Peptide models 4. Topological features of molecular mechanics and ab initio 2D-ramachandran maps

An improved two-rotor function for conformational potential energy surfaces of 20 amino acid diamides

Predicting the three-dimensional structure of a protein from its amino acid sequence requires a complete understanding of the molecular forces that influences the protein folding process. Each possible conformation has its corresponding potential energy, which characterizes its thermodynamic stability. This is needed to identify the primary intra- and inter-molecular interactions, so that we can reduce the dimensionality of the problem, and create a relatively simple representation of the system. Investigating this problem using quantum chemical methods produces accurate results; however, this also entails large computational resources. In this study, an improved two-rotor potential energy function is proposed to represent the backbone interactions in amino acids through a linear combination of a Fourier series and a mixture of Gaussian functions. This function is applied to approximate the 20 amino acid diamide Ramachandran-type PESs, and results yielded an average RMSE of 2.36 kJ mol−1, which suggest that the mathematical model precisely captures the general topology of the conformational potential energy surface. Furthermore, this paper provides insights on the conformational preferences of amino acid diamides through local minima geometries and energy ranges, using the improved mathematical model. The proposed mathematical model presents a simpler representation that attempts to provide a framework on building polypeptide models from individual amino acid functions, and consequently, a novel method for rapid but accurate evaluation of potential energies for biomolecular simulations.

A comprehensive conformational space analysis of N-formyl-l-tryptophanamide system by using a genetic algorithm for multi-modal search

The conformational space of protected amino acid HCO-Tryptophane-NH₂ was explored by using a new optimization procedure, in order to localize the stable minima on its potential energy surface (PES). The genetic algorithm based on the Multi-Niche Crowding (MNC) technique was used initially to generate a set of optimized structures for title compound. Resulting structures from the genetic algorithm technique will be used hereafter as input conformers at a hierarchy of increasingly more accurate electronic structure calculations (RHF/6-31G+(d) and DFT/B3LYP/6-31G+(d) geometry optimizations). The lowest energy conformer γ_L(g+g+) presents a folded Backbone that is stabilized by strong hydrogen bond noted C₇. This links the carbonyl oxygen of the formyl group and the hydrogen of the amine group. There are further interactions from one hand between the carbonyl oxygen of the formyl group and the neighboring CH group on the pyrrole ring and from other hand between the N-terminus hydrogen and the indole ring in accordance with the experimental results. This work includes also a comparison between the theoretical calculations and the experimental results of X-ray crystallography extracted from protein data bank (PDB).

Conformational Preferences of N-Acetyl-l-leucine-N‘-methylamide. Gas-Phase and Solution Calculations on the Model Dipeptide

A DFT study of N-acetyl-l-leucine-N'-methylamide conformers in the gas phase and in solution was carried out. The theoretical computational analysis revealed 43 different conformations at the B3LYP/6-31G(d) level of theory in the gas phase. In addition, the effects of three solvents (water, acetonitrile, and chloroform) were included in the calculations using the isodensity polarizable continuum model (IPCM) and the Poisson-Boltzmann self-consistent reaction field (PB-SCRF) method. The stability order of the different conformers in solution has been analyzed. The theoretical results were compared with some experimental data (X-ray, IR, and NMR).

Thermodynamic Functions of Conformational Changes: Conformational Network of Glycine Diamide Folding, Entropy Lowering, and Informational Accumulation

A refined grid of a conformational potential energy surface (PES) and a conformational entropy surface for glycine diamide was generated by ab initio molecular computations. The possible network of reaction paths was recognized in terms of the linear combinations of internal coordinates corresponding to conrotatory and disrotatory modes of motions. Such a Woodward-Hoffmann-like path selection principle was detected for the folding of this peptide from extended to some virtually cyclic structure. It seemed reasonable to assume that this principle (or its generalized form) might be applicable to protein folding. A reaction path network was projected on the potential energy, and a continuous entropy surface was constructed under the condition of reduced dimensionality. The low entropy of the folded conformation indicated an information accumulation between 326% and 1414% with respect to the fully extended or unfolded structure. It is found that the location of existing and 'latent' critical points on the surface is revealed by the extrema and inflection points of the entropy curve.

