Cα Coordinates Research Articles

DeepBBQ: A Deep Learning Approach to the Protein Backbone Reconstruction.

Coarse-grained models have provided researchers with greatly improved computational efficiency in modeling structures and dynamics of biomacromolecules, but, to be practically useful, they need fast and accurate conversion methods back to the all-atom representation. Reconstruction of atomic details may also be required in the case of some experimental methods, like electron microscopy, which may provide Cα-only structures. In this contribution, we present a new method for recovery of all backbone atom positions from just the Cα coordinates. Our approach, called deepBBQ, uses a deep convolutional neural network to predict a single internal coordinate per peptide plate, based on Cα trace geometric features, and then proceeds to recalculate the cartesian coordinates based on the assumption that the peptide plate atoms lie in the same plane. Extensive comparison with similar programs shows that our solution is accurate and cost-efficient. The deepBBQ program is available as part of the open-source bioinformatics toolkit Bioshell and is free for download and the documentation is available online.

DiAMoNDBack: Diffusion-Denoising Autoregressive Model for Non-Deterministic Backmapping of Cα Protein Traces.

Coarse-grained molecular models of proteins permit access to length and time scales unattainable by all-atom models and the simulation of processes that occur on long time scales, such as aggregation and folding. The reduced resolution realizes computational accelerations, but an atomistic representation can be vital for a complete understanding of mechanistic details. Backmapping is the process of restoring all-atom resolution to coarse-grained molecular models. In this work, we report DiAMoNDBack (Diffusion-denoising Autoregressive Model for Non-Deterministic Backmapping) as an autoregressive denoising diffusion probability model to restore all-atom details to coarse-grained protein representations retaining only Cα coordinates. The autoregressive generation process proceeds from the protein N-terminus to C-terminus in a residue-by-residue fashion conditioned on the Cα trace and previously backmapped backbone and side-chain atoms within the local neighborhood. The local and autoregressive nature of our model makes it transferable between proteins. The stochastic nature of the denoising diffusion process means that the model generates a realistic ensemble of backbone and side-chain all-atom configurations consistent with the coarse-grained Cα trace. We train DiAMoNDBack over 65k+ structures from the Protein Data Bank (PDB) and validate it in applications to a hold-out PDB test set, intrinsically disordered protein structures from the Protein Ensemble Database (PED), molecular dynamics simulations of fast-folding mini-proteins from DE Shaw Research, and coarse-grained simulation data. We achieve state-of-the-art reconstruction performance in terms of correct bond formation, avoidance of side-chain clashes, and the diversity of the generated side-chain configurational states. We make the DiAMoNDBack model publicly available as a free and open-source Python package.

Mathematical and Machine Learning Approaches for Classification of Protein Secondary Structure Elements from Cα Coordinates.

Determining Secondary Structure Elements (SSEs) for any protein is crucial as an intermediate step for experimental tertiary structure determination. SSEs are identified using popular tools such as DSSP and STRIDE. These tools use atomic information to locate hydrogen bonds to identify SSEs. When some spatial atomic details are missing, locating SSEs becomes a hinder. To address the problem, when some atomic information is missing, three approaches for classifying SSE types using Cα atoms in protein chains were developed: (1) a mathematical approach, (2) a deep learning approach, and (3) an ensemble of five machine learning models. The proposed methods were compared against each other and with a state-of-the-art approach, PCASSO.

Predicting the Assembly of the Transmembrane Domains of Viral Channel Forming Proteins and Peptide Drug Screening Using a Docking Approach.

