Main-chain Dihedral Angles Research Articles

Unveiling interatomic distances influencing the reaction coordinates in alanine dipeptide isomerization: An explainable deep learning approach.

The present work shows that the free energy landscape associated with alanine dipeptide isomerization can be effectively represented by specific interatomic distances without explicit reference to dihedral angles. Conventionally, two stable states of alanine dipeptide in vacuum, i.e., C7eq (β-sheet structure) and C7ax (left handed α-helix structure), have been primarily characterized using the main chain dihedral angles, φ (C-N-Cα-C) and ψ (N-Cα-C-N). However, our recent deep learning combined with the "Explainable AI" (XAI) framework has shown that the transition state can be adequately captured by a free energy landscape using φ and θ (O-C-N-Cα) [Kikutsuji et al., J. Chem. Phys. 156, 154108 (2022)]. In the perspective of extending these insights to other collective variables, a more detailed characterization of the transition state is required. In this work, we employ interatomic distances and bond angles as input variables for deep learning rather than the conventional and more elaborate dihedral angles. Our approach utilizes deep learning to investigate whether changes in the main chain dihedral angle can be expressed in terms of interatomic distances and bond angles. Furthermore, by incorporating XAI into our predictive analysis, we quantified the importance of each input variable and succeeded in clarifying the specific interatomic distance that affects the transition state. The results indicate that constructing a free energy landscape based on the identified interatomic distance can clearly distinguish between the two stable states and provide a comprehensive explanation for the energy barrier crossing.

Exhaustive Mapping of the Conformational Space of Natural Dipeptides by the DFT-D3//COSMO-RS Method.

We extensively mapped energy landscapes and conformations of 22 (including three His protonation states) proteinogenic α-amino acids in trans configuration and the corresponding 484 (222) dipeptides. To mimic the environment in a protein chain, the N- and C-termini of the studied systems were capped with acetyl and N-methylamide groups, respectively. We systematically varied the main chain dihedral angles (ϕ, ψ) by 40° steps and all side chain angles by 90° or 120° steps. We optimized the molecular geometries with the GFN2-xTB semiempirical (SQM) method and performed single point density functional theory calculations at the BP86-D3/DGauss-DZVP//COSMO-RS level in water, 1-octanol, N,N-dimethylformamide, and n-hexane. For each restrained (nonequilibrium) structure, we also calculated energy gradients (in water) and natural atomic charges. The exhaustive and unprecedented QM-based sampling enabled us to construct Ramachandran plots of quantum mechanical (QM(BP86-D3)//COSMO-RS) energies calculated on SQM structures, for all 506 (484 dipeptides and 22 amino acids) studied systems. We showed how the character of an amino acid side chain influences the conformational space of single amino acids and dipeptides. With clustering techniques, we were able to identify unique minima of amino acids and dipeptides (i.e., minima on the GFN2-xTB potential energy surfaces) and analyze the distribution of their BP86-D3//COSMO-RS conformational energies in all four solvents. We also derived an empirical formula for the number of unique minima based on the overall number of rotatable bonds within each peptide. The final peptide conformer data set (PeptideCs) comprises over 400 million structures, all of them annotated with QM(BP86-D3)//COSMO-RS energies. Thanks to its completeness and unbiased nature, the PeptideCs can serve, inter alia, as a data set for the validation of new methods for predicting the energy landscapes of protein structures. This data set may also prove to be useful in the development and reparameterization of biomolecular force fields. The data set is deposited at Figshare (10.25452/figshare.plus.19607172) and can be accessed using a simple web interface at http://peptidecs.uochb.cas.cz.

Mechanism for the Unfolding of the TOP7 Protein in Steered Molecular Dynamics Simulations as Revealed by Mutual Information Analysis.

