The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Charles L Brooks - One of the best experts on this subject based on the ideXlab platform.
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diversity and identity of mechanical properties of icosahedral viral capsids studied with elastic network Normal Mode Analysis
Journal of Molecular Biology, 2005Co-Authors: Florence Tama, Charles L BrooksAbstract:We analyze the mechanical properties and putative dynamical fluctuations of a variety of viral capsids comprising different sizes and quasi-equivalent symmetries by performing Normal Mode Analysis using the elastic network Model. The expansion of the capsid to a swollen state is studied using Normal Modes and is compared with the experimentally observed conformational change for three of the viruses for which experimental data exist. We show that a combination of one or two Normal Modes captures remarkably well the overall translation that dominates the motion between the two conformational states, and reproduces the overall conformational change. We observe for all of the viral capsids that the nature of the Modes is different. In particular for the T=7 virus, HK97, for which the shape of the capsid changes from spherical to faceted polyhedra, two Modes are necessary to accomplish the conformational transition. In addition, we extend our study to viral capsids with other T numbers, and discuss the similarities and differences in the features of virus capsid conformational dynamics. We note that the pentamers generally have higher flexibility and propensity to move freely from the other capsomers, which facilitates the shape adaptation that may be important in the viral life cycle.
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flexible multi scale fitting of atomic structures into low resolution electron density maps with elastic network Normal Mode Analysis
Journal of Molecular Biology, 2004Co-Authors: Florence Tama, Osamu Miyashita, Charles L BrooksAbstract:A novel method is presented for the quantitative flexible docking of high-resolution structure into low-resolution maps of macromolecular complexes from electron microscopy. This method uses a linear combination of low-frequency Normal Modes from elastic network description of the molecular framework in an iterative manner to deform the structure optimally to conform to the low-resolution electron density map. The methodology utilizes gradient following techniques in collective Normal Modes to locally optimize the overall correlation coefficient between computed and measured electron density. To evaluate the performance of our approach, several proteins, which undergo large conformational changes, have been studied. We demonstrate that refinement based on Normal Mode Analysis provides an accurate and fast alternative for the flexible fitting of high-resolution structure into a low-resolution density map. Additionally, we show that lower resolution (multi-scale) structural Models can be used for the Normal Mode searching in lieu of fully atomic Models with little loss of overall accuracy.
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dynamic reorganization of the functionally active ribosome explored by Normal Mode Analysis and cryo electron microscopy
Proceedings of the National Academy of Sciences of the United States of America, 2003Co-Authors: Florence Tama, Mikel Valle, Joachim Frank, Charles L BrooksAbstract:Combining structural data for the ribosome from x-ray crystallography and cryo-electron microscopy with dynamic Models based on elastic network Normal Mode Analysis, an atomically detailed picture of functionally important structural rearrangements that occur during translocation is elucidated. The dynamic Model provides a near-atomic description of the ratchet-like rearrangement of the 70S ribosome seen in cryo-electron microscopy, and permits the identification of bridging interactions that either facilitate the conformational switching or maintain structural integrity of the 50S/30S interface. Motions of the tRNAs residing in the A and P sites also suggest the early stages of tRNA translocation as a result of this ratchet-like movement. Displacement of the L1 stalk, alternately closing and opening the intersubunit space near the E site, is observed in the dynamic Model, in line with growing experimental evidence for the role of this structural component in facilitating the exiting of tRNA. Finally, a hinge-like transition in the 30S ribosomal subunit, similar to that observed in crystal structures of this complex, is also manifest as a dynamic Mode of the ribosome. The coincidence of these dynamic transitions with the individual Normal Modes of the ribosome and the good correspondence between these motions and those observed in experiment suggest an underlying principle of nature to exploit the shape of molecular assemblies such as the ribosome to provide robustness to functionally important motions.
Florence Tama - One of the best experts on this subject based on the ideXlab platform.
