Péter Hudáky

Solvation model induced structural changes in peptides. A quantum chemical study on Ramachandran surfaces and conformers of alanine diamide using the polarizable continuum model

Potential energy surfaces of the model peptide HCO‐L‐Ala‐NH2 were calculated using polarizable continuum model (PCM) for the description of aqueous solution at RHF/3‐21G, RHF/6‐31+G(d), and B3LYP/6‐31+G(d) levels of theory. Energy minima were optimized at all three levels as well as at B3LYP/PCM/6‐311++G(d,p) level of theory. Results were correlated to experimental data of protein structures retrieved from PDB SELECT. It is concluded that alanine residues of proteins are modeled better by PCM results than by gas‐phase calculations on the alanine diamide model (frequently called alanine dipeptide model). The currently available version of the PCM model implemented in Gaussian 03 provides a reasonable alternative to anticipate solvation effects without the computational costs of introducing explicit solvent molecules into the model system. Frequencies calculated at RHF/PCM/6‐31+G(d) and B3LYP/PCM/6‐31+G(d) levels of theory show high correlation; thus, RHF results have their own merit.

Peptide Models XXXI. Conformational Properties of Hydrophobic Residues Shaping the Core of Proteins. An Ab Initio Study of N-Formyl-L-Valinamide and N-Formyl-L-Phenylalaninamide

Employing introductory (3‐21G RHF) and medium‐size (6‐311++G** B3LYP) ab initio calculations, complete conformational libraries, containing as many as 27 conformers, have been determined for diamide model systems incorporating the amino acids valine (Val) and phenylalanine (Phe). Conformational and energetic properties of these libraries were analyzed. For example, significant correlation was found between relative energies from 6‐311++G** B3LYP and single‐point B3LYP/6‐311++G**//RHF/3‐21G calculations. Comparison of populations of molecular conformations of hydrophobic aromatic and nonaromatic residues, based on their ab initiorelative energies, with their natural abundance indicates that, at least for the hydrophobic core of proteins, the conformations of Val (Ile, Leu) and Phe (Tyr, Trp) are controlled by the local energetic preferences of the respective amino acids.

Stability Issues of Covalently and Noncovalently Bonded Peptide Subunits

The present study focuses on important questions associated with modeling of peptide and protein stability. Computing at different levels of theory (RHF, B3LYP) for a representative ensemble of conformers of di‐ and tripeptides of alanine, we found that the Gibbs Free Energy values correlate significantly with the total electronic energy of the molecules (0.922 ≤ R2). For noncovalently attached but interacting peptide subunits, such as [For‐NH2]2 or [For‐L‐Ala‐NH2]2, we have found, as expected, that the basis set superimposition error (BSSE) is large in magnitude for small basis set but significantly smaller when larger basis sets [e.g., B3LYP/6‐311++G(d,p)] are used. Stability of the two hydrogen bonds of antiparallel β‐pleated sheets were quantitatively determined as a function of the molecular structure, S10 and S14, computed as 4.0 ± 0.5 and 8.1 ± 1.1 kcal/mol, respectively. Finally, a suitable thermoneutral isodesmic reaction was introduced to scale both covalently and noncovalently attached peptide units onto a common stability scale. We found that a suitable isodesmic reaction can result in the total electronic energy as well as the Gibbs free energy of a molecule, from its “noninteracting” fragments, as accurate as a few tenths of a kcal per mol. The latter observation seems to hold for peptides regardless of their length (1 ≤ n ≤ 8) or the level of theory applied.

