Structure of Isolated Tryptophyl-Glycine Dipeptide and Tryptophyl-Glycyl-Glycine Tripeptide: Ab Initio SCC-DFTB-D Molecular Dynamics Simulations and High-Level Correlated ab Initio Quantum Chemical Calculations

Tracking the Amide I and αCOO- Terminal ν(C=O) Raman Bands in a Family of l-Glutamic Acid-Containing Peptide Fragments: A Raman and DFT Study

The E-hook of β-tubulin plays instrumental roles in cytoskeletal regulation and function. The last six C-terminal residues of the βII isotype, a peptide of amino acid sequence EGEDEA, extend from the microtubule surface and have eluded characterization with classic X-ray crystallographic techniques. The band position of the characteristic amide I vibration of small peptide fragments is heavily dependent on the length of the peptide chain, the extent of intramolecular hydrogen bonding, and the overall polarity of the fragment. The dependence of the E residue's amide I ν(C=O) and the αCOO- terminal ν(C=O) bands on the neighboring side chain, the length of the peptide fragment, and the extent of intramolecular hydrogen bonding in the structure are investigated here via the EGEDEA peptide. The hexapeptide is broken down into fragments increasing in size from dipeptides to hexapeptides, including EG, ED, EA, EGE, EDE, DEA, EGED, EDEA, EGEDE, GEDEA, and, finally, EGEDEA, which are investigated with experimental Raman spectroscopy and density functional theory (DFT) computations to model the zwitterionic crystalline solids (in vacuo). The molecular geometries and Boltzmann sum of the simulated Raman spectra for a set of energetic minima corresponding to each peptide fragment are computed with full geometry optimizations and corresponding harmonic vibrational frequency computations at the B3LYP/6-311++G(2df,2pd) level of theory. In absence of the crystal structure, geometry sampling is performed to approximate solid phase behavior. Natural bond order (NBO) analyses are performed on each energetic minimum to quantify the magnitude of the intramolecular hydrogen bonds. The extent of the intramolecular charge transfer is dependent on the overall polarity of the fragment considered, with larger and more polar fragments exhibiting the greatest extent of intramolecular charge transfer. A steady blue shift arises when considering the amide I band position moving linearly from ED to EDE to EDEA to GEDEA and, finally, to EGEDEA. However, little variation is observed in the αCOO- ν(C=O) band position in this family of fragments.

Neutral Peptides in the Gas Phase: Conformation and Aggregation Issues

Combined IR and UV laser spectroscopic techniques in molecular beams merged with theoretical approaches have proven to be an ideal tool to elucidate intrinsic structural properties on a molecular level. It offers the possibility to analyze structural changes, in a controlled molecular environment, when successively adding aggregation partners. By this, it further makes these techniques a valuable starting point for a bottom-up approach in understanding the forces shaping larger molecular systems. This bottom-up approach was successfully applied to neutral amino acids starting around the 1990s. Ever since, experimental and theoretical methods developed further, and investigations could be extended to larger peptide systems. Against this background, the review gives an introduction to secondary structures and experimental methods as well as a summary on theoretical approaches. Vibrational frequencies being characteristic probes of molecular structure and interactions are especially addressed. Archetypal biologically relevant secondary structures investigated by molecular beam spectroscopy are described, and the influences of specific peptide residues on conformational preferences as well as the competition between secondary structures are discussed. Important influences like microsolvation or aggregation behavior are presented. Beyond the linear α-peptides, the main results of structural analysis on cyclic systems as well as on β- and γ-peptides are summarized. Overall, this contribution addresses current aspects of molecular beam spectroscopy on peptides and related species and provides molecular level insights into manifold issues of chemical and biochemical relevance.