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Hybrid Electron Microscopy Normal Mode Analysis graphical interface and protocol
Journal of structural biology, 2014Co-Authors: Carlos Oscar S. Sorzano, José Miguel De La Rosa-trevín, Florence Tama, Slavica JonicAbstract:This article presents an integral graphical interface to the Hybrid Electron Microscopy Normal Mode Analysis (HEMNMA) approach that was developed for capturing continuous motions of large macromolecular complexes from single-particle EM images. HEMNMA was shown to be a good approach to analyze multiple conformations of a macromolecular complex but it could not be widely used in the EM field due to a lack of an integral interface. In particular, its use required switching among different software sources as well as selecting Modes for image Analysis was difficult without the graphical interface. The graphical interface was thus developed to simplify the practical use of HEMNMA. It is implemented in the open-source software package Xmipp 3.1 (http://xmipp.cnb.csic.es) and only a small part of it relies on MATLAB that is accessible through the main interface. Such integration provides the user with an easy way to perform the Analysis of macromolecular dynamics and forms a direct connection to the single-particle reconstruction process. A step-by-step HEMNMA protocol with the graphical interface is given in full details in Supplementary material. The graphical interface will be useful to experimentalists who are interested in studies of continuous conformational changes of macromolecular complexes beyond the Modeling of continuous heterogeneity in single particle reconstruction.
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diversity and identity of mechanical properties of icosahedral viral capsids studied with elastic network Normal Mode Analysis
Journal of Molecular Biology, 2005Co-Authors: Florence Tama, Charles L BrooksAbstract:We analyze the mechanical properties and putative dynamical fluctuations of a variety of viral capsids comprising different sizes and quasi-equivalent symmetries by performing Normal Mode Analysis using the elastic network Model. The expansion of the capsid to a swollen state is studied using Normal Modes and is compared with the experimentally observed conformational change for three of the viruses for which experimental data exist. We show that a combination of one or two Normal Modes captures remarkably well the overall translation that dominates the motion between the two conformational states, and reproduces the overall conformational change. We observe for all of the viral capsids that the nature of the Modes is different. In particular for the T=7 virus, HK97, for which the shape of the capsid changes from spherical to faceted polyhedra, two Modes are necessary to accomplish the conformational transition. In addition, we extend our study to viral capsids with other T numbers, and discuss the similarities and differences in the features of virus capsid conformational dynamics. We note that the pentamers generally have higher flexibility and propensity to move freely from the other capsomers, which facilitates the shape adaptation that may be important in the viral life cycle.
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flexible multi scale fitting of atomic structures into low resolution electron density maps with elastic network Normal Mode Analysis
Journal of Molecular Biology, 2004Co-Authors: Florence Tama, Osamu Miyashita, Charles L BrooksAbstract:A novel method is presented for the quantitative flexible docking of high-resolution structure into low-resolution maps of macromolecular complexes from electron microscopy. This method uses a linear combination of low-frequency Normal Modes from elastic network description of the molecular framework in an iterative manner to deform the structure optimally to conform to the low-resolution electron density map. The methodology utilizes gradient following techniques in collective Normal Modes to locally optimize the overall correlation coefficient between computed and measured electron density. To evaluate the performance of our approach, several proteins, which undergo large conformational changes, have been studied. We demonstrate that refinement based on Normal Mode Analysis provides an accurate and fast alternative for the flexible fitting of high-resolution structure into a low-resolution density map. Additionally, we show that lower resolution (multi-scale) structural Models can be used for the Normal Mode searching in lieu of fully atomic Models with little loss of overall accuracy.
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dynamic reorganization of the functionally active ribosome explored by Normal Mode Analysis and cryo electron microscopy
Proceedings of the National Academy of Sciences of the United States of America, 2003Co-Authors: Florence Tama, Mikel Valle, Joachim Frank, Charles L BrooksAbstract:Combining structural data for the ribosome from x-ray crystallography and cryo-electron microscopy with dynamic Models based on elastic network Normal Mode Analysis, an atomically detailed picture of functionally important structural rearrangements that occur during translocation is elucidated. The dynamic Model provides a near-atomic description of the ratchet-like rearrangement of the 70S ribosome seen in cryo-electron microscopy, and permits the identification of bridging interactions that either facilitate the conformational switching or maintain structural integrity of the 50S/30S interface. Motions of the tRNAs residing in the A and P sites also suggest the early stages of tRNA translocation as a result of this ratchet-like movement. Displacement of the L1 stalk, alternately closing and opening the intersubunit space near the E site, is observed in the dynamic Model, in line with growing experimental evidence for the role of this structural component in facilitating the exiting of tRNA. Finally, a hinge-like transition in the 30S ribosomal subunit, similar to that observed in crystal structures of this complex, is also manifest as a dynamic Mode of the ribosome. The coincidence of these dynamic transitions with the individual Normal Modes of the ribosome and the good correspondence between these motions and those observed in experiment suggest an underlying principle of nature to exploit the shape of molecular assemblies such as the ribosome to provide robustness to functionally important motions.
