Can conformational change be described by only a few normal modes?

Free Energy Surface and Molecular Mechanism of Slow Structural Transitions in Lipid Bilayers

Lipid membrane remodeling, crucial for many cellular processes, is governed by the coupling of membrane structure and shape fluctuations. Given the importance of the ∼ nm length scale, details of the transition intermediates for conformational change are not fully captured by a continuum-mechanical description. Slow dynamics and the lack of knowledge of reaction coordinates (RCs) for biasing methods pose a challenge for all-atom (AA) simulations. Here, we map system dynamics on Langevin dynamics in a normal mode space determined from an elastic network model representation for the lipid-water Hamiltonian. AA molecular dynamics (MD) simulations are used to determine model parameters, and Langevin dynamics predictions for bilayer structural, mechanical, and dynamic properties are validated against MD simulations and experiments. Transferability to describe the dynamics of a larger lipid bilayer and a heterogeneous membrane-protein system is assessed. A set of generic RCs for pore formation in two tensionless bilayers is obtained by coupling Langevin dynamics to the underlying energy landscape for membrane deformations. Structure evolution is carried out by AA MD, wherein the generic RCs are used in a path metadynamics or an umbrella sampling simulation to determine the thermodynamics of pore formation and its molecular determinants, such as the role of distinct bilayer motions, lipid solvation, and lipid packing.

Normal mode analysis and comparative study of intrinsic dynamics of alcohol oxidase enzymes from GMC protein family

Glucose-Methanol-Choline (GMC) family enzymes are very important in catalyzing the oxidation of a wide range of structurally diverse substrates. Enzymes that constitute the GMC family, share a common tertiary fold but < 25% sequence identity. Cofactor FAD, FAD binding signature motif, and similar structural scaffold of the active site are common features of oxidoreductase enzymes of the GMC family. Protein functionality mainly depends on protein three-dimensional structures and dynamics. In this study, we used the normal mode analysis method to search the intrinsic dynamics of GMC family enzymes. We have explored the dynamical behavior of enzymes with unique substrate catabolism and active site characteristics from different classes of the GMC family. Analysis of individual enzymes and comparative ensemble analysis of enzymes from different classes has shown conserved dynamic motion at FAD binding sites. The present study revealed that GMC enzymes share a strong dynamic similarity (Bhattacharyya coefficient >90% and root mean squared inner product >52%) despite low sequence identity across the GMC family enzymes. The study predicts that local deformation energy between atoms of the enzyme may be responsible for the catalysis of different substrates. This study may help that intrinsic dynamics can be used to make meaningful classifications of proteins or enzymes from different organisms.Communicated by Ramaswamy H. Sarma.

Analyzing the Geometry and Dynamics of Viral Structures: A Review of Computational Approaches Based on Alpha Shape Theory, Normal Mode Analysis, and Poisson-Boltzmann Theories

The current SARS-CoV-2 pandemic highlights our fragility when we are exposed to emergent viruses either directly or through zoonotic diseases. Fortunately, our knowledge of the biology of those viruses is improving. In particular, we have more and more structural information on virions, i.e., the infective form of a virus that includes its genomic material and surrounding protective capsid, and on their gene products. It is important to have methods that enable the analyses of structural information on such large macromolecular systems. We review some of those methods in this paper. We focus on understanding the geometry of virions and viral structural proteins, their dynamics, and their energetics, with the ambition that this understanding can help design antiviral agents. We discuss those methods in light of the specificities of those structures, mainly that they are huge. We focus on three of our own methods based on the alpha shape theory for computing geometry, normal mode analyses to study dynamics, and modified Poisson-Boltzmann theories to study the organization of ions and co-solvent and solvent molecules around biomacromolecules. The corresponding software has computing times that are compatible with the use of regular desktop computers. We show examples of their applications on some outer shells and structural proteins of the West Nile Virus.

Predicting allosteric sites using fast conformational sampling as guided by coarse-grained normal modes

To computationally identify cryptic binding sites for allosteric modulators, we have developed a fast and simple conformational sampling scheme guided by coarse-grained normal modes solved from the elastic network models followed by atomistic backbone and sidechain reconstruction. Despite the complexity of conformational changes associated with ligand binding, we previously showed that simply sampling along each of the lowest 30 modes can adequately restructure cryptic sites so they are detectable by pocket finding programs like Concavity. Here, we applied this method to study four classical examples of allosteric regulation (GluR2 receptor, GroEL chaperonin, GPCR, and myosin). Our method along with alternative methods has been utilized to locate known allosteric sites and predict new promising allosteric sites. Compared with other sampling methods based on extensive molecular dynamics simulation, our method is both faster (1-2 h for an average-size protein of ∼400 residues) and more flexible (it can be easily integrated with any structure-based pocket finding methods), so it is suitable for high-throughput screening of large datasets of protein structures at the genome scale.

Response of Terahertz Protein Vibrations to Ligand Binding: Calmodulin-Peptide Complexes as a Case Study

Terahertz vibrations are sensitive reporters of the structure and interactions of proteins. Ligand binding alters the nature and distribution of these collective vibrations. The ligand-induced changes in the terahertz protein vibrations contribute to the binding entropy and to the overall thermodynamic stability of the resultant protein-ligand complexes. Here, we have examined the response of the low-frequency (below 6 terahertz) collective vibrations of the calcium-loaded calmodulin (CaM) to binding to five different ligands, both in the presence and absence of water, using normal-mode analysis and molecular dynamics simulations. A comparison of the vibrational spectra of hydrated and dry systems reveals that protein-solvent interactions stiffen the terahertz protein vibrations and that these solvent-coupled collective vibrations contribute significantly to the hydration-sensitive variation in the vibrational entropy of CaM. In the absence of water, the low-frequency vibrations of CaM are stiffened by ligand binding. On the contrary, the number and the cumulative vibrational entropy of low-frequency vibrational modes (ω < 200 cm^-1) of the hydrated CaM are increased noticeably after binding to the peptides, indicating binding-induced softening of collective vibrations of the protein. Although the calculated and experimental binding affinities of the chosen complexes correlated reasonably well, no systematic correlation was observed between the protein vibrational entropy and the binding affinity. The results underscored the importance of the interplay of protein-ligand and solvent interactions in modulating the low-frequency vibrations of proteins.

