Assortative mixing in Protein Contact Networks and protein folding kinetics

Importance of Inter-residue Contacts for Understanding Protein Folding and Unfolding Rates, Remote Homology, and Drug Design

Inter-residue interactions in protein structures provide valuable insights into protein folding and stability. Understanding these interactions can be helpful in many crucial applications, including rational design of therapeutic small molecules and biologics, locating functional protein sites, and predicting protein-protein and protein-ligand interactions. The process of developing machine learning models incorporating inter-residue interactions has been improved recently. This review highlights the theoretical models incorporating inter-residue interactions in predicting folding and unfolding rates of proteins. Utilizing contact maps to depict inter-residue interactions aids researchers in developing computer models for detecting remote homologs and interface residues within protein-protein complexes which, in turn, enhances our knowledge of the relationship between sequence and structure of proteins. Further, the application of contact maps derived from inter-residue interactions is highlighted in the field of drug discovery. Overall, this review presents an extensive assessment of the significant models that use inter-residue interactions to investigate folding rates, unfolding rates, remote homology, and drug development, providing potential future advancements in constructing efficient computational models in structural biology.

Revisiting structural organization of proteins at high temperature from a network perspective

Interactions between distantly placed amino acids in the primary chain (long-range) play a very crucial role in the formation and stabilization of the tertiary structure of a protein, while interactions between closely placed amino acids in the primary chain (short-range) mostly stabilize the secondary structures. Every protein needs to maintain marginal stability in order to perform its physiological functions in its native environment. The requirements for this stability in mesophilic and thermophilic proteins are different. Thermophilic proteins need to form more interactions as well as more stable interactions to survive in the extreme environment, they live in. Here, we aim to find out how the interacting amino acids in three-dimensional space are positioned in the primary chains in thermophilic and mesophilic. How does this arrangement help thermophiles to maintain their structural integrity at high temperatures? Working on a dataset of 1560 orthologous pairs we perceive that thermophiles are not only enriched with long-range interactions, they feature bigger connected clusters and higher network densities compared to their mesophilic orthologs, at higher interaction strengths between the amino acids. Moreover, we have observed the enrichment of different types of interactions at different secondary structural regions.

Evaluating the active site-substrate interplay between x-ray crystal structure and molecular dynamics in chorismate mutase

Designing realistic quantum mechanical (QM) models of enzymes is dependent on reliably discerning and modeling residues, solvents, and cofactors important in crafting the active site microenvironment. Interatomic van der Waals contacts have previously demonstrated usefulness toward designing QM-models, but their measured values (and subsequent residue importance rankings) are expected to be influenceable by subtle changes in protein structure. Using chorismate mutase as a case study, this work examines the differences in ligand-residue interatomic contacts between an x-ray crystal structure and structures from a molecular dynamics simulation. Select structures are further analyzed using symmetry adapted perturbation theory to compute ab initio ligand-residue interaction energies. The findings of this study show that ligand-residue interatomic contacts measured for an x-ray crystal structure are not predictive of active site contacts from a sampling of molecular dynamics frames. In addition, the variability in interatomic contacts among structures is not correlated with variability in interaction energies. However, the results spotlight using interaction energies to characterize and rank residue importance in future computational enzymology workflows.

Amyotrophic lateral sclerosis disease-related mutations disrupt the dimerization of superoxide dismutase 1 - A comparative molecular dynamics simulation study

More than 150 genes are involved in amyotrophic lateral sclerosis (ALS), with superoxide dismutase 1 (SOD1) being one of the most studied. Mutations in SOD1 gene, which encodes the enzyme SOD1 is the second most prevalent and studied cause of familial ALS. SOD1 is a ubiquitous, homodimeric metalloenzyme that forms a critical component of the cellular defense against reactive oxygen species. Several mutations in the SOD1 enzyme cause misfolding, dimerization instability, and increased aggregate formation in ALS. However, there is a lack of information on the dimerization of SOD1 monomers and the mechanistic underpinnings on how the pathogenic mutations disrupt the dimerization mechanism. Here, we presented microsecond-scale molecular dynamics (MD) simulations to unravel how interface-based mutations compromise SOD1 dimerization and provide mechanistic understanding into the corresponding process using WT and three interface-based mutant systems (A4V, T54R, and I113T). Structural stability analysis showed that the mutant systems displayed disparate variations in the catalytic sites which may directly alter the stability and activity of the SOD1 enzyme. Based on the dynamic network analysis and principal component analysis, it has been identified that the mutations weakened the correlated motions along the dimer interface and altered the protein conformational behavior, thus weakening the stability of dimer formation. Moreover, the simulation results identified crucial residues such as G51, D52, G114, I151, and Q153 in establishing the dimerization interaction network, which were weakened or absent in the presence of interfacial mutants. Surface potential analysis on mutant systems also displayed changes in the dimerization potential, thus showing the unfavorable dimer formation. Furthermore, network analysis identified the hotspot residues necessary for SOD1 signal transduction which were surprisingly found in the catalytic sites rather than the anticipated dimerization interface.

