Determination of Signaling Pathways in Proteins through Network Theory: Importance of the Topology

Dynamically driven correlations in elastic net models reveal sequence of events and causality in proteins

An explicit analytic solution is given for the Langevin equation applied to the Gaussian Network Model of a protein subjected to both a random and a deterministic periodic force. Synchronous and asynchronous components of time correlation functions are derived and an expression for phase differences in the time correlations of residue pairs is obtained. The synchronous component enables the determination of dynamic communities within the protein structure. The asynchronous component reveals causality, where the time correlation function between residues i and j differs depending on whether i is observed before j or vice versa, resulting in directional information flow. Driver and driven residues in the allosteric process of cyclophilin A and human NAD-dependent isocitrate dehydrogenase are determined by a perturbation-scanning technique. Factors affecting phase differences between fluctuations of residues, such as network topology, connectivity, and residue centrality, are identified. Within the constraints of the isotropic Gaussian Network Model, our results show that asynchronicity increases with viscosity and distance between residues, decreases with increasing connectivity, and decreases with increasing levels of eigenvector centrality.

Complex networks with complex weights

In many studies, it is common to use binary (i.e., unweighted) edges to examine networks of entities that are either adjacent or not adjacent. Researchers have generalized such binary networks to incorporate edge weights, which allow one to encode node-node interactions with heterogeneous intensities or frequencies (e.g., in transportation networks, supply chains, and social networks). Most such studies have considered real-valued weights, despite the fact that networks with complex weights arise in fields as diverse as quantum information, quantum chemistry, electrodynamics, rheology, and machine learning. Many of the standard network-science approaches in the study of classical systems rely on the real-valued nature of edge weights, so it is necessary to generalize them if one seeks to use them to analyze networks with complex edge weights. In this paper, we examine how standard network-analysis methods fail to capture structural features of networks with complex edge weights. We then generalize several network measures to the complex domain and show that random-walk centralities provide a useful approach to examine node importances in networks with complex weights.

Catalytic Effects of Active Site Conformational Change in the Allosteric Activation of Imidazole Glycerol Phosphate Synthase

Imidazole glycerol phosphate synthase (IGPS) is a class-I glutamine amidotransferase (GAT) that hydrolyzes glutamine. Ammonia is produced and transferred to a second active site, where it reacts with N1-(5'-phosphoribosyl)-formimino-5-aminoimidazole-4-carboxamide ribonucleotide (PrFAR) to form precursors to purine and histidine biosynthesis. Binding of PrFAR over 25 Å away from the active site increases glutaminase efficiency by ∼4500-fold, primarily altering the glutamine turnover number. IGPS has been the focus of many studies on allosteric communication; however, atomic details for how the glutamine hydrolysis rate increases in the presence of PrFAR are lacking. We present a density functional theory study on 237-atom active site cluster models of IGPS based on crystallized structures representing the inactive and allosterically active conformations and investigate the multistep reaction leading to thioester formation and ammonia production. The proposed mechanism is supported by similar, well-studied enzyme mechanisms, and the corresponding energy profile is consistent with steady-state kinetic studies of PrFAR + IGPS. Additional active site models are constructed to examine the relationship between active site structural change and transition-state stabilization via energy decomposition schemes. The results reveal that the inactive IGPS conformation does not provide an adequately formed oxyanion hole structure and that repositioning of the oxyanion strand relative to the substrate is vital for a catalysis-competent oxyanion hole, with or without the hVal51 dihedral flip. These findings are valuable for future endeavors in modeling the IGPS allosteric mechanism by providing insight into the atomistic changes required for rate enhancement that can inform suitable reaction coordinates for subsequent investigations.

Combining structural and coevolution information to unveil allosteric sites

Understanding allosteric regulation in biomolecules is of great interest to pharmaceutical research and computational methods emerged during the last decades to characterize allosteric coupling. However, the prediction of allosteric sites in a protein structure remains a challenging task. Here, we integrate local binding site information, coevolutionary information, and information on dynamic allostery into a structure-based three-parameter model to identify potentially hidden allosteric sites in ensembles of protein structures with orthosteric ligands. When tested on five allosteric proteins (LFA-1, p38-α, GR, MAT2A, and BCKDK), the model successfully ranked all known allosteric pockets in the top three positions. Finally, we identified a novel druggable site in MAT2A confirmed by X-ray crystallography and SPR and a hitherto unknown druggable allosteric site in BCKDK validated by biochemical and X-ray crystallography analyses. Our model can be applied in drug discovery to identify allosteric pockets.

