Network and atomistic simulations unveil the structural determinants of mutations linked to retinal diseases

PyInteraph2 and PyInKnife2 to Analyze Networks in Protein Structural Ensembles

Due to the complex nature of noncovalent interactions and their long-range effects, analyzing protein conformations using network theory can be enlightening. Protein Structure Networks (PSNs) provide a convenient formalism to study protein structures in relation to essential properties such as key residues for structural stability, allosteric communication, and the effects of modifications of the protein. PSNs can be defined according to very different principles, and the available tools have limitations in input formats, supported models, and version control. Other outstanding problems are related to the definition of network cutoffs and the assessment of the stability of the network properties. The protein science community could benefit from a common framework to carry out these analyses and make them easier to reproduce, reuse, and evaluate. We here provide two open-source software packages, PyInteraph2 and PyInKnife2, to implement and analyze PSNs in a reproducible and documented manner. PyInteraph2 interfaces with multiple formats for protein ensembles and incorporates different network models with the possibility of integrating them into a macronetwork and performing various downstream analyses, including hubs, connected components, and several other centrality measures, and visualizes the networks or further analyzes them thanks to compatibility with Cytoscape.PyInKnife2 that supports the network models implemented in PyInteraph2. It employs a jackknife resampling approach to estimate the convergence of network properties and streamline the selection of distance cutoffs. We foresee that the modular structure of the code and the supported version control system will promote the transition to a community-driven effort, boost reproducibility, and establish common protocols in the PSN field. As developers, we will guarantee the introduction of new functionalities and maintenance, assistance, and training of new contributors.

In-depth molecular profiling of an intronic GNAO1 mutant as the basis for personalized high-throughput drug screening

BACKGROUND

The GNAO1 gene, encoding the major neuronal G protein Gαo, is mutated in a subset of pediatric encephalopathies. Most such mutations consist of missense variants.

METHODS

In this study, we present a precision medicine workflow combining next-generation sequencing (NGS) diagnostics, molecular etiology analysis, and personalized drug discovery.

FINDINGS

We describe a patient carrying a de novo intronic mutation (NM_020988.3:c.724-8G>A), leading to epilepsy-negative encephalopathy with motor dysfunction from the second decade. Our data show that this mutation creates a novel splice acceptor site that in turn causes an in-frame insertion of two amino acid residues, Pro-Gln, within the regulatory switch III region of Gαo. This insertion misconfigures the switch III loop and creates novel interactions with the catalytic switch II region, resulting in increased GTP uptake, defective GTP hydrolysis, and aberrant interactions with effector proteins. In contrast, intracellular localization, Gβγ interactions, and G protein-coupled receptor (GPCR) coupling of the Gαo[insPQ] mutant protein remain unchanged.

CONCLUSIONS

This in-depth analysis characterizes the heterozygous c.724-8G>A mutation as partially dominant negative, providing clues to the molecular etiology of this specific pathology. Further, this analysis allows us to establish and validate a high-throughput screening platform aiming at identifying molecules that could correct the aberrant biochemical functions of the mutant Gαo.

FUNDING

This work was supported by the Joint Seed Money Funding scheme between the University of Geneva and the Hebrew University of Jerusalem.

Quantitative systems pharmacology of the eye: Tools and data for ocular QSP

Good eyesight belongs to the most-valued attributes of health, and diseases of the eye are a significant healthcare burden. Case numbers are expected to further increase in the next decades due to an aging society. The development of drugs in ophthalmology, however, is difficult due to limited accessibility of the eye, in terms of drug administration and in terms of sampling of tissues for drug pharmacokinetics (PKs) and pharmacodynamics (PDs). Ocular quantitative systems pharmacology models provide the opportunity to describe the distribution of drugs in the eye as well as the resulting drug-response in specific segments of the eye. In particular, ocular physiologically-based PK (PBPK) models are necessary to describe drug concentration levels in different regions of the eye. Further, ocular effect models using molecular data from specific cellular systems are needed to develop dose-response correlations. We here describe the current status of PK/PBPK as well as PD models for the eyes and discuss cellular systems, data repositories, as well as animal models in ophthalmology. The application of the various concepts is highlighted for the development of new treatments for postoperative fibrosis after glaucoma surgery.