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.

Inhibition of mutant RAS-RAF interaction by mimicking structural and dynamic properties of phosphorylated RAS

Undruggability of RAS proteins has necessitated alternative strategies for the development of effective inhibitors. In this respect, phosphorylation has recently come into prominence as this reversible post-translational modification attenuates sensitivity of RAS towards RAF. As such, in this study, we set out to unveil the impact of phosphorylation on dynamics of HRAS^WT and aim to invoke similar behavior in HRAS^G12D mutant by means of small therapeutic molecules. To this end, we performed molecular dynamics (MD) simulations using phosphorylated HRAS and showed that phosphorylation of Y32 distorted Switch I, hence the RAS/RAF interface. Consequently, we targeted Switch I in HRAS^G12D by means of approved therapeutic molecules and showed that the ligands enabled detachment of Switch I from the nucleotide-binding pocket. Moreover, we demonstrated that displacement of Switch I from the nucleotide-binding pocket was energetically more favorable in the presence of the ligand. Importantly, we verified computational findings in vitro where HRAS^G12D/RAF interaction was prevented by the ligand in HEK293T cells that expressed HRAS^G12D mutant protein. Therefore, these findings suggest that targeting Switch I, hence making Y32 accessible might open up new avenues in future drug discovery strategies that target mutant RAS proteins.

Multi-Targeted Approaches and Drug Repurposing Reveal Possible SARS-CoV-2 Inhibitors

The COVID-19 pandemic caused by SARS-CoV-2 is unprecedented in recent memory owing to the non-stop escalation in number of infections and deaths in almost every country of the world. The lack of treatment options further worsens the scenario, thereby necessitating the exploration of already existing US FDA-approved drugs for their effectiveness against COVID-19. In the present study, we have performed virtual screening of nutraceuticals available from DrugBank against 14 SARS-CoV-2 proteins. Molecular docking identified several inhibitors, two of which, rutin and NADH, displayed strong binding affinities and inhibitory potential against SARS-CoV-2 proteins. Further normal model-based simulations were performed to gain insights into the conformational transitions in proteins induced by the drugs. The computational analysis in the present study paves the way for experimental validation and development of multi-target guided inhibitors to fight COVID-19.

From System Modeling to System Analysis: The Impact of Resolution Level and Resolution Distribution in the Computer-Aided Investigation of Biomolecules

The ever increasing computer power, together with the improved accuracy of atomistic force fields, enables researchers to investigate biological systems at the molecular level with remarkable detail. However, the relevant length and time scales of many processes of interest are still hardly within reach even for state-of-the-art hardware, thus leaving important questions often unanswered. The computer-aided investigation of many biological physics problems thus largely benefits from the usage of coarse-grained models, that is, simplified representations of a molecule at a level of resolution that is lower than atomistic. A plethora of coarse-grained models have been developed, which differ most notably in their granularity; this latter aspect determines one of the crucial open issues in the field, i.e. the identification of an optimal degree of coarsening, which enables the greatest simplification at the expenses of the smallest information loss. In this review, we present the problem of coarse-grained modeling in biophysics from the viewpoint of system representation and information content. In particular, we discuss two distinct yet complementary aspects of protein modeling: on the one hand, the relationship between the resolution of a model and its capacity of accurately reproducing the properties of interest; on the other hand, the possibility of employing a lower resolution description of a detailed model to extract simple, useful, and intelligible information from the latter.

Predicting cryptic ligand binding sites based on normal modes guided conformational sampling

To greatly expand the druggable genome, fast and accurate predictions of cryptic sites for small molecules binding in target proteins are in high demand. In this study, we have developed a fast and simple conformational sampling scheme guided by normal modes solved from the coarse-grained elastic models followed by atomistic backbone refinement and side-chain repacking. Despite the observations of complex and diverse conformational changes associated with ligand binding, we found that simply sampling along each of the lowest 30 modes is near optimal for adequately restructuring cryptic sites so they can be detected by existing pocket finding programs like fpocket and concavity. We further trained machine-learning protocols to optimize the combination of the sampling-enhanced pocket scores with other dynamic and conservation scores, which only slightly improved the performance. As assessed based on a training set of 84 known cryptic sites and a test set of 14 proteins, our method achieved high accuracy of prediction (with area under the receiver operating characteristic curve >0.8) comparable to the CryptoSite server. Compared with CryptoSite and other methods based on extensive molecular dynamics simulation, our method is much faster (1-2 hours for an average-size protein) and simpler (using only pocket scores), so it is suitable for high-throughput processing of large datasets of protein structures at the genome scale.