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Normal Mode Analysis with simplified Models to investigate the global dynamics of biological systems
Protein and Peptide Letters, 2003Co-Authors: Florence TamaAbstract:Dynamical properties of macromolecules are increasingly being recognized as significantly contributing to biological functions, including catalysis, regulation of activity, etc. In this review, theoretical approaches to the study of dynamics of biological systems and their application are discussed. In particular, simplified Models for the Normal Mode Analysis are described.
Slavica Jonic - One of the best experts on this subject based on the ideXlab platform.
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hybrid electron microscopy Normal Mode Analysis with scipion
Protein Science, 2020Co-Authors: Mohamad Harastani, Carlos Oscar S. Sorzano, Slavica JonicAbstract:Hybrid Electron Microscopy Normal Mode Analysis (HEMNMA) method was introduced in 2014. HEMNMA computes Normal Modes of a reference Model (an atomic structure or an electron microscopy map) of a molecular complex and uses this Model and its Normal Modes to analyze single-particle images of the complex to obtain information on its continuous conformational changes, by determining the full distribution of conformational variability from the images. An advantage of HEMNMA is a simultaneous determination of all parameters of each image (particle conformation, orientation, and shift) through their iterative optimization, which allows applications of HEMNMA even when the effects of conformational changes dominate those of orientational changes. HEMNMA was first implemented in Xmipp and was using MATLAB for statistical Analysis of obtained conformational distributions and for fitting of underlying trajectories of conformational changes. A HEMNMA implementation independent of MATLAB is now available as part of a plugin of Scipion V2.0 (http://scipion.i2pc.es). This plugin, named ContinuousFlex, can be installed by following the instructions at https://pypi.org/project/scipion-em-continuousflex. In this article, we present this new HEMNMA software, which is user-friendly, totally free, and open-source. STATEMENT FOR A BROADER AUDIENCE: This article presents Hybrid Electron Microscopy Normal Mode Analysis (HEMNMA) software that allows analyzing single-particle images of a complex to obtain information on continuous conformational changes of the complex, by determining the full distribution of conformational variability from the images. The HEMNMA software is user-friendly, totally free, open-source, and available as part of ContinuousFlex plugin (https://pypi.org/project/scipion-em-continuousflex) of Scipion V2.0 (http://scipion.i2pc.es).
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Hybrid Electron Microscopy Normal Mode Analysis graphical interface and protocol
Journal of structural biology, 2014Co-Authors: Carlos Oscar S. Sorzano, José Miguel De La Rosa-trevín, Florence Tama, Slavica JonicAbstract:This article presents an integral graphical interface to the Hybrid Electron Microscopy Normal Mode Analysis (HEMNMA) approach that was developed for capturing continuous motions of large macromolecular complexes from single-particle EM images. HEMNMA was shown to be a good approach to analyze multiple conformations of a macromolecular complex but it could not be widely used in the EM field due to a lack of an integral interface. In particular, its use required switching among different software sources as well as selecting Modes for image Analysis was difficult without the graphical interface. The graphical interface was thus developed to simplify the practical use of HEMNMA. It is implemented in the open-source software package Xmipp 3.1 (http://xmipp.cnb.csic.es) and only a small part of it relies on MATLAB that is accessible through the main interface. Such integration provides the user with an easy way to perform the Analysis of macromolecular dynamics and forms a direct connection to the single-particle reconstruction process. A step-by-step HEMNMA protocol with the graphical interface is given in full details in Supplementary material. The graphical interface will be useful to experimentalists who are interested in studies of continuous conformational changes of macromolecular complexes beyond the Modeling of continuous heterogeneity in single particle reconstruction.
