Coarse-grained Elastic Network Models Research Articles

Enhanced Conformational Sampling with an Adaptive Coarse-Grained Elastic Network Model Using Short-Time All-Atom Molecular Dynamics.

Compared to all-atom molecular dynamics (AA-MD) simulations, coarse-grained (CG) MD simulations can significantly reduce calculation costs. However, existing CG-MD methods are unsuitable for sampling structures that depart significantly from the initial structure without any biased force. In this study, we developed a new adaptive CG elastic network model (ENM), in which the dynamic cross-correlation coefficient based on short-time AA-MD of at most ns order is considered. By applying Bayesian optimization to search for a suitable parameter among the vast parameter space of adaptive CG-ENM, we succeeded in reducing the searching cost to approximately 10% of those for random sampling and exhaustive sampling. To evaluate the performance of adaptive CG-ENM, we applied the new methodology to adenylate kinase (ADK) and glutamine binding protein (GBP) in the apo state. The results showed that the structural ensembles explored by adaptive CG-ENM could be considerably more diverse than those by conventional ENMs with enhanced sampling such as temperature replica exchange MD and long-time AA-MD of 1 μs. In particular, some of the structures sampled by adaptive ENM are relatively close to the holo-type structures of ADK and GBP. Furthermore, as a challenging task, to demonstrate the advantages of the CG model with lower calculation cost, we applied our new methodology to a larger biomolecule, integrin (αV) in the inactive state. Then, we sampled various structural ensembles, including extended structures that are apparently different from inactive ones.

Modeling coronavirus spike protein dynamics: implications for immunogenicity and immune escape

The ongoing COVID-19 pandemic is a global public health emergency requiring urgent development of efficacious vaccines. While concentrated research efforts have focused primarily on antibody-based vaccines that neutralize SARS-CoV-2, and several first-generation vaccines have either been approved or received emergency use authorization, it is forecasted that COVID-19 will become an endemic disease requiring updated second-generation vaccines. The SARS-CoV-2 surface spike (S) glycoprotein represents a prime target for vaccine development because antibodies that block viral attachment and entry, i.e., neutralizing antibodies, bind almost exclusively to the receptor-binding domain. Here, we develop computational models for a large subset of S proteins associated with SARS-CoV-2, implemented through coarse-grained elastic network models and normal mode analysis. We then analyze local protein domain dynamics of the S protein systems and their thermal stability to characterize structural and dynamical variability among them. These results are compared against existing experimental data and used to elucidate the impact and mechanisms of SARS-CoV-2 S protein mutations and their associated antibody binding behavior. We construct a SARS-CoV-2 antigenic map and offer predictions about the neutralization capabilities of antibody and S mutant combinations based on protein dynamic signatures. We then compare SARS-CoV-2 S protein dynamics to SARS-CoV and MERS-CoV S proteins to investigate differing antibody binding and cellular fusion mechanisms that may explain the high transmissibility of SARS-CoV-2. The outbreaks associated with SARS-CoV, MERS-CoV, and SARS-CoV-2 over the last two decades suggest that the threat presented by coronaviruses is ever-changing and long term. Our results provide insights into the dynamics-driven mechanisms of immunogenicity associated with coronavirus S proteins and present a new, to our knowledge, approach to characterize and screen potential mutant candidates for immunogen design, as well as to characterize emerging natural variants that may escape vaccine-induced antibody responses.

Estimating the Directional Flexibility of Proteins from Equilibrium Thermal Fluctuations.

The directional flexibility of proteins is an equilibrium molecular property which is accessible to both experiment and computation. Single molecule force spectroscopy (SMFS) experiments report effective directional spring constants to describe the collective anisotropic response of a protein structure to mechanical pulling forces applied along selected axes. On the other hand, computational methods have thus far employed either indirect force based nonequilibrium simulations or coarse-grained elastic network models (ENM) to predict protein directional spring constants. Here, we examine the ability of equilibrium atomistic Molecular Dynamics (MD) simulations to estimate the directional flexibility and mechanical anisotropy of proteins. MD-derived effective directional spring constants are found to correlate well with SMFS spring constants (ρ2 = 0.97-0.99; Adj R2 = 0.92-0.99) and unfolding forces (ρ2 = 0.85-0.97; Adj R2 = 0.63-0.91) for five different globular proteins. Specifically, the computed spring constants reproduce the mechanical anisotropy reported by SMFS along five different directions of green fluorescence protein (GFP) and six directions of the immunoglobulin-binding B1 domain of streptococcal protein G (GB1). Further, protein dynamics as captured in MD can be translated into spring constants which can distinguish the N-C directional flexibility of ubiquitin (Ub) from two structurally homologous small ubiquitin-like modifier (SUMO1 and SUMO2) isoforms. We apply our computational framework to study the mechanical anisotropy of Ub along the seven lysine-C-term directions which are functionally relevant. We show that Ub possesses two distinct flexibility scales along these directions which roughly differ by an order of magnitude. Further, our studies reveal that the mechanical anisotropy of Ub is modified in contrasting ways by the binding of two partner proteins (UBCH5A and UEV) which attach and recognize these biomolecular tag proteins. On the basis of equilibrium MD benchmarks for flexibility along 2485 bond vectors in Ub, we propose and validate a new covariance-propagation scheme to extract spring constants from ENM normal modes. We also critically examine the ability of ENM to predict directional flexibility of proteins and suggest modifications to improve these intuitive and scalable descriptions.