Emerging landscape of molecular interaction networks: Opportunities, challenges and prospects

Network biology finds application in interpreting molecular interaction networks and providing insightful inferences using graph theoretical analysis of biological systems. The integration of computational bio-modelling approaches with different hybrid network-based techniques provides additional information about the behaviour of complex systems. With increasing advances in high-throughput technologies in biological research, attempts have been made to incorporate this information into network structures, which has led to a continuous update of network biology approaches over time. The newly minted centrality measures accommodate the details of omics data and regulatory network structure information. The unification of graph network properties with classical mathematical and computational modelling approaches and technologically advanced approaches like machine-learning- and artificial intelligence-based algorithms leverages the potential application of these techniques. These computational advances prove beneficial and serve various applications such as essential gene prediction, identification of drug–disease interaction and gene prioritization. Hence, in this review, we have provided a comprehensive overview of the emerging landscape of molecular interaction networks using graph theoretical approaches. With the aim to provide information on the wide range of applications of network biology approaches in understanding the interaction and regulation of genes, proteins, enzymes and metabolites at different molecular levels, we have reviewed the methods that utilize network topological properties, emerging hybrid network-based approaches and applications that integrate machine learning techniques to analyse molecular interaction networks. Further, we have discussed the applications of these approaches in biomedical research with a note on future prospects.

Linking protein structural and functional change to mutation using amino acid networks

The function of a protein is strongly dependent on its structure. During evolution, proteins acquire new functions through mutations in the amino-acid sequence. Given the advance in deep mutational scanning, recent findings have found functional change to be position dependent, notwithstanding the chemical properties of mutant and mutated amino acids. This could indicate that structural properties of a given position are potentially responsible for the functional relevance of a mutation. Here, we looked at the relation between structure and function of positions using five proteins with experimental data of functional change available. In order to measure structural change, we modeled mutated proteins via amino-acid networks and quantified the perturbation of each mutation. We found that structural change is position dependent, and strongly related to functional change. Strong changes in protein structure correlate with functional loss, and positions with functional gain due to mutations tend to be structurally robust. Finally, we constructed a computational method to predict functionally sensitive positions to mutations using structural change that performs well on all five proteins with a mean precision of 74.7% and recall of 69.3% of all functional positions.

Evaluating the role of community detection in improving influence maximization heuristics

Both community detection and influence maximization are well-researched fields of network science. Here, we investigate how several popular community detection algorithms can be used as part of a heuristic approach to influence maximization. The heuristic is based on the community value, a node-based metric defined on the outputs of overlapping community detection algorithms. This metric is used to select nodes as high influence candidates for expanding the set of influential nodes. Our aim in this paper is twofold. First, we evaluate the performance of eight frequently used overlapping community detection algorithms on this specific task to show how much improvement can be gained compared to the originally proposed method of Kempe et al. Second, selecting the community detection algorithm(s) with the best performance, we propose a variant of the influence maximization heuristic with significantly reduced runtime, at the cost of slightly reduced quality of the output. We use both artificial benchmarks and real-life networks to evaluate the performance of our approach.

Network-based strategies for protein characterization

Protein structure characterization is fundamental to understand protein properties, such as folding process and protein resistance to thermal stress, up to unveiling organism pathologies (e.g., prion disease). In this chapter, we provide an overview on how the spectral properties of the networks reconstructed from the Protein Contact Map (PCM) can be used to generate informative observables. As a specific case study, we apply two different network approaches to an example protein dataset, for the aim of discriminating protein folding state, and for the reconstruction of protein 3D structure.

Entropy-based distance cutoff for protein internal contact networks

Protein structure networks (PSNs) have long been used to provide a coarse yet meaningful representation of protein structure, dynamics, and internal communication pathways. An important question is what criteria should be applied to construct the network so that to include relevant interresidue contacts while avoiding unnecessary connections. To address this issue, we systematically considered varying residue distance cutoff length and the probability threshold for contact formation to construct PSNs based on atomistic molecular dynamics in order to assess the amount of mutual information within the resulting representations. We found that the minimum in mutual information is universally achieved at the cutoff length of 5 Å, irrespective of the applied contact formation probability threshold in all considered, distinct proteins. Assuming that the optimal PSNs should be characterized by the least amount of redundancy, which corresponds to the minimum in mutual information, this finding suggests an objective criterion for cutoff distance and supports the existing preference towards its customary selection around 5 Å length, typically based to date on heuristic criteria.

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 β₂-adrenergic receptors.

Topology Results on Adjacent Amino Acid Networks of Oligomeric Proteins

In this chapter, we focus on topology measurements of the adjacent amino acid networks for a data set of oligomeric proteins and some of its subnetworks. The aim is to present many mathematical tools in order to understand the structures of proteins implicitly coded in such networks and subnetworks. We mainly investigate four important networks by computing the number of connected components, the degree distribution, and assortativity measures. We compare each result in order to prove that the four networks have quite independent topologies.

RBinds: A user-friendly server for RNA binding site prediction

RNA performs various biological functions by interacting with other molecules. The knowledge of RNA binding sites is essential for the understanding of RNA-protein or RNA-ligand complex structures and their mechanisms. However, the RNA binding site prediction study requires tedious programming scripts and manual handling. One user-friendly bioinformatics tool for RNA binding site prediction has been missing. This limitation motivated us to develop the RBinds, a user-friendly web server, to predict the RNA binding site using a simple graphical user interface. Some advanced features implemented in RBinds are (1) transforming the RNA structure to a network automatically; (2) analyzing the structural network properties to predict binding site; (3) constructing one annotated force-directed network; (4) providing a visualization tool for users to scale and rotate the structure; (5) offering the related tools to predict or simulate RNA structures. RBinds web server is a reliable and user-friendly tool and facilitates the RNA binding site study without installing programs locally. RBinds is freely accessible at http://zhaoserver.com.cn/RBinds/RBinds.html.