Toward Ab Initio Protein Folding: Inherent Secondary Structure Propensity of Short Peptides from the Bioinformatics and Quantum-Chemical Perspective

By combining bioinformatics with quantum-chemical calculations, we attempt to address quantitatively some of the physical principles underlying protein folding. The former allowed us to identify tripeptide sequences in existing protein three-dimensional structures with a strong preference for either helical or extended structure. The selected representatives of pro-helical and pro-extended sequences were converted into "isolated" tripeptides-capped at N- and C-termini-and these were subjected to an extensive conformational sampling and geometry optimization (typically thousands to tens of thousands of conformers for each tripeptide). For each conformer, the QM(DFT-D3)/COSMO-RS free-energy value was then calculated, G_conf(solv). The Δ G_conf(solv) is expected to provide an objective, unbiased, and quantitatively accurate measure of the conformational preference of the particular tripeptide sequence. It has been shown that irrespective of the helical vs extended preferences of the selected tripeptide sequences in context of the protein, most of the low-energy conformers of isolated tripeptides prefer the R-helical structure. Nevertheless, pro-helical tripeptides show slightly stronger helix preference than their pro-extended counterparts. Furthermore, when the sampling is repeated in the presence of a partner tripeptide to mimic the situation in a β-sheet, pro-extended tripeptides (exemplified by the VIV) show a larger free-energy benefit than pro-helical tripeptides (exemplified by the EAM). This effect is even more pronounced in a hydrophobic solvent, which mimics the less polar parts of a protein. This is in line with our bioinformatic results showing that the majority of pro-extended tripeptides are hydrophobic. The preference for a specific secondary structure by the studied tripeptides is thus governed by the plasticity to adopt to its environment. In addition, we show that most of the "naturally occurring" conformations of tripeptide sequences, i.e., those found in existing three-dimensional protein structures, are within ∼10 kcal·mol^-1 from their global minima. In summary, our "ab initio" data suggest that complex protein structures may start to emerge already at the level of their small oligopeptidic units, which is in line with a hierarchical nature of protein folding.

Computational study on single molecular spectroscopy of tyrosin-glycine, tryptophane-glycine and glycine-tryptophane

Quantum chemistry calculations play a fundamental role in revealing the molecular structures observed in gas-phase spectroscopic measurements. The supersonic jet cooling widely used in single molecular spectroscopy experiment is a non-equilibrium process and often causes confusion on the theoretical and experimental comparison. A computational approach is proposed here to account for the effect of the non-equilibrium cooling on the experimental spectra and applied to the cases of tyrosin-glycine (YG), tryptophane-glycine (WG) and glycine-tryptophane (GW). The low energy conformers of YG, WG and GW are obtained through thorough conformational searches. The structural features and equilibrium distributions of conformations and the energy barriers for conformer conversions are then determined. Three classes of transition energy barriers, high, medium and low, are found for the conversions among conformers with distinctly different, similar and the same structural types, respectively. The final conformation populations are determined by assuming an initial temperature of about 450 K and allowing for only the conformation conversion with a low energy barrier to occur during the rapid cooling process. The results provide a natural explanation for the numbers of YG, WG and GW conformations observed experimentally. The theoretical conformation assignments are also in good agreement with the experimental IR data.

Nonradiative Relaxation Mechanisms of UV Excited Phenylalanine Residues: A Comparative Computational Study

The present work is directed toward understanding the mechanisms of excited state deactivation in three neutral model peptides containing the phenylalanine residue. The excited state dynamics of theγL(g+)folded form of N-acetylphenylalaninylamide (NAPA B) and its amide-N-methylated derivative (NAPMA B) is reviewed and compared to the dynamics of the monohydrated structure of NAPA (NAPAH). The goal is to unravel how the environment, and in particular solvation, impacts the photodynamics of peptides. The systems are investigated using reaction path calculations and surface hopping nonadiabatic dynamics based on the coupled cluster doubles (CC2) method and time-dependent density functional theory. The work emphasizes the role that excitation transfer from the phenylππ*to amidenπ*state plays in the deactivation of the three systems and shows how the ease of out-of-plane distortions of the amide group determines the rate of population transfer between the two electronic states. The subsequent dynamics on thenπ*state is barrierless along several pathways and leads to fast deactivation to the ground electronic state.