Coarse-grained elastic network modelling: A fast and stable numerical tool to characterize mesenchymal stem cells subjected to AFM nanoindentation measurements

The knowledge of the mechanical properties is the starting point to study the mechanobiology of mesenchymal stem cells and to understand the relationships linking biophysical stimuli to the cellular differentiation process. In experimental biology, Atomic Force Microscopy (AFM) is a common technique for measuring these mechanical properties.In this paper we present an alternative approach for extracting common mechanical parameters, such as the Young's modulus of cell components, starting from AFM nanoindentation measurements conducted on human mesenchymal stem cells. In a virtual environment, a geometrical model of a stem cell was converted in a highly deformable Coarse-Grained Elastic Network Model (CG-ENM) to reproduce the real AFM experiment and retrieve the related force-indentation curve. An ad-hoc optimization algorithm perturbed the local stiffness values of the springs, subdivided in several functional regions, until the computed force-indentation curve replicated the experimental one. After this curve matching, the extraction of global Young's moduli was performed for different stem cell samples. The algorithm was capable to distinguish the material properties of different subcellular components such as the cell cortex and the cytoskeleton. The numerical results predicted with the elastic network model were then compared to those obtained from hertzian contact theory and Finite Element Method (FEM) for the same case studies, showing an optimal agreement and a highly reduced computational cost.The proposed simulation flow seems to be an accurate, fast and stable method for understanding the mechanical behavior of soft biological materials, even for subcellular levels of detail. Moreover, the elastic network modelling allows shortening the computational times to approximately 33% of the time required by a traditional FEM simulation performed using elements with size comparable to that of springs.

Coarse-Grained Simulation of Full-Length Integrin Activation

Integrin conformational dynamics are critical to their receptor and signaling functions in many cellular processes, including spreading, adhesion, and migration. However, assessing integrin conformations is both experimentally and computationally challenging because of limitations in resolution and dynamic sampling. Thus, structural changes that underlie transitions between conformations are largely unknown. Here, focusing on integrin αvβ3, we developed a modified form of the coarse-grained heterogeneous elastic network model (hENM), which allows sampling conformations at the onset of activation by formally separating local fluctuations from global motions. Both local fluctuations and global motions are extracted from all-atom molecular dynamics simulations of the full-length αvβ3 bent integrin conformer, but whereas the former are incorporated in the hENM as effective harmonic interactions between groups of residues, the latter emerge by systematically identifying and treating weak interactions between long-distance domains with flexible and anharmonic connections. The new hENM model allows integrins and single-point mutant integrins to explore various conformational states, including the initiation of separation between α- and β-subunit cytoplasmic regions, headpiece extension, and legs opening.

Modeling of Protein Structural Flexibility and Large-Scale Dynamics: Coarse-Grained Simulations and Elastic Network Models

Fluctuations of protein three-dimensional structures and large-scale conformational transitions are crucial for the biological function of proteins and their complexes. Experimental studies of such phenomena remain very challenging and therefore molecular modeling can be a good alternative or a valuable supporting tool for the investigation of large molecular systems and long-time events. In this minireview, we present two alternative approaches to the coarse-grained (CG) modeling of dynamic properties of protein systems. We discuss two CG representations of polypeptide chains used for Monte Carlo dynamics simulations of protein local dynamics and conformational transitions, and highly simplified structure-based elastic network models of protein flexibility. In contrast to classical all-atom molecular dynamics, the modeling strategies discussed here allow the quite accurate modeling of much larger systems and longer-time dynamic phenomena. We briefly describe the main features of these models and outline some of their applications, including modeling of near-native structure fluctuations, sampling of large regions of the protein conformational space, or possible support for the structure prediction of large proteins and their complexes.

Designed Elastic Networks: Models of Complex Protein Machinery.