We employed mutual information (MI) analysis to detect motions affecting the mechanical resistance of the human-engineered protein Top7. The results are based on the MI analysis of pair contact correlations measured in steered molecular dynamics (SMD) trajectories and their statistical dependence on global unfolding. This study is the first application of the MI analysis to SMD forced unfolding, and we furnish specific SMD recommendations for the utility of parameters and options in the TimeScapes package. The MI analysis provided a global overview of the effect of perturbation on the stability of the protein. We also employed a more conventional trajectory analysis for a detailed description of the mechanical resistance of Top7. Specifically, we investigated 1) the hydropathy of the interactions of structural segments, 2) the H2O concentration near residues relevant for unfolding, and 3) the changing hydrogen bonding patterns and main chain dihedral angles. The results show that the application of MI in the study of protein mechanical resistance can be useful for the engineering of more resistant mutants when combined with conventional analysis. We propose a novel mutation design based on the hydropathy of residues that would stabilize the unfolding region by mimicking its more stable symmetry mate. The proposed design process does not involve the introduction of covalent crosslinks, so it has the potential to preserve the conformational space and unfolding pathway of the protein.

Benchmark Force Fields for the Molecular Dynamic Simulation of G-Quadruplexes.

G-quadruplexes have drawn widespread attention for serving as a potential anti-cancer target and their application in material science. Molecular dynamics (MD) simulation is the key theoretical tool in the study of GQ’s structure-function relationship. In this article, we systematically benchmarked the five force fields of parmbsc0, parmbsc1, OL15, AMOEBA, and Drude2017 on the MD simulation of G-quadruplex from four aspects: structural stability, central ion channel stability, description of Hoogsteen hydrogen bond network, and description of the main chain dihedral angle. The results show that the overall performance of the Drude force field is the best. Although there may be a certain over-polarization effect, it is still the best choice for the MD simulation of G-quadruplexes.

Normal mode analysis calculation for a full-atom model with a smaller number of degrees of freedom for huge protein molecules.

The number of degrees of freedom (DOF), N, in normal mode analysis (NMA) calculations of proteins is a crucial problem in huge systems because the eigenvalue problem of an N-by-N matrix must be solved. If it were possible to perform the analysis with a smaller number of DOF for the same system with minimal deterioration in accuracy, this would make a significant impact on the computational study of protein dynamics. We examined two models in which the number of DOF was reduced. Both of them adopted a full-atom model with dihedral angles as independent variables. In one model, side-chain dihedral angles, χ’s, and a main-chain dihedral angle, ω, were fixed and only the main-chain dihedral angles, ϕ and ψ, were variable. In another model, the dihedral angles around virtual bonds that connect neighboring Cα atoms were tested. The number of DOFs for the two models was two and one per residue, respectively. The residue-by-residue fluctuation profiles for atoms and dihedral angles were well reproduced in both models. The motion of atoms in the individual lowest-frequency normal modes of the two models was also very similar to those of the original model in which all rotatable dihedral angles were variable. Consequently, these models could predict large-amplitude concerted motion. These results also imply that proteins in a full-atom model can undergo only limited large-scale conformational changes around the native conformation, and consequently, NMA results do not strongly depend on the independent variables adopted.

Structural and dynamical characteristics of tropomyosin epitopes as the major allergens in shrimp

Ingestion of marine invertebrates often causes food allergy, where the major allergens have been reported to be derived from tropomyosin (TM). Intact or the digestive fragments of food allergens generally show resistance to digestion, which is usually attributable to the structural stability (or rigidity). The difference in the structural and dynamical characteristics between the epitope and the non-epitope regions in TM has not yet been well understood. In the present study, molecular dynamics simulation was performed at constant pHs for shrimp TM. By analyzing the main-chain dihedral angle fluctuations and local α-helix contents, we found that the epitope regions are more stable than the non-epitope counterparts, providing a possible physical reason for the resistance to digestion in the epitopes regions. The difference of the structural stability between the epitope and the non-epitope regions was largest at low pHs, even though pH dependence of the structural stability in itself was not significant in both regions. The lower content of the Ala cluster in the epitope region is considered to cause the higher stability of the epitope region.

Intrinsic α helix propensities compact hydrodynamic radii in intrinsically disordered proteins.

