Normal Mode Analysis as a Routine Part of a Structural Investigation

Normal mode analysis (NMA) is a technique that can be used to describe the flexible states accessible to a protein about an equilibrium position. These states have been shown repeatedly to have functional significance. NMA is probably the least computationally expensive method for studying the dynamics of macromolecules, and advances in computer technology and algorithms for calculating normal modes over the last 20 years have made it nearly trivial for all but the largest systems. Despite this, it is still uncommon for NMA to be used as a component of the analysis of a structural study. In this review, we will describe NMA, outline its advantages and limitations, explain what can and cannot be learned from it, and address some criticisms and concerns that have been voiced about it. We will then review the most commonly used techniques for reducing the computational cost of this method and identify the web services making use of these methods. We will illustrate several of their possible uses with recent examples from the literature. We conclude by recommending that NMA become one of the standard tools employed in any structural study.

Download Full-text

ProMode-Oligomer: Database of Normal Mode Analysis in Dihedral Angle Space for a Full-Atom System of Oligomeric Proteins

The Open Bioinformatics Journal ◽

10.2174/1875036201206010009 ◽

2012 ◽

Vol 6 (1) ◽

pp. 9-19 ◽

Cited By ~ 3

Author(s):

Hiroshi Wako ◽

Shigeru Endo

Keyword(s):

Normal Mode ◽

Protein Complexes ◽

Normal Mode Analysis ◽

Normal Modes ◽

Point Of View ◽

Mode Analysis ◽

Dihedral Angles ◽

Oligomeric Proteins ◽

Displacement Vectors ◽

Atom System

The database ProMode-Oligomer (http://promode.socs.waseda.ac.jp/promode_oligomer) was constructed by collecting normal-mode-analysis (NMA) results for oligomeric proteins including protein-protein complexes. As in the ProMode database developed earlier for monomers and individual subunits of oligomers (Bioinformatics vol. 20, pp. 2035–2043, 2004), NMA was performed for a full-atom system using dihedral angles as independent variables, and we released the results (fluctuations of atoms, fluctuations of dihedral angles, correlations between atomic fluctuations, etc.). The vibrating oligomer is visualized by animation in an interactive molecular viewer for each of the 20 lowest-frequency normal modes. In addition, displacement vectors of constituent atoms for each normal mode were decomposed into two characteristic motions in individual subunits, i.e., internal and external (deformation and rigid-body movements of the individual subunits, respectively), and then the mutual movements of the subunits and the movement of atoms around the interface regions were investigated. These results released in ProMode-Oligomer are useful for characterizing oligomeric proteins from a dynamic point of view. The analyses are illustrated with immunoglobulin light- and heavy-chain variable domains bound to lysozyme and to a 12-residue peptide.

Download Full-text

Perturbed normal-mode analysis of induction times, relaxation times, and reaction rates in unimolecular reactions

Canadian Journal of Chemistry ◽

10.1139/v79-276 ◽

1979 ◽

Vol 57 (13) ◽

pp. 1723-1730 ◽

Cited By ~ 3

Author(s):

Andrew W. Yau ◽

Huw O. Pritchard

Keyword(s):

Normal Mode ◽

Transition Probabilities ◽

Normal Mode Analysis ◽

Relaxation Times ◽

Normal Modes ◽

Reaction Rates ◽

Mode Analysis ◽

Decomposition Reactions ◽

Induction Times ◽

Network Relationship

A perturbed normal-mode analysis is presented of the induction (or incubation) time, the relaxation rate, and the reaction rate of a diluted unimolecular system. At high temperature, the unimolecular rate approaches the Lindemann behaviour and the low-pressure rate is related to the normal modes of relaxation of the reactive states in a simple manner. In a step-ladder model system, the network relationship between the normal modes and the microscopic transition probabilities leads to explicit theoretical correlations between the respective experimental quantities. Illustrative calculations of such correlations are presented for the decomposition reactions of N2O and CO2 diluted in Ar at shock wave temperatures, and are compared with experiment.