Increasing the Sampling Efficiency of Protein Conformational Change by Combining a Modified Replica Exchange Molecular Dynamics and Normal Mode Analysis

Understanding conformational change at an atomic level is significant when determining a protein functional mechanism. Replica exchange molecular dynamics (REMD) is a widely used enhanced sampling method to explore protein conformational space. However, REMD with an explicit solvent model requires huge computational resources, immensely limiting its application. In this study, a variation of parallel tempering metadynamics (PTMetaD) with the omission of solvent-solvent interactions in exchange attempts and the use of low-frequency modes calculated by normal-mode analysis (NMA) as collective variables (CVs), namely ossPTMetaD, is proposed with the aim to accelerate MD simulations simultaneously in temperature and geometrical spaces. For testing the performance of ossPTMetaD, five protein systems with diverse biological functions and motion patterns were selected, including large-scale domain motion (AdK), flap movement (HIV-1 protease and BACE1), and DFG-motif flip in kinases (p38α and c-Abl). The simulation results showed that ossPTMetaD requires much fewer numbers of replicas than temperature REMD (T-REMD) with a reduction of ∼70% to achieve a similar exchange ratio. Although it does not obey the detailed balance condition, ossPTMetaD provides consistent results with T-REMD and experimental data. The high accessibility of the large conformational change of protein systems by ossPTMetaD, especially in simulating the very challenging DFG-motif flip of protein kinases, demonstrated its high efficiency and robustness in the characterization of the large-scale protein conformational change pathway and associated free energy profile.

Molecular Docking: Challenges, Advances and its Use in Drug Discovery Perspective

Molecular docking is a process through which small molecules are docked into the macromolecular structures for scoring its complementary values at the binding sites. It is a vibrant research area with dynamic utility in structure-based drug-designing, lead optimization, biochemical pathway and for drug designing being the most attractive tools. Two pillars for a successful docking experiment are correct pose and affinity prediction. Each program has its own advantages and drawbacks with respect to their docking accuracy, ranking accuracy and time consumption so a general conclusion cannot be drawn. Moreover, users don't always consider sufficient diversity in their test sets which results in certain programs to outperform others. In this review, the prime focus has been laid on the challenges of docking and troubleshooters in existing programs, underlying algorithmic background of docking, preferences regarding the use of docking programs for best results illustrated with examples, comparison of performance for existing tools and algorithms, state of art in docking, recent trends of diseases and current drug industries, evidence from clinical trials and post-marketing surveillance are discussed. These aspects of the molecular drug designing paradigm are quite controversial and challenging and this review would be an asset to the bioinformatics and drug designing communities.

Perturb-Scan-Pull: A Novel Method Facilitating Conformational Transitions in Proteins

Conformational transitions in proteins facilitate precise physiological functions. Therefore, it is crucial to understand the mechanisms underlying these processes to modulate protein function. Yet, studying structural and dynamical properties of proteins is notoriously challenging due to the complexity of the underlying potential energy surfaces (PES). We have previously developed the perturbation-response scanning (PRS) method to identify key residues that participate in the communication network responsible for specific conformational transitions. PRS is based on a residue-by-residue scan of the protein to determine the subset of residues/forces which provide the closest conformational change leading to a target conformational state, inasmuch as linear response theory applies to these motions. Here, we develop a novel method to further evaluate if conformational transitions may be triggered on the PES. We aim to study functionally relevant conformational transitions in proteins by using results obtained from PRS and feeding them as inputs to steered molecular dynamics simulations. The success and the transferability of the method are evaluated on three protein systems having different complexities of motion on the PES: calmodulin, adenylate kinase, and bacterial ferric binding protein. We find that the method captures the target conformation, while providing key residues and the optimum paths with relatively low free energy profiles.

Correlation Between Allosteric and Orthosteric Sites

Correlation between an allosteric site and its orthosteric site refers to the phenomenon that perturbations like ligand binding, mutation, or posttranslational modifications at the allosteric site leverage variation in the orthosteric site. Understanding this kind of correlation not only helps to disclose how information is transmitted in allosteric regulation but also provides clues for allosteric drug discovery. This chapter starts with an overview of correlation studies on allosteric and orthosteric sites and then introduces recent progress in evolutionary and simulation-based dynamic studies. Discussions and perspectives on future directions are also given.

Coarse-grained dynamics of supramolecules: Conformational changes in outer shells of Dengue viruses

While structural data on viruses are more and more common, information on their dynamics is much harder to obtain as those viruses form very large molecular complexes. In this paper, we propose a new method for computing the coarse-grained normal modes of such supra-molecules, NormalGo. A new formalism is developed to represent the Hessian of a quadratic potential using tensor products. This formalism is applied to the Tirion elastic potential, as well as to a Gō like potential. When combined with a fast method for computing a select set of eigenpairs of the Hessian, this new formalism enables the computation of thousands of normal modes of a full viral shell with more than one hundred thousand atoms in less than 2 h on a standard desktop computer. We then compare the two coarse-grained potentials. We show that, despite significant differences in their formulations, the Tirion and the Gō like potentials capture very similar dynamics characteristics of the molecule under study. However, we find that the Gō like potential should be preferred as it leads to less local deformations in the structure of the molecule during normal mode dynamics. Finally, we use NormalGo to characterize the structural transitions that occur when FAB fragments bind to the icosahedral outer shell of serotype 3 of the Dengue virus. We have identified residues at the surface of the outer shell that are important for the transition between the FAB-free and FAB-bound conformations, and therefore potentially useful for the design of antibodies to Dengue viruses.

Theoretical framework for analyzing structural compliance properties of proteins

We propose methods for directly analyzing structural compliance (SC) properties of elastic network models of proteins, and we also propose methods for extracting information about motion properties from the SC properties. The analysis of SC properties involves describing the relationships between the applied forces and the deformations. When decomposing the motion according to the magnitude of SC (SC mode decomposition), we can obtain information about the motion properties under the assumption that the lower SC mode motions or the softer motions occur easily. For practical applications, the methods are formulated in a general form. The parts where forces are applied and those where deformations are evaluated are separated from each other for enabling the analyses of allosteric interactions between the specified parts. The parts are specified not only by the points but also by the groups of points (the groups are treated as flexible bodies). In addition, we propose methods for quantitatively evaluating the properties based on the screw theory and the considerations of the algebraic structures of the basic equations expressing the SC properties. These methods enable quantitative discussions about the relationships between the SC mode motions and the motions estimated from two different conformations; they also help identify the key parts that play important roles for the motions by comparing the SC properties with those of partially constrained models. As application examples, lactoferrin and ATCase are analyzed. The results show that we can understand their motion properties through their lower SC mode motions or the softer motions.