Proteins that lack tertiary stability under normal conditions, known as intrinsically disordered, exhibit a wide range of biological activities. Molecular descriptions for the biology of intrinsically disordered proteins (IDPs) consequently rely on disordered structural models, which in turn require experiments that assess the origins to structural features observed. For example, while hydrodynamic size is mostly insensitive to sequence composition in chemically denatured proteins, IDPs show strong sequence-specific effects in the hydrodynamic radius (Rh ) when measured under normal conditions. To investigate sequence-modulation of IDP Rh , disordered ensembles generated by a hard sphere collision model modified with a structure-based parameterization of the solution energetics were used to parse the contributions of net charge, main chain dihedral angle bias, and excluded volume on hydrodynamic size. Ensembles for polypeptides 10-35 residues in length were then used to establish power-law scaling relationships for comparison to experimental Rh from 26 IDPs. Results showed the expected outcomes of increased hydrodynamic size from increases in excluded volume and net charge, and compaction from chain-solvent interactions. Chain bias representing intrinsic preferences for α helix and polyproline II (PPII ), however, modulated Rh with intricate dependence on the simulated propensities. PPII propensities at levels expected in IDPs correlated with heightened Rh sensitivity to even weak α helix propensities, indicating bias for common (φ, ψ) are important determinants of hydrodynamic size. Moreover, data show that IDP Rh can be predicted from sequence with good accuracy from a small set of physicochemical properties, namely intrinsic conformational propensities and net charge. Proteins 2017; 85:296-311. © 2016 Wiley Periodicals, Inc.

Amino Acids in Nine Ligand-Prefer Ramachandran Regions.

Several secondary structures, such as π-helix and left-handed helix, have been frequently identified at protein ligand-binding sites. A secondary structure is considered to be constrained to a specific region of dihedral angles. However, a comprehensive analysis of the correlation between main chain dihedral angles and ligand-binding sites has not been performed. We undertook an extensive analysis of the relationship between dihedral angles in proteins and their distance to ligand-binding sites, frequency of occurrence, molecular potential energy, amino acid composition, van der Waals contacts, and hydrogen bonds with ligands. The results showed that the values of dihedral angles have a strong preference for ligand-binding sites at certain regions in the Ramachandran plot. We discovered that amino acids preceding the ligand-prefer ϕ/ψ box residues are exposed more to solvents, whereas amino acids following ligand-prefer ϕ/ψ box residues form more hydrogen bonds and van der Waals contacts with ligands. Our method exhibited a similar performance compared with the program Ligsite-csc for both ligand-bound structures and ligand-free structures when just one ligand-binding site was predicted. These results should be useful for the prediction of protein ligand-binding sites and for analysing the relationship between structure and function.

Dihedral-based segment identification and classification of biopolymers I: proteins.

A new structure classification scheme for biopolymers is introduced, which is solely based on main-chain dihedral angles. It is shown that by dividing a biopolymer into segments containing two central residues, a local classification can be performed. The method is referred to as DISICL, short for Dihedral-based Segment Identification and Classification. Compared to other popular secondary structure classification programs, DISICL is more detailed as it offers 18 distinct structural classes, which may be simplified into a classification in terms of seven more general classes. It was designed with an eye to analyzing subtle structural changes as observed in molecular dynamics simulations of biomolecular systems. Here, the DISICL algorithm is used to classify two databases of protein structures, jointly containing more than 10 million segments. The data is compared to two alternative approaches in terms of the amount of classified residues, average occurrence and length of structural elements, and pair wise matches of the classifications by the different programs. In an accompanying paper (Nagy, G.; Oostenbrink, C. Dihedral-based segment identification and classification of biopolymers II: Polynucleotides. J. Chem. Inf. Model. 2013, DOI: 10.1021/ci400542n), the analysis of polynucleotides is described and applied. Overall, DISICL represents a potentially useful tool to analyze biopolymer structures at a high level of detail.