A de novo assembly algorithm is provided to propose the assembly of bitopic transmembrane domains (TMDs) of membrane proteins. The algorithm is probed using, in particular, viral channel forming proteins (VCPs) such as M2 of influenza A virus, E protein of severe acute respiratory syndrome corona virus (SARS-CoV), 6K of Chikungunya virus (CHIKV), SH of human respiratory syncytial virus (hRSV), and Vpu of human immunodeficiency virus type 2 (HIV-2). The generation of the structures is based on screening a 7-dimensional space. Assembly of the TMDs can be achieved either by simultaneously docking the individual TMDs or via a sequential docking. Scoring based on estimated binding energies (EBEs) of the oligomeric structures is obtained by the tilt to decipher the handedness of the bundles. The bundles match especially well for all-atom models of M2 referring to an experimentally reported tetrameric bundle. Docking of helical poly-peptides to experimental structures of M2 and E protein identifies improving EBEs for positively charged (K,R,H) and aromatic amino acids (F,Y,W). Data are improved when using polypeptides for which the coordinates of the amino acids are adapted to the Cα coordinates of the respective experimentally derived structures of the TMDs of the target proteins.

Automated Protein Secondary Structure Assignment from Cα Positions Using Neural Networks.

The assignment of secondary structure elements in protein conformations is necessary to interpret a protein model that has been established by computational methods. The process essentially involves labeling the amino acid residues with H (Helix), E (Strand), or C (Coil, also known as Loop). When particular atoms are absent from an input protein structure, the procedure becomes more complicated, especially when only the alpha carbon locations are known. Various techniques have been tested and applied to this problem during the last forty years. The application of machine learning techniques is the most recent trend. This contribution presents the HECA classifier, which uses neural networks to assign protein secondary structure types. The technique exclusively employs C coordinates. The Keras (TensorFlow) library was used to implement and train the neural network model. The BioShell toolkit was used to calculate the neural network input features from raw coordinates. The study’s findings show that neural network-based methods may be successfully used to take on structure assignment challenges when only C trace is available. Thanks to the careful selection of input features, our approach’s accuracy (above 97%) exceeded that of the existing methods.

Assigning secondary structure in proteins using AI.

Knowledge about protein structure assignment enriches the structural and functional understanding of proteins. Accurate and reliable structure assignment data is crucial for secondary structure prediction systems. Since the 1980s, various methods based on hydrogen bond analysis and atomic coordinate geometry, followed by machine learning, have been employed in protein structure assignment. However, the assignment process becomes challenging when missing atoms are present in the protein files. Our method proposed a multi-class classifier program named DLFSA for assigning protein secondary structure elements (SSE) using convolutional neural networks (CNNs). A fast and efficient GPU-based parallel procedure extracts fragments from protein files. The model implemented in this work is trained with a subset of the protein fragments and achieves 88.1% and 82.5% train and test accuracy, respectively. The model uses only Cα coordinates for secondary structure assignments. The model has been successfully tested on a few full-length proteins also. Results from the fragment-based studies demonstrate the feasibility of applying deep learning solutions for structure assignment problems.

Dissociation Process of a MDM2/p53 Complex Investigated by Parallel Cascade Selection Molecular Dynamics and the Markov State Model.

Recently, we efficiently generated dissociation pathways of a protein-ligand complex without applying force bias with parallel cascade selection molecular dynamics (PaCS-MD) and showed that PaCS-MD in combination with the Markov state model (MSM) yielded a binding free energy comparable to experimental values. In this work, we applied the same procedure to a complex of MDM2 protein and the transactivation domain of p53 protein (TAD-p53), the latter of which is known to be very flexible in the unbound state. Using 30 independent MD simulations in PaCS-MD, we successfully generated 25 dissociation pathways of the complex, which showed complete or partial unfolding of the helical region of TAD-p53 during the dissociation process within an average simulation time of 154.8 ± 46.4 ns. The standard binding free energy obtained in combination with one-dimensional-, three-dimensional (3D)- or Cα-MSM was in good agreement with those determined experimentally. Using 3D-MSM based on the center of mass position of TAD-p53 relative to MDM2, the dissociation rate constant was calculated, which was comparable to those measured experimentally. Cα-MSM based on all Cα coordinates of TAD-p53 reproduced the experimentally measured standard binding free energy, and dissociation and association rate constants. We conclude that the combination of PaCS-MD and MSM offers an efficient computational procedure to calculate binding free energies and kinetic rates.

