Normal Mode Analysis Techniques in Structural Biology

Abstract

The dynamic simulation of macromolecular systems with biologically relevant sizes and time scales is critical for understanding macromolecular function. In this context, normal mode analysis (NMA) approximates the complex dynamical behaviour of a macromolecule as a simple set of harmonic oscillators vibrating around a given equilibrium conformation. This technique, originated from classical mechanics, was first applied to investigate the dynamical properties of small biological systems more than 30 years ago. During this time, a wealth of evidence has accumulated to support NMA as a successful tool for simulating macromolecular motions at extended length scales. Today, NMA combined with coarse‐grained representations has become an efficient alternative to molecular dynamics simulations for studying the slow and large‐amplitude motions of macromolecular machines. Interesting insights into these systems can be obtained very quickly with NMA to characterise their flexibility, to predict the directions of their collective conformational changes, or to help in the interpretation of experimental structural data. The recently developed methods and applications of NMA together with an introduction of the underlying theory will be briefly reviewed here. Key Concepts: NMA computes all motions around an equilibrium conformation (normal modes). Normal modes are orthogonal displacement vectors with an associated frequency. The collective functional motions of the macromolecules are well described by lowest frequency modes. NMA inexpensive and accurately simulates the slow and large‐amplitude motions of biomolecules, but local reorganisations and the absolute time scale or amplitude of the motions are poorly predicted. NMA can be used to characterise macromolecular flexibility, to predict the directions of collective conformational changes, and to interpret structural experimental data.

Molecular ‘time‐machines’ to unravel key biological events for drug design

“…The high‐frequency modes usually describe the highly energetic motions, while low‐frequency normal modes relate to the low‐energy structural displacements. This way, NMA can reduce the dimensionality of the system (under study) and identify the essential (or important) conformational changes, including changes induced by binding, correlated motions, and allosteric regulation . NMA has shown to accurately describe the conformational changes of proteins in several cases, which agreed with the experiments .…”

“…Normal mode analysis (NMA) and molecular dynamics (MD) are two important computational methods that have been popularly employed to study the dynamics and conformational changes in proteins. NMA approximates the dynamic changes in biological systems as a simple set of harmonic oscillators vibrating around an equilibrium state (or an energy minima) . Each mode describes a state, where all particles of the system are vibrating with the same characteristic frequency, thus allowing most of the biological systems to be approximated as linear combinations of normal modes .…”

ALLO: A tool to discriminate and prioritize allosteric pockets

“…AlloPred uses Fpocket to identify pockets and generate the corresponding pocket descriptors. In addition to descriptors from Fpocket, it also integrates descriptors from a normal mode analysis (NMA) . This set of descriptors is then used to train an optimal SVM model.…”

Edge-based formulation of elastic network models

“…Typically, the analysis of (infinitesimal) motions involves diagonalization of H to determine the normal modes of the protein. While real potential energy surfaces of proteins are complex, highly nonlinear, and containing many minima [7], elastic models have been surprisingly effective for the analysis of slow equilibrium motions of proteins [8,9]. Another common use of ENMs is for the calculation of node fluctuations, which have shown good agreement with crystallographic B factors [10,11].…”