Random network behaviour of protein structures

The alteration of structural network upon transient association between proteins studied using graph theory

Proteins such as enzymes perform their function by predominant non-covalent bond interactions between transiently interacting units. There is an impact on the overall structural topology of the protein, albeit transient nature of such interactions, that enable proteins to deactivate or activate. This aspect of the alteration of the structural topology is studied by employing protein structural networks, which are node-edge representative models of protein structure, reported as a robust tool for capturing interactions between residues. Several methods have been optimized to collect meaningful, functionally relevant information by studying alteration of structural networks. In this article, different methods of comparing protein structural networks are employed, along with spectral decomposition of graphs to study the subtle impact of protein-protein interactions. A detailed analysis of the structural network of interacting partners is performed across a dataset of around 900 pairs of bound complexes and corresponding unbound protein structures. The variation in network parameters at, around, and far away from the interface are analyzed. Finally, we present interesting case studies, where an allosteric mechanism of structural impact is understood from communication-path detection methods. The results of this analysis are beneficial in understanding protein stability, for future engineering, and docking studies.

Surveying the Side-Chain Network Approach to Protein Structure and Dynamics: The SARS-CoV-2 Spike Protein as an Illustrative Case

Network theory-based approaches provide valuable insights into the variations in global structural connectivity between different dynamical states of proteins. Our objective is to review network-based analyses to elucidate such variations, especially in the context of subtle conformational changes. We present technical details of the construction and analyses of protein structure networks, encompassing both the non-covalent connectivity and dynamics. We examine the selection of optimal criteria for connectivity based on the physical concept of percolation. We highlight the advantages of using side-chain-based network metrics in contrast to backbone measurements. As an illustrative example, we apply the described network approach to investigate the global conformational changes between the closed and partially open states of the SARS-CoV-2 spike protein. These conformational changes in the spike protein is crucial for coronavirus entry and fusion into human cells. Our analysis reveals global structural reorientations between the two states of the spike protein despite small changes between the two states at the backbone level. We also observe some differences at strategic locations in the structures, correlating with their functions, asserting the advantages of the side-chain network analysis. Finally, we present a view of allostery as a subtle synergistic-global change between the ligand and the receptor, the incorporation of which would enhance drug design strategies.

Allosteric Regulation at the Crossroads of New Technologies: Multiscale Modeling, Networks, and Machine Learning

Allosteric regulation is a common mechanism employed by complex biomolecular systems for regulation of activity and adaptability in the cellular environment, serving as an effective molecular tool for cellular communication. As an intrinsic but elusive property, allostery is a ubiquitous phenomenon where binding or disturbing of a distal site in a protein can functionally control its activity and is considered as the "second secret of life." The fundamental biological importance and complexity of these processes require a multi-faceted platform of synergistically integrated approaches for prediction and characterization of allosteric functional states, atomistic reconstruction of allosteric regulatory mechanisms and discovery of allosteric modulators. The unifying theme and overarching goal of allosteric regulation studies in recent years have been integration between emerging experiment and computational approaches and technologies to advance quantitative characterization of allosteric mechanisms in proteins. Despite significant advances, the quantitative characterization and reliable prediction of functional allosteric states, interactions, and mechanisms continue to present highly challenging problems in the field. In this review, we discuss simulation-based multiscale approaches, experiment-informed Markovian models, and network modeling of allostery and information-theoretical approaches that can describe the thermodynamics and hierarchy allosteric states and the molecular basis of allosteric mechanisms. The wealth of structural and functional information along with diversity and complexity of allosteric mechanisms in therapeutically important protein families have provided a well-suited platform for development of data-driven research strategies. Data-centric integration of chemistry, biology and computer science using artificial intelligence technologies has gained a significant momentum and at the forefront of many cross-disciplinary efforts. We discuss new developments in the machine learning field and the emergence of deep learning and deep reinforcement learning applications in modeling of molecular mechanisms and allosteric proteins. The experiment-guided integrated approaches empowered by recent advances in multiscale modeling, network science, and machine learning can lead to more reliable prediction of allosteric regulatory mechanisms and discovery of allosteric modulators for therapeutically important protein targets.

