Coarse-grained Normal Mode Analysis Research Articles

Coarse-Graining Waters: Unveiling The Effective Hydrophilicity/Hydrophobicity of Individual Protein Atoms and The Roles of Waters' Hydrogens.

There have been many coarse-graining methods developed that aim to reduce the sizes of simulated systems and their computational costs. In this work, we develop a new coarse-graining method, called coarse-graining-delta (or δ-CG in short), that reduces the degrees of freedom of the potential energy surface by coarse-graining relative locations of atoms from their unit centers. Our method extends and generalizes the methods used in the coarse-grained normal mode analysis and enables us to study the roles of the individual removed atoms in a system, which have been difficult to study in molecular dynamics simulations. By applying δ-CG to coarse-grain three-point water molecules into single-point solvent particles, we successfully identify the effective hydrophilicity and hydrophobicity of all the individual protein atom types, which collectively correlate well with the known hydrophilic, hydrophobic, and amphipathic characteristics of amino acids. Moreover, our investigation shows that water's hydrogens have two roles in interacting with protein atoms. First, water molecules adjust their poses around different amino acids and their atoms, and the statistical preferences of the hydrogen poses near the atoms determine the effective hydrophilicity and hydrophobicity of the atoms, which have not been successfully addressed before. Second, the collective dynamics of the hydrogens assist the water molecules in escaping from the potential energy wells of the hydrophilic atoms. Our method also shows that coarse-graining a system mathematically leads to breaking antisymmetry of the nonbonded interactions; as a result, two interacting coarse-grained units exert different forces on each other. Our study indicates that the accuracy of coarse-grained force fields, such as the MARTINI force field and the UNRES force field, can be improved in two ways: (i) refining their potential energy functions and coefficients by analyzing the coarse-grained potential energy surface using δ-CG, and (ii) introducing non-antisymmetric interactions.

The DynaSig-ML Python package: automated learning of biomolecular dynamics-function relationships.

DynaSig-ML is open-source software available at https://github.com/gregorpatof/dynasigml_package.

Sequence-sensitive elastic network captures dynamical features necessary for miR-125a maturation

The Elastic Network Contact Model (ENCoM) is a coarse-grained normal mode analysis (NMA) model unique in its all-atom sensitivity to the sequence of the studied macromolecule and thus to the effect of mutations. We adapted ENCoM to simulate the dynamics of ribonucleic acid (RNA) molecules, benchmarked its performance against other popular NMA models and used it to study the 3D structural dynamics of human microRNA miR-125a, leveraging high-throughput experimental maturation efficiency data of over 26 000 sequence variants. We also introduce a novel way of using dynamical information from NMA to train multivariate linear regression models, with the purpose of highlighting the most salient contributions of dynamics to function. ENCoM has a similar performance profile on RNA than on proteins when compared to the Anisotropic Network Model (ANM), the most widely used coarse-grained NMA model; it has the advantage on predicting large-scale motions while ANM performs better on B-factors prediction. A stringent benchmark from the miR-125a maturation dataset, in which the training set contains no sequence information in common with the testing set, reveals that ENCoM is the only tested model able to capture signal beyond the sequence. This ability translates to better predictive power on a second benchmark in which sequence features are shared between the train and test sets. When training the linear regression model using all available data, the dynamical features identified as necessary for miR-125a maturation point to known patterns but also offer new insights into the biogenesis of microRNAs. Our novel approach combining NMA with multivariate linear regression is generalizable to any macromolecule for which relatively high-throughput mutational data is available.