Dewetting during Terahertz Vibrations of Nanoparticles

We use molecular simulations to demonstrate the formation of a vacuum layer around a vibrating nanoparticle in a liquid. This vacuum layer forms readily for high frequencies with respect to the characteristic vibrational (Einstein) frequency of the fluid, even with small amplitude vibrations. The opposite is true for low frequencies, where large amplitudes are required to demonstrate the vacuum layer. With the vacuum layer forming, the quality factor of the oscillations increases substantially. The findings provide an interpretation of our recent experiments that show the onset of high-quality resonances of nanoparticles in water ( Xiang et al. Nano Lett. 2016 , 16 , 3638 ) in the gigahertz to terahertz range.

Computational studies of G protein-coupled receptor complexes: Structure and dynamics

G protein-coupled receptors (GPCRs) are ubiquitously expressed transmembrane proteins associated with a wide range of diseases such as Alzheimer's, Parkinson, schizophrenia, and also implicated in in several abnormal heart conditions. As such, this family of receptors is regarded as excellent drug targets. However, due to the high number of intracellular signaling partners, these receptors have a complex interaction networks and it becomes challenging to modulate their function. Experimentally determined structures give detailed information on the salient structural properties of these signaling complexes but they are far away from providing mechanistic insights into the underlying process. This chapter presents some of the computational tools, namely molecular dynamics, molecular docking, and molecular modeling and related analyses methods that have been used to complement experimental findings.

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.

Peptide Inhibitors Targeting the Neisseria gonorrhoeae Pivotal Anaerobic Respiration Factor AniA

Neisseria gonorrhoeae causes the sexually transmitted infection gonorrhea, which is highly prevalent worldwide and has a major impact on reproductive and neonatal health. The superbug status of N. gonorrhoeae necessitates the development of drugs with different mechanisms of action. Here, we focused on targeting the nitrite reductase AniA, which is a pivotal component of N. gonorrhoeae anaerobic respiration and biofilm formation. Our studies showed that gonococci expressing AniA containing the altered catalytic residues D137A and H280A failed to grow under anaerobic conditions, demonstrating that the nitrite reductase function is essential. To facilitate the pharmacological targeting of AniA, new crystal structures of AniA were refined to 1.90-Å and 2.35-Å resolutions, and a phage display approach with libraries expressing randomized linear dodecameric peptides or heptameric peptides flanked by a pair of cysteine residues was utilized. Biopanning experiments led to the identification of 29 unique peptides, with 1 of them, C7-3, being identified multiple times. Evaluation of their ability to interact with AniA using enzyme-linked immunosorbent assay and computational docking studies revealed that C7-3 was the most promising inhibitor, binding near the type 2 copper site of the enzyme, which is responsible for interaction with nitrite. Subsequent enzymatic assays and biolayer interferometry with a synthetic C7-3 and its derivatives, C7-3m1 and C7-3m2, demonstrated potent inhibition of AniA. Finally, the MIC₅₀ value of C7-3 and C7-3m2 against anaerobically grown N. gonorrhoeae was 0.6 mM. We present the first peptide inhibitors of AniA, an enzyme that should be further exploited for antigonococcal drug development.

Evaluating the effect of mutations and ligand binding on transthyretin homotetramer dynamics

Native transthyretin (TTR) homotetramer dissociation is the first step of the fibrils formation process in amyloid disease. A large number of specific point mutations that destabilize TTR quaternary structure have shown pro-amyloidogenic effects. Besides, several compounds have been proposed as drugs in the therapy of TTR amyloidosis due to their TTR tetramer binding affinities, and therefore, contribution to its integrity. In the present paper we have explored key positions sustaining TTR tetramer dynamical stability. We have identified positions whose mutations alter the most the TTR tetramer equilibrium dynamics based on normal mode analysis and their response to local perturbations. We have found that these positions are mostly localized at β-strands E and F and EF-loop. The monomer-monomer interface is pointed out as one of the most vulnerable regions to mutations that lead to significant changes in the TTR-tetramer equilibrium dynamics and, therefore, induces TTR amyloidosis. Besides, we have found that mutations on residues localized at the dimer-dimer interface and/or at the T4 hormone binding site destabilize the tetramer more than the average. Finally, we were able to compare several compounds according to their effect on vibrations associated to the ligand binding. Our ligand comparison is discussed and analyzed in terms of parameters and measurements associated to TTR-ligand binding affinities and the stabilization of its native state.

Jumping between protein conformers using normal modes

The relationship between the normal modes of a protein and its functional conformational change has been studied for decades. However, using this relationship in a predictive context remains a challenge. In this work, we demonstrate that, starting from a given protein conformer, it is possible to generate in a single step model conformers that are less than 1 Å (C_α -RMSD) from the conformer which is the known endpoint of the conformational change, particularly when the conformational change is collective in nature. Such accurate model conformers can be generated by following either the so-called robust or the 50 lowest-frequency modes obtained with various Elastic Network Models (ENMs). Interestingly, the quality of many of these models compares well with actual crystal structures, as assessed by the ROSETTA scoring function and PROCHECK. The most accurate and best quality conformers obtained in the present study were generated by using the 50 lowest-frequency modes of an all-atom ENM. However, with less than ten robust modes, which are identified without any prior knowledge of the nature of the conformational change, nearly 90% of the motion described by the 50 lowest-frequency modes of a protein can be captured. Such results strongly suggest that exploring the robust modes of ENMs may prove efficient for sampling the functionally relevant conformational repertoire of many proteins. © 2017 Wiley Periodicals, Inc.