Chokepoints in Mechanical Coupling Associated with Allosteric Proteins: The Pyruvate Kinase Example

Although the critical role of allostery in controlling enzymatic processes is well appreciated, there is a current dearth in our understanding of its underlying mechanisms, including communication between binding sites. One potential key aspect of intersite communication is the mechanical coupling between residues in a protein. Here, we introduce a graph-based computational approach to investigate the mechanical coupling between distant parts of a protein, highlighting effective pathways via which protein motion can transfer energy between sites. In this method, each residue is treated as a node on a weighted, undirected graph, in which the edges are defined by locally correlated motions of those residues and weighted by the strength of the correlation. The method was validated against experimental data on allosteric regulation in the human liver pyruvate kinase as obtained from full-protein alanine-scanning mutagenesis (systematic mutation) studies, as well as computational data on two G-protein-coupled receptors. The method provides semiquantitative information on the regulatory importance of specific structural elements. It is shown that these elements are key for the mechanical coupling between distant parts of the protein by providing effective pathways for energy transfer. It is also shown that, although there are a multitude of energy transfer pathways between distant parts of a protein, these pathways share a few common nodes that represent effective "chokepoints" for the communication.

Uncovering GPCR and G Protein Function by Protein Structure Network Analysis

Protein structure network (PSN) analysis is one of the graph theory-based approaches currently used for investigating structural communication in biomolecular systems. Information on the system's dynamics can be provided by atomistic molecular dynamics (MD) simulations or coarse grained elastic network models paired with normal mode analysis (ENM-NMA). This chapter reports on selected applications of PSN analysis to uncover the structural communication in G protein coupled receptors (GPCRs) and G proteins. Strategies to highlight changes in structural communication caused by mutations, ligand and protein binding are described. Conserved amino acids, sites of misfolding mutations, or ligands acting as functional switches tend to behave as hubs in the native structure networks. Densely linked regions in the protein structure graphs could be identified as playing central roles in protein stability and function. Changes in the communication pathway fingerprints depending on the bound ligand or following amino acid mutation could be highlighted as well. A bridge between misfolding and misrouting could be established in rhodopsin mutants linked to inherited blindness. The analysis of native network perturbations by misfolding mutations served to infer key structural elements of protein responsiveness to small chaperones with implications for drug discovery.

Network-based modelling and percolation analysis of conformational dynamics and activation in the CDK2 and CDK4 proteins: dynamic and energetic polarization of the kinase lobes may determine divergence of the regulatory mechanisms

Network modeling and percolation analysis of conformational dynamics and energetics of regulatory mechanisms in cyclin-dependent kinases.

Percolation-like phase transitions in network models of protein dynamics

In broad terms, percolation theory describes the conditions under which clusters of nodes are fully connected in a random network. A percolation phase transition occurs when, as edges are added to a network, its largest connected cluster abruptly jumps from insignificance to complete dominance. In this article, we apply percolation theory to meticulously constructed networks of protein folding dynamics called Markov state models. As rare fluctuations are systematically repressed (or reintroduced), we observe percolation-like phase transitions in protein folding networks: whole sets of conformational states switch from nearly complete isolation to complete connectivity in a rapid fashion. We analyze the general and critical properties of these phase transitions in seven protein systems and discuss how closely dynamics on protein folding landscapes relate to percolation on random lattices.

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.

Communities in the iron superoxide dismutase amino acid network

Amino acid networks (AANs) analysis is a new way to reveal the relationship between protein structure and function. We constructed six different types of AANs based on iron superoxide dismutase (Fe-SOD) three-dimensional structure information. These Fe-SOD AANs have clear community structures when they were modularized by different methods. Especially, detected communities are related to Fe-SOD secondary structures. Regular structures show better correlations with detected communities than irregular structures, and loops weaken these correlations, which suggest that secondary structure is the unit element in Fe-SOD folding process. In addition, a comparative analysis of mesophilic and thermophilic Fe-SOD AANs' communities revealed that thermostable Fe-SOD AANs had more highly associated community structures than mesophilic one. Thermophilic Fe-SOD AANs also had more high similarity between communities and secondary structures than mesophilic Fe-SOD AANs. The communities in Fe-SOD AANs show that dense interactions in modules can help to stabilize thermophilic Fe-SOD.