Semiempirical Quantum Mechanical Methods for Noncovalent Interactions for Chemical and Biochemical Applications

Semiempirical (SE) methods can be derived from either Hartree-Fock or density functional theory by applying systematic approximations, leading to efficient computational schemes that are several orders of magnitude faster than ab initio calculations. Such numerical efficiency, in combination with modern computational facilities and linear scaling algorithms, allows application of SE methods to very large molecular systems with extensive conformational sampling. To reliably model the structure, dynamics, and reactivity of biological and other soft matter systems, however, good accuracy for the description of noncovalent interactions is required. In this review, we analyze popular SE approaches in terms of their ability to model noncovalent interactions, especially in the context of describing biomolecules, water solution, and organic materials. We discuss the most significant errors and proposed correction schemes, and we review their performance using standard test sets of molecular systems for quantum chemical methods and several recent applications. The general goal is to highlight both the value and limitations of SE methods and stimulate further developments that allow them to effectively complement ab initio methods in the analysis of complex molecular systems.

Isolated neutral peptides

This chapter examines the structural characterisation of isolated neutral amino-acids and peptides. After a presentation of the experimental and theoretical state-of-the-art in the field, a review of the major structures and shaping interactions is presented. Special focus is made on conformationally-resolved studies which enable one to go beyond simple structural characterisation; probing flexibility and excited-state photophysics are given as examples of promising future directions.

On the near UV photophysics of a phenylalanine residue: conformation-dependent ππ* state deactivation revealed by laser spectroscopy of isolated neutral dipeptides

The primary step of the near UV photophysics is investigated in pump–probe R2PI ns experiments carried out on specific conformers of model peptide chains.

Polarized Molecular Orbital Model Chemistry 3. The PMO Method Extended to Organic Chemistry

The polarized molecular orbital (PMO) method, a neglect-of-diatomic-differential-overlap (NDDO) semiempirical molecular orbital method previously parameterized for systems composed of O and H, is here extended to carbon. We modified the formalism and optimized all the parameters in the PMO Hamiltonian by using a genetic algorithm and a database containing both electrostatic and energetic properties; the new parameter set is called PMO2. The quality of the resulting predictions is compared to results obtained by previous NDDO semiempirical molecular orbital methods, both including and excluding dispersion terms. We also compare the PMO2 properties to SCC-DFTB calculations. Within the class of semiempirical molecular orbital methods, the PMO2 method is found to be especially accurate for polarizabilities, atomization energies, proton transfer energies, noncovalent complexation energies, and chemical reaction barrier heights and to have good across-the-board accuracy for a range of other properties, including dipole moments, partial atomic charges, and molecular geometries.

Comprehensive conformational studies of five tripeptides and a deduced method for efficient determinations of peptide structures

Thorough searches on the potential energy surfaces of five tripeptides, GGG, GYG, GWG, TGG, and MGG, were performed by considering all possible combinations of the bond rotational degrees of freedom with a semiempirical and ab initio combined computational approach. Structural characteristics of the obtained stable tripeptide conformers were carefully analyzed. Conformers of the five tripeptides were found to be closely connected with conformers of their constituting dipeptides and amino acids. A method for finding all important tripeptide conformers by optimizing a small number of trial structures generated by suitable superposition of the parent amino acid and dipeptide conformers is thus proposed. Applying the method to another five tripeptides, YGG, FGG, WGG, GFA, and GGF, studied before shows that the new approach is both efficient and reliable by providing the most complete ensembles of tripeptide conformers. The method is further generalized for application to larger peptides by introducing the breeding and mutation concepts in a genetic algorithm way. The generalized method is verified to be capable of finding tetrapeptide conformers with secondary structures of strands, helices, and turns, which are highly populated in larger peptides. This show some promise for the proposed method to be applied for the structural determination of larger peptides.

