Protein Contact Networks: An Emerging Paradigm in Chemistry

Extracting Dynamical Correlations and Identifying Key Residues for Allosteric Communication in Proteins by correlationplus

Extracting dynamical pairwise correlations and identifying key residues from large molecular dynamics trajectories or normal-mode analysis of coarse-grained models are important for explaining various processes like ligand binding, mutational effects, and long-distance interactions. Efficient and flexible tools to perform this task can provide new insights about residues involved in allosteric regulation and protein function. In addition, combining and comparing dynamical coupling information with sequence coevolution data can help to understand better protein function. To this aim, we developed a Python package called correlationplus to calculate, visualize, and analyze pairwise correlations. In this way, the package aids to identify key residues and interactions in proteins. The source code of correlationplus is available under LGPL version 3 at https://github.com/tekpinar/correlationplus. The current version of the package (0.2.0) can be installed with common installation methods like conda or pip in addition to source code installation. Moreover, docker images are also available for usage of the code without installation.

Perturbation of ACE2 Structural Ensembles by SARS-CoV-2 Spike Protein Binding

The human ACE2 enzyme serves as a critical first recognition point of coronaviruses, including SARS-CoV-2. In particular, the extracellular domain of ACE2 interacts directly with the S1 tailspike protein of the SARS-CoV-2 virion through a broad protein-protein interface. Although this interaction has been characterized by X-ray crystallography, these structures do not reveal significant differences in the ACE2 structure upon S1 protein binding. In this work, using several all-atom molecular dynamics simulations, we show persistent differences in the ACE2 structure upon binding. These differences are determined with the linear discriminant analysis (LDA) machine learning method and validated using independent training and testing datasets, including long trajectories generated by D. E. Shaw Research on the Anton 2 supercomputer. In addition, long trajectories for 78 potent ACE2-binding compounds, also generated by D. E. Shaw Research, were projected onto the LDA classification vector in order to determine whether the ligand-bound ACE2 structures were compatible with S1 protein binding. This allows us to predict which compounds are "apo-like" versus "complex-like" and to pinpoint long-range ligand-induced allosteric changes in the ACE2 structure.

Cheminformatic quantum mechanical enzyme model design: A catechol-O-methyltransferase case study

To accurately simulate the inner workings of an enzyme active site with quantum mechanics (QM), not only must the reactive species be included in the model but also important surrounding residues, solvent, or coenzymes involved in crafting the microenvironment. Our lab has been developing the Residue Interaction Network Residue Selector (RINRUS) toolkit to utilize interatomic contact network information for automated, rational residue selection and QM-cluster model generation. Starting from an x-ray crystal structure of catechol-O-methyltransferase, RINRUS was used to construct a series of QM-cluster models. The reactant, product, and transition state of the methyl transfer reaction were computed for a total of 550 models, and the resulting free energies of activation and reaction were used to evaluate model convergence. RINRUS-designed models with only 200-300 atoms are shown to converge. RINRUS will serve as a cornerstone for improved and automated cheminformatics-based enzyme model design.

pyProGA-A PyMOL plugin for protein residue network analysis

The field of protein residue network (PRN) research has brought several useful methods and techniques for structural analysis of proteins and protein complexes. Many of these are ripe and ready to be used by the proteomics community outside of the PRN specialists. In this paper we present software which collects an ensemble of (network) methods tailored towards the analysis of protein-protein interactions (PPI) and/or interactions of proteins with ligands of other type, e.g. nucleic acids, oligosaccharides etc. In parallel, we propose the use of the network differential analysis as a method to identify residues mediating key interactions between proteins. We use a model system, to show that in combination with other, already published methods, also included in pyProGA, it can be used to make such predictions. Such extended repertoire of methods allows to cross-check predictions with other methods as well, as we show here. In addition, the possibility to construct PRN models from various kinds of input is so far a unique asset of our code. One can use structural data as defined in PDB files and/or from data on residue pair interaction energies, either from force-field parameters or fragment molecular orbital (FMO) calculations. pyProGA is a free open-source software available from https://gitlab.com/Vlado_S/pyproga.

Activation-Induced Reorganization of Energy Transport Networks in the β2 Adrenergic Receptor

We compute energy exchange networks (EENs) through the β₂ adrenergic receptor (β₂AR), a G-protein coupled receptor (GPCR), in inactive and active states, based on the results of molecular dynamics simulations of this membrane bound protein. We introduce a new definition for the reorganization of EENs upon activation that depends on the relative change in rates of energy transfer across noncovalent contacts throughout the protein. On the basis of the reorganized network that we obtain for β₂AR upon activation, we identify a branched pathway between the agonist binding site and the cytoplasmic region, where a G-protein binds to the receptor when activated. The pathway includes all of the motifs containing molecular switches previously identified as contributing to the allosteric transition of β₂AR upon agonist binding. EENs and their reorganization upon activation are compared with structure-based contact networks computed for the inactive and active states of β₂AR.

