Capping parallel ß-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 ß-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.

The interactions of phenylalanines in ß-sheet-like structures from molecular orbital calculations using density functional theory (DFT), MP2, and CCSD(T) methods.

We present density functional theory calculations designed to evaluate the importance of π-stacking interactions to the stability of in-register Phe residues within parallel ß-sheets, such as amyloids. We have used a model of a parallel H-bonded tetramer of acetylPheNH2 as a model and both functionals that were specifically designed to incorporate dispersion effects (DFs), as well as, several traditional functionals which have not been so designed. None of the functionals finds a global minimum for the π-stacked conformation, although two of the DFs find this to be a local minimum. The stacked phenyls taken from the optimized geometries calculated for each functional have been evaluated using MP2 and CCSD(T) calculations for comparison. The results suggest that π-stacking does not make an important contribution to the stability of this system and (by implication) to amyloid formation.

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

We present a new classification of ß-turns specific to antiparallel ß-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 ß-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.

A reinvestigation of the dimer of para-benzoquinone and pyrimidine with MP2, CCSD(T), and DFT using functionals including those designed to describe dispersion.

We reevaluate the interaction of pyridine and p-benzoquinone using functionals designed to treat dispersion. We compare the relative energies of four different structures: stacked, T-shaped (identified for the first time), and two planar H-bonded geometries using these functionals (B97-D, ωB97x-D, M05, M05-2X, M06, M06L, and M06-2X), other functionals (PBE1PBE, B3LYP, X3LYP), MP2, and CCSD(T) using basis sets as large as cc-pVTZ. The functionals designed to treat dispersion behave erratically as the predictions of the most stable structure vary considerably. MP2 predicts the experimentally observed structure (H-bonded) to be the least stable, while single-point CCSD(T) at the MP2 optimized geometry correctly predicts the observed structure to be the most stable. We have confirmed the assignment of the experimental structure using new calculations of the vibrational frequency shifts previously used to identify the structure. The MP2/cc-pVTZ vibrational calculations are in excellent agreement with the observations. All methods used to calculate the energies provide vibrational shifts that agree with the observed structure even though most do not predict this structure to be most stable. The implications for evaluating possible π-stacking in biologically important systems are discussed.

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 ß-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 ß-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).

Comparison of some dispersion-corrected and traditional functionals with CCSD(T) and MP2 ab initio methods: dispersion, induction, and basis set superposition error.

We compare dispersion and induction interactions for noble gas dimers and for Ne, methane, and 2-butyne with HF and LiF using a variety of functionals (including some specifically parameterized to evaluate dispersion interactions) with ab initio methods including CCSD(T) and MP2. We see that inductive interactions tend to enhance dispersion and may be accompanied by charge-transfer. We show that the functionals do not generally follow the expected trends in interaction energies, basis set superposition errors (BSSE), and interaction distances as a function of basis set size. The functionals parameterized to treat dispersion interactions often overestimate these interactions, sometimes by quite a lot, when compared to higher level calculations. Which functionals work best depends upon the examples chosen. The B3LYP and X3LYP functionals, which do not describe pure dispersion interactions, appear to describe dispersion mixed with induction about as accurately as those parametrized to treat dispersion. We observed significant differences in high-level wavefunction calculations in a basis set larger than those used to generate the structures in many of the databases. We discuss the implications for highly parameterized functionals based on these databases, as well as the use of simple potential energy for fitting the parameters rather than experimentally determinable thermodynamic state functions that involve consideration of vibrational states.

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.

J-coupling constants for a trialanine peptide as a function of dihedral angles calculated by density functional theory over the full Ramachandran space.

We present 13 (3)J, seven (2)J and four (1)J coupling constants (24 in all) calculated using B3LYP/D95** as a function of the φ and ψ Ramachandran dihedral angles of the acetyl(Ala)(3)NH(2) capped trialanine peptide over the entire Ramachandran space. With the exception of three of these J couplings, all show significant dependence upon both dihedral angles. For each J coupling considered, a two dimensional grid with respect to φ and ψ angles can be used to interpolate the values for any pair of φ and ψ values. Such simple interpolation is shown to be very accurate. Most of these calculated J couplings should prove useful for improving the accuracy of the determination of peptide and protein structures from NMR measurements in solution over that provided by the common procedure of treating the J couplings as functions of a single dihedral angle by means of Karplus-type fittings.

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 importance of hydrogen bonding between the glutamine side chains to the formation of amyloid VQIVYK parallel beta-sheets: an ONIOM DFT/AM1 study.