Wordom update 2: A user-friendly program for the analysis of molecular structures and conformational ensembles

We present the second update of Wordom, a user-friendly and efficient program for manipulation and analysis of conformational ensembles from molecular simulations. The actual update expands some of the existing modules and adds 21 new modules to the update 1 published in 2011. The new adds can be divided into three sets that: 1) analyze atomic fluctuations and structural communication; 2) explore ion-channel conformational dynamics and ionic translocation; and 3) compute geometrical indices of structural deformation. Set 1 serves to compute correlations of motions, find geometrically stable domains, identify a dynamically invariant core, find changes in domain-domain separation and mutual orientation, perform wavelet analysis of large-scale simulations, process the output of principal component analysis of atomic fluctuations, perform functional mode analysis, infer regions of mechanical rigidity, analyze overall fluctuations, and perform the perturbation response scanning. Set 2 includes modules specific for ion channels, which serve to monitor the pore radius as well as water or ion fluxes, and measure functional collective motions like receptor twisting or tilting angles. Finally, set 3 includes tools to monitor structural deformations by computing angles, perimeter, area, volume, β-sheet curvature, radial distribution function, and center of mass. The ring perception module is also included, helpful to monitor supramolecular self-assemblies. This update places Wordom among the most suitable, complete, user-friendly, and efficient software for the analysis of biomolecular simulations. The source code of Wordom and the relative documentation are available under the GNU general public license at http://wordom.sf.net.

Structural communication between the GTPase Sec4p and its activator Sec2p: Determinants of GEF activity and early deformations to nucleotide release

Ras GTPases are molecular switches that cycle between OFF and ON states depending on the bound nucleotide (i.e. GDP-bound and GTP-bound, respectively).

The Rab GTPase, Sec4p, plays regulatory roles in multiple steps of intracellular vesicle trafficking. Nucleotide release is catalyzed by the Guanine Nucleotide Exchange Factor (GEF) Sec2p.

Here, the integration of structural information with molecular dynamics (MD) simulations addressed a number of questions concerning the intrinsic and stimulated dynamics of Sec2p and Sec4p as well as the chain of structural deformations leading to GEF-assisted activation of the Rab GTPase.

Sec2p holds an intrinsic ability to adopt the conformation found in the crystallographic complexes with Sec4p, thus suggesting that the latter selects and shifts the conformational equilibrium towards a pre-existing bound-like conformation of Sec2p.

The anchoring of Sec4p to a suitable conformation of Sec2p favors the Sec2p-assisted pulling on itself of the α1/switch 1 (SWI) loop and of SWI, which loose any contact with GDP. Those deformations of Sec4p would occur earlier. Formation of the final Sec2p-Sec4p hydrophobic interface, accomplishes later. Disruption of the nucleotide cage would cause firstly loss of interactions with the guanine ring and secondly loss of interactions with the phosphates.

The ease in sampling the energy landscape and adopting a bound-like conformation likely favors the catalyzing ability of GEFs for Ras GTPases.

PSNtools for standalone and web-based structure network analyses of conformational ensembles

Structure graphs, in which interacting amino acids/nucleotides correspond to linked nodes, represent cutting-edge tools to investigate macromolecular function.

The graph-based approach defined as Protein Structure Network (PSN) was initially implemented in the Wordom software and subsequently in the webPSN server. PSNs are computed either on a molecular dynamics (MD) trajectory (PSN-MD) or on a single structure. In the latter case, information on atomic fluctuations is inferred from the Elastic Network Model-Normal Mode Analysis (ENM-NMA) (PSN-ENM). While Wordom performs both PSN-ENM and PSN-MD analyses but without output post-processing, the webPSN server performs only single-structure PSN-EMN but assisting the user in input setup and output analysis.