Residue packing in globular and intrinsically disordered proteins.

Intrinsically disordered proteins (IDPs)/regions do not have well-defined secondary and tertiary structures, however, they are functional and it is critical to gain a deep understanding of their residue packing. The shape distributions methodology, which is usually utilized in pattern recognition, clustering, and classification studies in computer science, may be adopted to study the residue packing of the proteins. In this study, shape distributions of the globular proteins and IDPs were obtained to shed light on the residue packing of their structures. The shape feature that was used is the sphericity of tetrahedra obtained by Delaunay Tessellation of points of Cα coordinates. Then the sphericity probability distributions were compared by using Principal Component Analysis. This computational structural study shows that the set of IDPs constitute a more diverse set than the set of globular proteins in terms of the geometrical properties of their network structures.

Local Protein Structure Refinement via Molecular Dynamics Simulations with locPREFMD.

A method for the local refinement of protein structures that targets improvements in local stereochemistry while preserving the overall fold is presented. The method uses force field-based minimization and sampling via molecular dynamics simulations with a modified force field to bring bonds, angles, and torsion angles into an acceptable range for high-resolution protein structures. The method is implemented in the locPREFMD web server and was tested on computational models submitted to CASP11. Using MolProbity scores as the main assessment criterion, the locPREFMD method significantly improves the stereochemical quality of given input models close to the quality expected for experimental structures while maintaining the Cα coordinates of the initial model.

Predicting protein backbone chemical shifts from Cα coordinates: extracting high resolution experimental observables from low resolution models.

Given the demonstrated utility of coarse-grained modeling and simulations approaches in studying protein structure and dynamics, developing methods that allow experimental observables to be directly recovered from coarse-grained models is of great importance. In this work, we develop one such method that enables protein backbone chemical shifts (1HN, 1Hα, 13Cα, 13C, 13Cβ, and 15N) to be predicted from Cα coordinates. We show that our Cα-based method, LARMORCα, predicts backbone chemical shifts with comparable accuracy to some all-atom approaches. More importantly, we demonstrate that LARMORCα predicted chemical shifts are able to resolve native structure from decoy pools that contain both native and non-native models, and so it is sensitive to protein structure. As an application, we use LARMORCα to characterize the transient state of the fast-folding protein gpW using recently published NMR relaxation dispersion derived backbone chemical shifts. The model we obtain is consistent with the previously proposed model based on independent analysis of the chemical shift dispersion pattern of the transient state. We anticipate that LARMORCα will find utility as a tool that enables important protein conformational substates to be identified by “parsing” trajectories and ensembles generated using coarse-grained modeling and simulations.

A three dimensional visualisation approach to protein heavy-atom structure reconstruction.

BackgroundA commonly recurring problem in structural protein studies, is the determination of all heavy atom positions from the knowledge of the central α-carbon coordinates.ResultsWe employ advances in virtual reality to address the problem. The outcome is a 3D visualisation based technique where all the heavy backbone and side chain atoms are treated on equal footing, in terms of the Cα coordinates. Each heavy atom is visualised on the surfaces of a different two-sphere, that is centered at another heavy backbone and side chain atoms. In particular, the rotamers are visible as clusters, that display a clear and strong dependence on the underlying backbone secondary structure.ConclusionsWe demonstrate that there is a clear interdependence between rotameric states and secondary structure. Our method easily detects those atoms in a crystallographic protein structure which are either outliers or have been likely misplaced, possibly due to radiation damage. Our approach forms a basis for the development of a new generation, visualization based side chain construction, validation and refinement tools. The heavy atom positions are identified in a manner which accounts for the secondary structure environment, leading to improved accuracy.Electronic supplementary materialThe online version of this article (doi:10.1186/s12900-014-0027-8) contains supplementary material, which is available to authorized users.