We report DFT calculations indicating that beta-sheet formation involving the capped amino acid sequence VQIVYK is due (at least in part) to cooperative H-bonding between the glutamine side chains. The sequence VQIVYK has been reported to be essential for the aggregation of the tau protein into the amyloids associated with Alzheimer's disease and has been crystallized. Sheets containing only capped Q's form cooperative H-bonds between the side chains that enhance stabilization while keeping the backbones of the individual strands close to the quasi-planarity expected for a beta-sheet. Sheets containing only capped A's cannot form H-bonds between the side chains, do not interact cooperatively, and form helical structures that deviate considerably from the quasi-planarity expected for beta-sheets. Comparisons between the sheets made from capped VQIVYK's, Q's, and A's illustrate the importance of the cooperative H-bonds between the Q's to the stability of tau amyloids.

Ramachandran revisited. DFT energy surfaces of diastereomeric trialanine peptides in the gas phase and aqueous solution.

We report DFT calculations at the B3LYP/D95(d,p) level on the gas phase, aqueous solvation and solvated energies as functions of the central psi and phi dihedral angles (in steps of 5 degrees each) of acetyl-(L)Ala-(L)Ala-(L)Ala-NH(2) (3AL) and its diastereomer, acetyl-(L)Ala-(D)Ala-(L)Ala-NH(2) (3AD). In addition to structures without internal H-bonds (C(5) interactions are neglected), many (95) structures containing internal H-bonds were completely optimized. The only minima for non-H-bonding structures in the gas phase correspond to extended beta-strands for both diastereomers. Some (but not all) structures with internal H-bonds are more stable than those without them. The energy landscapes for the solvated species show multiple minima for the non-H-bonding species and a single minimum for the H-bonding species (3(10)-helix), suggesting that the equilibrium conformational mixture in water be composed of the extended beta-strand, polyproline II, 3(10)-helix, and alpha-helix-like (with no H-bonds) conformations which are all within about 1 kcal/mol of each other. Most H-bonding structures are destabilized relative to the non-H-bonding structures in aqueous solution, but some with large dipole moments are not. The large dipole moment of the alpha-helix-like conformation leads to its increased stability in water (vs the gas phase). Significant qualitative and quantitative differences are reported for the energy landscapes of the two diastereomers when one is compared with the mirror image of the other landscape (particularly in the beta-turn region), suggesting that the differences in the energies of the unfolded peptides need to be considered when considering the stabilities of folded peptides and proteins with single amino acid mutations.

Attractive strain: the disadvantages of rigid multiple H-bond donors and acceptors. A theoretical analysis of the hydrogen-bonding interactions in complexes of tetraazaanthracenedione with pyridylureas.

We report density functional theory calculations at the B3LYP/D95(d,p) level on the hydrogen-bonding complexes of tetraazaanthracenedione, 1, with N-(pyridin-2-yl)urea, 2H, or N-(6-aminopyridin-2-yl)urea, 2N. The interaction energy of the 1-2H complex exceeds that of 1-2N, despite the fact that 1-2N contains a strong N-H...O interaction in place of a weak C-H...O interaction in 1-2H. We show that the 1-2N interaction is weaker than the sum of the four normal individual H-bonding interactions because the steric constraints of the complex prevent the H-bonding donors and acceptors from optimally approaching each other to form the two central H-bonds. This steric phenomenon, which we call attractive strain, is likely present to some extent in most H-bonding systems that contain more than two H-bonds between rigid monomers. Attractive strain is unusually important in 1-2N. Attractive strain can be conceived of as an enthalpic cost for the entropic benefits of freezing the dihedral angles of the multiple H-bond donors and acceptors by designing rigid systems.

Amide I vibrational frequencies of alpha-helical peptides based upon ONIOM and density functional theory (DFT) studies.

We present ONIOM and pure DFT calculations on infrared spectra of alpha-helical-capped polyalanines. The calculations used two-layer ONIOM (B3LYP/D95**:AM1) calculations of the amide I vibrational frequencies for acetyl(ala)NNH2 (N=8, 10, 12-18) whose structures have been previously completely optimized by the same method. These are the first such calculations based upon structures of alpha-helical peptides that are completely optimized using DFT or molecular orbital methods. As the peptide becomes longer, the amide I band becomes both more intense and more red shifted. However, the individual absorptions that contribute most to the band vary between three patterns: one very intense absorption, two absorptions of similar intensity, and two strong absorptions where one is roughly twice as intense as the other. This pattern appears to be related to the relative number of H bonds in the individual H-bonding chains; however, there is one exception. Using 14C=O's to selectively decouple specific C=O's, we found that the couplings between the C=O's within each of the three individual H-bonding chains within the helices follow the same pattern previously reported for planar H-bonding chains of formamides. The coupling between the H-bonding chains appears to involve through-space coupling between the H-bonding chains. While decoupling individual C=O's always decreases the intensity of the amide I band, it leads to complex changes in the individual amide I absorptions that contribute to the band. Depending upon the position of the 14C=O, the amide I band can either red or blue shift. Moreover, the individual absorptions that contribute to the band can increase or decrease in intensity as well as shift. The patterns of the individual absorptions (mentioned above) also change. Using the C=O stretch of acetamide as a reference, we calculate the red shifts for the most intense absorptions to be much greater than predicted by the transition dipole method.