Here we release for the first time the standalone software PSNtools, which allows calculation and post-processing of PSN analyses carried out either on single structures or on conformational ensembles. Relevant unique and novel features of PSNtools are either comparisons of two networks or computations of consensus networks on sets of homologous/analogous macromolecular structures or conformational ensembles. Network comparisons and consensus serve to infer differences in functionally different states of the same system or network-based signatures in groups of bio-macromolecules sharing either the same functionality or the same fold.

In addition to the new software, here we release also an updated version of the webPSN server, which allows performing an interactive graphical analysis of PSN-MD, following the upload of the PSNtools output.

PSNtools, the auxiliary binary version of Wordom software, and the WebPSN server are freely available at http://webpsn.hpc.unimo.it/wpsn3.php.

Bcl-xL Dynamics under the Lens of Protein Structure Networks

Understanding the finely orchestrated interactions leading to or preventing programmed cell death (apoptosis) is of utmost importance in cancer research because the failure of these systems could eventually lead to the onset of the disease. In this regard, the maintenance of a delicate balance between the promoters and inhibitors of mitochondrial apoptosis is crucial, as demonstrated by the interplay among the Bcl-2 family members. In particular, B-cell lymphoma extra-large (Bcl-x_L) is a target of interest due to the forefront role of its dysfunctions in cancer development. Bcl-x_L prevents apoptosis by binding both the pro-apoptotic BH3-only proteins, like PUMA, and the noncanonical partners, such as p53, at different sites. An allosteric communication between the BH3-only protein binding pocket and the p53 binding site, mediating the release of p53 from Bcl-x_L upon PUMA binding, has been postulated and supported by nuclear magnetic resonance and other biophysical data. The molecular details of this mechanism, especially at the residue level, remain unclear. In this work, we investigated the distal communication between these two sites in Bcl-x_L in its free state and when bound to PUMA. We also evaluated how missense mutations of Bcl-x_L found in cancer samples might impair this communication and therefore the allosteric mechanism. We employed all-atom explicit solvent microsecond molecular dynamics simulations, analyzed through a Protein Structure Network approach and integrated with calculations of changes in free energies upon cancer-related mutations identified by genomics studies. We found a subset of candidate residues responsible for both maintaining protein stability and for conveying structural information between the two binding sites and hypothesized possible communication routes between specific residues at both sites.

Dynamics and structural communication in the ternary complex of fully phosphorylated V2 vasopressin receptor, vasopressin, and β-arrestin 1

G protein-coupled receptors (GPCRs) are critically regulated by arrestins, which not only desensitize G-protein signaling but also initiate a G protein-independent wave of signaling. The information from structure determination was herein exploited to build a structural model of the ternary complex, comprising fully phosphorylated V2 vasopressin receptor (V2R), the agonist arginine vasopressin (AVP), and β-arrestin 1 (β-arr1). Molecular simulations served to explore dynamics and structural communication in the ternary complex. Flexibility and mechanical profiles reflect fold of V2R and β-arr1. Highly conserved amino acids tend to behave as hubs in the structure network and contribute the most to the mechanical rigidity of V2R seven-helix bundle and of β-arr1. Two structurally and dynamically distinct receptor-arrestin interfaces assist the twist of the N- and C-terminal domains (ND and CD, respectively) of β-arr1 with respect to each other, which is linked to arrestin activation. While motion of the ND is essentially assisted by the fully phosphorylated C-tail of V2R (V2RCt), that of CD is assisted by the second and third intracellular loops and the cytosolic extensions of helices 5 and 6. In the presence of the receptor, the β-arr1 inter-domain twist angle correlates with the modes describing the essential subspace of the ternary complex. β-arr1 motions are also influenced by the anchoring to the membrane of the C-edge-loops in the β-arr1-CD. Overall fluctuations reveal a coupling between motions of the agonist binding site and of β-arr1-ND, which are in allosteric communication between each other. Mechanical rigidity points, often acting as hubs in the structure network and distributed along the main axis of the receptor helix bundle, contribute to establish a preferential communication pathway between agonist ligand and the ND of arrestin. Such communication, mediated by highly conserved amino acids, involves also the first amino acid in the arrestin C-tail, which is highly dynamic and is involved in clathrin-mediated GPCR internalization.

