen bond energy in situ in intra- and intermolecular multiple hydrogen bonds system

The results of evaluating the individual hydrogen bond (H-bond) strength are expected to be helpful for the rational design of new strategies for molecular recognition or supramolecular assemblies. Unfortunately, there is few obvious and unambiguous means of evaluating the energy of a single H-bond within a multiple H-bonds system. We present a local analytic model, ABEEMσπ H-bond energy (HBE) model based on ab initio calculations (MP2) as benchmark, to directly and rapidly evaluate the individual HBE in situ in inter- and intramolecular multiple H-bonds system. This model describes the HBE as the sum of electrostatic and van der Waals (vdW) interactions which all depend upon the geometry and environment, and the ambient environment of H-bond in the model is accounted fairly. Thus, it can fairly consider the cooperative effect and secondary effect. The application range of ABEEMσπ HBE model is rather wide. This work has discussed the individual H-bond in DNA base pair and protein peptide dimers. The results indicate that the interactions among donor H atom, acceptor atom as well as those atoms connected to them with 1,2 or 1,3 relationships are all important for evaluating the HBE, although the interaction between the donor H atom and the acceptor atom is large. Furthermore, our model quantitatively indicates the polarization ability of N, O, and S in a new style, and gives the percentage of the polarization effect in HBE, which can not be given by fixed partial charge force field.

Polarization of intraprotein hydrogen bond is critical to thermal stability of short helix

Simulation result for protein folding/unfolding is highly dependent on the accuracy of the force field employed. Even for the simplest structure of protein such as a short helix, simulations using the existing force fields often fail to produce the correct structural/thermodynamic properties of the protein. Recent research indicated that lack of polarization is at least partially responsible for the failure to successfully fold a short helix. In this work, we develop a simple formula-based atomic charge polarization model for intraprotein (backbone) hydrogen bonding based on the existing AMBER force field to study the thermal stability of a short helix (2I9M) by replica exchange molecular dynamics simulation. By comparison of the simulation results with those obtained by employing the standard AMBER03 force field, the formula-based atomic charge polarization model gave the helix melting curve in close agreement with the NMR experiment. However, in simulations using the standard AMBER force field, the helix was thermally unstable at the temperature of the NMR experiment, with a melting temperature almost below the freezing point. The difference in observed thermal stability from these two simulations is the effect of backbone intraprotein polarization, which was included in the formula-based atomic charge polarization model. The polarization of backbone hydrogen bonding thus plays a critical role in the thermal stability of helix or more general protein structures.

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 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.

The role of hydrophobic surfaces in altering water-mediated peptide-peptide interactions in an aqueous environment

Using Born-Oppenheimer molecular dynamics within the density functional framework, we calculated the effective force acting on water-mediated peptide-peptide interaction between antiparallel β-sheets in an aqueous environment and also in the vicinity of a hydrophobic surface. From the magnitude of the effective force (corresponding to the slope of the free energy as a function of the interpeptide distance) and its sign (a negative value indicates an effective attraction, whereas a positive value indicates an effective repulsion) we can elucidate the fundamental differences of the water-mediated peptide-peptide interactions in those two environments. The computed effective forces indicate that the water-mediated interaction between peptides in an aqueous environment is attractive in the range of interpeptide distance d = 7-8 Å when hydrophobic surfaces are not nearby. Due to the stabilization of the water molecules bridging between the two β-sheets, a free energy barrier exists between the direct and indirect (water-mediated) interpeptide interactions. However, when the peptides are in the proximity of hydrophobic surfaces, this free energy barrier decreases because the hydrophobic surfaces enhance the interpeptide attraction by the destabilization and ease-to-libration of the bridging water molecules between them.

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.

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.

Revealing noncovalent interactions

Molecular structure does not easily identify the intricate noncovalent interactions that govern many areas of biology and chemistry, including design of new materials and drugs. We develop an approach to detect noncovalent interactions in real space, based on the electron density and its derivatives. Our approach reveals the underlying chemistry that compliments the covalent structure. It provides a rich representation of van der Waals interactions, hydrogen bonds, and steric repulsion in small molecules, molecular complexes, and solids. Most importantly, the method, requiring only knowledge of the atomic coordinates, is efficient and applicable to large systems, such as proteins or DNA. Across these applications, a view of nonbonded interactions emerges as continuous surfaces rather than close contacts between atom pairs, offering rich insight into the design of new and improved ligands.

Investigation on the individual contributions of N-H...O=C and C-H...O=C interactions to the binding energies of beta-sheet models

In this article, the binding energies of 16 antiparallel and parallel beta-sheet models are estimated using the analytic potential energy function we proposed recently and the results are compared with those obtained from MP2, AMBER99, OPLSAA/L, and CHARMM27 calculations. The comparisons indicate that the analytic potential energy function can produce reasonable binding energies for beta-sheet models. Further comparisons suggest that the binding energy of the beta-sheet models might come mainly from dipole-dipole attractive and repulsive interactions and VDW interactions between the two strands. The dipole-dipole attractive and repulsive interactions are further obtained in this article. The total of N-H...H-N and C=O...O=C dipole-dipole repulsive interaction (the secondary electrostatic repulsive interaction) in the small ring of the antiparallel beta-sheet models is estimated to be about 6.0 kcal/mol. The individual N-H...O=C dipole-dipole attractive interaction is predicted to be -6.2 +/- 0.2 kcal/mol in the antiparallel beta-sheet models and -5.2 +/- 0.6 kcal/mol in the parallel beta-sheet models. The individual C(alpha)-H...O=C attractive interaction is -1.2 +/- 0.2 kcal/mol in the antiparallel beta-sheet models and -1.5 +/- 0.2 kcal/mol in the parallel beta-sheet models. These values are important in understanding the interactions at protein-protein interfaces and developing a more accurate force field for peptides and proteins.

An analytic potential energy function for the amide-amide and amide-water intermolecular hydrogen bonds in peptides

An analytic potential energy function is proposed and applied to evaluate the amide-amide and amide-water hydrogen-bonding interaction energies in peptides. The parameters in the analytic function are derived from fitting to the potential energy curves of 10 hydrogen-bonded training dimers. The analytic potential energy function is then employed to calculate the N-H...O=C, C-H...O=C, N-H...OH2, and C=O...HOH hydrogen-bonding interaction energies in amide-amide and amide-water dimers containing N-methylacetamide, acetamide, glycine dipeptide, alanine dipeptide, N-methylformamide, N-methylpropanamide, N-ethylacetamide and/or water molecules. The potential energy curves of these systems are therefore obtained, including the equilibrium hydrogen bond distances R(O...H) and the hydrogen-bonding energies. The function is also applied to calculate the binding energies in models of beta-sheets. The calculation results show that the potential energy curves obtained from the analytic function are in good agreement with those obtained from MP2/6-31+G** calculations by including the BSSE correction, which demonstrate that the analytic function proposed in this work can be used to predict the hydrogen-bonding interaction energies in peptides quickly and accurately.