Network analysis of hydroxymethylbilane synthase dynamics

Hydroxymethylbilane synthase (HMBS) is one of the key enzymes of the heme biosynthetic pathway that catalyzes porphobilinogen to form the linear tetrapyrrole 1-hydroxymethylbilane through four intermediate steps. Mutations in the human HMBS (hHMBS) can lead to acute intermittent porphyria (AIP), a lethal metabolic disorder. The molecular basis of importance of the amino acid residues at the catalytic site of hHMBS has been well studied. However, the role of non-active site residues toward the activity of the enzyme and hence the association of their mutations with AIP is not known. Network-based analyses of protein structures provide a systems approach to understand the correlations of the residues through a series of inter-residue interactions. We analyzed the dynamic network representation of HMBS protein derived from five molecular dynamics trajectories corresponding to the five steps of pyrrole polymerization. We analyzed the network clusters for each stage and identified the amino acid residues and interactions responsible for the structural stability and catalytic function of the protein. The analysis of high betweenness nodes and interaction paths from the active site help in understanding the molecular basis of the effect of non-active site AIP-causing mutations on the catalytic activity.

NAPS update: network analysis of molecular dynamics data and protein-nucleic acid complexes

Network theory is now a method of choice to gain insights in understanding protein structure, folding and function. In combination with molecular dynamics (MD) simulations, it is an invaluable tool with widespread applications such as analyzing subtle conformational changes and flexibility regions in proteins, dynamic correlation analysis across distant regions for allosteric communications, in drug design to reveal alternative binding pockets for drugs, etc. Updated version of NAPS now facilitates network analysis of the complete repertoire of these biomolecules, i.e., proteins, protein–protein/nucleic acid complexes, MD trajectories, and RNA. Various options provided for analysis of MD trajectories include individual network construction and analysis of intermediate time-steps, comparative analysis of these networks, construction and analysis of average network of the ensemble of trajectories and dynamic cross-correlations. For protein–nucleic acid complexes, networks of the whole complex as well as that of the interface can be constructed and analyzed. For analysis of proteins, protein–protein complexes and MD trajectories, network construction based on inter-residue interaction energies with realistic edge-weights obtained from standard force fields is provided to capture the atomistic details. Updated version of NAPS also provides improved visualization features, interactive plots and bulk execution. URL: http://bioinf.iiit.ac.in/NAPS/

Small Conformational Changes Underlie Evolution of Resistance to NNRTI in HIV Reverse Transcriptase

Despite achieving considerable success in reducing the number of fatalities due to acquired immunodeficiency syndrome, emergence of resistance against the reverse transcriptase (RT) inhibitor drugs remains one of the biggest challenges of the human immunodeficiency virus antiretroviral therapy (ART). Non-nucleoside reverse transcriptase inhibitors (NNRTIs) form a large class of drugs and a crucial component of ART. In NNRTIs, even a single resistance mutation is known to make the drugs completely ineffective. Additionally, several inhibitor-bound RTs with single resistance mutations do not exhibit any significant variations in their three-dimensional structures compared with the inhibitor-bound RT but completely nullify their inhibitory functions. This makes understanding the structural mechanism of these resistance mutations crucial for drug development. Here, we study several single resistance mutations in the allosteric inhibitor (nevirapine)-bound RT to analyze the mechanism of small structural changes leading to these large functional effects. In this study, we have shown that in absence of significant conformational variations in the inhibitor-bound wild-type RT and RT with single resistance mutations, the protein contact network analysis of their static structures, along with molecular dynamics simulations, can be a useful approach to understand the functional effect of small local conformational variations. The simple network analysis exposes the localized contact changes that lead to global rearrangement in the communication pattern within RT. Furthermore, these conformational changes have implications on the overall dynamics of RT. Using various measures, we show that a single resistance mutation can change the network structure and dynamics of RT to behave more like unbound RT, even in the presence of the inhibitor. This combined coarse-grained contact network and molecular dynamics approach promises to be a useful tool to analyze structure-function studies of proteins that show large functional changes with negligible variations in their overall conformation.

Quantitative description and classification of protein structures by a novel robust amino acid network: interaction selective network (ISN)

To quantitatively categorize protein structures, we developed a quantitative coarse-grained model of protein structures with a novel amino acid network, the interaction selective network (ISN), characterized by the links based on interactions in both the main and side chains. We found that the ISN is a novel robust network model to show the higher classification probability in the plots of average vertex degree (k) versus average clustering coefficient (C), both of which are typical network parameters for protein structures, and successfully distinguished between “all-α” and “all-β” proteins. On the other hand, one of the typical conventional networks, the α-carbon network (CAN), was found to be less robust than the ISN, and another typical network, atomic distance network (ADN), failed to distinguish between these two protein structures. Considering that the links in the CAN and ADN are defined by the interactions only between the main chain atoms and by the distance of the closest atom pair between the two amino acid residues, respectively, we can conclude that reflecting structural information from both secondary and tertiary structures in the network parameters improves the quantitative evaluation and robustness in network models, resulting in a quantitative and more robust description of three-dimensional protein structures in the ISN.