Interconnecting Flexibility, Structural Communication, and Function in RhoGEF Oncoproteins

Dbl family Rho guanine nucleotide exchange factors (RhoGEFs) play a central role in cell biology by catalyzing the exchange of guanosine 5'-triphosphate for guanosine 5'-diphosphate (GDP) on RhoA. Insights into the oncogenic constitutive activity of the Lbc RhoGEF were gained by analyzing the structure and dynamics of the protein in different functional states and in comparison with a close homologue, leukemia-associated RhoGEF. Higher intrinsic flexibility, less dense and extended structure network, and less stable allosteric communication pathways in Lbc, compared to the nonconstitutively active homologue, emerged as major determinants of the constitutive activity. Independent of the state, the essential dynamics of the two RhoGEFs is contributed by the last 10 amino acids of Dbl homology (DH) and the whole pleckstrin homology (PH) domains and tends to be equalized by the presence of RhoA. The catalytic activity of the RhoGEF relies on the scaffolding action of the DH domain that primarily turns the switch I (SWI) of RhoA on itself through highly conserved amino acids participating in the stability core and essential for function. Changes in the conformation of SWI and disorganization of the RhoA regions deputed to nucleotide binding are among the major RhoGEF effects leading to GDP release. Binding of RhoA reorganizes the allosteric communication on RhoGEF, strengthening the communication among the canonical RhoA binding site on DH, a secondary RhoA binding site on PH, and the binding site for heterotrimeric G proteins, suggesting dual roles for RhoA as a catalysis substrate and as a regulatory protein. The structure network-based analysis tool employed in this study proved to be useful for predicting potentially druggable regulatory sites in protein structures.

A novel p.(Glu111Val) missense mutation in GUCA1A associated with cone-rod dystrophy leads to impaired calcium sensing and perturbed second messenger homeostasis in photoreceptors

Guanylate Cyclase-Activating Protein 1 (GCAP1) regulates the enzymatic activity of the photoreceptor guanylate cyclases (GC), leading to inhibition or activation of the cyclic guanosine monophosphate (cGMP) synthesis depending on its Ca2+- or Mg2+-loaded state. By genetically screening a family of patients diagnosed with cone-rod dystrophy, we identified a novel missense mutation with autosomal dominant inheritance pattern (c.332A>T; p.(Glu111Val); E111V from now on) in the GUCA1A gene coding for GCAP1. We performed a thorough biochemical and biophysical investigation of wild type (WT) and E111V human GCAP1 by heterologous expression and purification of the recombinant proteins. The E111V substitution disrupts the coordination of the Ca2+ ion in the high-affinity site (EF-hand 3, EF3), thus significantly decreasing the ability of GCAP1 to sense Ca2+ (∼80-fold higher Kdapp compared to WT). Both WT and E111V GCAP1 form dimers independently on the presence of cations, but the E111V Mg2+-bound form is prone to severe aggregation over time. Molecular dynamics simulations suggest a significantly increased flexibility of both the EF3 and EF4 cation binding loops for the Ca2+-bound form of E111V GCAP1, in line with the decreased affinity for Ca2+. In contrast, a more rigid backbone conformation is observed in the Mg2+-bound state compared to the WT, which results in higher thermal stability. Functional assays confirm that E111V GCAP1 interacts with the target GC with a similar apparent affinity (EC50); however, the mutant shifts the GC inhibition out of the physiological [Ca2+] (IC50E111V ∼10 μM), thereby leading to the aberrant constitutive synthesis of cGMP under conditions of dark-adapted photoreceptors.