Download Full-text

Molecular replacement via normal mode analysis and homology modelling on the web

Acta Crystallographica Section A Foundations of Crystallography ◽

10.1107/s0108767305093141 ◽

2005 ◽

Vol 61 (a1) ◽

pp. c161-c161

Author(s):

K. Suhre ◽

J.-B. Claude ◽

C. Abergel ◽

C. Notredame ◽

Y.-H. Sanejouand ◽

...

Keyword(s):

Normal Mode ◽

Homology Modelling ◽

Normal Mode Analysis ◽

Mode Analysis ◽

Molecular Replacement ◽

The Web

Download Full-text

Normal Mode Analysis as a Routine Part of a Structural Investigation

Prime Archives in Molecular Sciences ◽

10.37247/pamolscs.1.2020.3 ◽

2020 ◽

Author(s):

Jacob A Bauer ◽

Jelena Pavlović ◽

Vladena Bauerová-Hlinková

Keyword(s):

Normal Mode ◽

Structural Investigation ◽

Normal Mode Analysis ◽

Mode Analysis

Download Full-text

Predicting protein functional motions: an old recipe with a new twist

10.1101/703652 ◽

2019 ◽

Cited By ~ 1

Author(s):

Sergei Grudinin ◽

Elodie Laine ◽

Alexandre Hoffmann

Keyword(s):

Normal Mode ◽

Conformational Changes ◽

Normal Mode Analysis ◽

Normal Modes ◽

Low Frequency ◽

Structural Heterogeneity ◽

Mode Analysis ◽

Protein Motions ◽

Wide Range ◽

Geometrical Constraints

Large macromolecules, including proteins and their complexes, very often adopt multiple conformations. Some of them can be seen experimentally, for example with X-ray crystallography or cryo-electron microscopy. This structural heterogeneity is not occasional and is frequently linked with specific biological function. Thus, the accurate description of macromolecular conformational transitions is crucial for understanding fundamental mechanisms of life’s machinery. We report on a real-time method to predict such transitions by extrapolating from instantaneous eigen-motions, computed using the normal mode analysis, to a series of twists. We demonstrate the applicability of our approach to the prediction of a wide range of motions, including large collective opening-closing transitions and conformational changes induced by partner binding. We also highlight particularly difficult cases of very small transitions between crystal and solution structures. Our method guaranties preservation of the protein structure during the transition and allows to access conformations that are unreachable with classical normal mode analysis. We provide practical solutions to describe localized motions with a few low-frequency modes and to relax some geometrical constraints along the predicted transitions. This work opens the way to the systematic description of protein motions, whatever their degree of collectivity. Our method is available as a part of the NOn-Linear rigid Block (NOLB) package at https://team.inria.fr/nano-d/software/nolb-normal-modes/.Significance StatementProteins perform their biological functions by changing their shapes and interacting with each other. Getting access to these motions is challenging. In this work, we present a method that generates plausible physics-based protein motions and conformations. We model a protein as a network of atoms connected by springs and deform it along the least-energy directions. Our main contribution is to perform the deformations in a nonlinear way, through a series of twists. This allows us to produce a wide range of motions, some of them previously inaccessible, and to preserve the structure of the protein during the motion. We are able to simulate the opening or closing of a protein and the changes it undergoes to adapt to a partner.

Download Full-text

Normal-mode linear analysis and initial conditions of capillary jets

Journal of Fluid Mechanics ◽

10.1017/s0022112008000724 ◽

2008 ◽

Vol 602 ◽

pp. 81-117 ◽

Cited By ~ 15

Author(s):

F. J. GARCÍA ◽

H. GONZÁLEZ

Keyword(s):