Boosting the Full Potential of PyMOL with Structural Biology Plugins

Over the past few decades, the number of available structural bioinformatics pipelines, libraries, plugins, web resources and software has increased exponentially and become accessible to the broad realm of life scientists. This expansion has shaped the field as a tangled network of methods, algorithms and user interfaces. In recent years PyMOL, widely used software for biomolecules visualization and analysis, has started to play a key role in providing an open platform for the successful implementation of expert knowledge into an easy-to-use molecular graphics tool. This review outlines the plugins and features that make PyMOL an eligible environment for supporting structural bioinformatics analyses.

Energy Transport and Its Function in Heptahelical Transmembrane Proteins

Photoproteins such as bacteriorhodopsin (bR) and rhodopsin (Rho) need to effectively dissipate photoinduced excess energy to prevent themselves from damage. Another well-studied seven transmembrane (TM) helices protein is the β₂ adrenergic receptor (β₂AR), a G protein-coupled receptor for which energy dissipation paths have been linked with allosteric communication. To study the vibrational energy transport in the active and inactive states of these proteins, a master equation approach [J. Chem. Phys.2020, 152, 045103] is employed, which uses scaling rules that allow us to calculate energy transport rates solely based on the protein structure. Despite their overall structural similarity, the three 7TM proteins reveal quite different strategies to redistribute excess energy. While bR quickly removes the energy using the TM7 helix as a "lightning rod", Rho exhibits a rather poor energy dissipation, which might eventually require the hydrolysis of the Schiff base between the protein and the retinal chromophore to prevent overheating. Heating the ligand adrenaline of β₂AR, the resulting energy transport network of the protein is found to change significantly upon switching from the active state to the inactive state. While the energy flow may highlight aspects of the inter-residue couplings of β₂AR, it seems not particularly suited to explain allosteric phenomena.

Time Evolution of the Millisecond Allosteric Activation of Imidazole Glycerol Phosphate Synthase

Deciphering the molecular mechanisms of enzymatic allosteric regulation requires the structural characterization of functional states and also their time evolution toward the formation of the allosterically activated ternary complex. The transient nature and usually slow millisecond time scale interconversion between these functional states hamper their experimental and computational characterization. Here, we combine extensive molecular dynamics simulations, enhanced sampling techniques, and dynamical networks to describe the allosteric activation of imidazole glycerol phosphate synthase (IGPS) from the substrate-free form to the active ternary complex. IGPS is a heterodimeric bienzyme complex whose HisH subunit is responsible for hydrolyzing glutamine and delivering ammonia for the cyclase activity in HisF. Despite significant advances in understanding the underlying allosteric mechanism, essential molecular details of the long-range millisecond allosteric activation of IGPS remain hidden. Without using a priori information of the active state, our simulations uncover how IGPS, with the allosteric effector bound in HisF, spontaneously captures glutamine in a catalytically inactive HisH conformation, subsequently attains a closed HisF:HisH interface, and finally forms the oxyanion hole in HisH for efficient glutamine hydrolysis. We show that the combined effector and substrate binding dramatically decreases the conformational barrier associated with oxyanion hole formation, in line with the experimentally observed 4500-fold activity increase in glutamine hydrolysis. The allosteric activation is controlled by correlated time-evolving dynamic networks connecting the effector and substrate binding sites. This computational strategy tailored to describe millisecond events can be used to rationalize the effect of mutations on the allosteric regulation and guide IGPS engineering efforts.

From Distinct to Differential Conformational Dynamics to Map Allosteric Communication Pathways in Proteins

Initiation of biological processes involving protein-ligand binding, transient protein-protein interactions, or amino acid modifications alters the conformational dynamics of proteins. Accompanying these biological processes are ensuing coupled atomic level conformational changes within the proteins. These conformational changes collectively connect multiple amino acid residues at distal allosteric, binding, and/or active sites. Local changes due to, for example, binding of a regulatory ligand at an allosteric site initiate the allosteric regulation. The allosteric signal propagates throughout the protein structure, causing changes at distal sites, activating, deactivating, or modifying the function of the protein. Hence, dynamical responses within protein structures to stimuli contain critical information on protein function. In this Perspective, we examine the description of allosteric regulation from protein dynamical responses and associated alternative and emerging computational approaches to map allosteric communication pathways between distal sites in proteins at the atomic level.

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.

