Approaching Elastic Network Models to Molecular Dynamics Flexibility

Scipion-EM-ProDy: A Graphical Interface for the ProDy Python Package within the Scipion Workflow Engine Enabling Integration of Databases, Simulations and Cryo-Electron Microscopy Image Processing

Macromolecular assemblies, such as protein complexes, undergo continuous structural dynamics, including global reconfigurations critical for their function. Two fast analytical methods are widely used to study these global dynamics, namely elastic network model normal mode analysis and principal component analysis of ensembles of structures. These approaches have found wide use in various computational studies, driving the development of complex pipelines in several software packages. One common theme has been conformational sampling through hybrid simulations incorporating all-atom molecular dynamics and global modes of motion. However, wide functionality is only available for experienced programmers with limited capabilities for other users. We have, therefore, integrated one popular and extensively developed software for such analyses, the ProDy Python application programming interface, into the Scipion workflow engine. This enables a wider range of users to access a complete range of macromolecular dynamics pipelines beyond the core functionalities available in its command-line applications and the normal mode wizard in VMD. The new protocols and pipelines can be further expanded and integrated into larger workflows, together with other software packages for cryo-electron microscopy image analysis and molecular simulations. We present the resulting plugin, Scipion-EM-ProDy, in detail, highlighting the rich functionality made available by its development.

Statistical Learning of Protein Elastic Network from Positional Covariance Matrix

Positional fluctuation and covariance during protein dynamics are key observables for understanding the molecular origin of biological functions. A frequently employed potential energy function for describing protein structural variation at the coarse-gained level is elastic network model (ENM). A long-standing issue in biomolecular simulation is thus the parametrization of ENM spring constants from the components of positional covariance matrix (PCM). Based on sensitivity analysis of PCM, the direct-coupling statistics of each spring, which is a specific combination of position fluctuation and covariance, is found to exhibit prominent signal of parameter dependence. This finding provides the basis for devising the objective function and the scheme of running through the effective one-dimensional optimization of every spring by self-consistent iteration. Formal derivation of the positional covariance statistical learning (PCSL) method also motivates the necessary data regularization for stable calculations. Robust convergence of PCSL is achieved in taking an all-atom molecular dynamics trajectory or an ensemble of homologous structures as input data. The PCSL framework can also be generalized with mixed objective functions to capture specific property such as the residue flexibility profile. Such physical chemistry-based statistical learning thus provides a useful platform for integrating the mechanical information encoded in various experimental or computational data.

Exploring the Conformational Impact of Glycine Receptor TM1-2 Mutations Through Coarse-Grained Analysis and Atomistic Simulations

Pentameric ligand-gated ion channels (PLGICs) are a family of proteins that convert chemical signals into ion fluxes through cellular membranes. Their structures are highly conserved across all kingdoms from bacteria to eukaryotes. Beyond their classical roles in neurotransmission and neurological disorders, PLGICs have been recently related to cell proliferation and cancer. Here, we focus on the best characterized eukaryotic channel, the glycine receptor (GlyR), to investigate its mutational patterns in genomic-wide tumor screens and compare them with mutations linked to hyperekplexia (HPX), a Mendelian neuromotor disease that disrupts glycinergic currents. Our analysis highlights that cancer mutations significantly accumulate across TM1 and TM2, partially overlapping with HPX changes. Based on 3D-clustering, conservation, and phenotypic data, we select three mutations near the pore, expected to impact GlyR conformation, for further study by molecular dynamics (MD). Using principal components from experimental GlyR ensembles as framework, we explore the motions involved in transitions from the human closed and desensitized structures and how they are perturbed by mutations. Our MD simulations show that WT GlyR spontaneously explores opening and re-sensitization transitions that are significantly impaired by mutations, resulting in receptors with altered permeability and desensitization properties in agreement with HPX functional data.

Phage display identification of nanomolar ligands for human NEDD4-WW3: Energetic and dynamic implications for the development of broad-spectrum antivirals

The recognition of PPxY viral Late domains by the third WW domain of the human HECT-E3 ubiquitin ligase NEDD4 (NEDD4-WW3) is essential for the budding of many viruses. Blocking these interactions is a promising strategy to develop broad-spectrum antivirals. As all WW domains, NEDD4-WW3 is a challenging therapeutic target due to the low binding affinity of its natural interactions, its high conformational plasticity, and its complex thermodynamic behavior. In this work, we set out to investigate whether high affinity can be achieved for monovalent ligands binding to the isolated NEDD4-WW3 domain. We show that a competitive phage-display set-up allows for the identification of high-affinity peptides showing inhibitory activity of viral budding. A detailed biophysical study combining calorimetry, nuclear magnetic resonance, and molecular dynamic simulations reveals that the improvement in binding affinity does not arise from the establishment of new interactions with the domain, but is associated to conformational restrictions imposed by a novel C-terminal -LFP motif in the ligand, unprecedented in the PPxY interactome. These results, which highlight the complexity of WW domain interactions, provide valuable insight into the key elements for high binding affinity, of interest to guide virtual screening campaigns for the identification of novel therapeutics targeting NEDD4-WW3 interactions.