Networks of Networks: An Essay on Multi-Level Biological Organization

The multi-level organization of nature is self-evident: proteins do interact among them to give rise to an organized metabolism, while in the same time each protein (a single node of such interaction network) is itself a network of interacting amino-acid residues allowing coordinated motion of the macromolecule and systemic effect as allosteric behavior. Similar pictures can be drawn for structure and function of cells, organs, tissues, and ecological systems. The majority of biologists are used to think that causally relevant events originate from the lower level (the molecular one) in the form of perturbations, that “climb up” the hierarchy reaching the ultimate layer of macroscopic behavior (e.g., causing a specific disease). Such causative model, stemming from the usual genotype-phenotype distinction, is not the only one. As a matter of fact, one can observe top-down, bottom-up, as well as middle-out perturbation/control trajectories. The recent complex network studies allow to go further the pure qualitative observation of the existence of both non-linear and non-bottom-up processes and to uncover the deep nature of multi-level organization. Here, taking as paradigm protein structural and interaction networks, we review some of the most relevant results dealing with between networks communication shedding light on the basic principles of complex system control and dynamics and offering a more realistic frame of causation in biology.

Dynamic residue interaction network analysis of the oseltamivir binding site of N1 neuraminidase and its H274Y mutation site conferring drug resistance in influenza A virus

Background

Oseltamivir (OTV)-resistant influenza virus exhibits His-to-Tyr mutation at residue 274 (H274Y) in N1 neuraminidase (NA). However, the molecular mechanisms by which the H274Y mutation in NA reduces its binding affinity to OTV have not been fully elucidated.

Methods

In this study, we used dynamic residue interaction network (dRIN) analysis based on molecular dynamics simulation to investigate the correlation between the OTV binding site of NA and its H274Y mutation site.

Results

dRIN analysis revealed that the OTV binding site and H274Y mutation site of NA interact via the three interface residues connecting them. H274Y mutation significantly enhanced the interaction between residue 274 and the three interface residues in NA, thereby significantly decreasing the interaction between OTV and its surrounding loop 150 residues. Thus, we concluded that such changes in residue interactions could reduce the binding affinity of OTV to NA, resulting in drug resistant influenza viruses. Using dRIN analysis, we succeeded in understanding the characteristic changes in residue interactions due to H274Y mutation, which can elucidate the molecular mechanism of reduction in OTV binding affinity to influenza NA. Finally, the dRIN analysis used in this study can be widely applied to various systems such as individual proteins, protein-ligand complexes, and protein-protein complexes, to characterize the dynamic aspects of the interactions.

Protein conformational switch discerned via network centrality properties

Network analysis has emerged as a powerful tool for examining structural biology systems. The spatial organization of the components of a biomolecular structure has been rendered as a graph representation and analyses have been performed to deduce the biophysical and mechanistic properties of these components. For proteins, the analysis of protein structure networks (PSNs), especially via network centrality measurements and cluster coefficients, has led to identifying amino acid residues that play key functional roles and classifying amino acid residues in general. Whether these network properties examined in various studies are sensitive to subtle (yet biologically significant) conformational changes remained to be addressed. Here, we focused on four types of network centrality properties (betweenness, closeness, degree, and eigenvector centralities) for conformational changes upon ligand binding of a sensor protein (constitutive androstane receptor) and an allosteric enzyme (ribonucleotide reductase). We found that eigenvector centrality is sensitive and can distinguish salient structural features between protein conformational states while other centrality measures, especially closeness centrality, are less sensitive and rather generic with respect to the structural specificity. We also demonstrated that an ensemble-informed, modified PSN with static edges removed (which we term PSN*) has enhanced sensitivity at discerning structural changes.

The Odd Faces of Oligomers: The Case of TRAF2-C, A Trimeric C-Terminal Domain of TNF Receptor-Associated Factor

TNF Receptor Associated Factor 2 (TRAF2) is a trimeric protein that belongs to the TNF receptor associated factor family (TRAFs). The TRAF2 oligomeric state is crucial for receptor binding and for its interaction with other proteins involved in the TNFR signaling. The monomer-trimer equilibrium of a C- terminal domain truncated form of TRAF2 (TRAF2-C), plays also a relevant role in binding the membrane, causing inward vesiculation. In this study, we have investigated the conformational dynamics of TRAF2-C through circular dichroism, fluorescence, and dynamic light scattering, performing temperature-dependent measurements. The data indicate that the protein retains its oligomeric state and most of its secondary structure, while displaying a significative increase in the heterogeneity of the tyrosines signal, increasing the temperature from ≈15 to ≈35 °C. The peculiar crowding of tyrosine residues (12 out of 18) at the three subunit interfaces and the strong dependence on the trimer concentration indicate that such conformational changes mainly involve the contact areas between each pair of monomers, affecting the oligomeric state. Molecular dynamic simulations in this temperature range suggest that the interfaces heterogeneity is an intrinsic property of the trimer that arises from the continuous, asymmetric approaching and distancing of its subunits. Such dynamics affect the results of molecular docking on the external protein surface using receptor peptides, indicating that the TRAF2-receptor interaction in the solution might not involve three subunits at the same time, as suggested by the static analysis obtainable from the crystal structure. These findings shed new light on the role that the TRAF2 oligomeric state might have in regulating the protein binding activity in vivo.

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.

Recent advances in user-friendly computational tools to engineer protein function

Progress in technology and algorithms throughout the past decade has transformed the field of protein design and engineering. Computational approaches have become well-engrained in the processes of tailoring proteins for various biotechnological applications. Many tools and methods are developed and upgraded each year to satisfy the increasing demands and challenges of protein engineering. To help protein engineers and bioinformaticians navigate this emerging wave of dedicated software, we have critically evaluated recent additions to the toolbox regarding their application for semi-rational and rational protein engineering. These newly developed tools identify and prioritize hotspots and analyze the effects of mutations for a variety of properties, comprising ligand binding, protein-protein and protein-nucleic acid interactions, and electrostatic potential. We also discuss notable progress to target elusive protein dynamics and associated properties like ligand-transport processes and allosteric communication. Finally, we discuss several challenges these tools face and provide our perspectives on the further development of readily applicable methods to guide protein engineering efforts.