In-silico phenotype prediction by normal mode variant analysis in TUBB4A-related disease

TUBB4A-associated disorder is a rare condition affecting the central nervous system. It displays a wide phenotypic spectrum, ranging from isolated late-onset torsion dystonia to a severe early-onset disease with developmental delay, neurological deficits, and atrophy of the basal ganglia and cerebellum, therefore complicating variant interpretation and phenotype prediction in patients carrying TUBB4A variants. We applied entropy-based normal mode analysis (NMA) to investigate genotype–phenotype correlations in TUBB4A-releated disease and to develop an in-silico approach to assist in variant interpretation and phenotype prediction in this disorder. Variants included in our analysis were those reported prior to the conclusion of data collection for this study in October 2019. All TUBB4A pathogenic missense variants reported in ClinVar and Pubmed, for which associated clinical information was available, and all benign/likely benign TUBB4A missense variants reported in ClinVar, were included in the analysis. Pathogenic variants were divided into five phenotypic subgroups. In-silico point mutagenesis in the wild-type modeled protein structure was performed for each variant. Wild-type and mutated structures were analyzed by coarse-grained NMA to quantify protein stability as entropy difference value (ΔG) for each variant. Pairwise ΔG differences between all variant pairs in each structural cluster were calculated and clustered into dendrograms. Our search yielded 41 TUBB4A pathogenic variants in 126 patients, divided into 11 partially overlapping structural clusters across the TUBB4A protein. ΔG-based cluster analysis of the NMA results revealed a continuum of genotype–phenotype correlation across each structural cluster, as well as in transition areas of partially overlapping structural clusters. Benign/likely benign variants were integrated into the genotype–phenotype continuum as expected and were clearly separated from pathogenic variants. We conclude that our results support the incorporation of the NMA-based approach used in this study in the interpretation of variant pathogenicity and phenotype prediction in TUBB4A-related disease. Moreover, our results suggest that NMA may be of value in variant interpretation in additional monogenic conditions.

The NRGTEN Python package: an extensible toolkit for coarse-grained normal mode analysis of proteins, nucleic acids, small molecules and their complexes.

The Najmanovich Research Group Toolkit for Elastic Networks (NRGTEN) is a Python toolkit that implements four different NMA models in addition to popular and novel metrics to benchmark and measure properties from these models. Furthermore, the toolkit is available as a public Python package and is easily extensible for the development or implementation of additional normal mode analysis models. The inclusion of the Elastic Network Contact Model developed in our group within NRGTEN is noteworthy, owing to its account for the specific chemical nature of atomic interactions. https://github.com/gregorpatof/nrgten_package/.

Probing the Conformational Change of Contractile Tails using Coarse-Grained Normal Mode Analysis

Significant development in nanotechnology is expected to come from understanding the mechanisms of biomolecular machines. Contractile tails are unique organelles present in certain biomolecular machines which aid in piercing a host membrane and injecting macromolecules inside the host. These tails consist of an inner tail tube with a spring-like sheath wrapped around it. The inner tail tube ends at a spike tip surrounded by a baseplate. During the injection mechanism the sheath undergoes a large conformational from an extended state to a contracted state,thereby pushing the tail tube like a needle through the membrane. This conformational change involves ∼1.3 million atoms and is estimated to be on the millisecond-to-second timescale. Recent efforts have yielded information regarding the structure of the sheath. Conventional methods such as molecular dynamics simulations are not possible for a system of this size. Instead, the collective motions can be observed using the anisotropic network model (ANM), a coarse-grained normal mode analysis method. The ANM model shows that the slowest, global modes are encoded within the sheath's structure. Using these modes we show how it is possible to observe a coarse grained representation of the contraction pathway. Furthermore the work presented could be applied to other large biological structures which undergo conformational changes.

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.

A Comparative Study of All-atom Molecular Dynamics Simulation and Coarse-grained Normal Mode Analysis in Identifying Pre-existing Residue Interaction Networks that Promote Coupled-Domain Dynamics in Escherichia coli Methionyl-tRNA Synthetase