An Exhaustive Conformational Analysis of N-Acetyl-l-cysteine-N-methylamide. Identification of the Complete Set of Interconversion Pathways on the ab Initio and DFT Potential Energy Hypersurface

The full conformational space of N-acetyl-l-cysteine-N-methylamide was explored by ab initio (RHF/ 6-31G(d)) and DFT (B3LYP/6-31G(d)) computations. Multidimensional conformational analysis predicts 81 structures in N-acetyl-l-cysteine-N-methylamide, but only 47 relaxed structures were previously determined at the RHF/3-21G level of theory. These structures were now optimized using RHF/6-31G(d) and B3LYP/6-31G(d) approaches. Seven conformational migrations were observed when recalculated at higher level of theory. Besides these major changes, only smaller conformational shifts were operative for the remaining stationary points. The exploration of the whole conformational space of N-acetyl-l-cysteine-N-methylamide, including the transition-state structures allowing the conformational interconversion among the low-energy forms, was analyzed in this study. Our results offer new insights into the influence of polar side chains on the conformational preferences of peptide structures.

Peptide models XLV: Conformational properties of N-formyl-L-methioninamide and its relevance to methionine in proteins

The conformational space of the most biologically significant backbone folds of a suitable methionine peptide model was explored by density functional computational method. Using a medium [6-31G(d)] and a larger basis set [6-311++G(2d,2p)], the systematic exploration of low-energy backbone structures restricted for the "L-region" in the Ramachandran map of N-formyl-L-methioninamide results in conformers corresponding to the building units of an extended backbone structure (betaL), an inverse gamma-turn (gammaL), or a right-handed helical structure (alphaL). However, no poly-proline II type (epsilonL) fold was found, indicating that this conformer has no intrinsic stability, and highlighting the effect of molecular environment in stabilizing this backbone structure. This is in agreement with the abundance of the epsilonL-type backbone conformation of methionine found in proteins. Stability properties (DeltaE) and distinct backbone-side-chain interactions support the idea that specific intramolecular contacts are operative in the selection of the lowest energy conformers. Apart from the number of different folds, all stable conformers are within a 10 kcal x mol(-1) energy range, indicating the highly flexible behavior of methionine. This conformational feature can be important in supporting catalytic processes, facilitating protein folding and dimerization via metal ion binding. In both of the biological examples discussed (HIV-1 reverse transcriptase and PcoC copper-resistant protein), the conformational properties of Met residues were found to be of key importance. Spatial proximity to other types of residues or the same type of residue seems to be crucial for the structural integrity of a protein, whether Met is buried or exposed.

On the flexibility of beta-peptides

The full conformational space was explored for an achiral and two chiral beta-peptide models: namely For-beta-Ala-NH2, For-beta-Abu-NH2, and For-beta-Aib-NH2. Stability and conformational properties of all three model systems were computed at different levels of theory: RHF/3-21G, B3LYP/6-311++G(d,p)//RHF/3-21G, B3LYP/6-311++G(d,p), MP2//B3LYP/6-311++G(d,p), CCSD//B3LYP/6-311++G(d,p), and CCSD(T)//B3LYP/6-311++G(d,p). In addition, ab initio E = E(phi, micro, psi) potential energy hypersurfaces of all three models were determined, and their topologies were analyzed to determine the inherent flexibility properties of these beta-peptide models. Fewer points were found and assigned than expected on the basis of Multidimensional Conformational Analysis (MDCA). Furthermore, it has been demonstrated, that the four-dimensional surface, E = E(phi, mu, psi), can be reduced into a three-dimensional one: E = E[phi, f(phi), psi]. This reduction of dimensionality of freedom of motion suggests that beta-peptides are less flexible than one would have thought. This agrees with experimental data published on the conformational properties of peptides composed of beta-amino acid residues.

Peptide models. XXXIII. Extrapolation of low-level Hartree-Fock data of peptide conformation to large basis set SCF, MP2, DFT, and CCSD(T) results. The Ramachandran surface of alanine dipeptide computed at various levels of theory