Residue Interaction Network Analysis Predicts a Val24-Ile31 Interaction May be Involved in Preventing Amyloid-Beta (1-42) Primary Nucleation

Alzheimer's disease (AD) patients could benefit from a more effective treatment than the current FDA-approved options. Because amyloid-beta (Aβ) is thought to play a central role in AD pathogenesis, many experimental drugs attempt to reduce Aβ-induced pathology. Preventing amyloid accumulation may be a more effective strategy than clearing Aβ plaques after they form. If preventing Aβ accumulation can treat or prevent AD, then understanding Aβ primary nucleation may aid rational drug design. This study examines Aβ residue interaction networks and reports network and structural observations that may provide insight into primary nucleation. While many studies identify structural features of Aβ that promote aggregation, this study reports features that may resist primary nucleation by examining Aβ42 studies in more and less polar solvents. In Aβ42 in a less polar solvent (PDB ID: 1IYT), Val24 and Ile31 have higher betweenness and residue centrality values. This may be due to a predicted interaction between Val24 and Ile31. Residues in the central hydrophobic cluster (CHC) of Aβ40 and Aβ42 had significantly higher betweenness values compared to the average betweenness of the structures, highlighting the CHC's reported role in oligomerization. The predicted interaction between Val24 and Ile31 may reduce the likelihood of primary nucleation of Aβ.

Impact of dimerization and N3 binding on molecular dynamics of SARS-CoV and SARS-CoV-2 main proteases

SARS-CoV-2 main protease is one of the major targets in drug development efforts against Covid-19. Even though several structures were reported to date, its dynamics is not understood well. In particular, impact of dimerization and ligand binding on the dynamics is an important issue to investigate. In this study, we performed molecular dynamics simulations of SARS-CoV and SARS-CoV-2 main proteases to investigate influence of dimerization on the dynamics by modeling monomeric and dimeric apo and holo forms. The dimerization causes an organization of the interdomain dynamics as well as some local structural changes. Moreover, we investigated impact of a peptide mimetic (N3) on the dynamics of SARS-CoV and SARS-CoV-2 Mpro. The ligand binding to the dimeric forms causes some key local changes at the dimer interface and it causes an allosteric interaction between the active sites of two protomers. Our results support the idea that only one protomer is active on SARS-CoV-2 due to this allosteric interaction. Additionally, we analyzed the molecular dynamics trajectories from graph theoretical perspective and found that the most influential residues – as measured by eigenvector centrality – are a group of residues in active site and dimeric interface of the protease. This study may form a bridge between what we know about the dynamics of SARS-CoV and SARS-CoV-2 Mpro. We think that enlightening allosteric communication of the active sites and the role of dimerization in SARS-CoV-2 Mpro can contribute to development of novel drugs against this global health problem as well as other similar proteases.

Communicated by Ramaswamy H. Sarma

Network constraints on the mixing patterns of binary node metadata

We consider the network constraints on the bounds of the assortativity coefficient, which aims to quantify the tendency of nodes with the same attribute values to be connected. The assortativity coefficient can be considered as the Pearson's correlation coefficient of node metadata values across network edges and lies in the interval [-1,1]. However, properties of the network, such as degree distribution and the distribution of node metadata values, place constraints upon the attainable values of the assortativity coefficient. This is important as a particular value of assortativity may say as much about the network topology as about how the metadata are distributed over the network-a fact often overlooked in literature where the interpretation tends to focus simply on the propensity of similar nodes to link to each other, without any regard on the constraints posed by the topology. In this paper we quantify the effect that the topology has on the assortativity coefficient in the case of binary node metadata. Specifically, we look at the effect that the degree distribution, or the full topology, and the proportion of each metadata value has on the extremal values of the assortativity coefficient. We provide the means for obtaining bounds on the extremal values of assortativity for different settings and demonstrate that under certain conditions the maximum and minimum values of assortativity are severely limited, which may present issues in interpretation when these bounds are not considered.

Disclosing Allostery Through Protein Contact Networks

Proteins are located in the twilight zone between chemistry and biology, where a peculiar kind of complexity starts. Proteins are the smallest 'devices' showing a sensible adaptation to their environment by the production of appropriate behavior when facing a specific stimulus. This fact qualifies (from the 'effector' side) proteins as nanomachines working as catalysts, motors, or switches. However (from the sensor side), the need to single out the 'specific stimulus' out of thermal noise qualifies proteins as information processing devices. Allostery corresponds to the modification of the configuration (in a broad sense) of the protein molecule in response to a specific stimulus in a non-strictly local way, thereby connecting the sensor and effector sides of the nanomachine. This is why the 'disclosing' of allostery phenomenon is at the very heart of protein function; in this chapter, we will demonstrate how a network-based representation of protein structure in terms of nodes (aminoacid residues) and edges (effective contacts between residues) is the natural language for getting rid of allosteric phenomena and, more in general, of protein structure/function relationships.

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.