CONFORMATIONAL PREFERENCES OF N-ACETYL–GLYCINE–GLYCINE–N′-METHYLAMIDE: A THEORETICAL STUDY

The conformational preferences of peptide models have been investigated to understand the protein folding mechanism and to develop the force field. Here, we report the minimum energy conformations for a model peptide, N-acetyl–glycine–glycine–N′-methylamide ( Ac–1Gly–2Gly–NHMe(I) ) at the HF/3-21G, HF/6-31G*, and the B3LYP/6-31G* level of theory. At the B3LYP/6-31G* level, the 31 minima were identified and the 10 β-turn structures among the minima were observed in gas-phase. The conformational preferences of Gly residue in the model peptide, I depend on its relative position and conformation of neighboring Gly residue. The Gly residue in this model dipeptide has an asymmetric energy profile as one of Gly residue adopts a specific conformation. This study sheds some lights on understanding the unique conformational preferences of Gly residue in protein including two consecutive Gly residues.

Are current semiempirical methods better than force fields? A study from the thermodynamics perspective

The semiempirical Hamiltonians MNDO, AM1, PM3, RM1, PDDG/MNDO, PDDG/PM3, and SCC-DFTB, when used as part of a hybrid QM/MM scheme for the simulation of biological molecules, were compared on their abilities to reproduce experimental ensemble averages at or near room temperatures for the model system alanine dipeptide in water. Free energy surfaces in the (phi, psi) dihedral angle space, (3)J(H(N),H(alpha)) NMR dipolar coupling constants, basin populations, and peptide-water radial distribution functions (RDF) were calculated from replica exchange simulations and compared to both experiment and fully classical force field calculations using the Amber ff99SB force field. In contrast with the computational chemist's intuitive idea that the more expensive a method the better its accuracy, the ff99SB force field results were more accurate than most of the semiempirical methods, with the exception of RM1. None of the methods, however, was able to accurately reproduce the experimental data. Analysis of the results indicate that the specific QM/MM interactions have little influence on the sampling of free energy surfaces, and the differences are well explained simply by the intrinsic properties of the various QM methods.

Extensive conformational searches of 13 representative dipeptides and an efficient method for dipeptide structure determinations based on amino acid conformers

Conformations of peptides are the basis for their property studies and the predictions of peptide structures are highly important in life science but very complex in practice. Here, thorough searches on the potential energy surfaces of 13 representative dipeptides by considering all possible combinations of the bond rotational degrees of freedom are performed using the density functional theory based methods. Careful analyses of the conformers of the 13 dipeptides and the corresponding amino acids reveal the connections between the structures of dipeptide and amino acids. A method for finding all important dipeptide conformers by optimizing a small number of trial structures generated by suitable superposition of the parent amino acid conformations is thus proposed. Applying the method to another eight dipeptides carefully examined by others shows that the new approach is both highly efficient and reliable by providing the most complete ensembles of dipeptide conformers and much improved agreements between the theoretical and experimental IR spectra. The method opens the door for the determination of the stable structures of all dipeptides with a manageable amount of effort. Preliminary result on the applicability of the method to the tripeptide structure determination is also presented. The results are the first step towards proving Anfinsen's hypothesis by revealing the relationships between the structures of the simplest peptide and its constituting amino acids. It implies that the structures of peptides are not only determined by their amino acid sequences, but also closely linked with the amino acid conformations.