At the dawn of the new millenium, new concepts are required for a more profound understanding of protein structures. Together with NMR and X-ray-based 3D-structure determinations in silico methods are now widely accepted. Homology-based modeling studies, molecular dynamics methods, and quantum mechanical approaches are more commonly used. Despite the steady and exponential increase in computational power, high level ab initio methods will not be in common use for studying the structure and dynamics of large peptides and proteins in the near future. We are presenting here a novel approach, in which low- and medium-level ab initio energy results are scaled, thus extrapolating to a higher level of information. This scaling is of special significance, because we observed previously on molecular properties such as energy, chemical shielding data, etc., determined at a higher theoretical level, do correlate better with experimental data, than those originating from lower theoretical treatments. The Ramachandran surface of an alanine dipeptide now determined at six different levels of theory [RHF and B3LYP 3-21G, 6-31+G(d) and 6-311++G(d,p)] serves as a suitable test. Minima, first-order critical points and partially optimized structures, determined at different levels of theory (SCF, DFT), were completed with high level energy calculations such as MP2, MP4D, and CCSD(T). For the first time three different CCSD(T) sets of energies were determined for all stable B3LYP/6-311++G(d,p) minima of an alanine dipeptide. From the simplest ab initio data (e.g., RHF/3-21G) to more complex results [CCSD(T)/6-311+G(d,p)//B3LYP/6-311++G(d,p)] all data sets were compared, analyzed in a comprehensive manner, and evaluated by means of statistics.

Computational study of conformational preferences of thioamide-containing azaglycine peptides

The effect of thioamide substitution on the conformational stability of an azaglycine-containing peptide, For-AzaGly-NH2 (1), was investigated for the sake of finding possible applications by using ab initio and DFT methods. As model compounds, For-[psiCSNH]-AzaGly-NH2 (2), For-AzaGly-[psiCSNH]-NH2 (3), and For-[psiCSNH]-AzaGly-[psiCSNH]-NH2 (4) were used. Two-dimensional phi-psi potential energy surfaces (PESs) for 2-4 were calculated at the B3LYP/6-31G*//HF/6-31G* level in gas (epsilon = 1.0) and in water (epsilon = 78.4) by applying the isodensity polarizable continuum model (IPCM) method. On the basis of these PESs, the minimum energy conformations for 2-4 were characterized at the B3LYP level with 6-31G*, 6-311G**, and 6-31+G** basis sets. The remarkable structural effect of thioamide substitution for 2-4 is that beta-strand structure is observed as a global or local minimum. The minima of 2-4 are also compared with those for glycine and thioamide-containing glycine peptides. Our theoretical results demonstrate that compounds 2-4 would be used to design controllable secondary structures.

Peptide model XXVIII: An exploratory ab initio and density functional study on the side-chain-backbone interaction in N-acetyl-L-cysteine- N-methylamide and N-formyl-L-cysteinamide in their γL-backbone conformations

A conformational and electronic study on the energetically preferred conformations (γL) of N- and C-protected L-cysteine (P-CONH-CH(CH2SH)-CONH-Q, where P and Q may be H or Me) was carried out. After restraining the backbone (BB) conformation to its global minimum (γL or C7eq), all nine possible side-chain (SC) conformations were subjected to geometry optimization at the HF/3–21G and the B3LYP/6–31G(d,p) levels of theory. Seven of the nine side-chain conformers were located on the potential-energy surface. All conformers were subjected to an AIM (atoms in molecules) analysis. This study indicates that three of the seven optimized conformers exhibited either or both SC [Formula: see text] BB- or BB [Formula: see text] SC-type intramolecular hydrogen bonding. Five conformers, however, had distances between a proton and a heteroatom that suggested hydrogen bonding.Key words: L-cysteine diamides, side-chain potential-energy surface, ab initio and DFT geometry optimization, AIM analysis, intramolecular hydrogen bonding.

Article

The ab initio conformational energy minima of the model tripeptide N-formyl-L-alanyl-L-alanine amide (ALA-ALA) were determined by ab initio RHF/4-21G and RHF/6-31G* gradient geometry refinement. For the current investigation, 11 664 RHF/4-21G structures were optimized, representing grid points in the four-dimensional (phi1, psi1, phi2, psi2) conformational space, which were constructed in 40° increments along the outer torsions phi1 and psi2 and in 30° increments along the inner torsions psi1 and phi2 of ALA-ALA. Two new energy minima, previously not reported, are described. The positions of the RHF/6-31G* energy minima in phi,psi-space can differ significantly from the corresponding RHF/4-21G locations, and both sets are not clustered in the centers but on the fringes of the most populated regions of phi, psi-space in protein crystal structures. Thus, the torsion angles of the ab initio energy minima are not those of the typical substructures of proteins: the most stable helices are not alphaR, and the torsion angles of the most stable bend forms are not those most frequently encountered in protein bends. Limitations of the dipeptide approximation are explored, illustrating how the conformational energies of an amino acid residue depend on the state of its neighbor.Key words: alanyl alanine amide, dipeptide approximation, model tripeptide, peptide models, structure of peptides.