Community Network Analysis of Allosteric Proteins

Community network analysis (CNA) of correlated protein motions allows modeling of signals propagation in allosteric proteic systems. From standard classical molecular dynamics (MD) simulations, protein motions can be analysed by means of mutual information between pairs of amino acid residues, providing dynamical weighted networks that contains fundamental information of the communication among amino acids. The CNA method has been successfully applied to a variety of allosteric systems including an enzyme, a nuclear receptor and a bacterial adaptive immune system, providing characterization of the allosteric pathways. This method is complementary to network analyses based on different metrics and it is particularly powerful for studying large proteic systems, as it provides a coarse-grained view of the communication flows within large and complex networks.

Investigating Conformational Dynamics and Allostery in the p53 DNA-Binding Domain Using Molecular Simulations

The p53 tumor suppressor is a multifaceted context-dependent protein, which is involved in multiple cellular pathways, with the ability to either keep the cells alive or to kill them through mechanisms such as apoptosis. To complicate this picture, cancer cells that express mutant p53 becomes addicted to the mutant activity, so that the mutant variant features a myriad of gain-of-function activities, opening different venues for therapy. This makes essential to think outside the box and apply new approaches to the study of p53 structure-(mis)function relationship to find new critical components of its pathway or to understand how known parts are interconnected, compete, or cooperate. In this context, I will here illustrate how to integrate different computational methods to the identification of possible allosteric effects transmitted from the DNA binding interface of p53 to regions for cofactor recruitment. The protocol can be extended to any other cases of study. Indeed, it does not necessarily apply only to the study of DNA-induced effects, but more broadly to the investigation of long-range effects induced by a biological partner that binds to a biomolecule of interest.

ANCA: A Web Server for Amino Acid Networks Construction and Analysis

Amino acid network (AAN) models empower us to gain insights into protein structures and functions by describing a protein 3D structure as a graph, where nodes represent residues and edges as amino acid interactions. Here, we present the ANCA, an interactive Web server for Amino Acids Network Construction and Analysis based on a single structure or a set of structures from the Protein Data Bank. The main purpose of ANCA is to provide a portal for three types of an environment-dependent residue contact energy (ERCE)-based network model, including amino acid contact energy network (AACEN), node-weighted amino acid contact energy network (NACEN), and edge-weighted amino acid contact energy network (EACEN). For comparison, the C-alpha distance-based network model is also included, which can be extended to protein–DNA/RNA complexes. Then, the analyses of different types of AANs were performed and compared from node, edge, and network levels. The network and corresponding structure can be visualized directly in the browser. The ANCA enables researchers to investigate diverse concerns in the framework of AAN, such as the interpretation of allosteric regulation and functional residues. The ANCA portal, together with an extensive help, is available at http://sysbio.suda.edu.cn/anca/.

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.

A quantum biochemistry investigation of the protein-protein interactions for the description of allosteric modulation on biomass-degrading chimera

The worldwide dependence of population on fossil fuels continues to have several harmful implications for the environment. Bioethanol is an excellent option for renewable fuel to replace the current greenhouse gas emitters. In addition, its production by enzymatic route has gained space among the industrial processes because it replaces the traditional acid treatment. Due to its high versatility, the xylanase family is used in this process as an accessory enzyme for degrading the lignocellulosic substrate of biomass. A chimera built by a xylanolytic domain (Xyl) and a xylose-binding protein (XBP) showed an experimentally improved catalytic efficiency and interdomain allosteric modulation after xylose binding. In this context, we performed a quantum biochemistry characterization of the interactions between these domains and dynamic cross-correlation (DCC) analysis after performing molecular dynamics (DM) simulations of the systems in the presence and absence of xylose in the XBP active site. We used the density functional theory (DFT) within the molecular fractionation with the conjugated caps (MFCC) approach to describe the pair energies, and the corresponding energy difference between the chimera domains responsible for the allosteric effect and amino acid DCC to evaluate the interdomain coupling differences between the energy states. The detailed energetic investigation together with the related structural and dynamics counterparts revealed the molecular mechanisms of chimeric improvement of the xylanase activity observed experimentally. This mechanism was correlated with greater stability and high connectivity at the interdomain interface in the xylose bound relative to the free chimera. We identify the contributions of hydrogen bonds, hydrophobic interactions and water-mediated interactions in the interdomain region responsible for stability together with the structural and dynamical elements related to the allosteric effect. Taken together, these observations led to a comprehensive understanding of the chimera's modulatory action that occurs through the formation of a highly connected interface that makes the essential movements related to xylanolytic activity in xylanase correlated to those of the xylose-binding protein.

Aptamers Which Target Proteins: What Proteotronics Suggests to Pharmaceutics

Aptamers represent a challenging field of research, relevant for diagnosis in macular degeneration, cancer, thrombosis and many inflammatory diseases, and promising in drug discovery and development. Their selection is currently performed by a stable in vitro technology, namely, SELEX. Furthermore, computationalstatistical tools have been developed to complement the SELEX selection; they work both in the preliminary stage of selection, by designing high affinity aptamers for the assigned target, and also in the final stage, analyzing the features of the best performers to implement the selection technique further. A massive use of the in silico approach is, at present, only restricted by the limited knowledge of the specific aptamer-target topology. Actually, only about fifty X-ray structures of aptamer-protein complexes have been experimentally resolved, highlighting how this knowledge has to be improved. The structure of biomolecules like aptamer-protein complexes can be represented by networks, from which several parameters can be extracted. This work briefly reviews the literature, discussing if and how general network parameters in the framework of Proteotronics and graph theory (such as electrical features, link number, free energy change, and assortativity), are important in characterizing the complexes, anticipating some features of the biomolecules. To better explain this topic, a case-study is proposed, constituted by a set of anti-angiopoietin (Ang2) aptamers, whose performances are known from the experiments, and for which two different types of conformers were predicted. A topological indicator is proposed, named Möbius (M), which combines local and global information, and seems able to discriminate between the two possible types of conformers, so that it can be considered as a useful complement to the in vitro screening for pharmaceutical aims.