Protein Fluctuations in Response to Random External Forces

Elastic network models (ENMs) have been widely used in the last decades to investigate protein motions and dynamics. There the intrinsic fluctuations based on the isolated structures are obtained from the normal modes of these elastic networks, and they generally show good agreement with the B-factors extracted from X-ray crystallographic experiments, which are commonly considered to be indicators of protein flexibility. In this paper, we propose a new approach to analyze protein fluctuations and flexibility, which has a more appropriate physical basis. It is based on the application of random forces to the protein ENM to simulate the effects of collisions of solvent on a protein structure. For this purpose, we consider both the Cα-atom coarse-grained anisotropic network model (ANM) and an elastic network augmented with points included for the crystallized waters. We apply random forces to these protein networks everywhere, as well as only on the protein surface alone. Despite the randomness of the directions of the applied perturbations, the computed average displacements of the protein network show a remarkably good agreement with the experimental B-factors. In particular, for our set of 919 protein structures, we find that the highest correlation with the B-factors is obtained when applying forces to the external surface of the water-augmented ANM (an overall gain of 3% in the Pearson’s coefficient for the entire dataset, with improvements up to 30% for individual proteins), rather than when evaluating the fluctuations obtained from the normal modes of a standard Cα-atom coarse-grained ANM. It follows that protein fluctuations should be considered not just as the intrinsic fluctuations of the internal dynamics, but also equally well as responses to external solvent forces, or as a combination of both.

Structure, mechanism and lipid-mediated remodeling of the mammalian Na+/H+ exchanger NHA2

The Na⁺/H⁺ exchanger SLC9B2, also known as NHA2, correlates with the long-sought-after Na⁺/Li⁺ exchanger linked to the pathogenesis of diabetes mellitus and essential hypertension in humans. Despite the functional importance of NHA2, structural information and the molecular basis for its ion-exchange mechanism have been lacking. Here we report the cryo-EM structures of bison NHA2 in detergent and in nanodiscs, at 3.0 and 3.5 Å resolution, respectively. The bison NHA2 structure, together with solid-state membrane-based electrophysiology, establishes the molecular basis for electroneutral ion exchange. NHA2 consists of 14 transmembrane (TM) segments, rather than the 13 TMs previously observed in mammalian Na⁺/H⁺ exchangers (NHEs) and related bacterial antiporters. The additional N-terminal helix in NHA2 forms a unique homodimer interface with a large intracellular gap between the protomers, which closes in the presence of phosphoinositol lipids. We propose that the additional N-terminal helix has evolved as a lipid-mediated remodeling switch for the regulation of NHA2 activity.

Parameterizing elastic network models to capture the dynamics of proteins

Coarse-grained normal mode analyses of protein dynamics rely on the idea that the geometry of a protein structure contains enough information for computing its fluctuations around its equilibrium conformation. This geometry is captured in the form of an elastic network (EN), namely a network of edges between its residues. The normal modes of a protein are then identified with the normal modes of its EN. Different approaches have been proposed to construct ENs, focusing on the choice of the edges that they are comprised of, and on their parameterizations by the force constants associated with those edges. Here we propose new tools to guide choices on these two facets of EN. We study first different geometric models for ENs. We compare cutoff-based ENs, whose edges have lengths that are smaller than a cutoff distance, with Delaunay-based ENs and find that the latter provide better representations of the geometry of protein structures. We then derive an analytical method for the parameterization of the EN such that its dynamics leads to atomic fluctuations that agree with experimental B-factors. To limit overfitting, we attach a parameter referred to as flexibility constant to each atom instead of to each edge in the EN. The parameterization is expressed as a non-linear optimization problem whose parameters describe both rigid-body and internal motions. We show that this parameterization leads to improved ENs, whose dynamics mimic MD simulations better than ENs with uniform force constants, and reduces the number of normal modes needed to reproduce functional conformational changes.

Transcription factor allosteric regulation through substrate coordination to zinc

The development of new synthetic biology circuits for biotechnology and medicine requires deeper mechanistic insight into allosteric transcription factors (aTFs). Here we studied the aTF UxuR, a homodimer of two domains connected by a highly flexible linker region. To explore how ligand binding to UxuR affects protein dynamics we performed molecular dynamics simulations in the free protein, the aTF bound to the inducer D-fructuronate or the structural isomer D-glucuronate. We then validated our results by constructing a sensor plasmid for D-fructuronate in Escherichia coli and performed site-directed mutagenesis. Our results show that zinc coordination is necessary for UxuR function since mutation to alanines prevents expression de-repression by D-fructuronate. Analyzing the different complexes, we found that the disordered linker regions allow the N-terminal domains to display fast and large movements. When the inducer is bound, UxuR can sample an open conformation with a more pronounced negative charge at the surface of the N-terminal DNA binding domains. In opposition, in the free and D-glucuronate bond forms the protein samples closed conformations, with a more positive character at the surface of the DNA binding regions. These molecular insights provide a new basis to harness these systems for biological systems engineering.