Inter-domain communication plays a key role in the function of modular proteins. Earlier studies have demonstrated that the coupling of domain motions is important in mediating site-to-site communications in modular proteins. In the present study, bioinformatics and molecular simulations were usedto trace “pre-existing” residue-residue interaction networks that mediate coupled-domain dynamics in multi-domain Escherichia coli methionyl-tRNA synthetase (Ec MetRS). In particular, a comparative study was carried out to evaluate the effectiveness of coarse-grained normal mode analysis and all-atom molecular dynamic simulation in predicting pre-existing pathways of inter-domain communications in this enzyme. Integration of dynamic information of residues with their evolutionary features (conserved and coevolved) demonstrated that multiple residue-residue interaction networks exist in Ec MetRS that promote dynamic coupling between the anticodon binding domain and the connective polypeptide I domain, which are > 50Å apart, through correlated motions. Mutation of residues on these pathways have distinct impact on the dynamics and function of this enzyme. Moreover, the present study revealed that the dynamic information obtained from the coarse-grained normal mode analysis is comparable to the atomistic molecular dynamics simulations in predicting the interaction networks that are essential for promoting coupled-domain dynamics in Ec MetRS. KEYWORDS: Domain-domain Communication; Molecular Dynamics; Methionyl-tRNA Synthetase; Normal Mode Analysis; Coupled-domain Dynamics; Course-grained Normal Mode Analysis; Aminoacyl tRNA Synthetases; Statistical Coupling Analysis

Investigation of intrinsic dynamics of enzymes involved in metabolic pathways using coarse-grained normal mode analysis

AbstractIntrinsic dynamics of proteins are known to play important roles in their function. In particular, collective dynamics of a protein, which are defined by the protein’s overall architecture, are important in promoting the active site conformation that favors substrate binding and effective catalysis. The primary sequence of a protein, which determines its three-dimensional structure, encodes unique dynamics. The intrinsic dynamics of a protein actually link protein structure to its function. In the present study, coarse-grained normal mode analysis was performed to examine the intrinsic dynamic patterns of 24 different enzymes involved in primary metabolic pathways. We observed that each metabolic enzyme exhibits unique patterns of motions, which are conserved across multiple species and functionally relevant. Dynamic cross-correlation matrices (DCCMs) are visibly identical for a given enzyme family but significantly different from DCCMs of other protein families, reinforcing that proteins with sim...

Applications of Normal Mode Analysis Methods in Computational Protein Design.

Recent advances in coarse-grained normal mode analysis methods make possible the large-scale prediction of the effect of mutations on protein stability and dynamics as well as the generation of biologically relevant conformational ensembles. Given the interplay between flexibility and enzymatic activity, the combined analysis of stability and dynamics using the Elastic Network Contact Model (ENCoM) method has ample applications in protein engineering in industrial and medical applications such as in computational antibody design. Here, we present a detailed tutorial on how to perform such calculations using ENCoM.

Toward High-Throughput Predictive Modeling of Protein Binding/Unbinding Kinetics

One of the unaddressed challenges in drug discovery is that drug potency determined in vitro is not a reliable indicator of drug activity in vivo. Accumulated evidence suggests that in vivo activity is more strongly correlated with the binding/unbinding kinetics than the equilibrium thermodynamics of protein-ligand interactions (PLIs). However, existing experimental and computational techniques are insufficient in studying the molecular details of kinetics processes of PLIs on a large scale. Consequently, we not only have limited mechanistic understanding of the kinetic processes but also lack a practical platform for high-throughput screening and optimization of drug leads on the basis of their kinetic properties. For the first time, we address this unmet need by integrating coarse-grained normal mode analysis with multitarget machine learning (MTML). To test our method, HIV-1 protease is used as a model system. We find that computational models based on the residue normal mode directionality displacement of PLIs can not only recapitulate the results from all-atom molecular dynamics simulations but also predict protein-ligand binding/unbinding kinetics accurately. When this is combined with energetic features, the accuracy of combined kon and koff prediction reaches 74.35%. Furthermore, our integrated model provides us with new insights into the molecular determinants of the kinetics of PLIs. We propose that the coherent coupling of conformational dynamics and thermodynamic interactions between the receptor and the ligand may play a critical role in determining the kinetic rate constants of PLIs. In conclusion, we demonstrate that residue normal mode directionality displacement can serve as a kinetic fingerprint to capture long-time-scale conformational dynamics of the binding/unbinding kinetics. When this is coupled with MTML, it is possible to screen and optimize compounds on the basis of their binding/unbinding kinetics in a high-throughput fashion. The further development of such computational tools will bridge one of the critical missing links between in vitro compound screening and in vivo drug activity.

