Cooperativity in Long α- and 310-Helical Polyalanines: Both Electrostatic and van der Waals Interactions Are Essential

PSIQUE: Protein Secondary Structure Identification on the Basis of Quaternions and Electronic Structure Calculations

The secondary structure is important in protein structure analysis, classification, and modeling. We have developed a novel method for secondary structure assignment, termed PSIQUE, based on the potential energy surface (PES) of polyalanine obtained using an infinitely long chain model and density functional theory calculations. First, uniform protein segments are determined in terms of a difference of quaternions between neighboring amino acids along the protein backbone. Then, the identification of the secondary structure motifs is carried out based on the minima found in the PES. PSIQUE shows good agreement with other secondary structure assignment methods. However, it provides better discrimination of subtle secondary structures (e.g., helix types) and termini and produces more uniform segments while also accounting for local distortions. Overall, PSIQUE provides a precise and reliable assignment of secondary structures, so it should be helpful for the detailed characterization of the protein structure.

From Compact to String-The Role of Secondary and Tertiary Structure in Charge-Induced Unzipping of Gas-Phase Proteins

In the gas phase, protein ions can adopt a broad range of structures, which have been investigated extensively in the past using ion mobility-mass spectrometry (IM-MS)-based methods. Compact ions with low number of charges undergo a Coulomb-driven transition to partially folded species when the charge increases, and finally form extended structures with presumably little or no defined structure when the charge state is high. However, with respect to the secondary structure, IM-MS methods are essentially blind. Infrared (IR) spectroscopy, on the other hand, is sensitive to such structural details and there is increasing evidence that helices as well as β-sheet-like structures can exist in the gas phase, especially for ions in low charge states. Very recently, we showed that also the fully extended form of highly charged protein ions can adopt a distinct type of secondary structure that features a characteristic C₅-type hydrogen bond pattern. Here we use a combination of IM-MS and IR spectroscopy to further investigate the influence of the initial, native conformation on the formation of these structures. Our results indicate that when intramolecular Coulomb-repulsion is large enough to overcome the stabilization energies of the genuine secondary structure, all proteins, regardless of their sequence or native conformation, form C₅-type hydrogen bond structures. Furthermore, our results suggest that in highly charged proteins the positioning of charges along the sequence is only marginally influenced by the basicity of individual residues. Graphical Abstract ᅟ.

Evidences for Cooperative Resonance-Assisted Hydrogen Bonds in Protein Secondary Structure Analogs

Cooperative behaviors of the hydrogen bonding networks in proteins have been discovered for a long time. The structural origin of this cooperativity, however, is still under debate. Here we report a new investigation combining excess infrared spectroscopy and density functional theory calculation on peptide analogs, represented by N-methylformamide (NMF) and N-methylacetamide (NMA). Interestingly, addition of the strong hydrogen bond acceptor, dimethyl sulfoxide, to the pure analogs caused opposite effects, namely red- and blue-shift of the N−H stretching infrared absorption in NMF and NMA, respectively. The contradiction can be reconciled by the marked lowering of the energy levels of the self-associates between NMA molecules due to a cooperative effect of the hydrogen bonds. On the contrary, NMF molecules cannot form long-chain cooperative hydrogen bonds because they tend to form dimers. Even more interestingly, we found excellent linear relationships between changes on bond orders of N−H/N−C/C = O and the hydrogen bond energy gains upon the formation of hydrogen bonding multimers in NMA, suggesting strongly that the cooperativity originates from resonance-assisted hydrogen bonds. Our findings provide insights on the structures of proteins and may also shed lights on the rational design of novel molecular recognition systems.