(Hyper)graph Kernels over Simplicial Complexes

Graph kernels are one of the mainstream approaches when dealing with measuring similarity between graphs, especially for pattern recognition and machine learning tasks. In turn, graphs gained a lot of attention due to their modeling capabilities for several real-world phenomena ranging from bioinformatics to social network analysis. However, the attention has been recently moved towards hypergraphs, generalization of plain graphs where multi-way relations (other than pairwise relations) can be considered. In this paper, four (hyper)graph kernels are proposed and their efficiency and effectiveness are compared in a twofold fashion. First, by inferring the simplicial complexes on the top of underlying graphs and by performing a comparison among 18 benchmark datasets against state-of-the-art approaches; second, by facing a real-world case study (i.e., metabolic pathways classification) where input data are natively represented by hypergraphs. With this work, we aim at fostering the extension of graph kernels towards hypergraphs and, more in general, bridging the gap between structural pattern recognition and the domain of hypergraphs.

A Time-Dependent Quantum Approach to Allostery and a Comparison With Light-Harvesting in Photosynthetic Phenomenon

The allosteric effect is one of the most important processes in regulating the function of proteins, and the elucidation of this phenomenon plays a significant role in understanding emergent behaviors in biological regulation. In this process, a perturbation, generated by a ligand in a part of the macromolecule (the allosteric site), moves along this system and reaches a specific (active) site, dozens of Ångströms away, with a great efficiency. The dynamics of this perturbation in the macromolecule can model precisely the allosteric process. In this article, we will be studying the general characteristics of allostery, using a time-dependent quantum approach to obtain rules that apply to this kind of process. Considering the perturbation as a wave that moves within the molecular system, we will characterize the allosteric process with three of the properties of this wave in the active site: (1) t_a, the characteristic time for reaching that site, (2) A_a, the amplitude of the wave in this site, and (3) B_a, its corresponding spectral broadening. These three parameters, together with the process mechanism and the perturbation efficiency in the process, can describe the phenomenon. One of the main purposes of this paper is to link the parameters t_a, A_a, and B_a and the perturbation efficiency to the characteristics of the system. There is another fundamental process for life that has some characteristics similar to allostery: the light-harvesting (LH) process in photosynthesis. Here, as in allostery, two distant macromolecular sites are involved—two sites dozens of Ångströms away. In both processes, it is particularly important that the perturbation is distributed efficiently without dissipating in the infinite degrees of freedom within the macromolecule. The importance of considering quantum effects in the LH process is well documented in literature, and the quantum coherences are experimentally proven by time-dependent spectroscopic techniques. Given the existing similarities between these two processes in macromolecules, in this work, we suggest using Quantum Mechanics (QM) to study allostery.

Drug Research Meets Network Science: Where Are We?

Network theory provides one of the most potent analysis tools for the study of complex systems. In this paper, we illustrate the network-based perspective in drug research and how it is coherent with the new paradigm of drug discovery. We first present data sources from which networks are built, then show some examples of how the networks can be used to investigate drug-related systems. A section is devoted to network-based inference applications, i.e., prediction methods based on interactomes, that can be used to identify putative drug-target interactions without resorting to 3D modeling. Finally, we present some aspects of Boolean networks dynamics, anticipating that it might become a very potent modeling framework to develop in silico screening protocols able to simulate phenotypic screening experiments. We conclude that network applications integrated with machine learning and 3D modeling methods will become an indispensable tool for computational drug discovery in the next years.

Identification of potential allosteric binding sites in cathepsin K based on intramolecular communication

Network theory methods and molecular dynamics (MD) simulations are accepted tools to study allosteric regulation. Indeed, dynamic networks built upon correlation analysis of MD trajectories provide detailed information about communication paths between distant sites. In this context, we aimed to understand whether the efficiency of intramolecular communication could be used to predict the allosteric potential of a given site. To this end, we performed MD simulations and network theory analyses in cathepsin K (catK), whose allosteric sites are well defined. To obtain a quantitative measure of the efficiency of communication, we designed a new protocol that enables the comparison between properties related to ensembles of communication paths obtained from different sites. Further, we applied our strategy to evaluate the allosteric potential of different catK cavities not yet considered for drug design. Our predictions of the allosteric potential based on intramolecular communication correlate well with previous catK experimental and theoretical data. We also discuss the possibility of applying our approach to other proteins from the same family.

An information gain-based approach for evaluating protein structure models

For three decades now, knowledge-based scoring functions that operate through the "potential of mean force" (PMF) approach have continuously proven useful for studying protein structures. Although these statistical potentials are not to be confused with their physics-based counterparts of the same name-i.e. PMFs obtained by molecular dynamics simulations-their particular success in assessing the native-like character of protein structure predictions has lead authors to consider the computed scores as approximations of the free energy. However, this physical justification is a matter of controversy since the beginning. Alternative interpretations based on Bayes' theorem have been proposed, but the misleading formalism that invokes the inverse Boltzmann law remains recurrent in the literature. In this article, we present a conceptually new method for ranking protein structure models by quality, which is (i) independent of any physics-based explanation and (ii) relevant to statistics and to a general definition of information gain. The theoretical development described in this study provides new insights into how statistical PMFs work, in comparison with our approach. To prove the concept, we have built interatomic distance-dependent scoring functions, based on the former and new equations, and compared their performance on an independent benchmark of 60,000 protein structures. The results demonstrate that our new formalism outperforms statistical PMFs in evaluating the quality of protein structural decoys. Therefore, this original type of score offers a possibility to improve the success of statistical PMFs in the various fields of structural biology where they are applied. The open-source code is available for download at https://gitlab.rpbs.univ-paris-diderot.fr/src/ig-score.