Convolution Neural Network-Based Prediction of Protein Thermostability

Most natural proteins exhibit poor thermostability, which limits their industrial application. Computer-aided rational design is an efficient purpose-oriented method that can improve protein thermostability. Numerous machine-learning-based methods have been designed to predict the changes in protein thermostability induced by mutations. However, all of these methods have certain limitations due to existing mutation coding methods that overlook protein sequence features. Here we propose a method to predict protein thermostability using convolutional neural networks based on an in-depth study of thermostability-related protein properties. This method comprises a three-dimensional coding algorithm, including protein mutation information and a strategy to extract neighboring features at protein mutation sites based on multiscale convolution. The accuracies on the S1615 and S388 data sets, which are widely used for protein thermostability predictions, reached 86.4 and 87%, respectively. The Matthews correlation coefficient was nearly double those produced using other methods. Furthermore, a model was constructed to predict the thermostability of Rhizomucor miehei lipase mutants based on the S3661 data set, a single amino acid mutation data set screened from the ProTherm protein thermodynamics database. Compared with the RIF strategy, which consists of three algorithms, i.e., Rosetta ddg monomer, I Mutant 3.0, and FoldX, the accuracy of the proposed method was higher (75.0 vs 66.7%), and the negative sample resolution was simultaneously enhanced. These results indicate that our prediction method more effectively assessed the protein thermostability and distinguished its features, making it a powerful tool to devise mutations that enhance the thermostability of proteins, particularly enzymes.

Folding with a protein's native shortcut network

A complex network approach to protein folding is proposed, wherein a protein's contact map is reconceptualized as a network of shortcut edges, and folding is steered by a structural characteristic of this network. Shortcut networks are generated by a known message passing algorithm operating on protein residue networks. It is found that the shortcut networks of native structures (SCN0s) are relevant graph objects with which to study protein folding at a formal level. The logarithm form of their contact order (SCN0_lnCO) correlates significantly with folding rate of two-state and nontwo-state proteins. The clustering coefficient of SCN0s (C_SCN0 ) correlates significantly with folding rate, transition-state placement and stability of two-state folders. Reasonable folding pathways for several model proteins are produced when C_SCN0 is used to combine protein segments incrementally to form the native structure. The folding bias captured by C_SCN0 is detectable in non-native structures, as evidenced by Molecular Dynamics simulation generated configurations for the fast folding Villin-headpiece peptide. These results support the use of shortcut networks to investigate the role protein geometry plays in the folding of both small and large globular proteins, and have implications for the design of multibody interaction schemes in folding models. One facet of this geometry is the set of native shortcut triangles, whose attributes are found to be well-suited to identify dehydrated intraprotein areas in tight turns, or at the interface of different secondary structure elements.

Understanding contact patterns of protein structures from protein contact map and investigation of unique patterns in the globin-like folded domains

Proteins are biochemical compounds made up of one or more polypeptides in a specific order, typically folded into a functionally active form. Proteins are categorized into four different structural classes according to the topology of α-helices and β-strands. In this study, we modeled these four structural classes as an undirected network depicting amino acids as nodes and interaction between them as edges. Results infer that basic protein classes can be easily recognized as well as distinguished by utilizing protein contact maps (PCM). Toward studying the globin-like fold, the helix-loop-helix region contacts were seen to be of a unique pattern, and these remained in all the folds. Further, the averaged diagonal contacts were analyzed and identified those contacts in α/β proteins were higher in comparison with the other class. Interesting, we noticed that anti-parallel beta sheets were dominant in all-β and α + β classes that lead to similar diagonal patterns. Network properties of all four basic classes were analyzed and found to possess small-world property. Findings infer that PCM may assist classify protein structure classes and it also helps in evaluating the predicted protein structures.

Role of Computational Methods in Going beyond X-ray Crystallography to Explore Protein Structure and Dynamics

Protein structural biology came a long way since the determination of the first three-dimensional structure of myoglobin about six decades ago. Across this period, X-ray crystallography was the most important experimental method for gaining atomic-resolution insight into protein structures. However, as the role of dynamics gained importance in the function of proteins, the limitations of X-ray crystallography in not being able to capture dynamics came to the forefront. Computational methods proved to be immensely successful in understanding protein dynamics in solution, and they continue to improve in terms of both the scale and the types of systems that can be studied. In this review, we briefly discuss the limitations of X-ray crystallography in studying protein dynamics, and then provide an overview of different computational methods that are instrumental in understanding the dynamics of proteins and biomacromolecular complexes.

NDDN: A Cloud-Based Neuroinformation Database for Developing Neuronal Networks

Electrical activity of developing dissociated neuronal networks is of immense significance for understanding the general properties of neural information processing and storage. In addition, the complexity and diversity of network activity patterns make them ideal candidates for developing novel computational models and evaluating algorithms. However, there are rare databases which focus on the changing network dynamics during development. Here, we describe the design and implementation of Neuroinformation Database for Developing Networks (NDDN), a repository for electrophysiological data collected from long-term cultured hippocampal networks. The NDDN contains over 15 terabytes of multielectrode array data consisting of 25,380 items collected from 105 culture batches. Metadata including culturing and recording information and stimulation/drug application protocols are linked to each data item. A Matlab toolbox named MEAKit is also provided with the NDDN to ease the analysis of downloaded data items. We expect that NDDN may contribute to both the fields of experimental and computational neuroscience.