Dihedral-Based Segment Identification and Classification of Biopolymers II: Polynucleotides

In an accompanying paper (Nagy, G.; Oostenbrink, C. Dihedral-based segment identification and classification of biopolymers I: Proteins. J. Chem. Inf. Model. 2013, DOI: 10.1021/ci400541d), we introduce a new algorithm for structure classification of biopolymeric structures based on main-chain dihedral angles. The DISICL algorithm (short for DIhedral-based Segment Identification and CLassification) classifies segments of structures containing two central residues. Here, we introduce the DISICL library for polynucleotides, which is based on the dihedral angles ε, ζ, and χ for the two central residues of a three-nucleotide segment of a single strand. Seventeen distinct structural classes are defined for nucleotide structures, some of which—to our knowledge—were not described previously in other structure classification algorithms. In particular, DISICL also classifies noncanonical single-stranded structural elements. DISICL is applied to databases of DNA and RNA structures containing 80,000 and 180,000 segments, respectively. The classifications according to DISICL are compared to those of another popular classification scheme in terms of the amount of classified nucleotides, average occurrence and length of structural elements, and pairwise matches of the classifications. While the detailed classification of DISICL adds sensitivity to a structure analysis, it can be readily reduced to eight simplified classes providing a more general overview of the secondary structure in polynucleotides.

A coupled two-dimensional main chain torsional potential for protein dynamics: generation and implementation

Main chain torsions of alanine dipeptide are parameterized into coupled 2-dimensional Fourier expansions based on quantum mechanical (QM) calculations at M06 2X/aug-cc-pvtz//HF/6-31G** level. Solvation effect is considered by employing polarizable continuum model. Utilization of the M06 2X functional leads to precise potential energy surface that is comparable to or even better than MP2 level, but with much less computational demand. Parameterization of the 2D expansions is against the full main chain torsion space instead of just a few low energy conformations. This procedure is similar to that for the development of AMBER03 force field, except unique weighting factor was assigned to all the grid points. To avoid inconsistency between quantum mechanical calculations and molecular modeling, the model peptide is further optimized at molecular mechanics level with main chain dihedral angles fixed before the calculation of the conformational energy on molecular mechanical level at each grid point, during which generalized Born model is employed. Difference in solvation models at quantum mechanics and molecular mechanics levels makes this parameterization procedure less straightforward. All force field parameters other than main chain torsions are taken from existing AMBER force field. With this new main chain torsion terms, we have studied the main chain dihedral distributions of ALA dipeptide and pentapeptide in aqueous solution. The results demonstrate that 2D main chain torsion is effective in delineating the energy variation associated with rotations along main chain dihedrals. This work is an implication for the necessity of more accurate description of main chain torsions in the future development of ab initio force field and it also raises a challenge to the development of quantum mechanical methods, especially the quantum mechanical solvation models.

Correlated motion of protein subdomains and large-scale conformational flexibility of RecA protein filament

Based on X-ray crystallographic data available at Protein Data Bank, we have built molecular dynamics (MD) models of homologous recombinases RecA from E. coli and D. radiodurans. Functional form of RecA enzyme, which is known to be a long helical filament, was approximated by a trimer, simulated in periodic water box. The MD trajectories were analyzed in terms of large-scale conformational motions that could be detectable by neutron and X-ray scattering techniques. The analysis revealed that large-scale RecA monomer dynamics can be described in terms of relative motions of 7 subdomains. Motion of C-terminal domain was the major contributor to the overall dynamics of protein. Principal component analysis (PCA) of the MD trajectories in the atom coordinate space showed that rotation of C-domain is correlated with the conformational changes in the central domain and N-terminal domain, that forms the monomer-monomer interface. Thus, even though C-terminal domain is relatively far from the interface, its orientation is correlated with large-scale filament conformation. PCA of the trajectories in the main chain dihedral angle coordinate space implicates a co-existence of a several different large-scale conformations of the modeled trimer. In order to clarify the relationship of independent domain orientation with large-scale filament conformation, we have performed analysis of independent domain motion and its implications on the filament geometry.