Structure and Dynamics of an Archeal Monoglyceride Lipase from Palaeococcus ferrophilus as Revealed by Crystallography and In Silico Analysis

The crystallographic analysis of a lipase from Palaeococcus ferrophilus (PFL) previously annotated as a lysophospholipase revealed high structural conservation with other monoglyceride lipases, in particular in the lid domain and substrate binding pockets. In agreement with this observation, PFL was shown to be active on various monoacylglycerols. Molecular Dynamics (MD) studies performed in the absence and in the presence of ligands further allowed characterization of the dynamics of this system and led to a systematic closure of the lid compared to the crystal structure. However, the presence of ligands in the acyl-binding pocket stabilizes intermediate conformations compared to the crystal and totally closed structures. Several lid-stabilizing or closure elements were highlighted, i.e., hydrogen bonds between Ser117 and Ile204 or Asn142 and its facing amino acid lid residues, as well as Phe123. Thus, based on this complementary crystallographic and MD approach, we suggest that the crystal structure reported herein represents an open conformation, at least partially, of the PFL, which is likely stabilized by the ligand, and it brings to light several key structural features prone to participate in the closure of the lid.

Structures of ISCth4 transpososomes reveal the role of asymmetry in copy-out/paste-in DNA transposition

Copy-out/paste-in transposition is a major bacterial DNA mobility pathway. It contributes significantly to the emergence of antibiotic resistance, often by upregulating expression of downstream genes upon integration. Unlike other transposition pathways, it requires both asymmetric and symmetric strand transfer steps. Here, we report the first structural study of a copy-out/paste-in transposase and demonstrate its ability to catalyze all pathway steps in vitro. X-ray structures of ISCth4 transposase, a member of the IS256 family of insertion sequences, bound to DNA substrates corresponding to three sequential steps in the reaction reveal an unusual asymmetric dimeric transpososome. During transposition, an array of N-terminal domains binds a single transposon end while the catalytic domain moves to accommodate the varying substrates. These conformational changes control the path of DNA flanking the transposon end and the generation of DNA-binding sites. Our results explain the asymmetric outcome of the initial strand transfer and show how DNA binding is modulated by the asymmetric transposase to allow the capture of a second transposon end and to integrate a circular intermediate.

Structure and elevator mechanism of the mammalian sodium/proton exchanger NHE9

Na+ /H+ exchangers (NHEs) are ancient membrane-bound nanomachines that work to regulate intracellular pH, sodium levels and cell volume. NHE activities contribute to the control of the cell cycle, cell proliferation, cell migration and vesicle trafficking. NHE dysfunction has been linked to many diseases, and they are targets of pharmaceutical drugs. Despite their fundamental importance to cell homeostasis and human physiology, structural information for the mammalian NHE was lacking. Here, we report the cryogenic electron microscopy structure of NHE isoform 9 (SLC9A9) from Equus caballus at 3.2 Å resolution, an endosomal isoform highly expressed in the brain and associated with autism spectrum (ASD) and attention deficit hyperactivity (ADHD) disorders. Despite low sequence identity, the NHE9 architecture and ion-binding site are remarkably similar to distantly related bacterial Na+ /H+  antiporters with 13 transmembrane segments. Collectively, we reveal the conserved architecture of the NHE ion-binding site, their elevator-like structural transitions, the functional implications of autism disease mutations and the role of phosphoinositide lipids to promote homodimerization that, together, have important physiological ramifications.

eBDIMS server: protein transition pathways with ensemble analysis in 2D-motion spaces

SUMMARY

Understanding how proteins transition between different conformers, and how conformers relate to each other in terms of structure and function, is not trivial. Here, we present an online tool for transition pathway generation between two protein conformations using Elastic Network Driven Brownian Dynamics Importance Sampling, a coarse-grained simulation algorithm, which spontaneously predicts transition intermediates trapped experimentally. In addition to path-generation, the server provides an interactive 2D-motion landscape graphical representation of the transitions or any additional conformers to explore their structural relationships.

AVAILABILITY AND IMPLEMENTATION

eBDIMS is available online: http://ebdims.biophysics.se/ or as standalone software: https://github.com/laura-orellana/eBDIMS, https://github.com/cabergh/eBDIMS.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Investigation of bound and unbound phosphoserine phosphatase conformations through elastic network models and molecular dynamics simulations

The human phosphoserine phosphatase (hPSP) catalyses the last step in the biosynthesis of L-serine. It involves conformational changes of the enzyme lid once the substrate, phosphoserine (PSer), is bound in the active site. Here, Elastic Network Model (ENM) is applied to the crystal structure of hPSP to probe the transition between open and closed conformations of hPSP. Molecular Dynamics (MD) simulations are carried out on several PSer-hPSP systems to characterise the intermolecular interactions and their effect on the dynamics of the enzyme lid. Systems involving either Ca⁺⁺ or Mg⁺⁺ are considered. The first ENM normal mode shows that an open-closed transition can be explained from a simple description of the enzyme in terms of harmonic potentials. Principal Component Analyses applied to the MD trajectories also highlight a trend for a closing/opening motion. Different PSer orientations inside the enzyme cavity are identified, i.e. either the carboxylate, the phosphate group of PSer, or both, are oriented towards the cation. The interaction patterns are analysed in terms of hydrogen bonds, electrostatics, and bond critical points of the electron density distributions. The latter approach yields a global description of the bonding intermolecular interactions. The PSer orientation determines the content of the cation coordination shell and the mobility of the substrate, while Lys158 and Thr182, involved in the reaction mechanism, are always in interaction with the substrate. Closed enzyme conformations involve Met52-Gln204, Arg49-Glu29, and Arg50-Glu29 interactions. Met52, as well as Arg49 and Arg50, also stabilize PSer inside the cavity. Communicated by Ramaswamy H. Sarma.