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.

"Infostery" analysis of short molecular dynamics simulations identifies highly sensitive residues and predicts deleterious mutations

Characterizing a protein mutational landscape is a very challenging problem in Biology. Many disease-associated mutations do not seem to produce any effect on the global shape nor motions of the protein. Here, we use relatively short all-atom biomolecular simulations to predict mutational outcomes and we quantitatively assess the predictions on several hundreds of mutants. We perform simulations of the wild type and 175 mutants of PSD95’s third PDZ domain in complex with its cognate ligand. By recording residue displacements correlations and interactions, we identify “communication pathways” and quantify them to predict the severity of the mutations. Moreover, we show that by exploiting simulations of the wild type, one can detect 80% of the positions highly sensitive to mutations with a precision of 89%. Importantly, our analysis describes the role of these positions in the inter-residue communication and dynamical architecture of the complex. We assess our approach on three different systems using data from deep mutational scanning experiments and high-throughput exome sequencing. We refer to our analysis as “infostery”, from “info” - information - and “steric” - arrangement of residues in space. We provide a fully automated tool, COMMA2 (www.lcqb.upmc.fr/COMMA2), that can be used to guide medicinal research by selecting important positions/mutations.

Uncovering GPCR and G Protein Function by Protein Structure Network Analysis

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

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.

Structural Determinants of Constitutive Activation of Gα Proteins: Transducin as a Paradigm

Heterotrimeric guanine nucleotide-binding proteins (Gα proteins) are intracellular nanomachines deputed to signal transduction. The switch-on process requires the release of bound GDP from a site at the interface between GTPase and helical domains. Nucleotide release is catalyzed by G protein Coupled Receptors (GPCRs). Here we investigate the functional dynamics of wild type (WT) and six constitutively active mutants (CAMs) of the Gα protein transducin (Gt) by combining atomistic molecular dynamics (MD) simulations with Maxwell-Demod discrete MD (MDdMD) simulations of the receptor-catalyzed transition between GDP-bound and nucleotide-free states. Compared to the WT, Gt CAMs increase the overall fluctuations of nucleotide and its binding site. This is accompanied by weakening of native links involving GDP, α1, the G boxes, β1-β3, and α5. Collectively, constitutive activation by the considered mutants seems to associate with weakening of the interfaces between α5 and the surrounding portions and the interface between GTPase (G) and helical (H) domains. These mutational effects associate with increases in the overall fluctuations of the G and H domains, which reflect on the collective motions of the protein. Gt CAMs, with prominence to G56P, T325A, and F332A, prioritize collective motions of the H domain overlapping with the collective motions associated with receptor-catalyzed nucleotide release. In spite of different local perturbations, the mechanisms of nucleotide exchange catalyzed by activating mutations and by receptor are expected to employ similar molecular switches in the nucleotide binding site and to share the detachment of the H domain from the G domain.

Molecular mechanism of carbon nanotube to activate Subtilisin Carlsberg in polar and non-polar organic media

In the work, we mainly used molecular dynamics (MD) simulation and protein structure network (PSN) to study subtilisin Carlsberg (SC) immobilized onto carbon nanotube (CNT) in water, acetonitrile and heptane solvents, in order to explore activation mechanism of enzymes in non-aqueous media. The result indicates that the affinity of SC with CNT follows the decreasing order of water > acetonitrile > heptane. The overall structure of SC and the catalytic triad display strong robustness to the change of environments, responsible for the activity retaining. However, the distances between two β-strands of substrate-binding pocket are significantly expanded by the immobilization in the increasing order of water < acetonitrile < heptane, contributing to the highest substrate-binding energy in heptane media. PSN analysis further reveals that the immobilization enhances structural communication paths to the substrate-binding pocket, leading to its larger change than the free-enzymes. Interestingly, the increase in the number of the pathways upon immobilization is not dependent on the absorbed extent but the desorbed one, indicating significant role of shifting process of experimental operations in influencing the functional region. In addition, some conserved and important hot-residues in the paths are identified, providing molecular information for functional modification.