PCASSO: a fast and efficient Cα-based method for accurately assigning protein secondary structure elements.

Proteins are often characterized in terms of their primary, secondary, tertiary, and quaternary structure. Algorithms such as define secondary structure of proteins (DSSP) can automatically assign protein secondary structure based on the backbone hydrogen-bonding pattern. However, the assignment of secondary structure elements (SSEs) becomes a challenge when only the Cα coordinates are available. In this work, we present protein C-alpha secondary structure output (PCASSO), a fast and accurate program for assigning protein SSEs using only the Cα positions. PCASSO achieves ∼95% accuracy with respect to DSSP and takes ∼0.1 s using a single processor to analyze a 1000 residue system with multiple chains. Our approach was compared with current state-of-the-art Cα-based methods and was found to outperform all of them in both speed and accuracy. A practical application is also presented and discussed.

COARSE-GRAINED MODELING OF PROTEIN UNFOLDING DYNAMICS.

We present a new dynamic elastic network model (DENM) that describes the unfolding process of a force-loaded protein. The protein interaction network and its potentials are constructed based on information of its native-state structure obtained from the Protein Data Bank, with network nodes positioned at the Cα coordinates of the protein backbone. Specifically, to mimic the unfolding process, i.e., to simulate the process of overcoming the local energy barrier on the free energy landscape with force loading, the noncovalent protein network bonds (i.e., hydrogen bonds, salt bridges, hydrophobic contacts, etc.) are broken one-by-one with a certain probability, while the strong covalent bonds along the backbone (i.e., peptide bonds, disulfide bonds, etc.) are kept intact. The jumping event from local energy minima (bonds breaking rate) are chosen according to Kramer's theory and the Bell model. Moreover, we exploit the self-similar structure of proteins at different scales to design an effective coarse-graining procedure for DENM with optimal parameter selection. The robustness of DENM is validated by coarse-grained molecular dynamics (MD) simulation against atomistic MD simulation of force-extension processes of the Fibrinogen and Titin Immunoglobulin proteins. We observe that the native structure of the proteins determines the total unfolding dynamics (including large deviations) and not just the fluctuations around the native state.

Improving threading algorithms for remote homology modeling by combining fragment and template comparisons

In this work, we develop a method called fragment comparison and the template comparison (FTCOM) for assessing the global quality of protein structural models for targets of medium and hard difficulty (remote homology) produced by structure prediction approaches such as threading or ab initio structure prediction. FTCOM requires the C(alpha) coordinates of full length models and assesses model quality based on fragment comparison and a score derived from comparison of the model to top threading templates. On a set of 361 medium/hard targets, FTCOM was applied to and assessed for its ability to improve on the results from the SP(3), SPARKS, PROSPECTOR_3, and PRO-SP(3)-TASSER threading algorithms. The average TM-score improves by 5-10% for the first selected model by the new method over models obtained by the original selection procedure in the respective threading methods. Moreover, the number of foldable targets (TM-score >or= 0.4) increases from least 7.6% for SP(3) to 54% for SPARKS. Thus, FTCOM is a promising approach to template selection. Proteins 2010. (c) 2010 Wiley-Liss, Inc.

Solution Structure of Factor I-like Modules from Complement C7 Reveals a Pair of Follistatin Domains in Compact Pseudosymmetric Arrangement