Large-Scale Conformational Changes and Protein Function: Breaking the in silico Barrier

Large-scale conformational changes are essential to link protein structures with their function at the cell and organism scale, but have been elusive both experimentally and computationally. Over the past few years developments in cryo-electron microscopy and crystallography techniques have started to reveal multiple snapshots of increasingly large and flexible systems, deemed impossible only short time ago. As structural information accumulates, theoretical methods become central to understand how different conformers interconvert to mediate biological function. Here we briefly survey current in silico methods to tackle large conformational changes, reviewing recent examples of cross-validation of experiments and computational predictions, which show how the integration of different scale simulations with biological information is already starting to break the barriers between the in silico, in vitro, and in vivo worlds, shedding new light onto complex biological problems inaccessible so far.

ProSNEx: a web-based application for exploration and analysis of protein structures using network formalism

ProSNEx (Protein Structure Network Explorer) is a web service for construction and analysis of Protein Structure Networks (PSNs) alongside amino acid flexibility, sequence conservation and annotation features. ProSNEx constructs a PSN by adding nodes to represent residues and edges between these nodes using user-specified interaction distance cutoffs for either carbon-alpha, carbon-beta or atom-pair contact networks. Different types of weighted networks can also be constructed by using either (i) the residue-residue interaction energies in the format returned by gRINN, resulting in a Protein Energy Network (PEN); (ii) the dynamical cross correlations from a coarse-grained Normal Mode Analysis (NMA) of the protein structure; (iii) interaction strength. Upon construction of the network, common network metrics (such as node centralities) as well as shortest paths between nodes and k-cliques are calculated. Moreover, additional features of each residue in the form of conservation scores and mutation/natural variant information are included in the analysis. By this way, tool offers an enhanced and direct comparison of network-based residue metrics with other types of biological information. ProSNEx is free and open to all users without login requirement at http://prosnex-tool.com.

ESR Resolves the C Terminus Structure of the Ligand-free Human Glutathione S-Transferase A1-1

Nitroxide- and Cu²⁺-based electron spin resonance (ESR) are combined to provide insight into the conformational states of the functionally important α-helix of the human glutathione S-transferase A1. Distance measurements on various spin-labeled dimeric human glutathione S-transferase A1-1 all result in bimodal distance distributions, indicating that the C-terminus exists in two distinct conformations in solution, one of which closely matches that found in the crystal structure of the ligand-bound enzyme. These measurements permit the generation of a model of the unliganded conformation. Room temperature ESR indicates that the second conformation has high mobility, potentially enabling the enzyme's high degree of substrate promiscuity. This model is then validated using computational modeling and further Cu²⁺-based ESR distance measurements. Cu²⁺-based ESR also provides evidence that the secondary structure of the second conformation is of helical nature. Addition of S-hexyl glutathione results in a shift in relative populations, favoring the state that is similar to the previously known structure of the ligand-bound enzyme.

Advances in coarse-grained modeling of macromolecular complexes

Recent progress in coarse-grained (CG) molecular modeling and simulation has facilitated an influx of computational studies on biological macromolecules and their complexes. Given the large separation of length-scales and time-scales that dictate macromolecular biophysics, CG modeling and simulation are well-suited to bridge the microscopic and mesoscopic or macroscopic details observed from all-atom molecular simulations and experiments, respectively. In this review, we first summarize recent innovations in the development of CG models, which broadly include structure-based, knowledge-based, and dynamics-based approaches. We then discuss recent applications of different classes of CG models to explore various macromolecular complexes. Finally, we conclude with an outlook for the future in this ever-growing field of biomolecular modeling.

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.

Computational Exploration of Conformational Transitions in Protein Drug Targets

Protein drug targets vary from highly structured to completely disordered; either way dynamics governs function. Hence, understanding the dynamical aspects of how protein targets function can enable improved interventions with drug molecules. Computational approaches offer highly detailed structural models of protein dynamics which are becoming more predictive as model quality and sampling power improve. However, the most advanced and popular models still have errors owing to imperfect parameter sets and often cannot access longer timescales of many crucial biological processes. Experimental approaches offer more certainty but can struggle to detect and measure lightly populated conformations of target proteins and subtle allostery. An emerging solution is to integrate available experimental data into advanced molecular simulations. In the future, molecular simulation in combination with experimental data may be able to offer detailed models of important drug targets such that improved functional mechanisms or selectivity can be accessed.