Generation and analysis of the conformational potential energy surfaces of N-acetyl-N-methyl-L-alanine-N'-methylamide. An exploratory ab initio study

Abstract N-methylation is a naturally occurring modification in small peptides, e.g. antibiotics that can effect the conformational preferences of the molecule as well as the ease of trans to cis isomerization of the involved peptide bond. In the present exploratory study we have calculated the potential energy surface of both N -acetyl- l -alanine- N ′-methylamide and N -acetyl- N -methyl- l -alanine- N ′-methylamide at the RHF/3-21G level of theory with a cis – trans or with a trans – trans peptide conformation. With respect to the non-methylated model system our results indicate that N-methylation reduces the number of observable backbone conformers in both amide configurations. The effect of methylation on the ease of trans to cis isomerization was assessed by calculating the energetics of the corresponding transition structures. An increase in the activation energies of the trans to cis isomerization of the relevant peptide bond was observed for the N-methylated moiety.

Deciphering factors which determine the Ramachandran surface of peptides. The application of isodesmic surfaces, ΔEID(ϕ,ψ), to analyze the contribution of rotating moieties to the shape of potential energy surfaces

Abstract A series of double rotors of the following types have been investigated via potential energy surfaces, E=E(ϕ,ψ), generated by ab initio Hartree–Fock molecular computations. Download : Download high-res image (10KB) Download : Download full-size image Series of triply substituted methyne (H–C) moieties are called upon to mimic, the conformational behaviour of peptides. In substituents Z1 and Z2 the “first atoms” were of sp3 and sp2 hybridization having Z1=−CH3, –CH2F and –NHCHO, as well as Z2=−CH3, –CH2F, –CHO and –CONH2. The R group was chosen to be –H or –F and in one case –CH3 in order to reproduce the alanine model peptide. All potential energy surfaces, E=E(ϕ,ψ), were generated in the form of grids where points were separated by 15° intervals along both ϕ and ψ variables. This led to a total of 625 SCF points (25×25) for each surface, since both the initial (0°) and final (360°) values of both periodic variables (ϕ and ψ) were included in the grid. The interaction between substituents introduced were monitored by isodesmic reactions computed at each of the 625 grid points leading to isodesmic energy surfaces: ΔEID(ϕ,ψ). Comparing the influence of the different Z1 and Z2 substituents, undoubtedly, the introduction of two adjacent peptide bonds led to the greatest effect on the conformational energy surface.

Peptide models XXXIV. Side-chain conformational potential energy surfaces associated with all major backbone folds of neutral tautomers of N- and C-protected l-histidine. An ab initio study on ethylimidazole and N-formyl-l-histidinamide

Abstract Both tautomers of N -formyl- l -histidinamide and ethylimidazole were subjected to conformational analysis at the ab initio RHF/6-31G(d) level of theory. Side-chain potential energy surfaces (PES) were calculated for the nine typical backbone conformations predicted by Multidimensional Conformational Analysis. The side-chain torsions of N -formyl- l -histidinamide ( χ 1 and χ 2 ) were characterized with respect to the shapes of the PES. All envisaged minima were fully optimized. For each conformer of N -formyl- l -histidinamide stabilization energy was calculated and compared to values determined for other amino acid residues.

A self-stabilized model of the chymotrypsin catalytic pocket. The energy profile of the overall catalytic cycle

A model of the catalytic triad of chymotrypsin is built assuring the arrangement and properties as they are within the complete enzyme. The model contains 18 amino acid residues of chymotrypsin and its substrate. A total of 135 atoms (including 70 heavy atoms) were subjected to full ab initio geometry optimizations through 127 individual steps along the reaction coordinate of the complete catalytic mechanism. It was shown that the described model of the catalytic apparatus forms a self‐stabilized molecule ensemble without the rest of the enzyme and substrate. According to the calculations, the formations of the first and second tetrahedral intermediates in the model have 20.3 and 15.7 kcal/mol activation energy barriers, respectively. Removing elements of the catalytic apparatus such as the (1) catalytic aspartate or (2) the anion hole, as well as (3) inserting a water molecule “early” in the catalytic process, or (4) introducing conformational rigidity of the substrate, results in an increase of the above energy barrier of the first catalytic step in the model by 6.4, 13.7, 3.7, and 4.1 kcal/mol, respectively. Based on the calculated process one can conclude that the catalytic reaction in this model is much more similar to the reaction in the enzyme than to the reference reaction. To our knowledge, this is the first model system that mimics the complete catalytic mechanism. Proteins 2006.

