GraSp-PSN: A web server for graph spectra based analysis of protein structure networks.

The function of a protein is most of the time achieved due to minute conformational changes in its structure due to ligand binding or environmental changes or other interactions. Hence the analysis of structure of proteins should go beyond the analysis of mere atom contacts and should include the emergent global structure as a whole. This can be achieved by graph spectra based analysis of protein structure networks. GraSp-PSN is a web server that can assist in (1) acquiring weighted protein structure network (PSN) and network parameters ranging from atomic level to global connectivity from the three dimensional coordinates of a protein, (2) generating scores for comparison of a pair of protein structures with detailed information of local to global connectivity, and (3) assigning perturbation scores to the residues and their interactions, that can prioritise them in terms of residue clusters. The methods implemented in the server are generic in nature and can be used for comparing networks in any discipline by uploading adjacency matrices in the server. The webserver can be accessed using the following link: https://pople.mbu.iisc.ac.in/.

Comparison of structural networks across homologous proteins.

Protein sequence determines its structure and function. The indirect relationship between protein function and structure lies deep-rooted in the structural topology that has evolved into performing optimal function. The evolution of structure and its interconnectivity has been conventionally studied by comparing the root means square deviation between protein structures at the backbone level. Two factors that are necessary for the quantitative comparison of non-covalent interactions are (a) explicit inclusion of the coordinates of side-chain atoms and (b) consideration of multiple structures from the conformational landscape to account for structural variability. We have recently addressed these fundamental issues by investigating the alteration of inter-residue interactions across an ensemble of protein structure networks through a graph spectral approach. In this study, we have developed a rigorous method to compare the structure networks of homologous proteins, with a wide range of sequence identity percentages. A range of dissimilarity measures that show the extent of change in the network across homologous structures are generated, which also includes the comparison of the protein structure variability. We discuss in detail, scenarios where the variation of structure is not accompanied by loss or gain of the overall network and its vice versa. The sequence-based phylogeny among the homologs is also compared with the lineage obtained from information from such a robust structure comparison. In summary, we can obtain a quantitative comparison score for the structure networks of homologous proteins, which also enables us to study the evolution of protein function based on the variation of their topologies.

Understanding structural variability in proteins using protein structural networks.

Proteins perform their function by accessing a suitable conformer from the ensemble of available conformations. The conformational diversity of a chosen protein structure can be obtained by experimental methods under different conditions. A key issue is the accurate comparison of different conformations. A gold standard used for such a comparison is the root mean square deviation (RMSD) between the two structures. While extensive refinements of RMSD evaluation at the backbone level are available, a comprehensive framework including the side chain interaction is not well understood. Here we employ protein structure network (PSN) formalism, with the non-covalent interactions of side chain, explicitly treated. The PSNs thus constructed are compared through graph spectral method, which provides a comparison at the local and at the global structural level. In this work, PSNs of multiple crystal conformers of single-chain, single-domain proteins, are subject to pair-wise analysis to examine the dissimilarity in their network topologies and in order to determine the conformational diversity of their native structures. This information is utilized to classify the structural domains of proteins into different categories. It is observed that proteins typically tend to retain structure and interactions at the backbone level. However, some of them also depict variability in either their overall structure or only in their inter-residue connectivity at the sidechain level, or both. Variability of sub-networks based on solvent accessibility and secondary structure is studied. The types of specific interactions are found to contribute differently to structure variability. An ensemble analysis by computing the mathematical variance of edge-weights across multiple conformers provided information on the contribution to overall variability from each edge of the PSN. Interactions that are highly variable are identified and their impact on structure variability has been discussed with the help of a case study. The classification based on the present side-chain network-based studies provides a framework to correlate the structure-function relationships in protein structures.

PASS2.7: a database containing structure-based sequence alignments and associated features of protein domain superfamilies from SCOPe.