A density functional theory study of vibrational coupling in the amide I band of beta-sheet models.

We report the first molecular orbital/density functional theory (DFT) calculations on the vibrational frequencies involved in the amide I band of completely geometrically optimized models for beta-sheet peptides based upon (up to 16) glycine residues. These calculations use the B3LYP/D95** level of DFT. The primary means of vibrational coupling occurs through H bond, rather than through space, interactions, which is consistent with a previous report on alpha-helical polyalanines and H-bonding chains of both formamides and 4-pyridones. We decoupled the C=O stretching vibrations using selected 14C substitutions to probe the coupling mechanism and to determine "natural" frequencies for individual 14C=Os. The intermolecular H-bonding interactions affect the geometries of the amide groups. Those near the center of H-bonding chains have long C=O bonds. The C=O bond lengths correlate with these "natural" frequencies, The frequencies obtained from the DFT calculations are generally more coupled, and the most intense are more red shifted than those calculated by transition dipole coupling (TDC). TDC inverts the order of the shifted frequencies compared to DFT in several cases.

Direct calculation of trans-hydrogen-bond 13C-15N 3-bond J-couplings in entire polyalanine alpha-helices. A density functional theory study.

We present the first trans-H-bond 13C-15N 3-bond J couplings calculated from entire neutral and protonated alpha-helical polyalanines. The neutral helices considered are those of the capped peptides, acetyl(Ala)NNH2, where N = 8, 16, 17, and 18, while the protonated peptides are the uncapped (Ala)17 protonated at three different positions. The calculated J values correlate well with O...H distances and somewhat less well with N...O distances, particularly if the terminal H-bonds are eliminated from the correlation. The J values calculated using the entire helix are about 6% lower in magnitude than those recently reported for H-bonding chains whose geometries were extracted from the same helices. Aqueous solvation favors protonation of the alpha-helix on the terminal COOH. Experimental measurements of the trans-H-bond 13C-15N 3-bond J couplings in acidic solution should be interpreted with this context.

The effect of aqueous solvation upon alpha-helix formation for polyalanines.

The incremental free energies of aqueous solution for acetyl(ala)NNH2 in its extended unfolded and alpha-helical conformations are compared using the SM5.2 solvation method of Cramer and Truhlar. A combination of density functional theory (DFT) at the B3LYP/D95(d,p) and AM1 has been employed using the ONIOM method. The incremental solvation energies of alpha-helical structures are very similar for both ONIOM and AM1 optimized structures as these structures do not significantly change upon solution. However, the conformations of the unfolded peptides change from extended beta-strand to polyproline II conformations upon aqueous solution. The incremental solvation free energy per residue of the polyproline II structure is about 2 kcal/mol/residue greater than that for the alpha-helix, representing an upper limit for the difference between the solvation energies. However, most of this difference disappears when the energy required to distort the optimized gas-phase extended beta-strand structure to the optimized polyproline II solution structure is included in the analysis, leaving an estimated difference in incremental solvation free energy of 0.3-0.5 kcal/mol favoring the unfolded structure. The solution structure sacrifices the stability derived from the intramolecular C5 H-bonds for more favorable interactions with the aqueous solvent.

Through hydrogen-bond vibrational coupling in hydrogen-bonding chains of 4-pyridones with implications for peptide amide I absorptions: density functional theory compared with transition dipole coupling.

We present B3LYP/D95** calculations on the C=O and N-H couplings in H-bonded chains of 4-pyridones. 14C-substitutions are used to decouple various vibrations for purposes of illustration. The coupled C=O vibrations bear analogy to the amide I bands of proteins and peptides. The coupling of the C=O's occurs primarily via the cooperative H-bonds rather than transition dipole coupling (TDC), as demonstrated by the fact that (1) the couplings are greater than previously reported for similar studies on formamides despite the larger distance between the C=O's in the pyridone chains (TDC coupling decreases with distance) and (2) the red shifts (also greater than for formamides) can be attributed to the changes in the geometries (particularly the C=O bond lengths) of the individual 4-pyridones in the H-bonding chains induced by the H-bonds and resulting polarization of the monomers.

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.

Intramolecular aromatic 1,5-hydrogen transfer in free radical reactions III. Reactivity of diaryl ketones, ethers, thioethers, sulfoxydes, and sulfones. An experimental and theoretical study.

[reaction: see text] Experiments show that free radical hydrogen shift is significant in the Pschorr cyclization of diphenyl ethers (X = O) and thioethers (X = S) and does not take place with sufoxides (X = SO) and sulfones (X = SO(2)). DFT calculations of the product ratios, activation energies, rate constants for H-transfers, and ring-closings at the UB3PW91/6-31G(d,p) level are in excellent agreement with the experimental results reported here and elsewhere in the literature.