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

Dynamics of proteins aggregation. I. Universal scaling in unbounded media

It is well understood that in some cases proteins do not fold correctly and, depending on their environment, even properly-folded proteins change their conformation spontaneously, taking on a misfolded state that leads to protein aggregation and formation of large aggregates. An important factor that contributes to the aggregation is the interactions between the misfolded proteins. Depending on the aggregation environment, the aggregates may take on various shapes forming larger structures, such as protein plaques that are often toxic. Their deposition in tissues is a major contributing factor to many neuro-degenerative diseases, such as Alzheimer's, Parkinson's, amyotrophic lateral sclerosis, and prion. This paper represents the first part in a series devoted to molecular simulation of protein aggregation. We use the PRIME, a meso-scale model of proteins, together with extensive discontinuous molecular dynamics simulation to study the aggregation process in an unbounded fluid system, as the first step toward MD simulation of the same phenomenon in crowded cellular environments. Various properties of the aggregates have been computed, including dynamic evolution of aggregate-size distribution, mean aggregate size, number of peptides that contribute to the formation of β sheets, number of various types of hydrogen bonds formed in the system, radius of gyration of the aggregates, and the aggregates' diffusivity. We show that many of such quantities follow dynamic scaling, similar to those for aggregation of colloidal clusters. In particular, at long times the mean aggregate size S(t) grows with time as, S(t) ∼ t^z, where z is the dynamic exponent. To our knowledge, this is the first time that the qualitative similarity between aggregation of proteins and colloidal aggregates has been pointed out.

Probing the role of electrostatics of polypeptide main-chain in protein folding by perturbing N-terminal residue stereochemistry: DFT study with oligoalanine models

Energetics of folding (ΔH_E→F, in kcal mol⁻¹) from the extended (E) structure to the folded (F) structure for Ia and Ib critically depend on the geometrical relationship between the backbone peptide units of the polypeptide structure.

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.

Conformational properties of oxazole-amino acids: effect of the intramolecular N-H···N hydrogen bond

Oxazole ring occurs in numerous natural peptides, but conformational properties of the amino acid residue containing the oxazole ring in place of the C-terminal amide bond are poorly recognized. A series of model compounds constituted by the oxazole-amino acids occurring in nature, that is, oxazole-alanine (L-Ala-Ozl), oxazole-dehydroalanine (ΔAla-Ozl), and oxazole-dehydrobutyrine ((Z)-ΔAbu-Ozl), was investigated using theoretical calculations supported by FTIR and NMR spectra and single-crystal X-ray diffraction. It was found that the main feature of the studied oxazole-amino acids is the stable conformation β2 with the torsion angles φ and ψ of -150°, -10° for L-Ala-Ozl, -180°, 0° for ΔAla-Ozl, and -120°, 0° for (Z)-ΔAbu-Ozl, respectively. The conformation β2 is stabilized by the intramolecular N-H···N hydrogen bond and predominates in the low polar environment. In the case of the oxazole-dehydroamino acids, the π-electron conjugation that is spread on the oxazole ring and C(α)═C(β) double bond is an additional stabilizing interaction. The tendency to adopt the conformation β2 clearly decreases with increasing the polarity of environment, but still the oxazole-dehydroamino acids are considered to be more rigid and resistant to conformational changes.

The interactions of phenylalanines in β-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 β-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.

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.

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.

Antifreeze glycoprotein agents: structural requirements for activity

Antifreeze glycoproteins (AFGPs) are considered to be the most efficient means to reduce ice damage to cell tissues since they are able to inhibit growth and crystallization of ice. The key element of antifreeze proteins is to act in a non-colligative manner which allows them to function at concentrations 300-500 times lowers than other dissolved solutes. During the past decade, AFGPs have demonstrated tremendous potential for many pharmaceutical and food applications. Presently, the only route to obtain AFGPs involves the time consuming and expensive process of isolation and purification from deep-sea polar fishes. Unfortunately, it is not amenable to mass production and commercial applications. The lack of understanding of the mechanism through which the AFGPs inhibit ice growth has also hampered the realization of industrial and biotechnological applications. Here we report the structural motifs that are essential for antifreeze activity of AFGPs, and propose a unified mechanism based on both recent studies of short alanine peptides and structure activity relationship of synthesized AFGPs.

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.