Role of Position K+4 in the Phosphorylation and Dephosphorylation Reaction Kinetics of the CheY Response Regulator

Two-component signaling is a primary method by which microorganisms interact with their environments. A kinase detects stimuli and modulates autophosphorylation activity. The signal propagates by phosphotransfer from the kinase to a response regulator, eliciting a response. Response regulators operate over a range of time scales, corresponding to their related biological processes. Response regulator active site chemistry is highly conserved, but certain variable residues can influence phosphorylation kinetics. An Ala-to-Pro substitution (K+4, residue 113) in the Escherichia coli response regulator CheY triggers a constitutively active phenotype; however, the A113P substitution is too far from the active site to directly affect phosphochemistry. To better understand the activating mechanism(s) of the substitution, we analyzed receiver domain sequences to characterize the evolutionary role of the K+4 position. Although most featured Pro, Leu, Ile, and Val residues, chemotaxis-related proteins exhibited atypical Ala, Gly, Asp, and Glu residues at K+4. Structural and in silico analyses revealed that CheY A113P adopted a partially active configuration. Biochemical data showed that A113P shifted CheY toward a more activated state, enhancing autophosphorylation. By characterizing CheY variants, we determined that this functionality was transmitted through a hydrophobic network bounded by the β5α5 loop and the α1 helix of CheY. This region also interacts with the phosphodonor CheA_P1, suggesting that binding generates an activating perturbation similar to the A113P substitution. Atypical residues like Ala at the K+4 position likely serve two purposes. First, restricting autophosphorylation may minimize background noise generated by intracellular phosphodonors such as acetyl phosphate. Second, optimizing interactions with upstream partners may help prime the receiver domain for phosphorylation.

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.

Concepts, Practices, and Interactive Tutorial for Allosteric Network Analysis of Molecular Dynamics Simulations

Over the past decade, concepts of network theory in combination with dynamical information from conformational ensembles have been widely applied to gain insights in understanding allosteric regulation in biomolecules. In this chapter, we introduce the basic theories and protocols used in protein dynamics network analysis through a series of interactive python Jupyter notebook scripts. While various network analysis methods exist in the literature, here we focus on the two popular methods based on correlated atomic motions and pairwise interaction energies. While the tutorial is based on a small prototypic protein, the workflow and protocol introduced here are optimized to handle large membrane proteins.

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.

Residue-Level Allostery Propagates through the Effective Coarse-Grained Hessian

The long-ranged coupling between residues that gives rise to allostery in a protein is built up from short-ranged physical interactions. Computational tools used to predict this coupling and its functional relevance have relied on the application of graph theoretical metrics to residue-level correlations measured from all-atom molecular dynamics simulations. The short-ranged interactions that yield these long-ranged residue-level correlations are quantified by the effective coarse-grained Hessian. Here we compute an effective harmonic coarse-grained Hessian from simulations of a benchmark allosteric protein, IGPS, and demonstrate the improved locality of this graph Laplacian over two other connectivity matrices. Additionally, two centrality metrics are developed that indicate the direct and indirect importance of each residue at producing the covariance between the effector binding pocket and the active site. The residue importance indicated by these two metrics is corroborated by previous mutagenesis experiments and leads to unique functional insights; in contrast to previous computational analyses, our results suggest that fP76-hK181 is the most important contact for conveying direct allosteric paths across the HisF-HisH interface. The connectivity around fD98 is found to be important at affecting allostery through indirect means.

Tuning Allostery through Integration of Disorder to Order with a Residue Network

In allostery, a signal from one site in a protein is transmitted to a second site to alter its function. Due to its ubiquity in biology and the potential for its exploitation in drug and protein design, the molecular basis of allosteric communication continues to be the subject of intense research. Although allosterically coupled sites are frequently characterized by disorder, how communication between disordered segments occurs remains obscure. Allosteric activation of Escherichia coli BirA dimerization occurs via coupled distant disorder-to-order transitions. In this work, combined structural and computational studies reveal an extensive residue network in BirA. Substitution of several network residues yields large perturbations to allostery. Force distribution analysis reveals that disruptions to the disorder-to-order transitions through amino acid substitution are manifested in shifts in the energy experienced by network residues as well as alterations in packing of an α-helix that plays a critical role in allostery. The combined results reveal a highly distributed allosteric mechanism that is robust to sequence change.

Energy Transport Pathways in Proteins: A Non-equilibrium Molecular Dynamics Simulation Study

To facilitate the observation of biomolecular energy transport in real time and with single-residue resolution, recent experiments by Baumann et al. ( Angew. Chem. Int. Ed. 2019 , 58 , 2899 , DOI: 10.1002/anie.201812995 ) have used unnatural amino acids β-(1-azulenyl)alanine (Azu) and azidohomoalanine (Aha) to site-specifically inject and probe vibrational energy in proteins. To aid the interpretation of such experiments, non-equilibrium molecular dynamics simulations of the anisotropic energy flow in proteins TrpZip2 and PDZ3 domains are presented. On this account, an efficient simulation protocol is established that accurately mimics the excitation and probing steps of Azu and Aha. The simulations quantitatively reproduce the experimentally found cooling times of the solvated proteins at room temperature and predict that the cooling slows by a factor 2 below the glass temperature of water. In PDZ3, vibrational energy is shown to travel from the initially excited peptide ligand via a complex network of inter-residue contacts and backbone transport to distal regions of the protein. The supposed connection of these energy transport pathways with pathways of allosteric communication is discussed.