Charge-Induced Unzipping of Isolated Proteins to a Defined Secondary Structure

Here we present a combined experimental and theoretical study on the secondary structure of isolated proteins as a function of charge state. In infrared spectra of the proteins ubiquitin and cytochrome c, amide I (C=O stretch) and amide II (N-H bend) bands can be found at positions that are typical for condensed-phase proteins. For high charge states a new band appears, substantially red-shifted from the amide II band observed at lower charge states. The observations are interpreted in terms of Coulomb-driven transitions in secondary structures from mostly helical to extended C5 -type hydrogen-bonded structures. Support for this interpretation comes from simple energy considerations as well as from quantum chemical calculations on model peptides. This transition in secondary structure is most likely universal for isolated proteins that occur in mass spectrometric experiments.

Observation of α-Helical Hydrogen-Bond Cooperativity in an Intact Protein

The presence and extent of hydrogen-bonding (H-bonding) cooperativity in proteins remains a fundamental question, which in the past has been studied extensively, mostly by infrared and fluorescence measurements on model peptides. We demonstrate that such cooperativity can be studied in an intact protein by hydrogen/deuterium exchange NMR spectroscopy. The method is based on the fact that substitution of NH by ND in a backbone amide group slightly weakens the N-H···O═C hydrogen bond. Our results show that such substitution at position i in an α-helix impacts the (1)H and (15)N chemical shifts of the amide sites of residues i - 3 to i + 3. Quantum mechanical calculations indicate that the upfield shifts of (1)H and (15)N resonances at site i, observed upon H/D exchanges at sites i - 3, i + 1, i + 2, and i + 3, correspond to a decrease of the ith backbone amide electric dipole moment, which weakens its H-bonding and long-range electrostatic interactions with other backbone amides in the α-helix. These results provide new quantitative insights into the cooperativity of H-bonding in protein α-helices.

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.

Helical α/β-depsipeptides with alternating residue types: conformational change from the 11-helix to the 14/15-helix

Short α/β-depsipeptides of which the third residue from the N-terminus is an (S)-lactic acid residue predominantly adopt 14/15-helical conformations analogous to the α-helix.

Generalized energy-based fragmentation approach and its applications to macromolecules and molecular aggregates

Conspectus The generalized energy-based fragmentation (GEBF) approach provides a very simple way of approximately evaluating the ground-state energy or properties of a large system in terms of ground-state energies of various small "electrostatically embedded" subsystems, which can be calculated with any traditional ab initio quantum chemistry (X) method (X = Hartree-Fock, density functional theory, and so on). Due to its excellent parallel efficiency, the GEBF approach at the X theory level (GEBF-X) allows full quantum mechanical (QM) calculations to be accessible for systems with hundreds and even thousands of atoms on ordinary workstations. The implementation of the GEBF approach at various theoretical levels can be easily done with existing quantum chemistry programs. This Account reviews the methodology, implementation, and applications of the GEBF-X approach. This method has been successfully applied to optimize the structures of various large systems including molecular clusters, polypeptides, proteins, and foldamers. Such investigations could allow us to elucidate the origin and nature of the cooperative interaction in secondary structures of long peptides or the driving force of the self-assembly processes of aromatic oligoamides. These GEBF-based QM calculations reveal that the structures and stability of various complex systems result from a subtle balance of many types of noncovalent interactions such as hydrogen bonding and van der Waals interactions. The GEBF-based ab initio molecular dynamics (AIMD) method also allows the investigation of dynamic behaviors of large systems on the order of tens of picoseconds. It was demonstrated that the conformational dynamics of two model peptides predicted by GEBF-based AIMD are noticeably different from those predicted by the classical force field MD method. With the target of extending QM calculations to molecular aggregates in the condensed phase, we have implemented the GEBF-based multilayer hybrid models, which could provide satisfactory descriptions of the binding energies between a solute molecule and its surrounding waters and the chain-length dependence of the conformational changes of oligomers in aqueous solutions. A coarse-grained polarizable molecular mechanics model, furnished with GEBF-X dipole moments of subsystems, exhibits some advantages of treating the electrostatic polarization with reduced computational costs. We anticipate that the GEBF approach will continue to develop with the ultimate goal of studying complicated phenomena at mesoscopic scales and serve as a practical tool to elucidate the structure and dynamics of chemical and biological systems.