The Bio3D packages for structural bioinformatics

Bio3D is a family of R packages for the analysis of biomolecular sequence, structure, and dynamics. Major functionality includes biomolecular database searching and retrieval, sequence and structure conservation analysis, ensemble normal mode analysis, protein structure and correlation network analysis, principal component, and related multivariate analysis methods. Here, we review recent package developments, including a new underlying segregation into separate packages for distinct analysis, and introduce a new method for structure analysis named ensemble difference distance matrix analysis (eDDM). The eDDM approach calculates and compares atomic distance matrices across large sets of homologous atomic structures to help identify the residue wise determinants underlying specific functional processes. An eDDM workflow is detailed along with an example application to a large protein family. As a new member of the Bio3D family, the Bio3D-eddm package supports both experimental and theoretical simulation-generated structures, is integrated with other methods for dissecting sequence-structure-function relationships, and can be used in a highly automated and reproducible manner. Bio3D is distributed as an integrated set of platform independent open source R packages available from: http://thegrantlab.org/bio3d/.

Complexity in Biological Organization: Deconstruction (and Subsequent Restating) of Key Concepts

The “magic” word complexity evokes a multitude of meanings that obscure its real sense. Here we try and generate a bottom-up reconstruction of the deep sense of complexity by looking at the convergence of different features shared by complex systems. We specifically focus on complexity in biology but stressing the similarities with analogous features encountered in inanimate and artefactual systems in order to track an integrative path toward a new “mainstream” of science overcoming the actual fragmentation of scientific culture.

Comparative Dynamics and Functional Mechanisms of the CYP17A1 Tunnels Regulated by Ligand Binding

As an important member of cytochrome P450 (CYP) enzymes, CYP17A1 is a dual-function monooxygenase with a critical role in the synthesis of many human steroid hormones, making it an attractive therapeutic target. The emerging structural information about CYP17A1 and the growing number of inhibitors for these enzymes call for a systematic strategy to delineate and classify mechanisms of ligand transport through tunnels that control catalytic activity. In this work, we applied an integrated computational strategy to different CYP17A1 systems with a panel of ligands to systematically study at the atomic level the mechanism of ligand-binding and tunneling dynamics. Atomistic simulations and binding free energy computations identify the dynamics of dominant tunnels and characterize energetic properties of critical residues responsible for ligand binding. The common transporting pathways including S, 3, and 2c tunnels were identified in CYP17A1 binding systems, while the 2c tunnel is a newly formed pathway upon ligand binding. We employed and integrated several computational approaches including the analysis of functional motions and sequence conservation, atomistic modeling of dynamic residue interaction networks, and perturbation response scanning analysis to dissect ligand tunneling mechanisms. The results revealed the hinge-binding and sliding motions as main functional modes of the tunnel dynamic, and a group of mediating residues as key regulators of tunnel conformational dynamics and allosteric communications. We have also examined and quantified the mutational effects on the tunnel composition, conformational dynamics, and long-range allosteric behavior. The results of this investigation are fully consistent with the experimental data, providing novel rationale to the experiments and offering valuable insights into the relationships between the structure and function of the channel networks and a robust atomistic model of activation mechanisms and allosteric interactions in CYP enzymes.

Modelling and Recognition of Protein Contact Networks by Multiple Kernel Learning and Dissimilarity Representations

Multiple kernel learning is a paradigm which employs a properly constructed chain of kernel functions able to simultaneously analyse different data or different representations of the same data. In this paper, we propose an hybrid classification system based on a linear combination of multiple kernels defined over multiple dissimilarity spaces. The core of the training procedure is the joint optimisation of kernel weights and representatives selection in the dissimilarity spaces. This equips the system with a two-fold knowledge discovery phase: by analysing the weights, it is possible to check which representations are more suitable for solving the classification problem, whereas the pivotal patterns selected as representatives can give further insights on the modelled system, possibly with the help of field-experts. The proposed classification system is tested on real proteomic data in order to predict proteins' functional role starting from their folded structure: specifically, a set of eight representations are drawn from the graph-based protein folded description. The proposed multiple kernel-based system has also been benchmarked against a clustering-based classification system also able to exploit multiple dissimilarities simultaneously. Computational results show remarkable classification capabilities and the knowledge discovery analysis is in line with current biological knowledge, suggesting the reliability of the proposed system.