Elastic network model of learned maintained contacts to predict protein motion

We present a novel elastic network model, lmcENM, to determine protein motion even for localized functional motions that involve substantial changes in the protein's contact topology. Existing elastic network models assume that the contact topology remains unchanged throughout the motion and are thus most appropriate to simulate highly collective function-related movements. lmcENM uses machine learning to differentiate breaking from maintained contacts. We show that lmcENM accurately captures functional transitions unexplained by the classical ENM and three reference ENM variants, while preserving the simplicity of classical ENM. We demonstrate the effectiveness of our approach on a large set of proteins covering different motion types. Our results suggest that accurately predicting a "deformation-invariant" contact topology offers a promising route to increase the general applicability of ENMs. We also find that to correctly predict this contact topology a combination of several features seems to be relevant which may vary slightly depending on the protein. Additionally, we present case studies of two biologically interesting systems, Ferric Citrate membrane transporter FecA and Arachidonate 15-Lipoxygenase.

Comparative Normal Mode Analysis of the Dynamics of DENV and ZIKV Capsids

Key steps in the life cycle of a virus, such as the fusion event as the virus infects a host cell and its maturation process, relate to an intricate interplay between the structure and the dynamics of its constituent proteins, especially those that define its capsid, much akin to an envelope that protects its genomic material. We present a comprehensive, comparative analysis of such interplay for the capsids of two viruses from the flaviviridae family, Dengue (DENV) and Zika (ZIKV). We use for that purpose our own software suite, DD-NMA, which is based on normal mode analysis. We describe the elements of DD-NMA that are relevant to the analysis of large systems, such as virus capsids. In particular, we introduce our implementation of simplified elastic networks and justify their parametrization. Using DD-NMA, we illustrate the importance of packing interactions within the virus capsids on the dynamics of the E proteins of DENV and ZIKV. We identify differences between the computed atomic fluctuations of the E proteins in DENV and ZIKV and relate those differences to changes observed in their high resolution structures. We conclude with a discussion on additional analyses that are needed to fully characterize the dynamics of the two viruses.

A multi-resolution model to capture both global fluctuations of an enzyme and molecular recognition in the ligand-binding site

In multi-resolution simulations, different system components are simultaneously modeled at different levels of resolution, these being smoothly coupled together. In the case of enzyme systems, computationally expensive atomistic detail is needed in the active site to capture the chemistry of ligand binding. Global properties of the rest of the protein also play an essential role, determining the structure and fluctuations of the binding site; however, these can be modeled on a coarser level. Similarly, in the most computationally efficient scheme only the solvent hydrating the active site requires atomistic detail. We present a methodology to couple atomistic and coarse-grained protein models, while solvating the atomistic part of the protein in atomistic water. This allows a free choice of which protein and solvent degrees of freedom to include atomistically. This multi-resolution methodology can successfully model stable ligand binding, and we further confirm its validity by exploring the reproduction of system properties relevant to enzymatic function. In addition to a computational speedup, such an approach can allow the identification of the essential degrees of freedom playing a role in a given process, potentially yielding new insights into biomolecular function. Proteins 2016; 84:1902-1913. © 2016 Wiley Periodicals, Inc.

Prediction and validation of protein intermediate states from structurally rich ensembles and coarse-grained simulations

Protein conformational changes are at the heart of cell functions, from signalling to ion transport. However, the transient nature of the intermediates along transition pathways hampers their experimental detection, making the underlying mechanisms elusive. Here we retrieve dynamic information on the actual transition routes from principal component analysis (PCA) of structurally-rich ensembles and, in combination with coarse-grained simulations, explore the conformational landscapes of five well-studied proteins. Modelling them as elastic networks in a hybrid elastic-network Brownian dynamics simulation (eBDIMS), we generate trajectories connecting stable end-states that spontaneously sample the crystallographic motions, predicting the structures of known intermediates along the paths. We also show that the explored non-linear routes can delimit the lowest energy passages between end-states sampled by atomistic molecular dynamics. The integrative methodology presented here provides a powerful framework to extract and expand dynamic pathway information from the Protein Data Bank, as well as to validate sampling methods in general.

Protein conformational changes are key to a wide range of cellular functions but remain difficult to access experimentally. Here the authors describe eBDIMS, a novel approach to predict intermediates observed in structural transition pathways from experimental ensembles.

On the Applicability of Elastic Network Models for the Study of RNA CUG Trinucleotide Repeat Overexpansion