A better prediction of conformational changes of proteins using minimally connected network models

Elastic network models have recently been used for studying low-frequency collective motions of proteins. These models simplify the complexity that arises from normal mode analysis by considering a simplified potential involving a few parameters. Two common parameters in most of the elastic network models are cutoff radius and force constant. Although the latter has been studied extensively and even elaborate new models were introduced, for the former usually an ad-hoc cutoff radius is considered. Moreover, the quality of the network models is usually assessed by evaluating their prediction against experimental B-factors. In this work, we consider various common elastic network models with different cutoff radii and assess them by their ability to predict conformational changes of proteins in complexes from unbound to bound state. This prediction is performed by perturbing the unbound structure using a number of low-frequency normal modes of its network model to optimally fit the bound structure. We evaluated a dataset of 30 proteins with distinct unbound and bound structures using this criterion. The results showed that, opposed to the common calibration process based on B-factors, a meaningful relationship exists between the quality of the prediction and model parameters. It was shown that the cutoff radius has a major role in this prediction and minimally connected network models, which use the shortest cutoff radius for which the network is stable, give the best results. It was also shown that by considering the first ten normal modes, the conformational changes can be predicted by about 25 percent. Hence, the evaluation process was extended to the case of considering the contribution of all normal modes in the prediction. The results indicated that minimally connected network models are superior, despite their simplicity, when any number of modes are considered in the prediction.

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.

Pushing the Backbone in Protein-Protein Docking

Conformational changes of proteins that occur upon binding typically confound computational docking algorithms. In this study, we test computational methods to capture protein backbone conformational change related to binding. To address how well existing algorithms can sample bound-like backbones, we query seven techniques including Monte Carlo-based sampling, molecular dynamics, and normal mode analysis. All methods tested rarely sample near-bound states from the unbound conformation. Nevertheless, the direction of the predicted motions overlap with the actual conformational change. We next forced the backbone from the unbound toward the bound conformation to create a family of docking energy landscapes. Seventy percent of docking targets succeed when the unbound backbones is pushed to within 0.6 Å of the bound. Current methods can capture an average of 22% of unbound-bound transitions through conformer selection methods and another 57% through induced-fit methodologies, delineating a stubborn gap (21%) in backbone motion not covered by any current approach.

Evolutionary Conserved Positions Define Protein Conformational Diversity

Conformational diversity of the native state plays a central role in modulating protein function. The selection paradigm sustains that different ligands shift the conformational equilibrium through their binding to highest-affinity conformers. Intramolecular vibrational dynamics associated to each conformation should guarantee conformational transitions, which due to its importance, could possibly be associated with evolutionary conserved traits. Normal mode analysis, based on a coarse-grained model of the protein, can provide the required information to explore these features. Herein, we present a novel procedure to identify key positions sustaining the conformational diversity associated to ligand binding. The method is applied to an adequate refined dataset of 188 paired protein structures in their bound and unbound forms. Firstly, normal modes most involved in the conformational change are selected according to their corresponding overlap with structural distortions introduced by ligand binding. The subspace defined by these modes is used to analyze the effect of simulated point mutations on preserving the conformational diversity of the protein. We find a negative correlation between the effects of mutations on these normal mode subspaces associated to ligand-binding and position-specific evolutionary conservations obtained from multiple sequence-structure alignments. Positions whose mutations are found to alter the most these subspaces are defined as key positions, that is, dynamically important residues that mediate the ligand-binding conformational change. These positions are shown to be evolutionary conserved, mostly buried aliphatic residues localized in regular structural regions of the protein like β-sheets and α-helix.

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.

cNMA: a framework of encounter complex-based normal mode analysis to model conformational changes in protein interactions

MOTIVATION

It remains both a fundamental and practical challenge to understand and anticipate motions and conformational changes of proteins during their associations. Conventional normal mode analysis (NMA) based on anisotropic network model (ANM) addresses the challenge by generating normal modes reflecting intrinsic flexibility of proteins, which follows a conformational selection model for protein-protein interactions. But earlier studies have also found cases where conformational selection alone could not adequately explain conformational changes and other models have been proposed. Moreover, there is a pressing demand of constructing a much reduced but still relevant subset of protein conformational space to improve computational efficiency and accuracy in protein docking, especially for the difficult cases with significant conformational changes.

METHOD AND RESULTS

With both conformational selection and induced fit models considered, we extend ANM to include concurrent but differentiated intra- and inter-molecular interactions and develop an encounter complex-based NMA (cNMA) framework. Theoretical analysis and empirical results over a large data set of significant conformational changes indicate that cNMA is capable of generating conformational vectors considerably better at approximating conformational changes with contributions from both intrinsic flexibility and inter-molecular interactions than conventional NMA only considering intrinsic flexibility does. The empirical results also indicate that a straightforward application of conventional NMA to an encounter complex often does not improve upon NMA for an individual protein under study and intra- and inter-molecular interactions need to be differentiated properly. Moreover, in addition to induced motions of a protein under study, the induced motions of its binding partner and the coupling between the two sets of protein motions present in a near-native encounter complex lead to the improved performance. A study to isolate and assess the sole contribution of intermolecular interactions toward improvements against conventional NMA further validates the additional benefit from induced-fit effects. Taken together, these results provide new insights into molecular mechanisms underlying protein interactions and new tools for dimensionality reduction for flexible protein docking.