Normal Mode ◽

Initial Conditions ◽

Normal Mode Analysis ◽

Normal Modes ◽

Linear Analysis ◽

Mode Analysis ◽

Initial Transient ◽

Exhaustive Study ◽

Capillary Jets ◽

Necessary And Sufficient

The normal-mode linear analysis of an axisymmetric infinite capillary jet is generalized to account for arbitrary initial conditions. An exhaustive study of the dispersion relation reveals the parametric behaviour of all eigenvalues and their corresponding normal modes. The two capillary modes (dominant and subdominant) are found to be necessary and sufficient to describe any possible non-recirculating initial conditions. An infinite set of other modes accounts for initial conditions with recirculating velocity field. The predictions of the normal-mode analysis are contrasted against previous computations of the initial-value problem, previous experiments, and our own one-dimensional numerical simulations. Contrary to the claim of some authors, the normal-mode analysis accurately predicts the initial transient with non-exponential growth of the disturbance amplitude observed in previous works. Simple and accurate formulae for the duration of the initial transient are deduced, with emphasis on improving the growth-rate measurement.

Download Full-text

Normal Mode Analysis: A Tool for Better Understanding Protein Flexibility and Dynamics with Application to Homology Models

10.5772/intechopen.94139 ◽

2020 ◽

Author(s):

Jacob A. Bauer ◽

Vladena Bauerová-Hlinková

Keyword(s):

Normal Mode ◽

Protein Complexes ◽

Normal Mode Analysis ◽

Computational Cost ◽

Protein Flexibility ◽

Systematic Investigation ◽

Mode Analysis ◽

Biological Macromolecules ◽

Elastic Network Model ◽

Large Proteins

Molecular dynamics (MD) and normal mode analysis (NMA) are very useful methods for characterizing various dynamic aspects of biological macromolecules. In comparison to MD, NMA is computationally less expensive which facilitates the quick and systematic investigation of protein flexibility and dynamics even for large proteins and protein complexes, whose structure was obtained experimentally or in silico. In particular, NMA can be used to describe the flexible states adopted by a protein around an equilibrium position. These states have been repeatedly shown to have biological relevance and functional significance. This chapter briefly characterizes NMA and describes the elastic network model, a schematic model of protein shape used to decrease the computational cost of this method. Finally, we will describe the applications of this technique to several large proteins and their complexes as well as its use in enhancing protein homology modeling.

Download Full-text

Normal Mode Solution for the Vibrational Motions of Long Flexible Booms on the RAE Satellite

Journal of Engineering for Industry ◽

10.1115/1.3428075 ◽

1971 ◽

Vol 93 (4) ◽

pp. 1280-1289

Author(s):

F. E. England ◽

P. F. Cunniff

Keyword(s):

Normal Mode ◽

Central Body ◽

Normal Mode Analysis ◽

Normal Modes ◽

Mode Analysis ◽

State Variables ◽

Computer Solution ◽

Thermal Bending ◽

Mode Solution ◽

Generalized Coordinate

A normal mode analysis is applied to the Radio Astronomy Explorer satellite which uses four 750 ft booms arranged in an “X” configuration. The state variables consist of three Euler angles of the central body, a damper boom angle and “8n” generalized coordinate for the four booms, in two orthogonal directions each, for each of the “n” normal modes selected. The following information is obtained from a computer solution: (a) the static deflection of the antenna booms, (b) the natural frequencies of the configuration, and (c) the steady-state dynamic deflections of the booms due to thermal bending. Results are compared with other approaches found in the literature.

Download Full-text

RAMAN SPECTRA OF TITANIUM DI-, TRI-, AND TETRA-CHLORIDES

International Journal of Modern Physics B ◽

10.1142/s021797920100886x ◽

2001 ◽

Vol 15 (28n30) ◽

pp. 3865-3868 ◽

Cited By ~ 2

Author(s):

H. MIYAOKA ◽

T. KUZE ◽

H. SANO ◽

H. MORI ◽

G. MIZUTANI ◽

...

Keyword(s):

Force Constant ◽

Raman Spectra ◽

Normal Mode ◽

Raman Band ◽

Normal Mode Analysis ◽

Force Constants ◽

Mode Analysis ◽

Oxidation Number

We have obtained the Raman spectra of TiCl n (n= 2, 3, and 4). Assignments of the observed Raman bands were made by a normal mode analysis. The force constants were determined from the observed Raman band frequencies. We have found that the Ti-Cl stretching force constant increases as the oxidation number of the Ti species increases.

Download Full-text