Understanding G Protein-Coupled Receptor Allostery via Molecular Dynamics Simulations: Implications for Drug Discovery

Unraveling the mystery of protein allostery has been one of the greatest challenges in both structural and computational biology. However, recent advances in computational methods, particularly molecular dynamics (MD) simulations, have led to its utility as a powerful and popular tool for the study of protein allostery. By capturing the motions of a protein's constituent atoms, simulations can enable the discovery of allosteric hot spots and the determination of the mechanistic basis for allostery. These structural and dynamic studies can provide a foundation for a wide range of applications, including rational drug design and protein engineering. In our laboratory, the use of MD simulations and network analysis assisted in the elucidation of the allosteric hotspots and intracellular signal transduction of G protein-coupled receptors (GPCRs), primarily on one of the adenosine receptor subtypes, A_2A adenosine receptor (A_2AAR). In this chapter, we describe a method for calculating the map of allosteric signal flow in different GPCR conformational states and illustrate how these concepts have been utilized in understanding the mechanism of GPCR allostery. These structural studies will provide valuable insights into the allosteric and orthosteric modulations that would be of great help to design novel drugs targeting GPCRs in pathological states.

Ultraslow Water-Mediated Transmembrane Interactions Regulate the Activation of A2A Adenosine Receptor

Water molecules inside a G-protein coupled receptor (GPCR) have recently been spotlighted in a series of crystal structures. To decipher the dynamics and functional roles of internal water molecules in GPCR activity, we studied the A2A adenosine receptor using microsecond molecular-dynamics simulations. Our study finds that the amount of water flux across the transmembrane (TM) domain varies depending on the receptor state, and that the water molecules of the TM channel in the active state flow three times more slowly than those in the inactive state. Depending on the location in solvent-protein interface as well as the receptor state, the average residence time of water in each residue varies from ∼O(10(2)) ps to ∼O(10(2)) ns. Especially, water molecules, exhibiting ultraslow relaxation (∼O(10(2)) ns) in the active state, are found around the microswitch residues that are considered activity hotspots for GPCR function. A continuous allosteric network spanning the TM domain, arising from water-mediated contacts, is unique in the active state, underscoring the importance of slow water molecules in the activation of GPCRs.

Comparative Study of Elastic Network Model and Protein Contact Network for Protein Complexes: The Hemoglobin Case

The overall topology and interfacial interactions play key roles in understanding structural and functional principles of protein complexes. Elastic Network Model (ENM) and Protein Contact Network (PCN) are two widely used methods for high throughput investigation of structures and interactions within protein complexes. In this work, the comparative analysis of ENM and PCN relative to hemoglobin (Hb) was taken as case study. We examine four types of structural and dynamical paradigms, namely, conformational change between different states of Hbs, modular analysis, allosteric mechanisms studies, and interface characterization of an Hb. The comparative study shows that ENM has an advantage in studying dynamical properties and protein-protein interfaces, while PCN is better for describing protein structures quantitatively both from local and from global levels. We suggest that the integration of ENM and PCN would give a potential but powerful tool in structural systems biology.

Uncoupling of an ammonia channel as a mechanism of allosteric inhibition in anthranilate synthase of Serratia marcescens: dynamic and graph theoretical analysis

Network modeling and molecular dynamic studies reveal the perturbation in communication pathways as a mechanism of allosteric inhibition in anthranilate synthase.

Scaling Laws in Spatial Network Formation

Geometric constraints impact the formation of a broad range of spatial networks, from amino acid chains folding to proteins structures to rearranging particle aggregates. How the network of interactions dynamically self-organizes in such systems is far from fully understood. Here, we analyze a class of spatial network formation processes by introducing a mapping from geometric to graph-theoretic constraints. Combining stochastic and mean field analyses yields an algebraic scaling law for the extent (graph diameter) of the resulting networks with system size, in contrast to logarithmic scaling known for networks without constraints. Intriguingly, the exponent falls between that of self-avoiding random walks and that of space filling arrangements, consistent with experimentally observed scaling of the radius of gyration of protein tertiary structures with their chain length.

NAPS: Network Analysis of Protein Structures

Traditionally, protein structures have been analysed by the secondary structure architecture and fold arrangement. An alternative approach that has shown promise is modelling proteins as a network of non-covalent interactions between amino acid residues. The network representation of proteins provide a systems approach to topological analysis of complex three-dimensional structures irrespective of secondary structure and fold type and provide insights into structure-function relationship. We have developed a web server for network based analysis of protein structures, NAPS, that facilitates quantitative and qualitative (visual) analysis of residue-residue interactions in: single chains, protein complex, modelled protein structures and trajectories (e.g. from molecular dynamics simulations). The user can specify atom type for network construction, distance range (in Å) and minimal amino acid separation along the sequence. NAPS provides users selection of node(s) and its neighbourhood based on centrality measures, physicochemical properties of amino acids or cluster of well-connected residues (k-cliques) for further analysis. Visual analysis of interacting domains and protein chains, and shortest path lengths between pair of residues are additional features that aid in functional analysis. NAPS support various analyses and visualization views for identifying functional residues, provide insight into mechanisms of protein folding, domain-domain and protein-protein interactions for understanding communication within and between proteins. URL:http://bioinf.iiit.ac.in/NAPS/.