AVAILABILITY AND IMPLEMENTATION

Source codes are available upon request.

Terahertz optical measurements of correlated motions with possible allosteric function

A suggested mechanism for allosteric response is the distortion of the energy landscape with agonist binding changing the protein structure's access to functional configurations. Intramolecular vibrations are indicative of the energy landscape and may have trajectories that enable functional conformational change. Here, we discuss the development of an optical method to measure the intramolecular vibrations in proteins, namely, crystal anisotropy terahertz microscopy, and the various approaches which can be used to identify the spectral data with specific structural motions.

Atomic torsional modal analysis for high-resolution proteins

We introduce a formulation for normal mode analyses of globular proteins that significantly improves on an earlier one-parameter formulation [M. M. Tirion, Phys. Rev. Lett. 77, 1905 (1996)] that characterized the slow modes associated with protein data bank structures. Here we develop that empirical potential function that is minimized at the outset to include two features essential to reproduce the eigenspectra and associated density of states in the 0 to 300cm-1 frequency range, not merely the slow modes. First, introduction of preferred dihedral-angle configurations via use of torsional stiffness constants eliminates anomalous dispersion characteristics due to insufficiently bound surface side chains and helps fix the spectrum thin tail frequencies (100-300cm-1). Second, we take into account the atomic identities and the distance of separation of all pairwise interactions, improving the spectrum distribution in the 20 to 300cm-1 range. With these modifications, not only does the spectrum reproduce that of full atomic potentials, but we obtain stable reliable eigenmodes for the slow modes and over a wide range of frequencies.

On the relationship between low-frequency normal modes and the large-scale conformational changes of proteins

Normal mode analysis is a computational technique that allows to study the dynamics of biological macromolecules. It was first applied to small protein cases, more than thirty years ago. The interest in this technique then raised when it was realized that it can provide insights about the large-scale conformational changes a protein can experience, for instance upon ligand binding. As it was also realized that studying highly simplified protein models can provide similar insights, meaning that this kind of analysis can be both quick and simple to handle, several applications were proposed, in the context of various structural biology techniques. This review focuses on these applications, as well as on how the functional relevance of the lowest-frequency modes of proteins was established.

Computing ensembles of transitions with molecular dynamics simulations

A molecular understanding of conformational change is important for connecting structure and function. Without the ability to sample on the meaningful large-scale conformational changes, the ability to infer biological function and to understand the effect of mutations and changes in environment is not possible. Our Dynamic Importance Sampling method (DIMS), part of the CHARMM simulation package, is a method that enables sampling over ensembles of transition intermediates. This chapter outlines the context for the method and the usage within the program.

WEBnm@ v2.0: Web server and services for comparing protein flexibility

BACKGROUND

Normal mode analysis (NMA) using elastic network models is a reliable and cost-effective computational method to characterise protein flexibility and by extension, their dynamics. Further insight into the dynamics-function relationship can be gained by comparing protein motions between protein homologs and functional classifications. This can be achieved by comparing normal modes obtained from sets of evolutionary related proteins.

RESULTS

We have developed an automated tool for comparative NMA of a set of pre-aligned protein structures. The user can submit a sequence alignment in the FASTA format and the corresponding coordinate files in the Protein Data Bank (PDB) format. The computed normalised squared atomic fluctuations and atomic deformation energies of the submitted structures can be easily compared on graphs provided by the web user interface. The web server provides pairwise comparison of the dynamics of all proteins included in the submitted set using two measures: the Root Mean Squared Inner Product and the Bhattacharyya Coefficient. The Comparative Analysis has been implemented on our web server for NMA, WEBnm@, which also provides recently upgraded functionality for NMA of single protein structures. This includes new visualisations of protein motion, visualisation of inter-residue correlations and the analysis of conformational change using the overlap analysis. In addition, programmatic access to WEBnm@ is now available through a SOAP-based web service. Webnm@ is available at http://apps.cbu.uib.no/webnma .

CONCLUSION

WEBnm@ v2.0 is an online tool offering unique capability for comparative NMA on multiple protein structures. Along with a convenient web interface, powerful computing resources, and several methods for mode analyses, WEBnm@ facilitates the assessment of protein flexibility within protein families and superfamilies. These analyses can give a good view of how the structures move and how the flexibility is conserved over the different structures.

High-resolution modeling of protein structures based on flexible fitting of low-resolution structural data

To circumvent the difficulty of directly solving high-resolution biomolecular structures, low-resolution structural data from Cryo-electron microscopy (EM) and small angle solution X-ray scattering (SAXS) are increasingly used to explore multiple conformational states of biomolecular assemblies. One promising venue to obtain high-resolution structural models from low-resolution data is via data-constrained flexible fitting. To this end, we have developed a new method based on a coarse-grained Cα-only protein representation, and a modified form of the elastic network model (ENM) that allows large-scale conformational changes while maintaining the integrity of local structures including pseudo-bonds and secondary structures. Our method minimizes a pseudo-energy which linearly combines various terms of the modified ENM energy with an EM/SAXS-fitting score and a collision energy that penalizes steric collisions. Unlike some previous flexible fitting efforts using the lowest few normal modes, our method effectively utilizes all normal modes so that both global and local structural changes can be fully modeled with accuracy. This method is also highly efficient in computing time. We have demonstrated our method using adenylate kinase as a test case which undergoes a large open-to-close conformational change. The EM-fitting method is available at a web server (http://enm.lobos.nih.gov), and the SAXS-fitting method is available as a pre-compiled executable upon request.

