Imre Jákli

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‐stucture 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.

Peptide models XXIV: An ab initio study on N-formyl-L-prolinamide with trans peptide bond. The existence or non-existence of αL and ϵL conformations

Abstract N-formyl-L-prolinamide was subjected to geometry optimization at three levels of theory: HF/3-21G, HF/6-31G (d) and B3LYP/6-31G (d). At all three levels of computation the global minimum was γ L (inverse γ -Turn) backbone conformation with two ring-puckered forms “UP” and “DOWN”. At HF/3-21G level of theory three backbone conformations were found γ L , ϵ L , and α L . At higher levels of theory the ϵ L , and α L conformations disappeared. The “UP” and “DOWN” ring-puckered forms, in the γ L backbone conformation, led to practically identical vibrational spectra at the B3LYP/6-31G (d) level of theory.

PEPTIDE MODELS XXII. A CONFORMATIONAL MODEL FOR AROMATIC AMINO ACID RESIDUES IN PROTEINS. A COMPREHENSIVE ANALYSIS OF ALL THE RHF/6-31+G CONFORMERS OF FOR-L-PHE-NH2

Abstract Phenylalanine is expected to have conformational features similar to the other three naturally occurring aromatic amino acid residues: Tyr, Trp and His. Previous ab initio structure determinations resulted in 19 different conformers of HCO–L–Phe–NH2 at the RHF/3–21G level of theory. The present work summarises the results of a comprehensive analysis incorporating RHF/3–21G, RHF/6–31+G*, RHF/6–31+G*//RHF/3–21G and B3LYP/6–311++G**//RHF/3–21G data as some of the previously established minima have vanished with the larger basis set, three out of the 19 stationary points having migrated during the optimisation. On top of that, the conformational building unit of the right-handed helix-like (αL) conformation and that of the polyproline II (eL) conformation are still missing from the E=E(φ,ψ) surface. The optimised ab initio structures are also analysed in the context of –Phe– conformers taken from a large X-ray database on non-homologous proteins incorporating a total of 158 664 amino acid residues.

Peptide models XXIII. Conformational model for polar side‐chain containing amino acid residues: A comprehensive analysis of RHF, DFT, and MP2 properties of HCO‐L‐SER‐NH2

Geometric and energetic properties of a diamide of serine, HCO‐NH‐L‐CH(CH2OH)CO‐NH2, are investigated by standard methods of computational quantum chemistry. Similarly to other amino acid residues, conformational properties of HCO‐L‐Ser‐NH2 can be derived from the analysis of its E=E(ϕ,ψ;χ1,χ2) hypersurface. Reoptimization of 44 RHF/3‐21G conformers at the RHF/6‐311++G** level resulted in 36 minima. For all conformers, geometrical properties, including variation of H‐bond parameters and structural shifts in the torsional space, are thoroughly investigated. Results from further single‐point energy calculations at the RHF, DFT, and MP2 levels, performed on the entire conformational data set, form a database of 224 energy values, perhaps the largest set calculated so far for any single amino acid diamide. A comprehensive analysis of this database reveals significant correlation among energies obtained at six levels of ab initio theory. Regression parameters provide an opportunity for extrapolation in order to predict the energy of a conformer at a high level by doing explicit ab initio computations only for a few selected conformers. The computed conformational and relative energy data are compared with structural and occurrence results derived from a nonhomologous protein database incorporating 1135 proteins.

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.

Peptide models XXI. Side-chain/backbone conformational interconversions in HCO-l-Ser-NH2. Tracing relaxation paths by ab initio modeling. An exploratory study

Abstract Conformational motion of HCO- l -Ser-NH2 takes place on the four-dimensional space of f(φ, ψ, χ1, χ2). For all backbone conformation types (such as the building unit of an α-helix, β-pleated sheet, inverse γ-turn, etc.), selected two-dimensional cross-sections ( f relax α l [χ 1 ,χ 2 ], f relax β l [χ 1 ,χ 2 ], f relax γ l [χ 1 ,χ 2 ] etc. ) of the above four-dimensional hyperspace were calculated as the HF/3-21G level of theory. The analysis of the above ab initio conformation energy maps made the tracing of some relaxation paths possible which led to the monitoring of the side-chain-induced backbone conformational shifts operative in HCO- l -Ser-NH2. For most peptide models the present surface analysis makes it possible to monitor the side-chain-induced backbone modification via relaxation paths.