Non-coding RNAs play a pivotal role in a number of diseases promoting an aberrant sequestration of nuclear RNA-binding proteins. In the particular case of myotonic dystrophy type 1 (DM1), a multisystemic autosomal dominant disease, the formation of large non-coding CUG repeats set up long-tract hairpins able to bind muscleblind-like proteins (MBNL), which trigger the deregulation of several splicing events such as cardiac troponin T (cTNT) and insulin receptor’s, among others. Evidence suggests that conformational changes in RNA are determinant for the recognition and binding of splicing proteins, molecular modeling simulations can attempt to shed light on the structural diversity of CUG repeats and to understand their pathogenic mechanisms. Molecular dynamics (MD) are widely used to obtain accurate results at atomistic level, despite being very time consuming, and they contrast with fast but simplified coarse-grained methods such as Elastic Network Model (ENM). In this paper, we assess the application of ENM (traditionally applied on proteins) for studying the conformational space of CUG repeats and compare it to conventional and accelerated MD conformational sampling. Overall, the results provided here reveal that ANM can provide useful insights into dynamic rCUG structures at a global level, and that their dynamics depend on both backbone and nucleobase fluctuations. On the other hand, ANM fail to describe local U-U dynamics of the rCUG system, which require more computationally expensive methods such as MD. Given that several limitations are inherent to both methods, we discuss here the usefulness of the current theoretical approaches for studying highly dynamic RNA systems such as CUG trinucleotide repeat overexpansions.

New generation of elastic network models

The intrinsic flexibility of proteins and nucleic acids can be grasped from remarkably simple mechanical models of particles connected by springs. In recent decades, Elastic Network Models (ENMs) combined with Normal Model Analysis widely confirmed their ability to predict biologically relevant motions of biomolecules and soon became a popular methodology to reveal large-scale dynamics in multiple structural biology scenarios. The simplicity, robustness, low computational cost, and relatively high accuracy are the reasons behind the success of ENMs. This review focuses on recent advances in the development and application of ENMs, paying particular attention to combinations with experimental data. Successful application scenarios include large macromolecular machines, structural refinement, docking, and evolutionary conservation.

Molecular dynamics simulations: advances and applications

Molecular dynamics simulations have evolved into a mature technique that can be used effectively to understand macromolecular structure-to-function relationships. Present simulation times are close to biologically relevant ones. Information gathered about the dynamic properties of macromolecules is rich enough to shift the usual paradigm of structural bioinformatics from studying single structures to analyze conformational ensembles. Here, we describe the foundations of molecular dynamics and the improvements made in the direction of getting such ensemble. Specific application of the technique to three main issues (allosteric regulation, docking, and structure refinement) is discussed.

Correlated motions are a fundamental property of β-sheets

Correlated motions in proteins can mediate fundamental biochemical processes such as signal transduction and allostery. The mechanisms that underlie these processes remain largely unknown due mainly to limitations in their direct detection. Here, based on a detailed analysis of protein structures deposited in the protein data bank, as well as on state-of-the art molecular simulations, we provide general evidence for the transfer of structural information by correlated backbone motions, mediated by hydrogen bonds, across β-sheets. We also show that the observed local and long-range correlated motions are mediated by the collective motions of β-sheets and investigate their role in large-scale conformational changes. Correlated motions represent a fundamental property of β-sheets that contributes to protein function.

iMODS: internal coordinates normal mode analysis server

Normal mode analysis (NMA) in internal (dihedral) coordinates naturally reproduces the collective functional motions of biological macromolecules. iMODS facilitates the exploration of such modes and generates feasible transition pathways between two homologous structures, even with large macromolecules. The distinctive internal coordinate formulation improves the efficiency of NMA and extends its applicability while implicitly maintaining stereochemistry. Vibrational analysis, motion animations and morphing trajectories can be easily carried out at different resolution scales almost interactively. The server is versatile; non-specialists can rapidly characterize potential conformational changes, whereas advanced users can customize the model resolution with multiple coarse-grained atomic representations and elastic network potentials. iMODS supports advanced visualization capabilities for illustrating collective motions, including an improved affine-model-based arrow representation of domain dynamics. The generated all-heavy-atoms conformations can be used to introduce flexibility for more advanced modeling or sampling strategies. The server is free and open to all users with no login requirement at http://imods.chaconlab.org.

A theoretical view of protein dynamics

Proteins are fascinating supramolecular structures, which are able to recognize ligands transforming binding information into chemical signals. They can transfer information across the cell, can catalyse complex chemical reactions, and are able to transform energy into work with much more efficiency than any human engine. The unique abilities of proteins are tightly coupled with their dynamic properties, which are coded in a complex way in the sequence and carefully refined by evolution. Despite its importance, our experimental knowledge of protein dynamics is still rather limited, and mostly derived from theoretical calculations. I will review here, in a systematic way, the current state-of-the-art theoretical approaches to the study of protein dynamics, emphasizing the most recent advances, examples of use and the expected lines of development in the near future.

Elastic Network Models of Nucleic Acids Flexibility

Elastic network models (ENMs) are a useful tool for describing large scale motions in protein systems. While they are well validated in the context of proteins, relatively little is known about their applicability to nucleic acids, whose different architecture does not necessarily warrant comparable performance. In this study we thoroughly evaluate and optimize the efficiency of popular ENMs for capturing RNA and DNA flexibility. We also introduce two alternative models in which the strength of elastic connections at a coarse-grained level is governed by distance distribution at atomic resolution. For each of the considered ENMs we report the optimal length of spring connections as well as the scaling of elastic force constants that provides the best agreement of vibrational frequencies with normal modes based on atomic force field. In order to determine the absolute values of force constants we introduce a novel method based on the overlap of pseudoinverse of Hessian matrices.