Peptide bond distortions from planarity: new insights from quantum mechanical calculations and peptide/protein crystal structures

By combining quantum-mechanical analysis and statistical survey of peptide/protein structure databases we here report a thorough investigation of the conformational dependence of the geometry of peptide bond, the basic element of protein structures. Different peptide model systems have been studied by an integrated quantum mechanical approach, employing DFT, MP2 and CCSD(T) calculations, both in aqueous solution and in the gas phase. Also in absence of inter-residue interactions, small distortions from the planarity are more a rule than an exception, and they are mainly determined by the backbone ψ dihedral angle. These indications are fully corroborated by a statistical survey of accurate protein/peptide structures. Orbital analysis shows that orbital interactions between the σ system of C(α) substituents and the π system of the amide bond are crucial for the modulation of peptide bond distortions. Our study thus indicates that, although long-range inter-molecular interactions can obviously affect the peptide planarity, their influence is statistically averaged. Therefore, the variability of peptide bond geometry in proteins is remarkably reproduced by extremely simplified systems since local factors are the main driving force of these observed trends. The implications of the present findings for protein structure determination, validation and prediction are also discussed.

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.

Counting peptide-water hydrogen bonds in unfolded proteins

It is often assumed that the peptide backbone forms a substantial number of additional hydrogen bonds when a protein unfolds. We challenge that assumption in this article. Early surveys of hydrogen bonding in proteins of known structure typically found that most, but not all, backbone polar groups are satisfied, either by intramolecular partners or by water. When the protein is folded, these groups form approximately two hydrogen bonds per peptide unit, one donor or acceptor for each carbonyl oxygen or amide hydrogen, respectively. But when unfolded, the backbone chain is often believed to form three hydrogen bonds per peptide unit, one partner for each oxygen lone pair or amide hydrogen. This assumption is based on the properties of small model compounds, like N-methylacetamide, or simply accepted as self-evident fact. If valid, a chain of N residues would have approximately 2N backbone hydrogen bonds when folded but 3N backbone hydrogen bonds when unfolded, a sufficient difference to overshadow any uncertainties involved in calculating these per-residue averages. Here, we use exhaustive conformational sampling to monitor the number of H-bonds in a statistically adequate population of blocked polyalanyl-six-mers as the solvent quality ranges from good to poor. Solvent quality is represented by a scalar parameter used to Boltzmann-weight the population energy. Recent experimental studies show that a repeating (Gly-Ser) polypeptide undergoes a denaturant-induced expansion accompanied by breaking intramolecular peptide H-bonds. Results from our simulations augment this experimental finding by showing that the number of H-bonds is approximately conserved during such expansion⇋compaction transitions.

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.

Understanding the influence of guest-host interactions on the conformation of short peptides in a hydrophobic cavity: a computational study

We performed a computational investigation to understand the conformational preferences of four short peptides in a self-assembled cage based on the experimental work by Y. Hatakeyama et al. (Angew. Chem. Int. Ed.2009, 48, 8695). For this purpose, we combined molecular dynamics simulations, Monte Carlo simulations, and quantum mechanical calculations to obtain energies and structures for several low-lying conformers of four peptides and the corresponding peptide-cage inclusion complexes. Our calculations at both B3LYP and MP2 levels show that for each peptide, the corresponding conformation within the host (as revealed by the crystal structure) does not represent the lowest-energy conformation of this peptide in vacuum. By comparing some low-lying conformers in vacuum and in the cavity (for the same peptide), we found that the cage has a significant influence on the conformational propensities of peptides. First, one carbonyl oxygen of each peptide tends to bind to one Zn(II) atom of the cage, forming a Zn-O bond. The formation of this bond leads to significant charge transfer from the cage to the peptide. Second, this Zn-O bond causes the peptide to go through some local conformational changes. For larger peptides, such as penta- and hexapeptides, our calculations also show that some of their conformers must undergo significant structural changes, due to the confinement of the host. This computational study reveals the noticeable influence of the guest-host interaction on the conformational preferences of short peptides.