Network pharmacology: a new approach for chinese herbal medicine research

The dominant paradigm of "one gene, one target, one disease" has influenced many aspects of drug discovery strategy. However, in recent years, it has been appreciated that many effective drugs act on multiple targets rather than a single one. As an integrated multidisciplinary concept, network pharmacology, which is based on system biology and polypharmacology, affords a novel network mode of "multiple targets, multiple effects, complex diseases" and replaces the "magic bullets" by "magic shotguns." Chinese herbal medicine (CHM) has been recognized as one of the most important strategies in complementary and alternative medicine. Though CHM has been practiced for a very long time, its effectiveness and beneficial contribution to public health has not been fully recognized. Also, the knowledge on the mechanisms of CHM formulas is scarce. In the present review, the concept and significance of network pharmacology is briefly introduced. The application and potential role of network pharmacology in the CHM fields is also discussed, such as data collection, target prediction, network visualization, multicomponent interaction, and network toxicology. Furthermore, the developing tendency of network pharmacology is also summarized, and its role in CHM research is discussed.

Role of long- and short-range hydrophobic, hydrophilic and charged residues contact network in protein's structural organization

Background

The three-dimensional structure of a protein can be described as a graph where nodes represent residues and the strength of non-covalent interactions between them are edges. These protein contact networks can be separated into long and short-range interactions networks depending on the positions of amino acids in primary structure. Long-range interactions play a distinct role in determining the tertiary structure of a protein while short-range interactions could largely contribute to the secondary structure formations. In addition, physico chemical properties and the linear arrangement of amino acids of the primary structure of a protein determines its three dimensional structure. Here, we present an extensive analysis of protein contact subnetworks based on the London van der Waals interactions of amino acids at different length scales. We further subdivided those networks in hydrophobic, hydrophilic and charged residues networks and have tried to correlate their influence in the overall topology and organization of a protein.

Results

The largest connected component (LCC) of long (LRN)-, short (SRN)- and all-range (ARN) networks within proteins exhibit a transition behaviour when plotted against different interaction strengths of edges among amino acid nodes. While short-range networks having chain like structures exhibit highly cooperative transition; long- and all-range networks, which are more similar to each other, have non-chain like structures and show less cooperativity. Further, the hydrophobic residues subnetworks in long- and all-range networks have similar transition behaviours with all residues all-range networks, but the hydrophilic and charged residues networks don’t. While the nature of transitions of LCC’s sizes is same in SRNs for thermophiles and mesophiles, there exists a clear difference in LRNs. The presence of larger size of interconnected long-range interactions in thermophiles than mesophiles, even at higher interaction strength between amino acids, give extra stability to the tertiary structure of the thermophiles. All the subnetworks at different length scales (ARNs, LRNs and SRNs) show assortativity mixing property of their participating amino acids. While there exists a significant higher percentage of hydrophobic subclusters over others in ARNs and LRNs; we do not find the assortative mixing behaviour of any the subclusters in SRNs. The clustering coefficient of hydrophobic subclusters in long-range network is the highest among types of subnetworks. There exist highly cliquish hydrophobic nodes followed by charged nodes in LRNs and ARNs; on the other hand, we observe the highest dominance of charged residues cliques in short-range networks. Studies on the perimeter of the cliques also show higher occurrences of hydrophobic and charged residues’ cliques.

Conclusions

The simple framework of protein contact networks and their subnetworks based on London van der Waals force is able to capture several known properties of protein structure as well as can unravel several new features. The thermophiles do not only have the higher number of long-range interactions; they also have larger cluster of connected residues at higher interaction strengths among amino acids, than their mesophilic counterparts. It can reestablish the significant role of long-range hydrophobic clusters in protein folding and stabilization; at the same time, it shed light on the higher communication ability of hydrophobic subnetworks over the others. The results give an indication of the controlling role of hydrophobic subclusters in determining protein’s folding rate. The occurrences of higher perimeters of hydrophobic and charged cliques imply the role of charged residues as well as hydrophobic residues in stabilizing the distant part of primary structure of a protein through London van der Waals interaction.

Interaction energy based protein structure networks

The three-dimensional structure of a protein is formed and maintained by the noncovalent interactions among the amino-acid residues of the polypeptide chain. These interactions can be represented collectively in the form of a network. So far, such networks have been investigated by considering the connections based on distances between the amino-acid residues. Here we present a method of constructing the structure network based on interaction energies among the amino-acid residues in the protein. We have investigated the properties of such protein energy-based networks (PENs) and have shown correlations to protein structural features such as the clusters of residues involved in stability, formation of secondary and super-secondary structural units. Further we demonstrate that the analysis of PENs in terms of parameters such as hubs and shortest paths can provide a variety of biologically important information, such as the residues crucial for stabilizing the folded units and the paths of communication between distal residues in the protein. Finally, the energy regimes for different levels of stabilization in the protein structure have clearly emerged from the PEN analysis.