Robust Heterogeneous Anisotropic Elastic Network Model Precisely Reproduces the Experimental B-factors of Biomolecules

A computational method called the progressive fluctuation matching (PFM) is developed for constructing robust heterogeneous anisotropic network models (HANMs) for biomolecular systems. An HANM derived through the PFM approach consists of harmonic springs with realistic positive force constants, and yields the calculated B-factors that are basically identical to the experimental ones. For the four tested protein systems including crambin, trypsin inhibitor, HIV-1 protease, and lysozyme, the root-mean-square deviations between the experimental and the computed B-factors are only 0.060, 0.095, 0.247, and 0.049 Å(2), respectively, and the correlation coefficients are 0.99 for all. By comparing the HANM/ANM normal modes to their counterparts derived from both an atomistic force field and an NMR structure ensemble, it is found that HANM may provide more accurate results on protein dynamics.

Exploration of conformational transition pathways from coarse-grained simulations

MOTIVATION

A new algorithm to trace conformational transitions in proteins is presented. The method uses discrete molecular dynamics as engine to sample protein conformational space. A multiple minima Go-like potential energy function is used in combination with several enhancing sampling strategies, such as metadynamics, Maxwell Demon molecular dynamics and essential dynamics. The method, which shows an unprecedented computational efficiency, is able to trace a wide range of known experimental transitions. Contrary to simpler methods our strategy does not introduce distortions in the chemical structure of the protein and is able to reproduce well complex non-linear conformational transitions. The method, called GOdMD, can easily introduce additional restraints to the transition (presence of ligand, known intermediate, known maintained contacts, …) and is freely distributed to the community through the Spanish National Bioinformatics Institute (http://mmb.irbbarcelona.org/GOdMD).

AVAILABILITY

Freely available on the web at http://mmb.irbbarcelona.org/GOdMD.

PIM: phase integrated method for normal mode analysis of biomolecules in a crystalline environment

In this study, a normal mode analysis, named phase integrated method (PIM), is developed for computing modes of biomolecules in a crystalline environment. PIM can calculate low-frequency modes on one or a few asymmetric units (AUs) and generate exact modes of a whole unit cell according to space group symmetry, while the translational symmetry between unit cells is maintained via the periodic boundary condition. Therefore, the method can dramatically reduce computational cost in mode calculation in the presence of crystal symmetry. PIM also has an option to map modes onto a single AU to form an orthonormalized mode set, which can be directly applied to normal-mode-based thermal parameter refinement in X-ray crystallography. The performance of PIM was tested on all 65 space groups available in protein crystals (one protein for each space group) and on another set of 83 ultra-high-resolution X-ray structures. The results showed that considering space group symmetry in mode calculation is crucial for accurately describing vibrational motion in a crystalline environment. Moreover, the optimal inter-AU packing stiffness was found to be about 60% of that of intra-AU interactions (non-bonded interaction only).

Optimization of Algorithms for Modeling Protein Structural Transitions from Sparse Long-Range Spin-Label Distance Constraints

Function-related structural transitions of proteins are often large-scale conformational changes that are related to essential dynamics of a protein, which in turn proceeds along a small number of slow normal modes. Hence, it should be possible to characterize such transitions by an equally small number of distance constraints. These constraints should contain the information how the backbone coordinates move along the active normal modes. Such an approach based on residue-level elastic network models for the protein backbone is optimized with respect to the fit algorithm, constraint selection, and parametrization of the elastic network model. A stable fitting algorithm can be based on energy equipartitioning among the modes in the active space. This stabilization allows for extending active space dimension beyond the number of available constraints, which improves fit quality for transitions with a normal mode spectrum of only slowly increasing frequencies. In constraint selection, discrimination between the active normal modes appears to be more important than achieving large distance changes between initial and final structure. Parametrization of the network model has only a small influence on fit quality, as long as scaling of force constants with the inverse sixth power of the distance between network nodes is maintained. Elastic network models with a uniform force constant below a cutoff distance perform significantly worse. With 50 distance constraints, the optimized approach covers more than 50% of the structural change for 44% of all test cases, between 25 and 50% for 22% of the cases, and it fails for 33%.

Comparing proteins by their internal dynamics: exploring structure-function relationships beyond static structural alignments

The growing interest for comparing protein internal dynamics owes much to the realisation that protein function can be accompanied or assisted by structural fluctuations and conformational changes. Analogously to the case of functional structural elements, those aspects of protein flexibility and dynamics that are functionally oriented should be subject to evolutionary conservation. Accordingly, dynamics-based protein comparisons or alignments could be used to detect protein relationships that are more elusive to sequence and structural alignments. Here we provide an account of the progress that has been made in recent years towards developing and applying general methods for comparing proteins in terms of their internal dynamics and advance the understanding of the structure-function relationship.