PDB2Graph: A toolbox for identifying critical amino acids map in proteins based on graph theory

The integrative and cooperative nature of protein structure involves the assessment of topological and global features of constituent parts. Network concept takes complete advantage of both of these properties in the analysis concomitantly. High compatibility to structural concepts or physicochemical properties in addition to exploiting a remarkable simplification in the system has made network an ideal tool to explore biological systems. There are numerous examples in which different protein structural and functional characteristics have been clarified by the network approach. Here, we present an interactive and user-friendly Matlab-based toolbox, PDB2Graph, devoted to protein structure network construction, visualization, and analysis. Moreover, PDB2Graph is an appropriate tool for identifying critical nodes involved in protein structural robustness and function based on centrality indices. It maps critical amino acids in protein networks and can greatly aid structural biologists in selecting proper amino acid candidates for manipulating protein structures in a more reasonable and rational manner. To introduce the capability and efficiency of PDB2Graph in detail, the structural modification of Calmodulin through allosteric binding of Ca(2+) is considered. In addition, a mutational analysis for three well-identified model proteins including Phage T4 lysozyme, Barnase and Ribonuclease HI, was performed to inspect the influence of mutating important central residues on protein activity.

Molecular dynamics simulations and modelling of the residue interaction networks in the BRAF kinase complexes with small molecule inhibitors: probing the allosteric effects of ligand-induced kinase dimerization and paradoxical activation

The computational analysis of residue interaction networks dissects the allosteric effects of inhibitor-induced BRAF kinase dimerization and paradoxical activation.

Analysis of core-periphery organization in protein contact networks reveals groups of structurally and functionally critical residues

The representation of proteins as networks of interacting amino acids, referred to as protein contact networks (PCN), and their subsequent analyses using graph theoretic tools, can provide novel insights into the key functional roles of specific groups of residues. We have characterized the networks corresponding to the native states of 66 proteins (belonging to different families) in terms of their core-periphery organization. The resulting hierarchical classification of the amino acid constituents of a protein arranges the residues into successive layers - having higher core order - with increasing connection density, ranging from a sparsely linked periphery to a densely intra-connected core (distinct from the earlier concept of protein core defined in terms of the three-dimensional geometry of the native state, which has least solvent accessibility). Our results show that residues in the inner cores are more conserved than those at the periphery. Underlining the functional importance of the network core, we see that the receptor sites for known ligand molecules of most proteins occur in the innermost core. Furthermore, the association of residues with structural pockets and cavities in binding or active sites increases with the core order. From mutation sensitivity analysis, we show that the probability of deleterious or intolerant mutations also increases with the core order. We also show that stabilization centre residues are in the innermost cores, suggesting that the network core is critically important in maintaining the structural stability of the protein. A publicly available Web resource for performing core-periphery analysis of any protein whose native state is known has been made available by us at http://www.imsc.res.in/ ~sitabhra/proteinKcore/index.html.

Time-dependent degree-degree correlations in epileptic brain networks: from assortative to dissortative mixing

We investigate the long-term evolution of degree-degree correlations (assortativity) in functional brain networks from epilepsy patients. Functional networks are derived from continuous multi-day, multi-channel electroencephalographic data, which capture a wide range of physiological and pathophysiological activities. In contrast to previous studies which all reported functional brain networks to be assortative on average, even in case of various neurological and neurodegenerative disorders, we observe large fluctuations in time-resolved degree-degree correlations ranging from assortative to dissortative mixing. Moreover, in some patients these fluctuations exhibit some periodic temporal structure which can be attributed, to a large extent, to daily rhythms. Relevant aspects of the epileptic process, particularly possible pre-seizure alterations, contribute marginally to the observed long-term fluctuations. Our findings suggest that physiological and pathophysiological activity may modify functional brain networks in a different and process-specific way. We evaluate factors that possibly influence the long-term evolution of degree-degree correlations.

Assembly constraints drive co-evolution among ribosomal constituents

Ribosome biogenesis, a central and essential cellular process, occurs through sequential association and mutual co-folding of protein-RNA constituents in a well-defined assembly pathway. Here, we construct a network of co-evolving nucleotide/amino acid residues within the ribosome and demonstrate that assembly constraints are strong predictors of co-evolutionary patterns. Predictors of co-evolution include a wide spectrum of structural reconstitution events, such as cooperativity phenomenon, protein-induced rRNA reconstitutions, molecular packing of different rRNA domains, protein-rRNA recognition, etc. A correlation between folding rate of small globular proteins and their topological features is known. We have introduced an analogous topological characteristic for co-evolutionary network of ribosome, which allows us to differentiate between rRNA regions subjected to rapid reconstitutions from those hindered by kinetic traps. Furthermore, co-evolutionary patterns provide a biological basis for deleterious mutation sites and further allow prediction of potential antibiotic targeting sites. Understanding assembly pathways of multicomponent macromolecules remains a key challenge in biophysics. Our study provides a 'proof of concept' that directly relates co-evolution to biophysical interactions during multicomponent assembly and suggests predictive power to identify candidates for critical functional interactions as well as for assembly-blocking antibiotic target sites.