SARS-CoV and SARS-CoV-2 main protease residue interaction networks change when bound to inhibitor N3

COVID-19 is a respiratory disease caused by the coronavirus SARS-CoV-2. SARS-CoV-2 has many similarities with SARS-CoV. Both viruses rely on a protease called the main protease, or M^pro, for replication. Therefore, inhibiting M^pro may be a successful strategy for treating COVID-19. Structures of the main proteases of SARS-CoV and SARS-CoV-2 with and without inhibitor N3 are available in the Protein Data Bank. Comparing these structures revealed residue interaction network changes associated with N3 inhibition. Comparing network clustering with and without inhibitor N3 identified the formation of a cluster of residues 17, 18, 30-33, 70, 95, 98, 103, 117, 122, and 177 as a network change in both viral proteases when bound to inhibitor N3. Betweenness and stress centrality differences as well as differences in bond energies and relative B-factors when comparing free M^pro to inhibitor-bound M^pro identified residues 131, 175, 182, and 185 as possibly conformationally relevant when bound to the inhibitor N3. Taken together, these results provide insight into conformational changes of betacoronavirus M^pros when bound to an inhibitor.

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.

Self-organized emergence of folded protein-like network structures from geometric constraints

The intricate three-dimensional geometries of protein tertiary structures underlie protein function and emerge through a folding process from one-dimensional chains of amino acids. The exact spatial sequence and configuration of amino acids, the biochemical environment and the temporal sequence of distinct interactions yield a complex folding process that cannot yet be easily tracked for all proteins. To gain qualitative insights into the fundamental mechanisms behind the folding dynamics and generic features of the folded structure, we propose a simple model of structure formation that takes into account only fundamental geometric constraints and otherwise assumes randomly paired connections. We find that despite its simplicity, the model results in a network ensemble consistent with key overall features of the ensemble of Protein Residue Networks we obtained from more than 1000 biological protein geometries as available through the Protein Data Base. Specifically, the distribution of the number of interaction neighbors a unit (amino acid) has, the scaling of the structure’s spatial extent with chain length, the eigenvalue spectrum and the scaling of the smallest relaxation time with chain length are all consistent between model and real proteins. These results indicate that geometric constraints alone may already account for a number of generic features of protein tertiary structures.

Non-symmetrical structural behavior of a symmetric protein: the case of homo-trimeric TRAF2 (tumor necrosis factor-receptor associated factor 2)

The oligomeric state of TRAF2 (tumor necrosis factor-receptor associated factor 2), a TNF (tumor necrosis factor) receptor-associated factor, is crucial for membrane binding and probably plays a fundamental role in regulating the protein function in vivo. In this study we have combined molecular dynamics with the protein contact network approach to characterize the interaction of the three identical subunits of TRAF2. The average structure obtained after a 225 ns simulation reveals that two clusters of different size are formed, one of which includes almost completely two subunits, while the third monomer appears to be more independent. This picture is also confirmed by the estimated average number of inter-subunit contacts and by the comparison of side chains mobility in each monomer. The analysis of equilibrium pressure-induced dissociation measurements supports such findings, indicating that the dimeric-monomeric (2 + 1) might be prevalent with respect to the trimeric configuration, especially in the case of more diluted samples. These findings suggest that the formation of monomeric species, which is crucial for the formation of intra-luminal vesicles, might depend on preferential asymmetric interactions among the three subunits.Communicated by Ramaswamy H. Sarma.

Exploring the potency of currently used drugs against HIV-1 protease of subtype D variant by using multiscale simulations

Acquired immune deficiency syndrome (AIDS) is caused by the human immunodeficiency virus (HIV), type 1 and 2. Further, the diversity in HIV-1 has given rise to many serotypes and recombinant strains. The currently used protease inhibitors have been developed for subtype B, although non-B subtype strains account for ∼ 90% of the global HIV infections. Subtype D is spreading rapidly and infecting a large population in North Africa and the Middle East. In the current study, molecular dynamics simulations in conjunction with the molecular mechanics/Poisson-Boltzmann surface area (MM-PBSA) scheme was used to investigate the potency of four drugs, namely atazanavir (ATV), darunavir (DRV), lopinavir (LPV) and tipranavir (TPV) against the subtype D variant. Our calculations predicted that the potency of the inhibitors decreased in the order TPV > ATV > DRV > LPV. TPV was found to be the most potent against subtype D due to an increase in van der Waals and electrostatic interactions and reduction in the desolvation energy compared to other inhibitors. This result is further supported by the hydrogen bond interactions between inhibitors and protease. Furthermore, our analyses suggested that the binding of TPV induced a more closed conformation of the flap compared to apo or other complexes. It was observed that TPV/PR^D has a lower cavity volume relative to the other three complexes leading to a tighter binding. The open conformation of the flap was observed for LPV/PR^D. We expect that this study might be useful for designing more potent inhibitors against HIV-1 subtype D. Communicated by Ramaswamy H. Sarma.

Role of protein-protein interactions in allosteric drug design for DNA methyltransferases

DNA methyltransferases (DNMTs) not only play key roles in epigenetic gene regulation, but also serve as emerging targets for several diseases, especially for cancers. Due to the multi-domains of DNMT structures, targeting allosteric sites of protein-protein interactions (PPIs) is becoming an attractive strategy in epigenetic drug discovery. This chapter aims to review the major contemporary approaches utilized for the drug discovery based on PPIs in different dimensions, from the enumeration of allosteric mechanism to the identification of allosteric pockets. These include the construction of protein structure networks (PSNs) based on molecular dynamics (MD) simulations, performing elastic network models (ENMs) and perturbation response scanning (PRS) calculation, the sequence-based conservation and coupling analysis, and the allosteric pockets identification. Furthermore, we complement this methodology by highlighting the role of computational approaches in promising practical applications for the computer-aided drug design, with special focus on two DNMTs, namely, DNMT1 and DNMT3A.