The role of weakly polar and H-bonding interactions in the stabilization of the conformers of FGG, WGG, and YGG: an aqueous phase computational study

The energetics of intramolecular interactions on the conformational potential energy surface of the terminally protected N-Ac-Phe-Gly-Gly-NHMe (FGG), N-Ac-Trp-Gly-Gly-NHMe (WGG), and N-Ac-Tyr-Gly-Gly-NHMe (YGG) tripeptides was investigated. To identify the representative conformations, simulated annealing molecular dynamics (MD) and density functional theory (DFT) methods were used. The interaction energies were calculated at the BHandHLYP/aug-cc-pVTZ level of theory. In the global minima, 10%, 31%, and 10% of the stabilization energy come from weakly polar interactions, respectively, in FGG, WGG, and YGG. In the prominent cases 46%, 62%, and 46% of the stabilization energy is from the weakly polar interactions, respectively, in FGG, WGG, and YGG. On average, weakly polar interactions account for 15%, 34%, and 9% of the stabilization energies of the FGG, WGG, and YGG conformers, respectively. Thus, weakly polar interactions can make an important energetic contribution to protein structure and function.

Non-covalent interactions in biomacromolecules

Non-covalent interactions play an important role in chemistry, physics and especially in biodisciplines. They determine the structure of biomacromolecules such as DNA and proteins and are responsible for the molecular recognition process. Theoretical evaluation of interaction energies is difficult; however, perturbation as well as variation (supermolecular) methods are briefly described. Accurate interaction energies can be obtained by complete basis set limit calculations providing a large portion of correlation energy is covered (e.g. by performing CCSD(T) calculations). The role of H-bonding and stacking interactions in the stabilisation of DNA, oligopeptides and proteins is described, and the importance of London dispersion energy is shown.

Spectroscopic Evidence for the Formation of Helical Structures in Gas-Phase Short Peptide Chains

Aminoisobutyric acid (Aib) is a synthetic amino acid known to favor the formation of 3(10) helical structures in condensed phases, namely, crystals. The intrinsic character of these helicogenic properties has been investigated on the Ac-Aib-Phe-Aib-NH2 molecule under isolated conditions, namely, in the gas phase, both experimentally by double-resonance IR/UV spectroscopy and theoretically by quantum chemistry. A convergent set of evidence, based on energetic, IR, and UV spectroscopic data as well as on analogies with the similar peptide Ac-Ala-Phe-Ala-NH2 previously studied, enables us to conclude the formation of an incipient 310 helix in these isolated systems.

Density-functional, density-functional tight-binding, and wave function calculations on biomolecular systems

Recently, two computational approaches that supply a density-functional-based quantum-chemical method with an empirical term accounting for London dispersion were introduced and found use in the studies of biomolecular systems, namely, DFT-D and SCC-DFTB-D. Here, we examine the performance and usability of these combined techniques for dealing with several tasks typically occurring in the research of biomolecules. The interaction energy of small biomolecular complexes agrees very well with the reference data yielded by correlated ab initio quantum chemical methods. In real-life studies aimed at interaction energy, structure, and infrared spectra, the mentioned methods provide results in good agreement with each other and with experiment (where available). The very favorable time demands of these approaches are discussed, and for each of them, a suitable area of use is proposed on the basis of the results of our analysis.

Mid- and Near-Infrared Spectra of Conformers of H-Pro-Trp-OH

We present near- and mid-infrared-UV double resonance spectra of the natural dipeptide H-Pro-Trp-OH. Two conformers are present in the supersonic expansion: a stretched conformer with fully extended backbone and a folded conformer with an OH...OCpep hydrogen bond. Both conformers are stabilized by dispersion interaction between indole ring and peptide backbone and a NHpep/Nproline contact. The vibrational and conformational assignment is supported by DFT and MP2 calculations. An adequate description of the energetic order of different conformers requires the explicit inclusion of dispersion and geometry optimization at the MP2 level. We will address the very sensitivity of the observed conformations to the structure of the end groups.