Comparative Investigation of Normal Modes and Molecular Dynamics of Hepatitis C NS5B Protein

Understanding dynamics of proteins has many practical implications in terms of finding a cure for many protein related diseases. Normal mode analysis and molecular dynamics methods are widely used physics-based computational methods for investigating dynamics of proteins. In this work, we studied dynamics of Hepatitis C NS5B protein with molecular dynamics and normal mode analysis. Principal components obtained from a 100 nanoseconds molecular dynamics simulation show good overlaps with normal modes calculated with a coarse-grained elastic network model. Coarse-grained normal mode analysis takes at least an order of magnitude shorter time. Encouraged by this good overlaps and short computation times, we analyzed further low frequency normal modes of Hepatitis C NS5B. Motion directions and average spatial fluctuations have been analyzed in detail. Finally, biological implications of these motions in drug design efforts against Hepatitis C infections have been elaborated.

The stability of the three transmembrane and the four transmembrane human vitamin K epoxide reductase models

3 transmembrane and 4 transmembrane helices models are suggested for the human vitamin K epoxide reductase (VKOR). In this study, we investigate the stability of the human 3 transmembrane/4 transmembrane VKOR models employing a coarse-grained normal mode analysis and molecular dynamics simulation. Based on the analysis of the mobility of each transmembrane domain, we suggest that the 3 transmembrane human VKOR model is more stable than the 4 transmembrane human VKOR model.

A Combined Coarse-Grained and All-Atom Molecular Simulation of the TRPV1 Channel

The transient receptor potential (TRP) channels act as key sensors of various chemical and physical stimuli in eukaryotic cells. Despite years of study, the molecular mechanisms of TRP channel activation remain unclear. To elucidate the structural, dynamic, and energetic basis of gating in TRPV1 (a founding member of the TRPV subfamily), we performed coarse-grained modeling and all-atom molecular dynamics (MD) simulation based on the recently solved high resolution structures of the open and closed form of TRPV1. Our coarse-grained normal mode analysis captures two key modes of collective motions involved in the TRPV1 gating transition, featuring a quaternary twist motion of the transmembrane domains (TMDs) relative to the intracellular domains (ICDs). Our transition pathway modeling predicts a sequence of structural movements that propagate from the ICDs to the TMDs via key interface domains (including the membrane proximal domain and the C-terminal domain), leading to sequential opening of the selectivity filter followed by the lower gate in the channel pore (confirmed by modeling conformational changes induced by the activation of ICDs). The above findings of coarse-grained modeling are robust to perturbation by lipids. Finally, our MD simulation of the ICD identifies key residues that contribute differently to the nonpolar energy of the open and closed state, and these residues are predicted to control the temperature sensitivity of TRPV1 gating. We will also report preliminary MD simulation results of the full-length TRPV1 channel.For reference, check out J Gen Physiol. 2015 May;145(5):443-56 (http://www.ncbi.nlm.nih.gov/pubmed/25918362).

A combined coarse-grained and all-atom simulation of TRPV1 channel gating and heat activation.

The transient receptor potential (TRP) channels act as key sensors of various chemical and physical stimuli in eukaryotic cells. Despite years of study, the molecular mechanisms of TRP channel activation remain unclear. To elucidate the structural, dynamic, and energetic basis of gating in TRPV1 (a founding member of the TRPV subfamily), we performed coarse-grained modeling and all-atom molecular dynamics (MD) simulation based on the recently solved high resolution structures of the open and closed form of TRPV1. Our coarse-grained normal mode analysis captures two key modes of collective motions involved in the TRPV1 gating transition, featuring a quaternary twist motion of the transmembrane domains (TMDs) relative to the intracellular domains (ICDs). Our transition pathway modeling predicts a sequence of structural movements that propagate from the ICDs to the TMDs via key interface domains (including the membrane proximal domain and the C-terminal domain), leading to sequential opening of the selectivity filter followed by the lower gate in the channel pore (confirmed by modeling conformational changes induced by the activation of ICDs). The above findings of coarse-grained modeling are robust to perturbation by lipids. Finally, our MD simulation of the ICD identifies key residues that contribute differently to the nonpolar energy of the open and closed state, and these residues are predicted to control the temperature sensitivity of TRPV1 gating. These computational predictions offer new insights to the mechanism for heat activation of TRPV1 gating, and will guide our future electrophysiology and mutagenesis studies.