Weiliang Zhu - One of the best experts on this subject based on the ideXlab platform.
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increasing the sampling efficiency of protein conformational change by combining a modified replica exchange molecular dynamics and Normal Mode Analysis
Journal of Chemical Theory and Computation, 2021Co-Authors: Cheng Peng, Jinan Wang, Yulong Shi, Weiliang ZhuAbstract: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.
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exploring transition pathway and free energy profile of large scale protein conformational change by combining Normal Mode Analysis and umbrella sampling molecular dynamics
Journal of Physical Chemistry B, 2014Co-Authors: Jinan Wang, Qiang Shao, Yingtao Liu, Zhuo Yang, Benjamin P Cossins, Hualiang Jiang, Kaixian Chen, Jiye Shi, Weiliang ZhuAbstract:Large-scale conformational changes of proteins are usually associated with the binding of ligands. Because the conformational changes are often related to the biological functions of proteins, understanding the molecular mechanisms of these motions and the effects of ligand binding becomes very necessary. In the present study, we use the combination of Normal-Mode Analysis and umbrella sampling molecular dynamics simulation to delineate the atomically detailed conformational transition pathways and the associated free-energy landscapes for three well-known protein systems, viz., adenylate kinase (AdK), calmodulin (CaM), and p38α kinase in the absence and presence of respective ligands. For each protein under study, the transient conformations along the conformational transition pathway and thermodynamic observables are in agreement with experimentally and computationally determined ones. The calculated free-energy profiles reveal that AdK and CaM are intrinsically flexible in structures without obvious en...
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exploring transition pathway and free energy profile of large scale protein conformational change by combining Normal Mode Analysis and umbrella sampling molecular dynamics
Journal of Physical Chemistry B, 2014Co-Authors: Jinan Wang, Qiang Shao, Yingtao Liu, Zhuo Yang, Benjamin P Cossins, Hualiang Jiang, Kaixian Chen, Jiye Shi, Weiliang ZhuAbstract:Large-scale conformational changes of proteins are usually associated with the binding of ligands. Because the conformational changes are often related to the biological functions of proteins, understanding the molecular mechanisms of these motions and the effects of ligand binding becomes very necessary. In the present study, we use the combination of Normal-Mode Analysis and umbrella sampling molecular dynamics simulation to delineate the atomically detailed conformational transition pathways and the associated free-energy landscapes for three well-known protein systems, viz., adenylate kinase (AdK), calmodulin (CaM), and p38α kinase in the absence and presence of respective ligands. For each protein under study, the transient conformations along the conformational transition pathway and thermodynamic observables are in agreement with experimentally and computationally determined ones. The calculated free-energy profiles reveal that AdK and CaM are intrinsically flexible in structures without obvious energy barrier, and their ligand binding shifts the equilibrium from the ligand-free to ligand-bound conformation (population shift mechanism). In contrast, the ligand binding to p38α leads to a large change in free-energy barrier (ΔΔG ≈ 7 kcal/mol), promoting the transition from DFG-in to DFG-out conformation (induced fit mechanism). Moreover, the effect of the protonation of D168 on the conformational change of p38α is also studied, which reduces the free-energy difference between the two functional states of p38α and thus further facilitates the conformational interconversion. Therefore, the present study suggests that the detailed mechanism of ligand binding and the associated conformational transition is not uniform for all kinds of proteins but correlated to their respective biological functions.
Ivet Bahar - One of the best experts on this subject based on the ideXlab platform.