Semi-empirical molecular orbital methods including dispersion corrections for the accurate prediction of the full range of intermolecular interactions in biomolecules

Semi-empirical calculations including an empirical dispersive correction are used to calculate intermolecular interaction energies and structures for a large database containing 156 biologically relevant molecules (hydrogen-bonded DNA base pairs, interstrand base pairs, stacked base pairs and amino acid base pairs) for which MP2 and CCSD(T) complete basis set (CBS) limit estimates of the interaction energies are available. The dispersion corrected semi-empirical methods are parameterised against a small training set of 22 complexes having a range of biologically important non-covalent interactions. For the full molecule set (156 complexes), compared to the high-level ab initio database, the mean unsigned errors of the interaction energies at the corrected semi-empirical level are 1.1 (AM1-D) and 1.2 (PM3-D) kcal mol(-1), being a significant improvement over existing AM1 and PM3 methods (8.6 and 8.2 kcal mol(-1)). Importantly, the new semi-empirical methods are capable of describing the diverse range of biological interactions, most notably stacking interactions, which are poorly described by both current AM1 and PM3 methods and by many DFT functionals. The new methods require no more computer time than existing semi-empirical methods and therefore represent an important advance in the study of important biological interactions.

Resolution of Identity Density Functional Theory Augmented with an Empirical Dispersion Term (RI-DFT-D): A Promising Tool for Studying Isolated Small Peptides

Resolution of identity standard density functional theory augmented with a damped empirical dispersion term (RI-DFT-D) calculations have been carried out on a set of lowest energy minima of tryptophyl-glycine (Trp-Gly) and tryptophyl-glycyl-glycine (Trp-Gly-Gly) peptides. RI-DFT-D (TPSS/TZVP) results are in excellent agreement with benchmark data based on the CCSD(T) method. Experimental spectra could be assigned according to the calculated IR frequencies. Central processing unit (CPU) time requirements are only slightly higher than those needed for the DFT calculations. Consequently, RI-DFT-D theory seems to be a promising methodology for studying oligopeptides with accuracy comparable to ab initio quantum chemical calculations.

On the Copper(II) Ion Coordination by Prion Protein HGGGW Pentapeptide Model

The interaction of the octapeptide domain of the prion protein with the transition-metal-ion Cu2+ was studied at the DFT level by using the HGGGW pentapeptide as a model to mimic the PHGGGWGQ octarepeat sequence. Ten complexes, in which the metal ion exhibits different coordinations, were considered. Our results indicate that the lowest-energy structure is characterized by a tetracoordinated metal center and that this tendency of the ion to assume the square planar geometry is strong enough to prevent the addition of a further water molecule in its coordination sphere. The role of tryptophan was found to cause a lowering of the system energy due to the stabilizing effect of the electrostatic interaction between the Trp aromatic indole and histidine imidazole rings.

Charge Transfer Study through the Determination of the Ionization Energies of Tetrapeptides X3-Tyr, X = Gly, Ala, or Leu. Influence of the Inclusion of One Glycine in Alanine and Leucine Containing Peptides

The energies of the fundamental and several excited states of tetrapeptide radical cations were determined at the outer valence Green's function (OVGF) level, at three geometries corresponding to the lowest energy conformations: two for the neutral and one for the cation. The conformations were optimized at the density functional theory level within the B3LYP framework. It was found that, from a purely energetic point of view, a charge initially created on the tyrosine chromophore could migrate without any geometrical change and without further activation once the excited electronic state of the ionized chromophore was formed. This migration could reach the NH(2) terminus for the neutral conformations but should stop at the adjacent peptide link for the cation conformation. These results stress the probable influence of the electronic coupling between the states rather than the existence of a barrier on the charge pathway to explain the difference between the peptides in the charge-transfer process leading to the loss of an iminium [NH(2)=CHR](+) cation. The dissociation energy of the asymptote related to the formation of this NH(2) terminus iminium cation was calculated for few species and it appears that the excess energy available for dissociation is significant when starting from the lowest energy conformations of the neutral or the cation, provided that the charge transfer is effective. It was also found that the amino acids did not conserve their energetic properties and their zero order energy levels turned to a complete new energetic scheme corresponding to the conformation of the peptide.