NPPD: A Protein-Protein Docking Scoring Function Based on Dyadic Differences in Networks of Hydrophobic and Hydrophilic Amino Acid Residues

Protein-protein docking (PPD) predictions usually rely on the use of a scoring function to rank docking models generated by exhaustive sampling. To rank good models higher than bad ones, a large number of scoring functions have been developed and evaluated, but the methods used for the computation of PPD predictions remain largely unsatisfactory. Here, we report a network-based PPD scoring function, the NPPD, in which the network consists of two types of network nodes, one for hydrophobic and the other for hydrophilic amino acid residues, and the nodes are connected when the residues they represent are within a certain contact distance. We showed that network parameters that compute dyadic interactions and those that compute heterophilic interactions of the amino acid networks thus constructed allowed NPPD to perform well in a benchmark evaluation of 115 PPD scoring functions, most of which, unlike NPPD, are based on some sort of protein-protein interaction energy. We also showed that NPPD was highly complementary to these energy-based scoring functions, suggesting that the combined use of conventional scoring functions and NPPD might significantly improve the accuracy of current PPD predictions.

Small-world networks of residue interactions in the Abl kinase complexes with cancer drugs: topology of allosteric communication pathways can determine drug resistance effects

Computational modelling of efficiency and robustness of the residue interaction networks and allosteric pathways in kinase structures can characterize protein kinase sensitivity to drug binding and drug resistance effects.

Assortative and disassortative mixing investigated using the spectra of graphs

We investigate the impact of degree-degree correlations on the spectra of networks. Even though density distributions exhibit drastic changes depending on the (dis)assortative mixing and the network architecture, the short-range correlations in eigenvalues exhibit universal random matrix theory predictions. The long-range correlations turn out to be a measure of randomness in (dis)assortative networks. The analysis further provides insight into the origin of high degeneracy at the zero eigenvalue displayed by a majority of biological networks.

Structure-based network analysis of activation mechanisms in the ErbB family of receptor tyrosine kinases: the regulatory spine residues are global mediators of structural stability and allosteric interactions

The ErbB protein tyrosine kinases are among the most important cell signaling families and mutation-induced modulation of their activity is associated with diverse functions in biological networks and human disease. We have combined molecular dynamics simulations of the ErbB kinases with the protein structure network modeling to characterize the reorganization of the residue interaction networks during conformational equilibrium changes in the normal and oncogenic forms. Structural stability and network analyses have identified local communities integrated around high centrality sites that correspond to the regulatory spine residues. This analysis has provided a quantitative insight to the mechanism of mutation-induced “superacceptor” activity in oncogenic EGFR dimers. We have found that kinase activation may be determined by allosteric interactions between modules of structurally stable residues that synchronize the dynamics in the nucleotide binding site and the αC-helix with the collective motions of the integrating αF-helix and the substrate binding site. The results of this study have pointed to a central role of the conserved His-Arg-Asp (HRD) motif in the catalytic loop and the Asp-Phe-Gly (DFG) motif as key mediators of structural stability and allosteric communications in the ErbB kinases. We have determined that residues that are indispensable for kinase regulation and catalysis often corresponded to the high centrality nodes within the protein structure network and could be distinguished by their unique network signatures. The optimal communication pathways are also controlled by these nodes and may ensure efficient allosteric signaling in the functional kinase state. Structure-based network analysis has quantified subtle effects of ATP binding on conformational dynamics and stability of the EGFR structures. Consistent with the NMR studies, we have found that nucleotide-induced modulation of the residue interaction networks is not limited to the ATP site, and may enhance allosteric cooperativity with the substrate binding region by increasing communication capabilities of mediating residues.

Thermostability of in vitro evolved Bacillus subtilis lipase A: a network and dynamics perspective

Proteins in thermophilic organisms remain stable and function optimally at high temperatures. Owing to their important applicability in many industrial processes, such thermostable proteins have been studied extensively, and several structural factors attributed to their enhanced stability. How these factors render the emergent property of thermostability to proteins, even in situations where no significant changes occur in their three-dimensional structures in comparison to their mesophilic counter-parts, has remained an intriguing question. In this study we treat Lipase A from Bacillus subtilis and its six thermostable mutants in a unified manner and address the problem with a combined complex network-based analysis and molecular dynamic studies to find commonality in their properties. The Protein Contact Networks (PCN) of the wild-type and six mutant Lipase A structures developed at a mesoscopic scale were analyzed at global network and local node (residue) level using network parameters and community structure analysis. The comparative PCN analysis of all proteins pointed towards important role of specific residues in the enhanced thermostability. Network analysis results were corroborated with finer-scale molecular dynamics simulations at both room and high temperatures. Our results show that this combined approach at two scales can uncover small but important changes in the local conformations that add up to stabilize the protein structure in thermostable mutants, even when overall conformation differences among them are negligible. Our analysis not only supports the experimentally determined stabilizing factors, but also unveils the important role of contacts, distributed throughout the protein, that lead to thermostability. We propose that this combined mesoscopic-network and fine-grained molecular dynamics approach is a convenient and useful scheme not only to study allosteric changes leading to protein stability in the face of negligible over-all conformational changes due to mutations, but also in other molecular networks where change in function does not accompany significant change in the network structure.