Development of a new physics-based internal coordinate mechanics force field and its application to protein loop modeling

We report the development of internal coordinate mechanics force field (ICMFF), new force field parameterized using a combination of experimental data for crystals of small molecules and quantum mechanics calculations. The main features of ICMFF include: (a) parameterization for the dielectric constant relevant to the condensed state (ε = 2) instead of vacuum, (b) an improved description of hydrogen-bond interactions using duplicate sets of van der Waals parameters for heavy atom-hydrogen interactions, and (c) improved backbone covalent geometry and energetics achieved using novel backbone torsional potentials and inclusion of the bond angles at the C(α) atoms into the internal variable set. The performance of ICMFF was evaluated through loop modeling simulations for 4-13 residue loops. ICMFF was combined with a solvent-accessible surface area solvation model optimized using a large set of loop decoys. Conformational sampling was carried out using the biased probability Monte Carlo method. Average/median backbone root-mean-square deviations of the lowest energy conformations from the native structures were 0.25/0.21 Å for four residues loops, 0.84/0.46 Å for eight residue loops, and 1.16/0.73 Å for 12 residue loops. To our knowledge, these results are significantly better than or comparable with those reported to date for any loop modeling method that does not take crystal packing into account. Moreover, the accuracy of our method is on par with the best previously reported results obtained considering the crystal environment. We attribute this success to the high accuracy of the new ICM force field achieved by meticulous parameterization, to the optimized solvent model, and the efficiency of the search method.

Infrared spectroscopy of the alanine dipeptide analog in liquid water with DFT-MD. Direct evidence for P(II)/beta conformations

Following our previous work [J. Phys. Chem. B. Lett., 2009, 113, 10059], DFT-based molecular dynamics (DFTMD) simulations of 2-Ala peptide (i.e. Ac-Ala-NHMe dialanine peptide analog with methyl group caps at the extremities) immersed in liquid water at room temperature are reported. Our goal here is the theoretical calculation of the infrared spectrum of aqueous 2-Ala, in order to provide a definitive understanding of the average conformation adopted by this peptide in the liquid phase, taking into account solute and solvent at the same theoretical level of representation. We find that the experimental Amide I-II band predominantly results from a mixture of partially unfolded P(II) and unfolded beta conformational equilibrium of aqueous 2-Ala at room temperature.

UV resonance Raman investigation of the conformations and lowest energy allowed electronic excited states of tri- and tetraalanine: charge transfer transitions

UV resonance Raman excitation profiles and Raman depolarization ratios were measured for trialanine and tetraalanine between 198 and 210 nm. Excitation within the pi --> pi* electronic transitions of the peptide bond results in UVRR spectra dominated by amide peptide bond vibrations. In addition to the resonance enhancement of the normal amide vibrations, we find enhancement of the symmetric terminal COO(-) vibration. The Ala(3) UVRR AmIII(3) band frequencies indicate that poly-proline II and 2.5(1) helix conformations and type II turns are present in solution. We also find that the conformation of the interior peptide bond of Ala(4) is predominantly poly-proline-II-like. The Raman excitation profiles of both Ala(3) and Ala(4) reveal a charge transfer electronic transition at 202 nm, where electron transfer occurs from the terminal nonbonding carboxylate orbital to the adjacent peptide bond pi* orbital. Raman depolarization ratio measurements support this assignment. An additional electronic transition is found in Ala(4) at 206 nm.

Sidechain conformational dependence of hydrogen exchange in model peptides

Peptide hydrogens that are exposed to solvent in protein X-ray structures exhibit a billion-fold range in hydroxide-catalyzed exchange rates, and these rates have previously been shown to be predictable by continuum dielectric methods to within a factor of 7, based on single protein conformations. When using a protein coil library to model the Boltzmann-weighted conformational distribution for the various N-acetyl-[X-Ala]-N-methylamides and N-acetyl-[Ala-Y]-N-methylamides, the acidity of the central amide in the individual conformers of each peptide spans nearly a million-fold range. Nevertheless, population averaging of these conformer acidities predicts the standard sidechain-dependent hydrogen exchange correction factors for nonpolar model peptides to within a factor of 30% (10(0.11)) with a correlation coefficient r=0.91. Comparison with the analogous continuum dielectric calculations for the other N-acetyl-[X-Y]-N-methylamides indicates that deviations from the isolated residue hypothesis of classical polymer theory predict appreciable errors in the exchange rates for conformationally disordered peptides when the standard sidechain-dependent hydrogen exchange rate correction factors are assumed to be independently additive. Although electronic polarizability generally dominates the dielectric shielding for the approximately 10ps lifetime of peptide ionization, evidence is presented for modest contributions from rapid intrarotamer conformational reorganization of Asn and Gln sidechains.