gRINN: a tool for calculation of residue interaction energies and protein energy network analysis of molecular dynamics simulations

Atomistic molecular dynamics (MD) simulations generate a wealth of information related to the dynamics of proteins. If properly analyzed, this information can lead to new insights regarding protein function and assist wet-lab experiments. Aiming to identify interactions between individual amino acid residues and the role played by each in the context of MD simulations, we present a stand-alone software called gRINN (get Residue Interaction eNergies and Networks). gRINN features graphical user interfaces (GUIs) and a command-line interface for generating and analyzing pairwise residue interaction energies and energy correlations from protein MD simulation trajectories. gRINN utilizes the features of NAMD or GROMACS MD simulation packages and automatizes the steps necessary to extract residue-residue interaction energies from user-supplied simulation trajectories, greatly simplifying the analysis for the end-user. A GUI, including an embedded molecular viewer, is provided for visualization of interaction energy time-series, distributions, an interaction energy matrix, interaction energy correlations and a residue correlation matrix. gRINN additionally offers construction and analysis of Protein Energy Networks, providing residue-based metrics such as degrees, betweenness-centralities, closeness centralities as well as shortest path analysis. gRINN is free and open to all users without login requirement at http://grinn.readthedocs.io.

Thermostability of Lipase A and Dynamic Communication Based on Residue Interaction Network

OBJECTIVE

Dynamic communication caused by mutation affects protein stability. The main objective of this study is to explore how mutations affect communication and to provide further insight into the relationship between heat resistance and signal propagation of Bacillus subtilis lipase (Lip A).

METHODS

The relationship between dynamic communication and Lip A thermostability is studied by long-time MD simulation and residue interaction network. The Dijkstra algorithm is used to get the shortest path of each residue pair. Subsequently, time-series frequent paths and spatio-temporal frequent paths are mined through an Apriori-like algorithm.

RESULTS

Time-series frequent paths show that the communication between residue pairs, both in wild-type lipase (WTL) and mutant 6B, becomes chaotic with an increase in temperature; however, more residues in 6B can maintain stable communication at high temperature, which may be associated with the structural rigidity. Furthermore, spatio-temporal frequent paths reflect the interactions among secondary structures. For WTL at 300K, β7, αC, αB, the longest loop, αA and αF contact frequently. The 310-helix between β3 and αA is penetrated by spatio-temporal frequent paths. At 400K, only αC can be frequently transmitted. For 6B, when at 300K, αA and αF are in more tight contact by spatio-temporal frequent paths though I157M and N166Y. Moreover, the rigidity of the active site His156 and the C-terminal of Lip A are increased, as reflected by the spatio-temporal frequent paths. At 400K, αA and αF, 310-helix between β3 and αA, the longest loop, and the loop where the active site Asp133 is located can still maintain stable communication.

CONCLUSION

From the perspective of residue dynamic communication, it is obviously found that mutations cause changes in interactions between secondary structures and enhance the rigidity of the structure, contributing to the thermal stability and functional activity of 6B.

Integration of network models and evolutionary analysis into high-throughput modeling of protein dynamics and allosteric regulation: theory, tools and applications

Proteins are dynamical entities that undergo a plethora of conformational changes, accomplishing their biological functions. Molecular dynamics simulation and normal mode analysis methods have become the gold standard for studying protein dynamics, analyzing molecular mechanism and allosteric regulation of biological systems. The enormous amount of the ensemble-based experimental and computational data on protein structure and dynamics has presented a major challenge for the high-throughput modeling of protein regulation and molecular mechanisms. In parallel, bioinformatics and systems biology approaches including genomic analysis, coevolution and network-based modeling have provided an array of powerful tools that complemented and enriched biophysical insights by enabling high-throughput analysis of biological data and dissection of global molecular signatures underlying mechanisms of protein function and interactions in the cellular environment. These developments have provided a powerful interdisciplinary framework for quantifying the relationships between protein dynamics and allosteric regulation, allowing for high-throughput modeling and engineering of molecular mechanisms. Here, we review fundamental advances in protein dynamics, network theory and coevolutionary analysis that have provided foundation for rapidly growing computational tools for modeling of allosteric regulation. We discuss recent developments in these interdisciplinary areas bridging computational biophysics and network biology, focusing on promising applications in allosteric regulations, including the investigation of allosteric communication pathways, protein–DNA/RNA interactions and disease mutations in genomic medicine. We conclude by formulating and discussing future directions and potential challenges facing quantitative computational investigations of allosteric regulatory mechanisms in protein systems.