Seeking structural specificity: direct modulation of pentameric ligand-gated ion channels by alcohols and general anesthetics

Alcohols and other anesthetic agents dramatically alter neurologic function in a wide range of organisms, yet their molecular sites of action remain poorly characterized. Pentameric ligand-gated ion channels, long implicated in important direct effects of alcohol and anesthetic binding, have recently been illuminated in renewed detail thanks to the determination of atomic-resolution structures of several family members from lower organisms. These structures provide valuable models for understanding and developing anesthetic agents and for allosteric modulation in general. This review surveys progress in this field from function to structure and back again, outlining early evidence for relevant modulation of pentameric ligand-gated ion channels and the development of early structural models for ion channel function and modulation. We highlight insights and challenges provided by recent crystal structures and resulting simulations, as well as opportunities for translation of these newly detailed models back to behavior and therapy.

Evaluation of Protein Elastic Network Models Based on an Analysis of Collective Motions

Elastic network models (ENMs) are valuable tools for investigating collective motions of proteins, and a rich variety of simple models have been proposed over the past decade. A good representation of the collective motions requires a good approximation of the covariances between the fluctuations of the individual atoms. Nevertheless, most studies have validated such models only by the magnitudes of the single-atom fluctuations they predict. In the present study, we have quantified the agreement between the covariance structure predicted by molecular dynamics (MD) simulations and those predicted by a representative selection of proposed coarse-grained ENMs. We then contrast this approach with the comparison to MD-predicted atomic fluctuations and comparison to crystallographic B-factors. While all the ENMs yield approximations to the MD-predicted covariance structure, we report large and consistent differences between proposed models. We also find that the ability of the ENMs to predict atomic fluctuations is correlated with their ability to capture the covariance structure. In contrast, we find that the models that agree best with B-factors model collective motions less reliably and recommend against using B-factors as a benchmark.

Elastic network normal mode dynamics reveal the GPCR activation mechanism

G-protein-coupled receptors (GPCR) are a family of membrane-embedded metabotropic receptors which translate extracellular ligand binding into an intracellular response. Here, we calculate the motion of several GPCR family members such as the M2 and M3 muscarinic acetylcholine receptors, the A2A adenosine receptor, the β2 -adrenergic receptor, and the CXCR4 chemokine receptor using elastic network normal modes. The normal modes reveal a dilation and a contraction of the GPCR vestibule associated with ligand passage, and activation, respectively. Contraction of the vestibule on the extracellular side is correlated with cavity formation of the G-protein binding pocket on the intracellular side, which initiates intracellular signaling. Interestingly, the normal modes of rhodopsin do not correlate well with the motion of other GPCR family members. Electrostatic potential calculation of the GPCRs reveal a negatively charged field around the ligand binding site acting as a siphon to draw-in positively charged ligands on the membrane surface. Altogether, these results expose the GPCR activation mechanism and show how conformational changes on the cell surface side of the receptor are allosterically translated into structural changes on the inside.

Improved flexible refinement of protein docking in CAPRI rounds 22-27

Since the fourth evaluation for critical assessment of prediction of interactions (CAPRI), we have made improvements in three major areas in our refinement approach, namely the treatment of conformational flexibility, the binding free energy model, and the search algorithm. First, we incorporated backbone flexibility into our previous approach, which only optimized rigid backbone poses with limited side-chain flexibility. Here, we formulated and solved the conformational search as a hierarchical optimization problem (involving rigid-body poses, backbone flexibility, and side-chain flexibility). Second, we used continuum electrostatic calculations to include solvation effects in the binding free energy model. Finally, we eliminated sloppy modes (directions in which the free energy is essentially constant) to improve the efficiency of the search. With these improvements, we produced correct predictions for 6 of the 10 latest CAPRI targets, including one high, three medium, and two acceptable accuracy predictions. Compared to our previous performance in CAPRI, substantial improvements have been made for targets requiring homology modeling.

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.

Structural insight into the binding complex: β-arrestin/CCR5 complex

The chemokine receptor 5 (CCR5) belongs to the superfamily of serpentine G protein-coupled receptors (GPCRs). The DRY motif (Asp, Arg, Tyr) of the intracellular loop 2 (ICL2), which is highly conserved in the GPCRs has been shown to be essential for the stability of folding of CCR5 and the interaction with β-arrestin. But the molecular mechanism by which it recognizes and interacts with β-arrestin has not been elucidated. In the present study, we described the active state of the β-arrestin structure using normal mode analysis and characterized the binding cleft of CCR5-ICL2 with β-arrestin using SABRE© docking tool and molecular dynamics simulation. Based on our computational results, we proposed a mode of binding between the ICL2 loop of CCR5 and β-arrestin structure, and modeled the energetically stable β-arrestin/CCR5 complex. In view of CCR5's importance as a therapeutic target for the treatment of HIV, this observation provides novel insight into the β-arrestin/CCR5 pathway. As a result, the current computational study of the detailed β-arrestin/CCR5 binding complex could provide the rationale for the development of next generation of HIV peptide inhibitors as therapeutic agents.