ENCoM server: exploring protein conformational space and the effect of mutations on protein function and stability.

ENCoM is a coarse-grained normal mode analysis method recently introduced that unlike previous such methods is unique in that it accounts for the nature of amino acids. The inclusion of this layer of information was shown to improve conformational space sampling and apply for the first time a coarse-grained normal mode analysis method to predict the effect of single point mutations on protein dynamics and thermostability resulting from vibrational entropy changes. Here we present a web server that allows non-technical users to have access to ENCoM calculations to predict the effect of mutations on thermostability and dynamics as well as to generate geometrically realistic conformational ensembles. The server is accessible at: http://bcb.med.usherbrooke.ca/encom.

Protein engineering in the 21st century.

Protein engineering, the process by which novel proteins with desired properties are developed, has grown by leaps and bounds since the first examples of protein mutagenesis were described over three decades ago. In the last 30 years, protein engineers have successfully created a wide range of proteins tailored to specific industrial, medical, and research applications. Yet challenges remain that prevent the engineering of complex protein functions on demand. With the aim of creating a forum for the protein engineering community, the inaugural Protein Engineering Canada Conference was held on June 20–22, 2014, in Ottawa, Canada. Over the course of the 2-day conference, 115 protein scientists from over 30 institutions representing 5 countries shared ideas, networked with colleagues, and learned about exciting new research covering a broad array of topics such as enzyme engineering, computational protein design, X-ray crystallography, protein NMR, molecular modeling, and protein evolution. This special issue highlights the breadth of research that was covered during the Protein Engineering Canada Conference by including previously unpublished research articles submitted by speakers as well as some selections that were submitted directly to Protein Science.

Vibrational entropy differences between mesophile and thermophile proteins and their use in protein engineering.

We recently introduced ENCoM, an elastic network atomic contact model, as the first coarse-grained normal mode analysis method that accounts for the nature of amino acids and can predict the effect of mutations on thermostability based on changes vibrational entropy. In this proof-of-concept article, we use pairs of mesophile and thermophile homolog proteins with identical structures to determine if a measure of vibrational entropy based on normal mode analysis can discriminate thermophile from mesophile proteins. We observe that in around 60% of cases, thermophile proteins are more rigid at equivalent temperatures than their mesophile counterpart and this difference can guide the design of proteins to increase their thermostability through series of mutations. We observe that mutations separating thermophile proteins from their mesophile orthologs contribute independently to a decrease in vibrational entropy and discuss the application and implications of this methodology to protein engineering.

Collective Variable Approaches for Single Molecule Flexible Fitting and Enhanced Sampling