Elastic network normal modes provide a basis for protein structure refinement

It is well recognized that thermal motions of atoms in the protein native state, the fluctuations about the minimum of the global free energy, are well reproduced by the simple elastic network models (ENMs) such as the anisotropic network model (ANM). Elastic network models represent protein dynamics as vibrations of a network of nodes (usually represented by positions of the heavy atoms or by the C(α) atoms only for coarse-grained representations) in which the spatially close nodes are connected by harmonic springs. These models provide a reliable representation of the fluctuational dynamics of proteins and RNA, and explain various conformational changes in protein structures including those important for ligand binding. In the present paper, we study the problem of protein structure refinement by analyzing thermal motions of proteins in non-native states. We represent the conformational space close to the native state by a set of decoys generated by the I-TASSER protein structure prediction server utilizing template-free modeling. The protein substates are selected by hierarchical structure clustering. The main finding is that thermal motions for some substates, overlap significantly with the deformations necessary to reach the native state. Additionally, more mobile residues yield higher overlaps with the required deformations than do the less mobile ones. These findings suggest that structural refinement of poorly resolved protein models can be significantly enhanced by reduction of the conformational space to the motions imposed by the dominant normal modes.

Elastic Network Models are Robust to Variations in Formalism

Understanding the functions of biomolecules requires insight not only from structures, but from dynamics as well. Often, the most interesting processes occur on time scales too slow for exploration by conventional molecular dynamics (MD) simulations. For this reason, alternative computational methods such as elastic network models (ENMs) have become increasingly popular. These simple, coarse-grained models represent molecules as beads connected by harmonic springs; the system's motions are solved analytically by normal mode analysis. In the past few years, many different formalisms for performing ENM calculations have emerged, and several have been optimized using all-atom MD simulations. In contrast to other studies, we have compared the various formalisms in a systematic, quantitative way. In this study, we optimize many ENM functional forms using a uniform dataset containing only long (> 1 μs) all-atom MD simulations. Our results show that all models once optimized produce spring constants for immediate neighboring residues that are orders of magnitude stiffer than more distal contacts. In addition, the statistical significance of ENM performance varied with model resolution. We also show that fitting long trajectories does not improve ENM performance due to a problem inherent in all network models tested: they underestimate the relative importance of the most concerted motions. Finally, we characterize ENMs' resilience by tessellating the parameter space to show that broad ranges of parameters produce similar quality predictions. Taken together our data reveals that choice of spring function and parameters are not vital to performance of a network model and that simple parameters can by derived "by hand" when no data is available for fitting, thus illustrating the robustness of these models.

Characterization of Protein Conformational Changes with Sparse Spin-Label Distance Constraints

The combination of site-directed spin labeling with pulse EPR distance measurements can provide a moderate number of distance constraints on the nanometer length scale for proteins in different states. By adapting an existing algorithm (Zheng, W.; Brooks, B. R. Biophys. J. 2006, 90, 4327) to the problem, we address the question to what extent conformational change can be characterized when the protein structure is known for one of the states, whereas only a sparse set of distance constraints between spin labels is available for the other state. We find that the type and general direction of the conformational change can be recognized, while the amplitude may be uncertain.

FlexE: Using elastic network models to compare models of protein structure

It is often valuable to compare protein structures to determine how similar they are. Structure comparison methods such as RMSD and GDT-TS are based solely on fixed geometry and do not take into account the intrinsic flexibility or energy landscape of the protein. We propose a method, which we call FlexE, that is based on a simple elastic network model and uses the deformation energy as measure of the similarity between two structures. FlexE can distinguish biologically relevant conformational changes from random changes, while existing geometry-based methods cannot. Additionally, FlexE incorporates the concept of thermal energy, which provides a rational way to determine when two models are "the same". FlexE provides a unique measure of the similarity between protein structures that is complementary to existing methods.

iMod: multipurpose normal mode analysis in internal coordinates

MOTIVATION

Dynamic simulations of systems with biologically relevant sizes and time scales are critical for understanding macromolecular functioning. Coarse-grained representations combined with normal mode analysis (NMA) have been established as an alternative to atomistic simulations. The versatility and efficiency of current approaches normally based on Cartesian coordinates can be greatly enhanced with internal coordinates (IC).

RESULTS

Here, we present a new versatile tool chest to explore conformational flexibility of both protein and nucleic acid structures using NMA in IC. Consideration of dihedral angles as variables reduces the computational cost and non-physical distortions of classical Cartesian NMA methods. Our proposed framework operates at different coarse-grained levels and offers an efficient framework to conduct NMA-based conformational studies, including standard vibrational analysis, Monte-Carlo simulations or pathway exploration. Examples of these approaches are shown to demonstrate its applicability, robustness and efficiency.

CONTACT

pablo@chaconlab.org

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Coarse-grained representation of protein flexibility. Foundations, successes, and shortcomings

Flexibility is the key magnitude to understand the variety of functions of proteins. Unfortunately, its experimental study is quite difficult, and in fact, most experimental procedures are designed to reduce flexibility and allow a better definition of the structure. Theoretical approaches have become then the alternative but face serious timescale problems, since many biologically relevant deformation movements happen in a timescale that is far beyond the possibility of current atomistic models. In this complex scenario, coarse-grained simulation methods have emerged as a powerful and inexpensive alternative. Along this chapter, we will review these coarse-grained methods, and explain their physical foundations and their range of applicability.