A mechanistic understanding of allosteric immune escape pathways in the HIV-1 envelope glycoprotein

The HIV-1 envelope (Env) spike, which consists of a compact, heterodimeric trimer of the glycoproteins gp120 and gp41, is the target of neutralizing antibodies. However, the high mutation rate of HIV-1 and plasticity of Env facilitates viral evasion from neutralizing antibodies through various mechanisms. Mutations that are distant from the antibody binding site can lead to escape, probably by changing the conformation or dynamics of Env; however, these changes are difficult to identify and define mechanistically. Here we describe a network analysis-based approach to identify potential allosteric immune evasion mechanisms using three known HIV-1 Env gp120 protein structures from two different clades, B and C. First, correlation and principal component analyses of molecular dynamics (MD) simulations identified a high degree of long-distance coupled motions that exist between functionally distant regions within the intrinsic dynamics of the gp120 core, supporting the presence of long-distance communication in the protein. Then, by integrating MD simulations with network theory, we identified the optimal and suboptimal communication pathways and modules within the gp120 core. The results unveil both strain-dependent and -independent characteristics of the communication pathways in gp120. We show that within the context of three structurally homologous gp120 cores, the optimal pathway for communication is sequence sensitive, i.e. a suboptimal pathway in one strain becomes the optimal pathway in another strain. Yet the identification of conserved elements within these communication pathways, termed inter-modular hotspots, could present a new opportunity for immunogen design, as this could be an additional mechanism that HIV-1 uses to shield vulnerable antibody targets in Env that induce neutralizing antibody breadth.

Ensemble-based characterization of unbound and bound states on protein energy landscape

Physicochemical description of numerous cell processes is fundamentally based on the energy landscapes of protein molecules involved. Although the whole energy landscape is difficult to reconstruct, increased attention to particular targets has provided enough structures for mapping functionally important subspaces associated with the unbound and bound protein structures. The subspace mapping produces a discrete representation of the landscape, further called energy spectrum. We compiled and characterized ensembles of bound and unbound conformations of six small proteins and explored their spectra in implicit solvent. First, the analysis of the unbound-to-bound changes points to conformational selection as the binding mechanism for four proteins. Second, results show that bound and unbound spectra often significantly overlap. Moreover, the larger the overlap the smaller the root mean square deviation (RMSD) between the bound and unbound conformational ensembles. Third, the center of the unbound spectrum has a higher energy than the center of the corresponding bound spectrum of the dimeric and multimeric states for most of the proteins. This suggests that the unbound states often have larger entropy than the bound states. Fourth, the exhaustively long minimization, making small intrarotamer adjustments (all-atom RMSD ≤ 0.7 Å), dramatically reduces the distance between the centers of the bound and unbound spectra as well as the spectra extent. It condenses unbound and bound energy levels into a thin layer at the bottom of the energy landscape with the energy spacing that varies between 0.8-4.6 and 3.5-10.5 kcal/mol for the unbound and bound states correspondingly. Finally, the analysis of protein energy fluctuations showed that protein vibrations itself can excite the interstate transitions, including the unbound-to-bound ones.

The exomer cargo adaptor features a flexible hinge domain

Exomer is a cargo adaptor that mediates the sorting of specific plasma membrane proteins into vesicles at the trans-Golgi network. Cargo adaptors must bind to multiple partners, including their cargo, regulatory proteins, and the membrane surface. During biogenesis of a vesicle, the membrane makes a transition from a relatively flat surface to one of high curvature, requiring cargo adaptors to somehow maintain protein-protein and protein-membrane interactions on a changing membrane environment. Here, we present the crystal structure of a tetrameric Chs5/Bch1 exomer complex and use small-angle X-ray scattering to demonstrate its flexibility in solution. The structural data suggest that the complex flexes primarily around the dimeric N-terminal domain of the Chs5 subunits, which adopts a noncanonical β sandwich fold. We propose that this flexible hinge domain enables exomer to maintain interactions in the context of a dynamic membrane environment.

Normal-mode-analysis-guided investigation of crucial intersubunit contacts in the cAMP-dependent gating in HCN channels

Protein structures define a complex network of atomic interactions in three dimensions. Direct visualization of the structure and analysis of the interaction potential energy are not straightforward approaches to pinpoint the atomic contacts that are crucial for protein function. We used the tetrameric hyperpolarization-activated cAMP-regulated (HCN) channel as a model system to study the intersubunit contacts in cAMP-dependent gating. To obtain a systematic survey of the contacts between each pair of residues, we used normal-mode analysis, a computational approach for studying protein dynamics, and constructed the covariance matrix for C-α atoms. The significant contacts revealed by covariance analysis were further investigated by means of mutagenesis and functional assays. Among the mutant channels that show phenotypes different from those of the wild-type, we focused on two mutant channels that express opposite changes in cAMP-dependent gating. Subsequent biochemical assays on isolated C-terminal fragments, including the cAMP binding domain, revealed only minimal effects on cAMP binding, suggesting the necessity of interpreting the cAMP-dependent allosteric regulation at the whole-channel level. For this purpose, we applied the patch-clamp fluorometry technique and observed correlated changes in the dynamic, state-dependent cAMP binding in the mutant channels. This study not only provides further understanding of the intersubunit contacts in allosteric coupling in the HCN channel, it also illustrates an effective strategy for delineating important atomic contacts within a structure.

Multiscale Coarse-Graining via Normal Mode Analysis

A multiscale coarse-graining method called the normal-mode analysis based fluctuation matching (NMA-FM) is developed for constructing coarse-grained models of biomolecular systems. In the framework of normal-mode analysis, an arbitrary fine-grained model can be systematically converted to a more coarse-grained model, while the crucial low-frequency motions of the fine-grained system are able to be reproduced in the coarse-grained modeling. The method relies on the technique of fluctuation matching that has been devised earlier for parametrizing heterogeneous elastic network models based on data from atomistic molecular dynamics simulations. The new approach is quite efficient since it avoids expensive atomistic molecular dynamics simulations and can start from already coarse-grained elastic network models. In the practical aspect, the method is suitable for conformational analyses of large biomacromolecules and calculations of mechanical properties of biomaterials, which is demonstrated by the studied systems including an amyloid dimer, lysozyme and adenylate kinase proteins, and the S2 subdomain of myosin.