The inherent flexibility of peptides and protein fragments quantitized by CD in conjunction with CCA

ECD spectroscopy is traditionally used for rapid, non‐atomic level structure analysis of natural products such as peptides and proteins. Unlike globular proteins, peptides less frequently adopt a single 3D‐fold in a time average manner. Moreover, they exhibit an ensemble of conformers composed of a multitude of substantially different structures. In principle, both ECD‐ and vibrational circular dichroism (VCD)‐spectroscopy are sensitive enough to pick up structural information on these dynamic ensembles. However, the interpretation of the raw spectral data of these highly dynamic molecular systems can be cumbersome. The herein presented Convex Constraint Analysis Plus method, or CCA+ for short (http://www.chem.elte.hu/departments/protnmr/cca/), provides a unique opportunity for spectral ensemble analysis of peptides, glycopeptides, peptidomimetics, and other foldamers. The precision and accuracy of the approach is presented here through different peptide model systems. An interesting temperature and pH dependent folding and unfolding of a miniprotein (e.g. Tc5b variant) is also described. Analysis of CD spectra sets strongly affected by solvent and ion type is also introduced to account for severe environmental‐induced structure influencing effect(s). The deconvolution makes always possible the quantitative data analysis even when the interpretation of the deconvolution resulted in pure CD curves is complex. Copyright

Atropisomerism of the Asn α radicals revealed by ramachandran surface topology

C radicals are typically trigonal planar and thus achiral, regardless of whether they originate from a chiral or an achiral C-atom (e.g., C-H + (•)OH → C• + H2O). Oxidative stress could initiate radical formation in proteins when, for example, the H-atom is abstracted from the Cα-carbon of an amino acid residue. Electronic structure calculations show that such a radical remains achiral when formed from the achiral Gly, or the chiral but small Ala residues. However, when longer side-chain containing proteogenic amino acid residues are studied (e.g., Asn), they provide radicals of axis chirality, which in turn leads to atropisomerism observed for the first time for peptides. The two enantiomeric extended backbone structures, •βL and •βD, interconvert via a pair of enantiotopic reaction paths, monitored on a 4D Ramachandran surface, with two distinct transition states of very different Gibbs-free energies: 37.4 and 67.7 kJ/mol, respectively. This discovery requires the reassessment of our understanding on radical formation and their conformational and stereochemical behavior. Furthermore, the atropisomerism of proteogenic amino acid residues should affect our understanding on radicals in biological systems and, thus, reframes the role of the D-residues as markers of molecular aging.

Four faces of the interaction between ions and aromatic rings

Non‐covalent interactions between ions and aromatic rings play an important role in the stabilization of macromolecular complexes; of particular interest are peptides and proteins containing aromatic side chains (Phe, Trp, and Tyr) interacting with negatively (Asp and Glu) and positively (Arg and Lys) charged amino acid residues. The structures of the ion–aromatic‐ring complexes are the result of an interaction between the large quadrupole moment of the ring and the charge of the ion. Four attractive interaction types are proposed to be distinguished based on the position of the ion with respect to the plane of the ring: perpendicular cation–π (CP⊥), co‐planar cation–π (CP∥), perpendicular anion–π (AP⊥), and co‐planar anion–π (AP∥). To understand more than the basic features of these four interaction types, a systematic, high‐level quantum chemical study is performed, using the X– + C6H6, M+ + C6H6, X– + C6F6, and M+ + C6F6 model systems with X− = H−, F−, Cl−, HCOO−, CH3COO− and M+ = H+, Li+, Na+, NH4+ , CH3 NH3+ , whereby C6H6 and C6F6 represent an electron‐rich and an electron‐deficient π system, respectively. Benchmark‐quality interaction energies with small uncertainties, obtained via the so‐called focal‐point analysis (FPA) technique, are reported for the four interaction types. The computations reveal that the interactions lead to significant stabilization, and that the interaction energy order, given in kcal mol−1 in parentheses, is CP⊥ (23–37) > AP⊥ (14–21) > CP∥ (9–22) > AP∥ (6–16). A natural bond orbital analysis performed leads to a deeper qualitative understanding of the four interaction types. To facilitate the future quantum chemical characterization of ion–aromatic‐ring interactions in large biomolecules, the performance of three density functional theory methods, B3LYP, BHandHLYP, and M06‐2X, is tested against the FPA benchmarks, with the result that the M06‐2X functional performs best.

Quantum Chemical Calculations on Small Protein Models

After the definition of the peptide bond and its strength, as measured by its amidicity values the Ramachandran type potential energy surface (PES) of the backbone was investigated. Various alternatives, such as fitting mathematical functions the PES and its toroidal representation were discussed. A brief review of small peptides and oligopeptides was presented from a historic point of view. Peptide radicals as the cause of aging and numerous diseases were also outline. Finally it was concluded that the ultimate peptide and protein folding problem can be expected only after the chemical problem is rephrased as a mathematical problem.