It is now well established that proteins and nucleic acids undergo local and global conformational fluctuations to perform a variety of cellular functions such as signal transduction, transport, and catalysis.1 Many experimental techniques such as X-ray crystallography, nuclear magnetic resonance (NMR) spectroscopy, small-angle X-ray scattering (SAXS), and single-particle electron microscopy (EM) have indeed provided structural evidence at different resolutions to support the view of multiple functional states of biomolecules. Yet it remains difficult to characterize the vast conformational repertoire of biomolecules via experimental methods alone. Therefore, biophysical theory, modeling, and simulation techniques rooted in statistical mechanics are often useful for a detailed molecular understanding of biomolecular structures.2−5 Despite the limitations of molecular mechanics interaction potentials, computational methods can now be combined with low-resolution structural data to generate experimentally consistent conformational ensembles as well as to probe underlying mechanistic questions. Analyses of structural data for different functional states of biomolecules have revealed large-scale conformational rearrangements on the scales of entire domains. This means that a large group of atoms collectively move in a concerted way to facilitate functional movements. Traditionally, one relatively less expensive computational method to analyze collective motions in proteins has been to carry out normal-mode analysis (NMA) of equilibrium structures, because low-frequency modes are typically indicative of high-amplitude/large-scale motions.6−8 Such global and collective modes are robust, independent of sequence detail, and are intrinsically accessible to each biomolecule because they are encoded in their global shape.9−13 Given that the total number of degrees-of-freedom (DOF) in biomolecules is very large, NMA provides an efficient way to describe biomolecular dynamics in a reduced number of variables. As was originally pointed out by Hayward and Go,6 this reduction in dimensionality has led to the concept of an important subspace of variables, “collective variables (CVs)”, that are well-suited to characterize the dynamics of biomolecules. Interestingly, the concept of CVs as reaction coordinates has been recently extended to atomistic molecular dynamics (MD) simulations,14 which has significantly increased their capability in capturing long time-scale motions. This is chiefly possible because sampling in these CVs can be carried out more extensively in comparison to all possible DOF. Such methods are typically referred to as enhanced sampling techniques because they increase the likelihood of observation of a rare biomolecular event. The range of studies in which NMA and MD simulations have played a central role is immense, and it is not possible to do justice to all such studies in this focused Review. However, we refer the reader to pertinent comprehensive literature on those subjects along the way. Therefore, we have limited the scope of this Review to some specific applications of NMA, and enhanced sampling via temperature-acceleration in the context of flexible fitting to low-resolution EM data on macromolecular complexes. Particularly, we concentrate on two methods in this Review: (a) normal mode flexible fitting (NMFF)15,16 for structural refinement into EM maps; and (b) temperature-accelerated molecular dynamics (TAMD)17,18 for conformational exploration and flexible fitting. We first discuss theoretical underpinnings of all-atom and coarse-grained NMA of protein structures, which is followed by highlights of various successful applications. The theory and applications of NMA for flexible fitting of protein structures into EM maps are described thereafter. This is immediately followed by a discussion of the importance of enhanced sampling in biomolecular simulations, and how dynamics in these systems can be explored by evolving CVs via temperature acceleration, for example. Specifically, we discuss in detail various aspects of TAMD. During these discussions, we further highlight a few of the many cases where NMA and TAMD have alleviated difficulties faced by other methods in understanding large-scale functional excursions in biomolecules. This Review concludes with a brief overview and future outlook for these methods.

Incorporating Explicitly Treated Surface Water Produces Better Alignments Between Experimental and Predicted Anisotropic B-Factors

X-ray crystallography has been the gold standard for the determination of protein structures. Other than providing the definition of the positions for each atom, it also yields information on protein dynamics but this aspect has been under appreciated. The B-factors in high-resolution structures are anisotropic and reflect not only the amplitude but also the direction of the atomic vibrations. This trove of information on protein dynamics presented by experimental anisotropic B-factors (or anisotropic displacement parameter, ADP) is invaluable for the study of the intriguing relationship among structure, dynamics, and function. Here starting from the definition of atom positions, we apply normal mode analysis (NMA), a computational approach for studying protein dynamics, to predict the ADPs and then align them with experimental measurements. We use both coarse-grained NMA approaches and the NMA based on canonical all-atom force fields. By comparing the accuracy of these methods, we find that the all-atom NMA and the NMA based on portioning the all-atom Hessian matrix give the best results. Moreover, adding a layer of explicitly treated water molecules on protein surface consistently makes the energy minimized structure closer to the native structure and improves the accuracy of the ADP results. The above observations could be attributed to the significant impacts on protein dynamics by surface water and the intrinsic differences in physical-chemical properties from bulk water. This study illustrates the importance of incorporating surface water in the study of protein dynamics and provides useful information for the emerging technique of ADP-based refinement of medium-to-low resolution structures.