Recently, the design of mechanical networks with protein-inspired responses has become increasingly popular. Here, we review contributions which were motivated by studies of protein dynamics employing coarse-grained elastic network models. First, the concept of evolutionary optimization that we developed to design network structures which execute prescribed tasks is explained. We then review what presumably marks the origin of the idea to design complex functional networks which encode protein-inspired behavior, namely the design of an elastic network structure which emulates the cycles of ATP-powered conformational motion in protein machines. Two recent applications are reviewed. First, the construction of a model molecular motor, whose operation incorporates both the tight coupling power stroke as well as the loose coupling Brownian ratchet mechanism, is discussed. Second, the evolutionary design of network structures which encode optimal long-range communication between remote sites and represent mechanical models of allosteric proteins is presented. We discuss the prospects of designed protein-mimicking elastic networks as model systems to elucidate the design principles and functional signatures underlying the operation of complex protein machinery.

Flexible fitting to cryo-electron microscopy maps with coarse-grained elastic network models

Cryo-electron microscopy has become an important tool for protein structure determination in recent decades. Since proteins may exist in multiple conformational states, combining high resolution X-ray or NMR structures with cryo-electron microscopy maps is a useful approach to obtain proteins in different functional states. Flexible fitting methods used in cryo-electron microscopy aim to obtain an unknown protein conformation from a high resolution structure and a cryo-electron microscopy map. Since all-atom flexible fitting is computationally expensive, many efficient flexible fitting algorithms that utilize coarse-grained elastic network models have been proposed. In this study, we investigated performance of three coarse-grained elastic network model-based flexible fitting methods (EMFF, iModFit, NMFF) using 25 protein pairs at four resolutions. This study shows that the application of coarse-grained elastic network models to flexible fitting of cryo-electron microscopy maps can provide fast and fruitful models of various conformational states of proteins.

Comparisons of Protein Dynamics from Experimental Structure Ensembles, Molecular Dynamics Ensembles, and Coarse-Grained Elastic Network Models.

Predicting protein motions is important for bridging the gap between protein structure and function. With growing numbers of structures of the same or closely related proteins becoming available, it is now possible to understand more about the intrinsic dynamics of a protein with principal component analysis (PCA) of the motions apparent within ensembles of experimental structures. In this paper, we compare the motions extracted from experimental ensembles of 50 different proteins with the modes of motion predicted by several types of coarse-grained elastic network models (ENMs) which additionally take into account more details of either the protein geometry or the amino acid specificity. We further compare the structural variations in the experimental ensembles with the motions sampled in molecular dynamics (MD) simulations for a smaller subset of 17 proteins with available trajectories. We find that the correlations between the motions extracted from MD trajectories and experimental structure ensembles are slightly different than those for the ENMs, possibly reflecting potential sampling biases. We find that there are small gains in the predictive power of the ENMs in reproducing motions present in either experimental or MD ensembles by accounting for the protein geometry rather than the amino acid specificity of the interactions.

Altered dynamics upon oligomerization corresponds to key functional sites.

It is known that over half of the proteins encoded by most organisms function as oligomeric complexes. Oligomerization confers structural stability and dynamics changes in proteins. We investigate the effects of oligomerization on protein dynamics and its functional significance for a set of 145 multimeric proteins. Using coarse-grained elastic network models, we inspect the changes in residue fluctuations upon oligomerization and then compare with residue conservation scores to identify the functional significance of these changes. Our study reveals conservation of about ½ of the fluctuations, with ¼ of the residues increasing in their mobilities and ¼ having reduced fluctuations. The residues with dampened fluctuations are evolutionarily more conserved and can serve as orthosteric binding sites, indicating their importance. We also use triosephosphate isomerase as a test case to understand why certain enzymes function only in their oligomeric forms despite the monomer including all required catalytic residues. To this end, we compare the residue communities (groups of residues which are highly correlated in their fluctuations) in the monomeric and dimeric forms of the enzyme. We observe significant changes to the dynamical community architecture of the catalytic core of this enzyme. This relates to its functional mechanism and is seen only in the oligomeric form of the protein, answering why proteins are oligomeric structures. Proteins 2017; 85:1422-1434. © 2017 Wiley Periodicals, Inc.

Multiscale design of coarse-grained elastic network-based potentials for the μ opioid receptor.