HOMOLOGY MODELING OF BUFFALO (<i>BUBALUS BUBALIS</i>) INTERFERON-TAU PROTEIN

Interferon-Tau (IFNt) contributes towards maternal recognition of pregnancy in ruminants (like, cattle, buffalo, goat, giraffe). IFNt has been extensively studied in most of the ruminants except for buffalo Bubalus bubalis). The present study has been undertaken to predict the secondary structure of Interferon-tau in buffalo. The available amino acid sequence of bubaline IFNt (sequence database of SwissProt) was subjected to protein-BLAST to find similar sequences with high scores and low e-values. The ovine IFNt sequence (PDB code: 1B5L) was selected for further computational analysis of the bubaline IFNt sequence to predict the secondary and tertiary structure. The secondary structure of the modeled bubaline IFNt was predicted using STRIDE. The 3D structure was generated using academic version of MODELER9v6. The probability density functions (pdf) were used to restrain Cα-Cα distances, main chain N-O distances as well as main-chain and side-chain dihedral angles. The energy minimization and van der waal contacts were taken care of using ACCELRYS DS Modeling 2.0. The residue profiles of the obtained three-dimensional models were checked by VERIFY3D. The energetic architecture and the correctness of the generated model revealed that the predicted secondary model was correct and acceptable. The predicted structure of the bubaline IFNt constructed through homology modeling from ovine IFNt, could be used for further profiling the species specific difference in IFNt activity.

Statistical analysis of protein molecules

AbstractIn this paper, entropy and auto-correlation values of main chain dihedral angles of 22,356 protein molecules are calculated and found to lie within a well-specified range for most proteins. Also, the entropy values obey a Gaussian distribution, which indicates that entropy plays a crucial role in evolution and conservation of protein tertiary structures. A comparison of the auto-correlation values of the dihedral angles of the entire protein molecule with those of the alpha helices and beta sheets indicates that random coils play an important role in determining the tertiary structure of protein molecules.

A New Efficient Method for Generating Conformations of Unfolded Proteins with Diverse Main-Chain Dihedral-Angle Distributions

A new method for generating polypeptide-chain conformations has been developed for studying structural characteristics of unfolded proteins. It enables us to generate a large number of conformations very rapidly by avoiding atomic collisions efficiently with the use of main-chain dihedral-angle distributions derived from a crystal-structure database of proteins. In addition, combining main-chain dihedral-angle distributions for the amino acid residues incorporated in different secondary structures, we can obtain diverse conformational ensembles with different structural features. Structural characteristics of proteins denatured in high-concentration denaturant solution were analyzed by comparing predictions from this method with results from solution X-ray scattering (SXS) measurement. Analysis of the dependence of the mean square radius (Rsq) of protein on the number of residues and the shape of its Kratky profile has confirmed that the highly denaturing solvent serves as a good solvent in accordance with previous reports. It was also found that, in order for a conformational ensemble to reproduce experimental data, the percentage in which main-chain dihedral angles are found in the α region must be in the range of 20-40%. It agrees with studies on the (3)JHNα coupling constant using the multidimensional NMR method. These results confirm that our method for generating diverse conformations of polypeptide chains is very useful to the conformational analysis of unfolded protein, because it enables us to analyze comprehensively both of the local structural features obtained from NMR and the global ones obtained from SXS.

Signature of n→π* interactions in α‐helices

The oxygen of a peptide bond has two lone pairs of electrons. One of these lone pairs is poised to interact with the electron-deficient carbon of the subsequent peptide bond in the chain. Any partial covalency that results from this n→π* interaction should induce pyramidalization of the carbon (C'(i)) toward the oxygen (O(i-1)). We searched for such pyramidalization in 14 peptides that contain both α- and β-amino acid residues and that assume a helical structure. We found that the α-amino acid residues, which adopt the main chain dihedral angles of an α-helix, display dramatic pyramidalization but the β-amino acid residues do not. Thus, we conclude that O(i-1) and C'(i) are linked by a partial covalent bond in α-helices. This finding has important ramifications for the folding and conformational stability of α-helices in isolation and in proteins.