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Normal Mode Analysis of biomolecular structures functional mechanisms of membrane proteins
Chemical Reviews, 2010Co-Authors: Ivet Bahar, Timothy R Lezon, Ahmet Bakan, Indira H ShrivastavaAbstract:1.1. Protein Dynamics and Allostery 1.1.1. Dynamic Equilibrium between Pre-existing Conformations The ability of macromolecules to sample an ensemble of conformations has been evident for decades, starting from the statistical mechanical theory and simulations of polymers.1–3 A polymer chain of N atoms enjoys 3N – 6 internal degrees of freedom, which gives rise to infinitely many conformations. Even a simple Model of N = 100 atoms where bond lengths and bond angles are fixed, and dihedral angles are restricted to discrete isomeric states—say three states per bond—has access to 3N–3 = 1.9 × 1046 conformations. Proteins, too, are polymers, and have access to ensembles of conformations. The main structural difference between proteins and other chain molecules is that, under physiological conditions, proteins sample a significantly narrower distribution of conformations compared to disordered polymers. Their conformational variations are confined to the neighborhood of a global energy minimum that defines their “native state”. While the native state has been traditionally viewed as a “unique structure” selected or encoded by the particular amino acid sequence, it is now established by theory, computations, and experiments, after the work of pioneering scientists in the field,4–15 that the native state actually represents an ensemble of microstates: these microstates maintain the overall “fold” and usually share common secondary structure, but they differ in their detailed atomic coordinates. Differences are manifested by variations in bond lengths, bond angles, dihedral angles, loop conformations, substructure packing, or even entire domain or subunit positions and orientations. Importantly, these microstates are not static: there is a dynamic equilibrium which allows for continual interconversions between them while maintaining their probability distribution. These “jigglings and wigglings of atoms” as expressed by Feynman,16 and clearly observed in molecular dynamics (MD) simulations, were originally viewed as random events, or stochastic properties, hardly relevant to biological function. They essentially account for local relaxation phenomena in the nanoseconds regime, which may facilitate, for example, the diffusion of oxygen into the heme cavity of myoglobin17 or the permeation of ions across selectivity filters in ion channels.18–20 However, recent studies indicate that these thermal fluctuations may not only passively facilitate but also actively drive concerted domain movements and/or allosteric interactions, such as those required for substrate binding, ion channel gating, or catalytic function.15,21–34 Figure 1 provides an overview of the broad range of equilibrium motions accessible under native state conditions, ranging from bond length vibrations, of the order of femtoseconds, to coupled movements of multimeric substructures, of the order of milliseconds or seconds. Figure 1 Equilibrium motions of proteins. Motions accessible near native state conditions range from femtoseconds (bond length vibrations) to milliseconds or slower (concerted movements of multiple subunits; passages between equilibrium substates). X-ray crystallographic ... 1.1.2. Functional Significance of Collective Motions In the last two decades, there has been a surge in the number of studies based on principal components Analysis (PCA)36 of biomolecular structures and dynamics. These studies have proven useful in unraveling the collective Modes, and in particular those at the low frequency end of the Mode spectrum, that underlie the equilibrium dynamics of proteins.37 Normal Mode Analysis (NMA) of equilibrium structures,38,39 essential dynamics Analysis (EDA) of the covariance matrices retrieved from MD runs,40 and singular value decomposition (SVD) of MD or Monte Carlo (MC) trajectories41–43 all fall in this category of PCA-based methods. Recently, a server has been developed to efficiently perform such calculations using a variety of input structures.44 PCA-based studies provide increasing support to the view that the apparently random fluctuations of proteins under native state conditions conceal contributions from highly cooperative movements (e.g., concerted opening and closing of domains) that are directly relevant to biological function. Functional movements indeed involve passages between collections of microstates or substates that coexist in a dynamic equilibrium (Figure 2). The most cooperative motions usually occur at the low frequency end of the Mode spectrum. These Modes engage large substructures, if not the entire structure, hence their designation as global or essential Modes. They are intrinsically accessible to biomolecules, arising solely from structure. In a sense, in the same way as sequence encodes structure, structure encodes the equilibrium dynamics. We refer to these global movements that are collectively encoded by the 3-dimensional (3D) structure as intrinsic motions of the examined protein, intrinsic to the protein fold or topology of native contacts. Biomolecular structures conceivably evolved to favor the global Modes that help them achieve their biological or allosteric functions.21 Briefly, the emerging paradigm is structure-encodes-dynamics-encodes-function, and an evolutionary pressure originating from functional dynamics requirements may have selected the relatively small space of functional structures. Figure 2 Energy profile of the native state Modeled at different resolutions. N denotes the native state, Modeled at a coarse-grained scale as a single energy minimum. A more detailed examination of the structure and energetics reveals two or more substates (S1, ... The predisposition of proteins to undergo functional changes in structure is now supported by numerous experimental and computational studies, and an increasing amount of data demonstrates that allosteric responses are driven by intrinsically accessible motions.15,23,24,45–51 These studies have brought a new understanding to the role of collective dynamics in protein functions, demonstrating in particular how the functions of membrane proteins such as signal transduction, pore opening, ion gating, or substrate translocation are enabled by the cooperative movements of symmetrically arranged subunits. These findings are in support of the original Monod–Wyman–Changeux (MWC) view of allosteric effects,52,53 the main tenets of which are predisposition of the structure to access alternative conformations via cooperative changes in structure (simultaneously engaging all subunits) and selection from this pool of accessible conformation to achieve biological function in the presence of ligand/substrate binding. Recent findings on the relevance of global Modes to functional dynamics are presented below for select, widely studied membrane proteins. The goal here is to review NMA-based computational methods and their applications to membrane proteins. We will also discuss recent developments for improving the methodology and its implementation in structure refinement and drug discovery methods.