Structure network analysis to gain insights into GPCR function

G protein coupled receptors (GPCRs) are allosteric proteins whose functioning fundamentals are the communication between the two poles of the helix bundle. Protein structure network (PSN) analysis is one of the graph theory-based approaches currently used to investigate the structural communication in biomolecular systems. Information on system's dynamics can be provided by atomistic molecular dynamics (MD) simulations or coarse grained elastic network models paired with normal mode analysis (ENM–NMA). The present review article describes the application of PSN analysis to uncover the structural communication in G protein coupled receptors (GPCRs). Strategies to highlight changes in structural communication upon misfolding, dimerization and activation are described. Focus is put on the ENM–NMA-based strategy applied to the crystallographic structures of rhodopsin in its inactive (dark) and signalling active (meta II (MII)) states, highlighting changes in structure network and centrality of the retinal chromophore in differentiating the inactive and active states of the receptor.

Use of network model to explore dynamic and allosteric properties of three GPCR homodimers

We used an elastic network model and protein structure network to study three class A GPCR homodimers.

Protein-Protein Interface and Disease: Perspective from Biomolecular Networks

Protein-protein interactions are involved in many important biological processes and molecular mechanisms of disease association. Structural studies of interfacial residues in protein complexes provide information on protein-protein interactions. Characterizing protein-protein interfaces, including binding sites and allosteric changes, thus pose an imminent challenge. With special focus on protein complexes, approaches based on network theory are proposed to meet this challenge. In this review we pay attention to protein-protein interfaces from the perspective of biomolecular networks and their roles in disease. We first describe the different roles of protein complexes in disease through several structural aspects of interfaces. We then discuss some recent advances in predicting hot spots and communication pathway analysis in terms of amino acid networks. Finally, we highlight possible future aspects of this area with respect to both methodology development and applications for disease treatment.

(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.

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.

PyInteraph: a framework for the analysis of interaction networks in structural ensembles of proteins

In the last years, a growing interest has been gathering around the ability of Molecular Dynamics (MD) to provide insight into the paths of long-range structural communication in biomolecules. The knowledge of the mechanisms related to structural communication helps in the rationalization in atomistic details of the effects induced by mutations, ligand binding, and the intrinsic dynamics of proteins. We here present PyInteraph, a tool for the analysis of structural ensembles inspired by graph theory. PyInteraph is a software suite designed to analyze MD and structural ensembles with attention to binary interactions between residues, such as hydrogen bonds, salt bridges, and hydrophobic interactions. PyInteraph also allows the different classes of intra- and intermolecular interactions to be represented, combined or alone, in the form of interaction graphs, along with performing network analysis on the resulting interaction graphs. The program also integrates the network description with a knowledge-based force field to estimate the interaction energies between side chains in the protein. It can be used alone or together with the recently developed xPyder PyMOL plugin through an xPyder-compatible format. The software capabilities and associated protocols are here illustrated by biologically relevant cases of study. The program is available free of charge as Open Source software via the GPL v3 license at http://linux.btbs.unimib.it/pyinteraph/.

Network analysis to uncover the structural communication in GPCRs

Protein structure network (PSN) analysis is one of the graph theory-based approaches currently used to investigate the structural communication in biomolecular systems. Information on system dynamics can be provided by atomistic molecular dynamics simulations or coarse-grained Elastic Network Models paired with Normal Mode Analysis (ENM-NMA). This chapter describes the application of PSN analysis to uncover the structural communication in G protein-coupled receptors (GPCRs). Strategies to highlight changes in structural communication upon misfolding mutations, dimerization, and activation are described. Focus is put on the ENM-NMA-based strategy applied to the crystallographic structures of rhodopsin in its inactive (dark) and signaling active (meta II (MII)) states, highlighting clear changes in the PSN and the centrality of the retinal chromophore in differentiating the inactive and active states of the receptor.