Protein Residue Networks from Energetic and Geometric Data: Are They Identical?

Protein residue networks (PRN) from energetic and geometric data are probably not identical. PRNs constructed from ab initio pair interaction energies are analyzed for the first time and compared to PRN based on center of mass separation. We use modern, previously unused algorithms such as global and local efficiencies to quantitatively confirm that both types of PRNs do exhibit small-world character. The main novelty finding is that interaction energy-based PRNs preserve small-world character even when clustered. A node hierarchy independent of the cutoff energy used for the edge creation is characteristic for them. Efficiency centrality identifies hubs responsible for such behavior. The interaction energy-based PRNs seem to comply with the scale-free network model with respect to efficiency centrality distribution as opposed to distance based PRNs. Community detection is introduced into protein network research as an extension beyond cluster analysis to study tertiary and quaternary structures.

Allostery and cooperativity in multimeric proteins: bond-to-bond propensities in ATCase

Aspartate carbamoyltransferase (ATCase) is a large dodecameric enzyme with six active sites that exhibits allostery: its catalytic rate is modulated by the binding of various substrates at distal points from the active sites. A recently developed method, bond-to-bond propensity analysis, has proven capable of predicting allosteric sites in a wide range of proteins using an energy-weighted atomistic graph obtained from the protein structure and given knowledge only of the location of the active site. Bond-to-bond propensity establishes if energy fluctuations at given bonds have significant effects on any other bond in the protein, by considering their propagation through the protein graph. In this work, we use bond-to-bond propensity analysis to study different aspects of ATCase activity using three different protein structures and sources of fluctuations. First, we predict key residues and bonds involved in the transition between inactive (T) and active (R) states of ATCase by analysing allosteric substrate binding as a source of energy perturbations in the protein graph. Our computational results also indicate that the effect of multiple allosteric binding is non linear: a switching effect is observed after a particular number and arrangement of substrates is bound suggesting a form of long range communication between the distantly arranged allosteric sites. Second, cooperativity is explored by considering a bisubstrate analogue as the source of energy fluctuations at the active site, also leading to the identification of highly significant residues to the T ↔ R transition that enhance cooperativity across active sites. Finally, the inactive (T) structure is shown to exhibit a strong, non linear communication between the allosteric sites and the interface between catalytic subunits, rather than the active site. Bond-to-bond propensity thus offers an alternative route to explain allosteric and cooperative effects in terms of detailed atomistic changes to individual bonds within the protein, rather than through phenomenological, global thermodynamic arguments.

Molecular dynamics simulations of the glucocorticoid receptor DNA-binding domain suggest a role of the lever-arm mobility in transcriptional output

One of the first and essential steps in gene expression regulation involves the recruitment of transcription factors (TFs) to specific response elements located at enhancers and/or promoters of targeted genes. These DNA elements have a certain variability in both sequence and length, which may affect the final transcriptional output. The molecular mechanisms in which TFs integrate the subtle differences within specific recognition sequences to offer different transcriptional responses is still largely unknown. Here we used molecular dynamics simulations to study the DNA binding behavior of the glucocorticoid receptor (GR), a ligand-regulated TF with pleiotropic effects in almost all cells. By comparing the behavior of the wild type receptor and a well characterized Ala477Thr substitution within the rat GR DNA binding domain, we found that the region that connects the two-zinc fingers (i.e. the lever arm) would likely play a key role in GR transcriptional output.

Computational study to understand the energy transfer pathways within amicyanin

Vibrational energy diffusivities between the residues present in Amicyanin copper protein are calculated and presented in form of communication map. From those results energy flow pathways from the copper metal ion to the inter protein residue Glu31 are identified. Our finding suggests many different pathways are possible and copper metal ion in oxidized and reduced state switches the pathways. Our finding also suggests the cooperative nature of surrounding residues and water molecules towards selecting the pathways. The major transport channels in the oxidised state are, Cu²⁺---> MET28---> LYS29---> TYR30---> GLU31 and Cu²⁺---> MET98---> TYR30--- > GLU31. And in the reduced state Cu⁺---> CYS9---> TYR30---> GLU31 and Cu⁺---> MET28---> LYS2---> TYR30---> GLU31. We studied further the interaction energies between the copper ion and neighbouring residues using B3LYP/QZVP method. Both the methods complement each other in predicting the energy flow pathways and the cooperative nature of residues.