Computational modeling of allosteric regulation in the hsp90 chaperones: a statistical ensemble analysis of protein structure networks and allosteric communications

A fundamental role of the Hsp90 chaperone in regulating functional activity of diverse protein clients is essential for the integrity of signaling networks. In this work we have combined biophysical simulations of the Hsp90 crystal structures with the protein structure network analysis to characterize the statistical ensemble of allosteric interaction networks and communication pathways in the Hsp90 chaperones. We have found that principal structurally stable communities could be preserved during dynamic changes in the conformational ensemble. The dominant contribution of the inter-domain rigidity to the interaction networks has emerged as a common factor responsible for the thermodynamic stability of the active chaperone form during the ATPase cycle. Structural stability analysis using force constant profiling of the inter-residue fluctuation distances has identified a network of conserved structurally rigid residues that could serve as global mediating sites of allosteric communication. Mapping of the conformational landscape with the network centrality parameters has demonstrated that stable communities and mediating residues may act concertedly with the shifts in the conformational equilibrium and could describe the majority of functionally significant chaperone residues. The network analysis has revealed a relationship between structural stability, global centrality and functional significance of hotspot residues involved in chaperone regulation. We have found that allosteric interactions in the Hsp90 chaperone may be mediated by modules of structurally stable residues that display high betweenness in the global interaction network. The results of this study have suggested that allosteric interactions in the Hsp90 chaperone may operate via a mechanism that combines rapid and efficient communication by a single optimal pathway of structurally rigid residues and more robust signal transmission using an ensemble of suboptimal multiple communication routes. This may be a universal requirement encoded in protein structures to balance the inherent tension between resilience and efficiency of the residue interaction networks.

Functional versatility and structural adaptability of the Hsp90 chaperones are regulated by allosteric interactions that allow for diverse functions including modulation of ATP hydrolysis and binding with cochaperones and client proteins. By integrating molecular simulations and network-based approaches we have characterized conformational dynamics and allosteric interactions in different functional forms of Hsp90. The network centrality analysis and structural mapping of allosteric communications have revealed a small-world organization of the interaction network that is mediated by functionally important residues of the Hsp90 activity. We have found that effective allosteric communications in the Hsp90 chaperone may be provided by structurally stable residues that exhibit high centrality properties. Nucleotide-specific rewiring of the network topology and assortative organization of functional residues may protect the active form of the chaperone from random perturbations and detrimental mutations. These results have confirmed that allosteric interactions in the Hsp90 chaperone may be determined by a small-world network of functional residues that can regulate the network efficiency and resiliency by modulating the statistical ensemble of communication pathways in response to functional requirements of the ATPase cycle.

Amino acid contact energy networks impact protein structure and evolution

One of the most challenging tasks in structural proteomics is to understand the relationship between protein structure, biological function, and evolution. An understanding of amino acid networks based on protein topology has an important role in the study of this relationship; however, the relationship between network parameters underlying protein topology with structural properties or evolutionary rate is still unknown. To investigate this further, we modeled the three dimensional structure of proteins as amino acid contact energy networks (AACENs) with nodes represented as amino acid residues and edges established according to environment-dependent residue-residue contact energies. Five other types of networks were also constructed to investigate their topological parameters and compare their effect on protein structure and evolution: (1) a random contact network (RCN), (2) a rewiring network with the same degree of distribution as AACEN (RNDD), (3) long-range contact energy networks with and without the backbone connectivity (LCEN_BBs and LCENs), and (4) short range contact energy networks (SCENs). The results indicated that the long-range link percentage and the network clustering coefficient showed a significantly positive and negative correlation, respectively, with protein secondary structure density. In addition, the long-range link percentage and network diameter had a significantly positive and negative correlation, respectively, with evolutionary rate. According to our knowledge, this is the first study to identify the potential role of long-range links and network diameter in protein evolution.

The construction of an amino acid network for understanding protein structure and function

Amino acid networks (AANs) are undirected networks consisting of amino acid residues and their interactions in three-dimensional protein structures. The analysis of AANs provides novel insight into protein science, and several common amino acid network properties have revealed diverse classes of proteins. In this review, we first summarize methods for the construction and characterization of AANs. We then compare software tools for the construction and analysis of AANs. Finally, we review the application of AANs for understanding protein structure and function, including the identification of functional residues, the prediction of protein folding, analyzing protein stability and protein-protein interactions, and for understanding communication within and between proteins.

Residue interaction network analysis of Dronpa and a DNA clamp

Topology is an essential aspect of protein structure. The network paradigm is increasingly used to describe the topology and dynamics of proteins. In this paper, the effect of topology on residue interaction network was investigated for two different proteins: Dronpa and a DNA clamp, which have cylindrical and toroidal topologies, respectively. Network metrics including characteristic path lengths, clustering coefficients, and diameters were calculated to investigate their global topology parameters such as small-world properties and packing density. Measures of centrality including betweenness, closeness, and residue centrality were computed to predict residues critical to function. Additionally, the detailed topology of the hydrophobic pocket in Dronpa, and communication pathways across the interface in the DNA clamp, were investigated using the network. The results are presented and discussed with regard to existing residue interaction network properties of globular proteins and elastic network models on Dronpa and the DNA clamp. The topological principle underlying residue interaction networks provided insight into the architectural organization of proteins.