Despite progress in computer modeling, most biological processes are still out of reach when using all-atom (AA) models. Coarse-grained (CG) models allow classical molecular dynamics (MD) simulations to be accelerated. Although simplification of spatial resolution at different levels is often investigated, simplification of the CG potential in itself has been less common. CG potentials are often similar to AA potentials. In this work, we consider the design and reliability of purely mechanical CG models of the μ opioid receptor (μOR), a G protein-coupled receptor (GPCR). In this sense, CG force fields (FF) consist of a set of holonomic constraints guided by an elastic network model (ENM). Even though ENMs are used widely to perform normal mode analysis (NMA), they are not often implemented as a single FF in the context of MD simulations. In this work, various ENM-like potentials were investigated by varying their force constant schemes and connectivity patterns. A method was established to systematically parameterize ENM-like potentials at different spatial resolutions by using AA data. To do so, new descriptors were introduced. The choice of conformation descriptors that also include flexibility information is important for a reliable parameterization of ENMs with different degrees of sensitivity. Hence, ENM-like potentials, with specific parameters, can be sufficient to accurately reproduce AA MD simulations of μOR at highly coarse-grained resolutions. Therefore, the essence of the flexibility properties of μOR can be captured with simple models at different CG spatial resolutions, opening the way to mechanical approaches to understanding GPCR functions. Graphical Abstract All atom structure, residue interaction network and coarse-grained elastic network models of the μ opioid receptor (μOR).

Approach to the unfolding and folding dynamics of add A-riboswitch upon adenine dissociation using a coarse-grained elastic network model.

Riboswitches are noncoding mRNA segments that can regulate the gene expression via altering their structures in response to specific metabolite binding. We proposed a coarse-grained Gaussian network model (GNM) to examine the unfolding and folding dynamics of adenosine deaminase (add) A-riboswitch upon the adenine dissociation, in which the RNA is modeled by a nucleotide chain with interaction networks formed by connecting adjoining atomic contacts. It was shown that the adenine binding is critical to the folding of the add A-riboswitch while the removal of the ligand can result in drastic increase of the thermodynamic fluctuations especially in the junction regions between helix domains. Under the assumption that the native contacts with the highest thermodynamic fluctuations break first, the iterative GNM simulations showed that the unfolding process of the adenine-free add A-riboswitch starts with the denature of the terminal helix stem, followed by the loops and junctions involving ligand binding pocket, and then the central helix domains. Despite the simplified coarse-grained modeling, the unfolding dynamics and pathways are shown in close agreement with the results from atomic-level MD simulations and the NMR and single-molecule force spectroscopy experiments. Overall, the study demonstrates a new avenue to investigate the binding and folding dynamics of add A-riboswitch molecule which can be readily extended for other RNA molecules.

Atomistic analysis of ATP hydrolysis effect on a dynein walking mechanism

Dynein is a microtubule motor protein that is highly involved in cell motility. Although its atomic structure was recently reported, it has been believed that dynein, like other motor proteins, generates a large swing motion powered by ATP hydrolysis. In this paper, we have analyzed ATP hydrolysis effect on the walking mechanism of dynein at the atomic level using a Ca coarse-grained elastic network model. Normal mode analysis (NMA) revealed that the detachment of the linker from the head of dynein, which is triggered by ATP hydrolysis, facilitates the main swing motion of dynein in two ways: allowing the bending motion as an extra degree-of-freedom (topologically) and lowering the energy barrier between the closed and open forms (energetically). This large conformational transition pathway is successfully generated by Elastic network interpolation (ENI). Comparison between the ENI pathway and the NMA results clearly elucidates the role of ATP hydrolysis in motor proteins as well as the swing motion of dynein in atomic detail.

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.

Mechanical Mass-Spring Model for Understanding Globular Motion of Proteins

AbstractThe conformational (structural) change of proteins plays an essential role in their functions. Experiments have been conducted to try to understand the conformational change of proteins, but they have not been successful in providing information on the atomic scale. Simulation methods have been developed to understand the conformational change at an atomic scale in detail. Coarse-grained methods have been developed to calculate protein dynamics with computational efficiency when compared with than all-atom models. A structure-based mass-spring model called the elastic network model (ENM) showed excellent performance in various protein studies. Coarse-grained ENM was modified in various ways to improve the computational efficiency, and consequently to reduce required computational cost for studying the large-scale protein structures. Our previous studies report a modified mass-spring model, which was developed based on condensation method applicable to ENM, and show that the model is able to accurately predict the fluctuation behavior of proteins. We applied this modified mass-spring model to analyze the conformational changes in proteins. We consider two model proteins as an example, where these two proteins exhibit different functions and molecular sizes. It is shown that the modified mass-spring model allows for accurately predicting the pathways of conformation changes for proteins. Our model provides structural insights into the conformation change of proteins related to the biological functions of large protein complexes.