Time-resolved observation of protein allosteric communication

Allostery represents a fundamental mechanism of biological regulation that is mediated via long-range communication between distant protein sites. Although little is known about the underlying dynamical process, recent time-resolved infrared spectroscopy experiments on a photoswitchable PDZ domain (PDZ2S) have indicated that the allosteric transition occurs on multiple timescales. Here, using extensive nonequilibrium molecular dynamics simulations, a time-dependent picture of the allosteric communication in PDZ2S is developed. The simulations reveal that allostery amounts to the propagation of structural and dynamical changes that are genuinely nonlinear and can occur in a nonlocal fashion. A dynamic network model is constructed that illustrates the hierarchy and exceeding structural heterogeneity of the process. In compelling agreement with experiment, three physically distinct phases of the time evolution are identified, describing elastic response ([Formula: see text] ns), inelastic reorganization ([Formula: see text] ns), and structural relaxation ([Formula: see text]s). Issues such as the similarity to downhill folding as well as the interpretation of allosteric pathways are discussed.

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.

An optimal distance cutoff for contact-based Protein Structure Networks using side-chain centers of mass

Proteins are highly dynamic entities attaining a myriad of different conformations. Protein side chains change their states during dynamics, causing clashes that are propagated at distal sites. A convenient formalism to analyze protein dynamics is based on network theory using Protein Structure Networks (PSNs). Despite their broad applicability, few efforts have been devoted to benchmarking PSN methods and to provide the community with best practices. In many applications, it is convenient to use the centers of mass of the side chains as nodes. It becomes thus critical to evaluate the minimal distance cutoff between the centers of mass which will provide stable network properties. Moreover, when the PSN is derived from a structural ensemble collected by molecular dynamics (MD), the impact of the MD force field has to be evaluated. We selected a dataset of proteins with different fold and size and assessed the two fundamental properties of the PSN, i.e. hubs and connected components. We identified an optimal cutoff of 5 Å that is robust to changes in the force field and the proteins. Our study builds solid foundations for the harmonization and standardization of the PSN approach.

Molecular Mechanism of Nucleotide-Dependent Allosteric Regulation in AMP-Activated Protein Kinase

The AMP-activated protein kinase (AMPK), a central enzyme in the regulation of energy homeostasis, is an important drug target for type 2 diabetes, obesity, and cancer. Binding of adenosine nucleotides to the regulatory γ-subunit tightly regulates the activity of this enzyme. Though recent crystal structures of AMPK have provided important insights into the allosteric activation of AMPK, molecular details of the regulatory mechanism of AMPK activation is still elusive. Here, we have performed extensive all-atom molecular dynamics (MD) simulations and shown that the kinase domain (KD) and γ-subunit come closer resulting in a more compact heterotrimeric AMPK complex in AMP-bound state compared to the ATP-bound state. The binding of ATP at site 3 of regulatory γ-subunit allosterically inhibits AMPK by destabilizing different regulatory regions of α-subunit: the autoinhibitory domain, the linker region, and the activation loop of the kinase core. The catalytically important residues experience a change in mechanical stress, and major rearrangements in community structure derived from residue-residue interaction energy-based network are observed in KD and α-linker region upon binding of different nucleotides. Our results also highlight the role of conserved charged residues forming an ionic network near the site 3 of γ-subunit in allosteric communications.

The adaptive nature of protein residue networks

Protein residue networks PRNs are used to describe proteins. These networks are usually based on an average structure for the protein. However, proteins are dynamic entities that are affected by their surroundings. In this work, we study the effect of temperatures above and below the protein dynamical transition temperature(≈200 K), on three important network parameters gleaned from weighted PRNs for the solvated β-lactamase inhibitory protein BLIP: the betweenness centrality B, the closeness centrality C, and the clustering coefficient CC. The B and C values will be extracted for each node from PRNs at six different temperatures: 150 K, 180 K, 200 K, 220 K, 250 K, and 310 K respectively. The average value for the CC for each PRN will also be calculated at each temperature, respectively. We find that at temperatures ≤200 K, the network nodes with the most significant B and C values tend to have lower relative solvent accessibility RSA values, and to fall within the protein secondary structure elements (α helices and β sheets). At temperatures >200 K, the significant nodes in terms of B and C tend to have larger RSA values, and to fall on the connecting loops in the protein. The average CC decreases in value for the PRNs up to 200 K, and then remains basically constant above 200 K. This clearly shows that any conclusions based on static PRNs should be handled with care. The dynamic nature of proteins and its coupling to the surrounding environment should be taken into consideration when using the PRN paradigm. Proteins 2017; 85:917-923. © 2016 Wiley Periodicals, Inc.