Factor I-like modules (FIMs) of complement proteins C6, C7, and factor I participate in protein-protein interactions critical to the progress of a complement-mediated immune response to infections and other trauma. For instance, the carboxyl-terminal FIM pair of C7 (C7-FIMs) binds to the C345C domain of C5 and its activated product, C5b, during self-assembly of the cytolytic membrane-attack complex. FIMs share sequence similarity with follistatin domains (FDs) of known three-dimensional structure, suggesting that FIM structures could be reliably modeled. However, conflicting disulfide maps, inconsistent orientations of subdomains within FDs, and the presence of binding partners in all FD structures led us to determine the three-dimensional structure of C7-FIMs by NMR spectroscopy. The solution structure reveals that each FIM within C7 contains a small amino-terminal FOLN subdomain connected to a larger carboxyl-terminal KAZAL domain. The open arrangement of the subdomains within FIMs resembles that of first FDs within structures of tandem FDs but differs from the more compact subdomain arrangement of second or third FDs. Unexpectedly, the two C7-FIMs pack closely together with an approximate 2-fold rotational symmetry that is rarely seen in module pairs and has not been observed in FD-containing proteins. Interfaces between subdomains and between modules include numerous hydrophobic and electrostatic contributions, suggesting that this is a physiologically relevant conformation that persists in the context of the parent protein. Similar interfaces were predicted in a homology-based model of the C6-FIM pair. The C7-FIM structures also facilitated construction of a model of the single FIM of factor I.

Stability of ligand-binding domain dimer assembly controls kainate receptor desensitization

AMPA and kainate receptors mediate fast synaptic transmission. AMPA receptor ligand-binding domains form dimers, which are key functional units controlling ion-channel activation and desensitization. Dimer stability is inversely related to the rate and extent of desensitization. Kainate and AMPA receptors share common structural elements, but functional measurements suggest that subunit assembly and gating differs between these subtypes. To investigate this, we constructed a library of GluR6 kainate receptor mutants and directly measured changes in kainate receptor dimer stability by analytical ultracentrifugation, which, combined with electrophysiological experiments, revealed an inverse correlation between dimer stability and the rate of desensitization. We solved crystal structures for a series of five GluR6 mutants, to understand the molecular mechanisms for dimer stabilization. We demonstrate that the desensitized state of kainate receptors acts as a deep energy well offsetting the stabilizing effects of dimer interface mutants, and that the deactivation of kainate receptor responses is dominated by entry into desensitized states. Our results show how neurotransmitter receptors with similar structures and gating mechanisms can exhibit strikingly different functional properties.

A Structural Model of the GDP Dissociation Inhibitor Rab Membrane Extraction Mechanism

Rab GDP dissociation inhibitors (GDI)-facilitated extraction of prenylated Rab proteins from membranes plays an important role in vesicular membrane trafficking. The investigated thermodynamic properties of yeast Rab.GDI and Rab.MRS6 complexes demonstrated differences in the Rab binding properties of the closely related Rab GDI and MRS6 proteins, consistent with their functional diversity. The importance of the Rab C terminus and its prenylation for GDI/MRS6 binding was demonstrated using both biochemical and structural data. The presented structures of the apo-form yeast Rab GDI and its two complexes with unprenylated Rab proteins, together with the earlier published structures of the prenylated Ypt1.GDI, provide evidence of allosteric regulation of the GDI lipid binding site opening, which plays a key role in the proposed mechanism of GDI-mediated Rab extraction. We suggest a model for the interaction of GDI with prenylated Rab proteins that incorporates a stepwise increase in affinity as the three different partial interactions are successively formed.

Using molecular principal axes for structural comparison: determining the tertiary changes of a FAB antibody domain induced by antigenic binding