4.0-Å resolution cryo-EM structure of the mammalian chaperonin TRiC/CCT reveals its unique subunit arrangement

The essential double-ring eukaryotic chaperonin TRiC/CCT (TCP1-ring complex or chaperonin containing TCP1) assists the folding of approximately 5-10% of the cellular proteome. Many TRiC substrates cannot be folded by other chaperonins from prokaryotes or archaea. These unique folding properties are likely linked to TRiC's unique heterooligomeric subunit organization, whereby each ring consists of eight different paralogous subunits in an arrangement that remains uncertain. Using single particle cryo-EM without imposing symmetry, we determined the mammalian TRiC structure at 4.7-A resolution. This revealed the existence of a 2-fold axis between its two rings resulting in two homotypic subunit interactions across the rings. A subsequent 2-fold symmetrized map yielded a 4.0-A resolution structure that evinces the densities of a large fraction of side chains, loops, and insertions. These features permitted unambiguous identification of all eight individual subunits, despite their sequence similarity. Independent biochemical near-neighbor analysis supports our cryo-EM derived TRiC subunit arrangement. We obtained a Calpha backbone model for each subunit from an initial homology model refined against the cryo-EM density. A subsequently optimized atomic model for a subunit showed approximately 95% of the main chain dihedral angles in the allowable regions of the Ramachandran plot. The determination of the TRiC subunit arrangement opens the way to understand its unique function and mechanism. In particular, an unevenly distributed positively charged wall lining the closed folding chamber of TRiC differs strikingly from that of prokaryotic and archaeal chaperonins. These interior surface chemical properties likely play an important role in TRiC's cellular substrate specificity.

Precise side-chain conformation analysis of l-phenylalanine in α-helical polypeptide by quantum-chemical calculation and 13C CP-MAS NMR measurement

To clarify the positive role of side-chain conformation in the stability of protein secondary structure (main-chain conformation), we successfully calculated the optimization structure of a well-defined α-helical octadecapeptide composed of l-alanine (Ala) and l-phenylalanine (Phe) residues, H–(Ala) 8–Phe–(Ala) 9–OH, based on the molecular orbital calculation with density functional theory (DFT/B3LYP/6-31G(d)). From the total energy and the precise secondary structural parameters such as main-chain dihedral angles and hydrogen-bond parameters of the optimized structure, we confirmed that the conformational stability of an α-helix is affected dominantly by the side-chain conformation ( χ 1) of the Phe residue in this system: model A ( T form: around 180° of χ 1) is most stable in α-helix and model B ( G + form: around −60° of χ 1) is next stable, but model C ( G − form: around 60° of χ 1) is less stable. In addition, we demonstrate that the stable conformation of poly( l-phenylalanine) is an α-helix with the side-chain T form, by comparison of the carbonyl 13C chemical shift measured by 13C CP-MAS NMR and the calculated one.

Textbook of Structural Biology, by Anders Liljas, Lars Liljas, Jure Piskur, Göran Lindblom, Poul Nissen, and Morten Kjeldgaard

Textbook of Structural Biology, by Anders Liljas, Lars Liljas, Jure Piskur, Göran Lindblom, Poul Nissen, and Morten Kjeldgaard

Neuro-swarm hybridization for protein tertiary structure prediction

This paper describes a new approach for predicting tertiary structure of protein using artificial neural network and particle swarm optimization technique. The paper is concetrated around the well known Ab-initio approach for global minimisation of energy function. It predicts the native structure of protein by finding the main chain dihedral angles; through the optimization of CHARMM energy function, using particle swarm optimization algorithm. Side chain dihedral angle are predicted using three layered artificial neural network, realised with back propagation algorithm. This approach has merit as it reduces the dimensionality of the search space and computationally outperforms all other classical technique in atleast 80% cases.