Nonlinear backbone torsional pair correlations in proteins

Protein allostery requires dynamical structural correlations. Physical origin of which, however, remain elusive despite intensive studies during last two and half decades. Based on analysis of molecular dynamics (MD) simulation trajectories for ten proteins with different sizes and folds, we found that nonlinear backbone torsional pair (BTP) correlations, which are mainly spatially long-ranged and are dominantly executed by loop residues, exist extensively in most analyzed proteins. Examination of torsional motion for correlated BTPs suggested that such nonlinear correlations are mainly associated aharmonic torsional state transitions and in some cases strongly anisotropic local torsional motion of participating torsions, and occur on widely different and relatively longer time scales. In contrast, correlations between backbone torsions in stable α helices and β strands are mainly linear and spatially short-ranged, and are more likely to associate with harmonic local torsional motion. Further analysis revealed that the direct cause of nonlinear contributions are heterogeneous linear correlations. These findings implicate a general search strategy for novel allosteric modulation sites of protein activities.

Prediction of allosteric sites and mediating interactions through bond-to-bond propensities

Allostery is a fundamental mechanism of biological regulation, in which binding of a molecule at a distant location affects the active site of a protein. Allosteric sites provide targets to fine-tune protein activity, yet we lack computational methodologies to predict them. Here we present an efficient graph-theoretical framework to reveal allosteric interactions (atoms and communication pathways strongly coupled to the active site) without a priori information of their location. Using an atomistic graph with energy-weighted covalent and weak bonds, we define a bond-to-bond propensity quantifying the non-local effect of instantaneous bond fluctuations propagating through the protein. Significant interactions are then identified using quantile regression. We exemplify our method with three biologically important proteins: caspase-1, CheY, and h-Ras, correctly predicting key allosteric interactions, whose significance is additionally confirmed against a reference set of 100 proteins. The almost-linear scaling of our method renders it suitable for high-throughput searches for candidate allosteric sites.

Water-Mediated Energy Dynamics in a Homodimeric Hemoglobin

We examine energy dynamics in the unliganded and liganded states of the homodimeric hemoglobin from Scapharca inaequivalvis (HbI), which exhibits cooperativity mediated by the cluster of water molecules at the interface upon ligand binding and dissociation. We construct and analyze a dynamic network in which nodes representing the residues, hemes, and water cluster are connected by edges that represent energy transport times, as well as a nonbonded network (NBN) indicating regions that respond rapidly to local strain within the protein via nonbonded interactions. One of the two largest NBNs includes the Lys30-Asp89 salt bridge critical for stabilizing the dimer. The other includes the hemes and surrounding residues, as well as, in the unliganded state, the cluster of water molecules between the globules. Energy transport in the protein appears to be controlled by the Lys30-Asp89 salt bridge critical for stabilizing the dimer, as well as the interface water cluster in the unliganded state. Possible connections between energy transport dynamics in response to local strain identified here and allosteric transitions in HbI are discussed.

Allosteric Pathways in the PPARγ-RXRα nuclear receptor complex

Understanding the nature of allostery in DNA-nuclear receptor (NR) complexes is of fundamental importance for drug development since NRs regulate the transcription of a myriad of genes in humans and other metazoans. Here, we investigate allostery in the peroxisome proliferator-activated/retinoid X receptor heterodimer. This important NR complex is a target for antidiabetic drugs since it binds to DNA and functions as a transcription factor essential for insulin sensitization and lipid metabolism. We find evidence of interdependent motions of Ω-loops and PPARγ-DNA binding domain with contacts susceptible to conformational changes and mutations, critical for regulating transcriptional functions in response to sequence-dependent DNA dynamics. Statistical network analysis of the correlated motions, observed in molecular dynamics simulations, shows preferential allosteric pathways with convergence centers comprised of polar amino acid residues. These findings are particularly relevant for the design of allosteric modulators of ligand-dependent transcription factors.

Dynamic Transmission of Protein Allostery without Structural Change: Spatial Pathways or Global Modes?

We examine the contrast between mechanisms for allosteric signaling that involve structural change, and those that do not, from the perspective of allosteric pathways. In particular we treat in detail the case of fluctuation-allostery by which amplitude modulation of the thermal fluctuations of the elastic normal modes conveys the allosteric signal, and address the question of what an allosteric pathway means in this case. We find that a perturbation theory of thermal elastic solids and nonperturbative approach (by super-coarse-graining elasticity into internal bending modes) have opposite signatures in their structure of correlated pathways. We illustrate the effect from analysis of previous results from GlxR of Corynebacterium glutamicum, an example of the CRP/FNR transcription family of allosteric homodimers. We find that the visibility of both correlated pathways and disconnected sites of correlated motion in this protein suggests that mechanisms of local elastic stretch and bend are recruited for the purpose of creating and controlling allosteric cooperativity.