BackgroundComparison of different protein x-ray structures has previously been made in a number of different ways; for example, by visual examination, by differences in the locations of secondary structures, by explicit superposition of structural elements, e.g. α-carbon atom locations, or by procedures that utilize a common symmetry element or geometrical feature of the structures to be compared.ResultsA new approach is applied to determine the structural changes that an antibody protein domain experiences upon its interaction with an antigenic target. These changes are determined with the use of two different, however comparable, sets of principal axes that are obtained by diagonalizing the second-order tensors that yield the moments-of-geometry as well as an ellipsoidal characterization of domain shape, prior to and after interaction. Determination of these sets of axes for structural comparison requires no internal symmetry features of the domains, depending solely upon their representation in three-dimensional space. This representation may involve atomic, Cα, or residue centroid coordinates. The present analysis utilizes residue centroids. When the structural changes are minimal, the principal axes of the domains, prior to and after interaction, are essentially comparable and consequently may be used for structural comparison. When the differences of the axes cannot be neglected, but are nevertheless slight, a smaller relatively invariant substructure of the domains may be utilized for comparison. The procedure yields two distance metrics for structural comparison. First, the displacements of the residue centroids due to antigenic binding, referenced to the ellipsoidal principal axes, are noted. Second, changes in the ellipsoidal distances with respect to the non-interacting structure provide a direct measure of the spatial displacements of the residue centroids, towards either the interior or exterior of the domain.ConclusionWith use of x-ray data from the protein data bank (PDB), these two metrics are shown to highlight, in a manner different from before, the structural changes that are induced in the overall domains as well as in the H3 loops of the complementarity-determining regions (CDR) upon FAB antibody binding to a truncated and to a synthetic hemagglutinin viral antigenic target.

The Conformationally Dynamic C Helix of the RIα Subunit of Protein Kinase A Mediates Isoform-specific Domain Reorganization upon C Subunit Binding

Different isoforms of the full-length protein kinase A (PKA) regulatory subunit homodimer (R2) and the catalytic (C) subunit-bound holoenzyme (R2C2) have very different global structures despite similar molecular weights and domain organization within their primary sequences. To date, it has been the linker sequence between the R subunit dimerization/docking domain and cAMP-binding domain A that has been implicated in modulating domain interactions to give rise to these differences in global structure. The small angle solution scattering data presented here for three different isoforms of PKA heterodimer (deltaR-C) complexes reveal a role for another conformationally dynamic sequence in modulating inter-subunit and domain interactions, the C helix that connects the cAMP-binding domains A and B of the R subunit. The deltaR-C heterodimer complexes studied here were each formed with a monomeric N-terminal deletion mutant of the R subunit (deltaR) that contains the inhibitor sequence and both cAMP-binding domains. The scattering data show that type IIalpha and type IIbeta deltaR-C heterodimers are relatively compact and globular, with the C subunit contacting the inhibitor sequence and both cAMP-binding domains. In contrast, the type Ialpha heterodimer is significantly more extended, with the C subunit interacting with the inhibitor sequence and cAMP-binding domain A, whereas domain B extends out such that its surface is almost completely solvent exposed. These data implicate the C helix of RIalpha in modulating isoform-specific interdomain communication in the PKA holoenzyme, adding another layer of structural complexity to our understanding of signaling dynamics in this multisubunit, multidomain protein kinase.

PALSSE: A program to delineate linear secondary structural elements from protein structures

BackgroundThe majority of residues in protein structures are involved in the formation of α-helices and β-strands. These distinctive secondary structure patterns can be used to represent a protein for visual inspection and in vector-based protein structure comparison. Success of such structural comparison methods depends crucially on the accurate identification and delineation of secondary structure elements.ResultsWe have developed a method PALSSE (Predictive Assignment of Linear Secondary Structure Elements) that delineates secondary structure elements (SSEs) from protein Cα coordinates and specifically addresses the requirements of vector-based protein similarity searches. Our program identifies two types of secondary structures: helix and β-strand, typically those that can be well approximated by vectors. In contrast to traditional secondary structure algorithms, which identify a secondary structure state for every residue in a protein chain, our program attributes residues to linear SSEs. Consecutive elements may overlap, thus allowing residues located at the overlapping region to have more than one secondary structure type.ConclusionPALSSE is predictive in nature and can assign about 80% of the protein chain to SSEs as compared to 53% by DSSP and 57% by P-SEA. Such a generous assignment ensures almost every residue is part of an element and is used in structural comparisons. Our results are in agreement with human judgment and DSSP. The method is robust to coordinate errors and can be used to define SSEs even in poorly refined and low-resolution structures. The program and results are available at .