Screening for mechanical responses of proteins using coarse-grained elastic network models

Screening for mechanical responses of proteins using coarse-grained elastic network models

Simple Elastic Network Models for Exhaustive Analysis of Long Double-Stranded DNA Dynamics with Sequence Geometry Dependence.

Simple elastic network models of DNA were developed to reveal the structure-dynamics relationships for several nucleotide sequences. First, we propose a simple all-atom elastic network model of DNA that can explain the profiles of temperature factors for several crystal structures of DNA. Second, we propose a coarse-grained elastic network model of DNA, where each nucleotide is described only by one node. This model could effectively reproduce the detailed dynamics obtained with the all-atom elastic network model according to the sequence-dependent geometry. Through normal-mode analysis for the coarse-grained elastic network model, we exhaustively analyzed the dynamic features of a large number of long DNA sequences, approximately ∼150 bp in length. These analyses revealed positive correlations between the nucleosome-forming abilities and the inter-strand fluctuation strength of double-stranded DNA for several DNA sequences.

Oncogenic mutations weaken the interactions that stabilize the p110α-p85α heterodimer in phosphatidylinositol 3-kinase α.

Phosphatidylinositol 3-kinase (PI3K) α is a heterodimeric lipid kinase that catalyzes the conversion of phosphoinositol-4,5-bisphosphate to phosphoinositol-3,4,5-trisphosphate. The PI3Kα signaling pathway plays an important role in cell growth, proliferation, and survival. This pathway is activated in numerous cancers, where the PI3KCA gene, which encodes for the p110α PI3Kα subunit, is mutated. Its mutation often results in gain of enzymatic activity; however, the mechanism of activation by oncogenic mutations remains unknown. Here, using computational methods, we show that oncogenic mutations that are far from the catalytic site and increase the enzymatic affinity destabilize the p110α-p85α dimer. By affecting the dynamics of the protein, these mutations favor the conformations that reduce the autoinhibitory effect of the p85α nSH2 domain. For example, we determined that, in all of the mutants, the nSH2 domain shows increased positional heterogeneity as compared with the wild-type, as demonstrated by changes in the fluctuation profiles computed by normal mode analysis of coarse-grained elastic network models. Analysis of the interdomain interactions of the wild-type and mutants at the p110α-p85α interface obtained with molecular dynamics simulations suggest that all of the tumor-associated mutations effectively weaken the interactions between p110α and p85α by disrupting key stabilizing interactions. These findings have important implications for understanding how oncogenic mutations change the conformational multiplicity of PI3Kα and lead to increased enzymatic activity. This mechanism may apply to other enzymes and/or macromolecular complexes that play a key role in cell signaling.

Hamiltonian replica exchange combined with elastic network analysis to enhance global domain motions in atomistic molecular dynamics simulations.

Coarse-grained elastic network models (ENM) of proteins offer a low-resolution representation of protein dynamics and directions of global mobility. A Hamiltonian-replica exchange molecular dynamics (H-REMD) approach has been developed that combines information extracted from an ENM analysis with atomistic explicit solvent MD simulations. Based on a set of centers representing rigid segments (centroids) of a protein, a distance-dependent biasing potential is constructed by means of an ENM analysis to promote and guide centroid/domain rearrangements. The biasing potentials are added with different magnitude to the force field description of the MD simulation along the replicas with one reference replica under the control of the original force field. The magnitude and the form of the biasing potentials are adapted during the simulation based on the average sampled conformation to reach a near constant biasing in each replica after equilibration. This allows for canonical sampling of conformational states in each replica. The application of the methodology to a two-domain segment of the glycoprotein 130 and to the protein cyanovirin-N indicates significantly enhanced global domain motions and improved conformational sampling compared with conventional MD simulations.

Simulating Large-Scale Conformational Changes of Proteins by Accelerating Collective Motions Obtained from Principal Component Analysis

Enhanced sampling methods remain of continuing interest over the past decades because they are able to explore conformational space of proteins much more extensively than conventional molecular dynamics (MD) simulations. In this paper, we report a new sampling method that utilizes a few collective modes obtained from principal component analysis (PCA) to guide the MD simulations. Two multidomain proteins, bacteriophage T4 lysozyme and human vinculin, are studied to test the method. By updating the PCA modes with a proper frequency, our method can sample large-amplitude conformational changes of the proteins much more efficiently than standard MD. Since those PCA modes are calculated from structural ensembles generated by all-atom simulations, the method may overcome an inherent limitation called "tip effect" that would possibly appear in those sampling techniques based on coarse-grained elastic network models. The algorithm proposed here is potentially very useful in developing tools for flexible fitting of protein structures integrating cryo-electron microscope or small-angle X-ray scattering data.