(Dis)similarity Index To Compare Correlated Motions in Molecular Simulations

Molecular dynamics (MD) simulations are widely used to complement or guide experimental studies in the characterization of protein dynamics, thanks to improvements in force-field accuracy, along with in the software and hardware to sample the conformational landscape of proteins. Among the different applications of MD simulations, the study of correlated motions is largely employed for different purposes. Several metrics have been developed to describe correlated motions in the MD ensemble, such as methods based on Pearson Correlation or Mutual Information. Cross-correlation analysis of MD trajectories is indeed appealing not only to identify residues characterized by coupled fluctuations in protein structures but also since it can be used to extrapolate motions along directions in which major conformational changes should occur, for example on longer time scales than the ones that are actually simulated. Nevertheless, most of the MD studies employ average correlation maps and mostly in a qualitative way, even when different systems or different replicates of the same system are compared. The broad application of correlation metrics in the analysis of MD simulations, especially for comparative purposes, requires a step forward toward more quantitative and accurate comparisons. We thus here employed a simple but effective index, which is based on a normalized Frobenius norm of the differences between protein correlation maps, to compare correlated motions. We applied this index for a quantitative comparison of correlated motions from MD simulations of seven proteins of different size and fold. We also employed the index to assess the robustness of correlation description when multi-replicate MD simulations of a same system are used, and we compared our index to metrics for comparison of structural ensembles such as Root Mean Square Inner Product and the Bhattacharyya Coefficient.

MDN: A Web Portal for Network Analysis of Molecular Dynamics Simulations

We introduce a web portal that employs network theory for the analysis of trajectories from molecular dynamics simulations. Users can create protein energy networks following methodology previously introduced by our group, and can identify residues that are important for signal propagation, as well as measure the efficiency of signal propagation by calculating the network coupling. This tool, called MDN, was used to characterize signal propagation in Escherichia coli heat-shock protein 70-kDa. Two variants of this protein experimentally shown to be allosterically active exhibit higher network coupling relative to that of two inactive variants. In addition, calculations of partial coupling suggest that this quantity could be used as part of the criteria to determine pocket druggability in drug discovery studies.

Integrating atomistic molecular dynamics simulations, experiments, and network analysis to study protein dynamics: strength in unity

In the last years, we have been observing remarkable improvements in the field of protein dynamics. Indeed, we can now study protein dynamics in atomistic details over several timescales with a rich portfolio of experimental and computational techniques. On one side, this provides us with the possibility to validate simulation methods and physical models against a broad range of experimental observables. On the other side, it also allows a complementary and comprehensive view on protein structure and dynamics. What is needed now is a better understanding of the link between the dynamic properties that we observe and the functional properties of these important cellular machines. To make progresses in this direction, we need to improve the physical models used to describe proteins and solvent in molecular dynamics, as well as to strengthen the integration of experiments and simulations to overcome their own limitations. Moreover, now that we have the means to study protein dynamics in great details, we need new tools to understand the information embedded in the protein ensembles and in their dynamic signature. With this aim in mind, we should enrich the current tools for analysis of biomolecular simulations with attention to the effects that can be propagated over long distances and are often associated to important biological functions. In this context, approaches inspired by network analysis can make an important contribution to the analysis of molecular dynamics simulations.

Weighted protein residue networks based on joint recurrences between residues

BACKGROUND

Weighted and un-weighted protein residue networks can predict key functional residues in proteins based on the closeness centrality C and betweenness centrality B values for each residue. A static snapshot of the protein structure, and a cutoff distance, are used to define edges between the network nodes. In this work we apply the weighted network approach to study the β-Lactamase Inhibitory Protein (BLIP). Joint recurrences extracted from molecular dynamics MD trajectory positions of the protein residue carbon alpha atoms are used to define edge weights between nodes, and no cutoff distance is used. The results for B and C from our approach are compared with those extracted from an un-weighted network, and a weighted network that uses interatomic contacts to define edge weights between nodes, respectively.

RESULTS

The joint recurrence weighted network approach performs well in pointing out key protein residues. Furthermore, it seems to emphasize residues with medium to high relative solvent accessibility that lie in loop regions between secondary structure elements of the protein.

CONCLUSIONS

Protein residue networks that use joint recurrences extracted from molecular dynamics simulations of a solvated protein perform well in pointing to hotspot residues and hotspot clusters. This approach uses no distance cutoff threshold, and does not exclude any interactions between the residues, including water-mediated interactions.