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Normal Mode Analysis theory and applications to biological and chemical systems
2005Co-Authors: Qiang Cui, Ivet BaharAbstract:Normal Mode theory and harmonic potential approximations Konrad Hinsen All-atom Normal Mode calculations of large molecular systems using iterative methods Liliane Mouawad and David Perahia The Gaussian network Model: Theory and applications A.J. Radar, Chakra Chennubhotla, Lee-Wei Yang, Ivet Bahar Normal Mode Analysis of macromolecules: from enzyme activity site to molecular machines Guohui Li, Adam Van Wynsbergh, Omar N.A. Demerdash, Qiang Cui Functional information from slow Mode shapes Yves-Henri Sanejouand Unveiling molecular mechanisms of biological functions in large macromolecular assemblies using elastic network Normal Mode Analysis Florence Tama, Charles L. Brooks III Applications of Normal Mode Analysis in structural refinement of supramolecular complexes Jianpeng Ma Normal Mode Analysis in studying protein motions with x-ray crystallography George N. Phillips, Jr. Optimizing the parameters of the Gaussian network Model for ATP-binding proteins Taner Z. Sen, Robert L. Jernigan Effects of sequence, cyclization, and superhelical stress on the internet motions of DNA Atsushi Matsumoto, Wilma K. Olson Symmetry in Normal Mode Analysis of icosahedral viruses Herman W.T. van Vlijmen Extension of the Normal Mode concept: Principal component Analysis, jumping-among-minima Model, and their applications to experimental data Analysis Akio Kitao Imaginary-frequency, unstable instantaneous Normal Modes, the potential energy landscape, and diffusion in liquids T.Keyes Driven molecular dynamics for Normal Modes of biomolecules without the Hessian, and beyond Martina Kaledin, Alexey L. Kaledin, Alex Brown, and Joel Bowman Probing vibrational energy relaxation in proteins using Normal Modes Hiroshi Fujisaki, Lintao Bu, and John E. Straub Anharmonic decay of vibrational state in proteins Xin Yu, David M. Leitner Collective coordinate approaches to extended conformational sampling Michael Nilges, Rogher Abseher Using collective coordinates to guide conformational sampling in atomic simulations Haiyan Liu, Zhiyong Zhang, Jianbin He, Yunyu Shi
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coarse grained Normal Mode Analysis in structural biology
Current Opinion in Structural Biology, 2005Co-Authors: Ivet Bahar, A J RaderAbstract:The realization that experimentally observed functional motions of proteins can be predicted by coarse-grained Normal Mode Analysis has renewed interest in applications to structural biology. Notable applications include the prediction of biologically relevant motions of proteins and supramolecular structures driven by their structure-encoded collective dynamics; the refinement of low-resolution structures, including those determined by cryo-electron microscopy; and the identification of conserved dynamic patterns and mechanically key regions within protein families. Additionally, hybrid methods that couple atomic simulations with deformations derived from coarse-grained Normal Mode Analysis are able to sample collective motions beyond the range of conventional molecular dynamics simulations. Such applications have provided great insight into the underlying principles linking protein structures to their dynamics and their dynamics to their functions.