Sequence alignments are models that capture the structural, functional and evolutionary relationships between proteins. Structure-guided sequence alignments are helpful in the case of distantly related proteins with poor sequence identity, thus rendering routine sequence alignment methods ineffective. Protein Alignment organized as Structural Superfamilies or PASS2 database provides such sequence alignments of protein domains within a superfamily as per the Structural Classification of Proteins extended (SCOPe) database. The current update of PASS2 (i.e. PASS2.7) is following the latest release of SCOPe (2.07) and we provide data for 14 323 protein domains that are <40% identical and are organized into 2024 superfamilies. Several useful features derived from the alignments, such as conserved secondary structural motifs, HMMs and residues conserved across the superfamily, are also reported. Protein domains that are deviant from the rest of the members of a superfamily may compromise the quality of the alignment, and we found this to be the case in ∼7% of the total superfamilies we considered. To improve the alignment by objectively identifying such 'outliers', in this update, we have used a k-means-based unsupervised machine learning method for clustering superfamily members, where features provided were length of domains aligned, Cα-RMSD derived from the rigid-body superposition of all members and gaps contributed to the alignment by each domain. In a few cases, we have split the superfamily as per the clusters predicted and provided complete data for each cluster. A new feature included in this update is absolutely conserved interactions (ACIs) between residue backbones and side chains, which are obtained by aligning protein structure networks using structure-guided sequence alignments of superfamilies. ACIs provide valuable information about functionally important residues and the structure-function relationships of proteins. The ACIs and the corresponding conserved networks for backbone and sidechain have been marked on the superimposed structure separately. DATABASE URL: The updated version of the PASS2 database is available at http://caps.ncbs.res.in/pass2/.

Network Re-Wiring During Allostery and Protein-Protein Interactions: A Graph Spectral Approach.

The process of allostery is often guided by subtle changes in the non-covalent interactions between residues of a protein. These changes may be brought about by minor perturbations by natural processes like binding of a ligand or protein-protein interaction. The challenge lies in capturing minute changes at the residue interaction level and following their propagation at local as well as global distances. While macromolecular effects of the phenomenon of allostery are inferred from experiments, a computational microscope can elucidate atomistic-level details leading to such macromolecular effects. Network formalism has served as an attractive means to follow this path and has been pursued further for the past couple of decades. In this chapter some concepts and methods are summarized, and recent advances are discussed. Specifically, the changes in strength of interactions (edge weight) and their repercussion on the overall protein organization (residue clustering) are highlighted. In this review, we adopt a graph spectral method to probe these subtle changes in a quantitative manner. Further, the power of this method is demonstrated for capturing re-ordering of side-chain interactions in response to ligand binding, which culminates into formation of a protein-protein complex in ß2-adrenergic receptors.

From Quantum Chemistry to Networks in Biology: A Graph Spectral Approach to Protein Structure Analyses.

In this perspective article, we present a multidisciplinary approach for characterizing protein structure networks. We first place our approach in its historical context and describe the manner in which it synthesizes concepts from quantum chemistry, biology of polymer conformations, matrix mathematics, and percolation theory. We then explicitly provide the method for constructing the protein structure network in terms of noncovalently interacting amino acid side chains and show how a mine of information can be obtained from the graph spectra of these networks. Employing suitable mathematical approaches, such as the use of a weighted, Laplacian matrix to generate the spectra, enables us to develop rigorous methods for network comparison and to identify crucial nodes responsible for the network integrity through a perturbation approach. Our scoring methods have several applications in structural biology that are elusive to conventional methods of analyses. Here, we discuss the instances of (a) protein structure comparison that includes the details of side chain connectivity, (b) contribution to node clustering as a function of bound ligand, explaining the global effect of local changes in phenomena such as allostery, and (c) identification of crucial amino acids for structural integrity, derived purely from the spectra of the graph. We demonstrate how our method enables us to obtain valuable information on key proteins involved in cellular functions and diseases such as GPCR and HIV protease and discuss the biological implications. We then briefly describe how concepts from percolation theory further augment our analyses. In our concluding perspective for future developments, we suggest a further unifying approach to protein structure analyses and a judicious choice of questions to employ our methods for larger, more complex networks, such as metabolic and disease networks.

Validation of protein structure models using network similarity score.

Accurate structural validation of proteins is of extreme importance in studies like protein structure prediction, analysis of molecular dynamic simulation trajectories and finding subtle changes in very similar structures. The benchmarks for today's structure validation are scoring methods like global distance test-total structure (GDT-TS), TM-score and root mean square deviations (RMSD). However, there is a lack of methods that look at both the protein backbone and side-chain structures at the global connectivity level and provide information about the differences in connectivity. To address this gap, a graph spectral based method (NSS-network similarity score) which has been recently developed to rigorously compare networks in diverse fields, is adopted to compare protein structures both at the backbone and at the side-chain noncovalent connectivity levels. In this study, we validate the performance of NSS by investigating protein structures from X-ray structures, modeling (including CASP models), and molecular dynamics simulations. Further, we systematically identify the local and the global regions of the structures contributing to the difference in NSS, through the components of the score, a feature unique to this spectral based scoring scheme. It is demonstrated that the method can quantify subtle differences in connectivity compared to a reference protein structure and can form a robust basis for protein structure comparison. Additionally, we have also introduced a network-based method to analyze fluctuations in side chain interactions (edge-weights) in an ensemble of structures, which can be an useful tool for the analysis of MD trajectories.