Peptide models XXXV. Protonated and deprotonated N-Formyl-l-histidinamide: an ab initio study on side-chain potential energy surfaces of all major backbone conformers

Abstract Charged forms of N -Formyl- l -histidinamide and ethylimidazole molecules were subjected to conformational analysis at the ab initio RHF/6-31G(d) level of theory. Side-chain potential energy surfaces, E = E bb ( χ 1 , χ 2 ), were calculated at the nine typical backbone conformations (bb=α L , α D , β L , γ L , γ D , δ L , δ D , e L and e D ) given by multidimensional conformational analysis (MDCA). Envisaged minima obtained from the topological analysis of E = E bb ( χ 1 , χ 2 ) surfaces and from MDCA were fully optimized. Electrostatic interaction between charged side-chain and polar peptide bonds is discussed. Stabilization energy was calculated for each conformer of N -Formyl- l -histidinamide and scored relative to the stabilization energy of other amino acids.

AMINO ACID CONFORMATIONAL ANALYSES OF PROTEINS (ACAP PROGRAM)

Abstract The secondary structure analysis of proteins is a powerful tool, efficiently supporting spectroscopic (CD, IR, NMR) and biochemical research projects. However, the precise location of the different secondary structural elements in a sequence incorporates some subjectivity. A linearized notation of a uniform and objective description of protein backbone structures was developed. This involves a three-dimensional to one-dimensional transformation (3D → 1D). The classification is based on a step-by-step comparison performed between reference conformers (also called template values) and backbone sub-conformations of the protein. The readily provided structure templates may be modified, but the procedure still remains objective and uniform. This linearized notation of protein structures provides a description of the three-dimensional backbone conformation without relying on the traditional concept of secondary structure. Previously, the sequence analysis (primary structure) of proteins resulted in the identification of the 20 natural amino acid residues. Similarly, the backbone conformation analysis of the same proteins confirmed the presence of nine basically different subconformers. This recognition and the application of the linearized notation of the 3D structure makes easier the comparison of proteins at the levels of primary to tertiary structure.

Toward direct determination of conformations of protein building units from multidimensional NMR experiments VI. Chemical shift analysis of his to gain 3D structure and protonation state information

NMR–chemical shift structure correlations were investigated by using GIAO‐RB3LYP/6‐311++G(2d,2p) formalism. Geometries and chemical shifts (CSI values) of 103 different conformers of N′‐formyl‐L‐histidinamide were determined including both neutral and charged protonation forms. Correlations between amino acid torsional angle values and chemical shifts were investigated for the first time for an aromatic and polar amino acid residue whose side chain may carry different charges. Linear correlation coefficients of a significant level were determined between chemical shifts and dihedral angles for CSI[1Hα]/φ, CSI[13Cα]/φ, and CSI[13Cα]/ψ. Protonation of the imidazole ring induces the upfield shift of CSI[13Cα] for positively charged histidines and an opposite effect for the negative residue. We investigated the correspondence of theoretical and experimental 13Cα, 13Cβ, and 1Hα chemical shifts and the nine basic conformational building units characteristic for proteins. These three chemical shift values allow the identification of conformational building units at 80% accuracy. These results enable the prediction of additional regular secondary structural elements (e.g., polyProlineII, inverse γ‐turns) and loops beyond the assignment of chemical shifts to α‐helices and β‐pleated sheets. Moreover, the location of the His residue can be further specified in a β‐sheet. It is possible to determine whether the appropriate residue is located at the middle or in a first/last β‐strand within a β‐sheet based on calculated CSI values. Thus, the attractive idea of establishing local residue specific backbone folding parameters in peptides and proteins by employing chemical shift information (e.g., 1Hα and 13Cα) obtained from selected heteronuclear correlation NMR experiments (e.g., 2D‐HSQC) is reinforced.