Normal Mode Analysis Techniques in Structural Biology


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.

Keywords: normal mode analysis; dynamic simulation; conformational changes; X‐ray/NMR structure; coarse-grained

Figure 1.

Dynamics of biological molecules and computational approaches that can be used to investigate dynamical properties.

Figure 2.

Normal mode theory. (a) Description of a simple harmonic oscillator: A particle m is attached to a spring with a force constant k and its displacement is x. (b) Normal mode analysis: harmonic approximation of the potential energy surface. For any biological system, the real energy surface is rugged (dotted line) but for the normal mode analysis, the surface is approximated as a harmonic surface (plain line). (c) Normal mode coordinates are independent (uncoupled) but not Cartesian coordinates (coupled). Although the contour lines represent the equipotential points of a parabolic force field in a two‐dimensional space, the blue and red axis correspond to Cartesian (X) and normal mode (q) systems of coordinates, respectively. When some particle is released at any of the normal mode axes, its trajectory stays on this axis. In contrast, when the particle is released at some other point, its motion needs to be described by both Cartesian axes. (d) Simple normal mode vectors for the water molecule. Each arrow represents the direction of motion that each atom will undergo as obtained from normal mode theory. The three distinct motions predicted by NMA for the water molecule, i.e. symmetric and asymmetric stretching modes plus a bending mode, are in agreement with experimental observations.

Figure 3.

Normal mode analysis applied to a biological macromolecule. Representative atomic displacements corresponding to collective and local motions are shown for the adenylate kinase protein (chain A from PDB ID 4ake), the enzyme that catalyses the reaction: 2ADP↔ATP+AMP. Numbers are the mode indices sorted from low to high frequencies. Whereas the arrows represent the direction and relative amplitude of the motions, the different colours indicate the regions that are moving together. In the lowest frequency normal modes (collective motions), large groups of atoms experience a concerted motion, whereas in higher‐frequency modes (local modes), only some small groups are moving together (local motions). It is worth noting that the arrow lengths have been normalised for visualisation purposes, otherwise local motions should be smaller. These images were generated with the iMODS server (López‐Blanco et al., ) (

Figure 4.

Conformational open‐to‐closed transition pathway of the GroEL protein based on NMA. Starting from the open monomer (chain A from PDB ID 1sx4) (coloured structure at top left corner), a combination of low‐frequency modes were used iteratively to generate the intermediate structures (middle and bottom rows). Only those modes that reduced the differences with the closed conformation (chain H from PDB ID 1sx4) (grey) were employed. This transition was generated with the morphing tool of iMODS server (

Figure 5.

Flexible fitting of an atomic structure into a low‐resolution density map based on NMA. The high‐resolution structure of the thermosome (PDB ID 1a6d) (rainbow colours) has been flexibly fitted into a low‐resolution cryo‐Electron Microscopy density map (EMDB 1396) (grey transparency) with iMODFIT (Lopéz‐Blanco and Chacón, ) by using the low‐frequency modes to maximise the overlap between the map and the structure.



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Further Reading

Dill KA and Bromberg S (2003) Molecular Driving Forces: Statistical Thermodynamics in Chemistry and Biology. New York and London: Garland Science.

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López‐Blanco, José Ramón, Miyashita, Osamu, Tama, Florence, and Chacón, Pablo(Oct 2014) Normal Mode Analysis Techniques in Structural Biology. In: eLS. John Wiley & Sons Ltd, Chichester. [doi: 10.1002/9780470015902.a0020204.pub2]