Metabolic networks classification and knowledge discovery by information granulation

Graphs are powerful structures able to capture topological and semantic information from data, hence suitable for modelling a plethora of real-world (complex) systems. For this reason, graph-based pattern recognition gained a lot of attention in recent years. In this paper, a general-purpose classification system in the graphs domain is presented. When most of the information of the available patterns can be encoded in edge labels, an information granulation-based approach is highly discriminant and allows for the identification of semantically meaningful edges. The proposed classification system has been tested on the entire set of organisms (5299) for which metabolic networks are known, allowing for both a perfect mirroring of the underlying taxonomy and the identification of most discriminant metabolic reactions and pathways. The widespread diffusion of graph (network) structures in biology makes the proposed pattern recognition approach potentially very useful in many different fields of application. More specifically, the possibility to have a reliable metric to compare different metabolic systems is instrumental in emerging fields like microbiome analysis and, more in general, for proposing metabolic networks as a universal phenotype spanning the entire tree of life and in direct contact with environmental cues.

Dynamical important residue network (DIRN): network inference via conformational change

MOTIVATION

Protein residue interaction network has emerged as a useful strategy to understand the complex relationship between protein structures and functions and how functions are regulated. In a residue interaction network, every residue is used to define a network node, adding noises in network post-analysis and increasing computational burden. In addition, dynamical information is often necessary in deciphering biological functions.

RESULTS

We developed a robust and efficient protein residue interaction network method, termed dynamical important residue network, by combining both structural and dynamical information. A major departure from previous approaches is our attempt to identify important residues most important for functional regulation before a network is constructed, leading to a much simpler network with the important residues as its nodes. The important residues are identified by monitoring structural data from ensemble molecular dynamics simulations of proteins in different functional states. Our tests show that the new method performs well with overall higher sensitivity than existing approaches in identifying important residues and interactions in tested proteins, so it can be used in studies of protein functions to provide useful hypotheses in identifying key residues and interactions.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

(Hyper)Graph Embedding and Classification via Simplicial Complexes

This paper investigates a novel graph embedding procedure based on simplicial complexes. Inherited from algebraic topology, simplicial complexes are collections of increasing-order simplices (e.g., points, lines, triangles, tetrahedrons) which can be interpreted as possibly meaningful substructures (i.e., information granules) on the top of which an embedding space can be built by means of symbolic histograms. In the embedding space, any Euclidean pattern recognition system can be used, possibly equipped with feature selection capabilities in order to select the most informative symbols. The selected symbols can be analysed by field-experts in order to extract further knowledge about the process to be modelled by the learning system, hence the proposed modelling strategy can be considered as a grey-box. The proposed embedding has been tested on thirty benchmark datasets for graph classification and, further, we propose two real-world applications, namely predicting proteins’ enzymatic function and solubility propensity starting from their 3D structure in order to give an example of the knowledge discovery phase which can be carried out starting from the proposed embedding strategy.

Investigating Phosphorylation-Induced Conformational Changes in WNK1 Kinase by Molecular Dynamics Simulations

The With-No-Lysine (WNK) kinase is considered to be a master regulator for various cation-chloride cotransporters involved in maintaining cell-volume and ion homeostasis. Here, we have investigated the phosphorylation-induced structural dynamics of the WNK1 kinase bound to an inhibitor via atomistic molecular dynamics simulations. Results from our simulations show that the phosphorylation at Ser³⁸² could stabilize the otherwise flexible activation loop (A-loop). The intrahelix salt-bridge formed between Arg²⁶⁴ and Glu²⁶⁸ in the unphosphorylated system is disengaged after the phosphorylation, and Glu²⁶⁸ reorients itself and forms a stable salt-bridge with Arg³⁴⁸. The dynamic cross-correlation analysis shows that phosphorylation diminishes anticorrelated motions and increases correlated motions between different domains. Structural network analysis reveals that the phosphorylation causes structural rearrangements and shortens the communication path between the αC-helix and catalytic loop, making the binding pocket more suitable for accommodating the ligand. Overall, we have characterized the structural changes in the WNK kinase because of phosphorylation in the A-loop, which might help in designing rational drugs.

Tensor Algebra-based Geometrical (3D) Biomacro-Molecular Descriptors for Protein Research: Theory, Applications and Comparison with other Methods

In this report, a new type of tridimensional (3D) biomacro-molecular descriptors for proteins are proposed. These descriptors make use of multi-linear algebra concepts based on the application of 3-linear forms (i.e., Canonical Trilinear (Tr), Trilinear Cubic (TrC), Trilinear-Quadratic-Bilinear (TrQB) and so on) as a specific case of the N-linear algebraic forms. The definition of the kth 3-tuple similarity-dissimilarity spatial matrices (Tensor's Form) are used for the transformation and for the representation of the existing chemical information available in the relationships between three amino acids of a protein. Several metrics (Minkowski-type, wave-edge, etc) and multi-metrics (Triangle area, Bond-angle, etc) are proposed for the interaction information extraction, as well as probabilistic transformations (e.g., simple stochastic and mutual probability) to achieve matrix normalization. A generalized procedure considering amino acid level-based indices that can be fused together by using aggregator operators for descriptors calculations is proposed. The obtained results demonstrated that the new proposed 3D biomacro-molecular indices perform better than other approaches in the SCOP-based discrimination and the prediction of folding rate of proteins by using simple linear parametrical models. It can be concluded that the proposed method allows the definition of 3D biomacro-molecular descriptors that contain orthogonal information capable of providing better models for applications in protein science.