Contribution of the empirical dispersion correction on the conformation of short alanine peptides obtained by gas-phase QM calculations

In this work we analyze the effect of the inclusion of an empirical dispersion term to standard DFT (DFT-D) in the prediction of the conformational energy of the alanine dipeptide (Ala2) and in assessing the relative stabilities of short polyala-nine peptides in helical conformations, i.e., α and 310 helices, from Ala4 to Ala16. The Ala2 conformational energies obtained with the dispersion-corrected GGA functional B97-D are compared to previously published high level MP2 data. Meanwhile, the B97-D performance on larger polyalanine peptides is compared to MP2, B3LYP and RHF calculations obtained at a lower level of theory. Our results show that electron correlation affects the conformational energies of short peptides with a weight that increases with the peptide length. Indeed, while the contribution of vdW forces is significant for larger peptides, in the case of Ala2 it is negligible when compared to solvent effects. Even for short peptides, the inclusion of an empirical dispersion term greatly improves accuracy of DFT methods, providing results that correlate very well with the MP2 reference at no additional computational cost.

Mapping enzymatic catalysis using the effective fragment molecular orbital method: towards all ab initio biochemistry

We extend the Effective Fragment Molecular Orbital (EFMO) method to the frozen domain approach where only the geometry of an active part is optimized, while the many-body polarization effects are considered for the whole system. The new approach efficiently mapped out the entire reaction path of chorismate mutase in less than four days using 80 cores on 20 nodes, where the whole system containing 2398 atoms is treated in the ab initio fashion without using any force fields. The reaction path is constructed automatically with the only assumption of defining the reaction coordinate a priori. We determine the reaction barrier of chorismate mutase to be kcal mol⁻¹ for MP2/cc-pVDZ and for MP2/cc-pVTZ in an ONIOM approach using EFMO-RHF/6-31G(d) for the high and low layers, respectively.

Comparison of some dispersion-corrected and traditional functionals as applied to peptides and conformations of cyclohexane derivatives

We compare the energetic and structural properties of fully optimized α-helical and antiparallel β-sheet polyalanines and the energetic differences between axial and equatorial conformations of three cyclohexane derivatives (methyl, fluoro, and chloro) as calculated using several functionals designed to treat dispersion (B97-D, ωB97x-D, M06, M06L, and M06-2X) with other traditional functionals not specifically parametrized to treat dispersion (B3LYP, X3LYP, and PBE1PBE) and with experimental results. Those functionals developed to treat dispersion significantly overestimate interaction enthalpies of folding for the α-helix and predict unreasonable structures that contain Ramachandran φ and ψ and C = O...N H-bonding angles that are out of the bounds of databases compiled the β-sheets. These structures are consistent with overestimation of the interaction energies. For the cyclohexanes, these functionals overestimate the stabilities of the axial conformation, especially when used with smaller basis sets. Their performance improves when the basis set is improved from D95∗∗ to aug-cc-pVTZ (which would not be possible with systems as large as the peptides).

Performance comparison of computational methods for modeling alpha-helical structures

Geometry optimization results are reported for secondary structural elements of small proteins and polypeptides. Emphasis is placed on how well molecular mechanics as well as semiempirical, ab initio, and density functional methods describe α-helical and related structures in purely theoretical models (Gly10, Ile10) as well as in realistic models (an α-helical region of calmodulin, and the complete structure of a small protein). Many of the methods examined here were found to provide unsatisfactory descriptions of the hydrogen-bonding interactions within polypeptide-type structures, as the α-helical canonical secondary structure motif was not reproduced accurately. Ab initio and DFT methods provided reasonable results only when solvation models were included, although Hartree-Fock failed even with solvation in one of the test cases; among the semiempirical methods, one of the PM6 implementations performed very well.