NOLB Normal Modes


NOn-Linear rigid Block NMA approach (NOLB)  a new conceptually simple and computationally efficient method for non-linear normal mode analysis.

Cover Image for JCTC May issue, 2017


The key observation of our method is that the angular velocity of a residue can be interpreted as the result of an implicit force, such that the motion of the residue can be considered as a pure rotation about a certain center.

Linear Normal Modes of a protein-DNA complex

Linear Normal Modes of a protein-DNA complex

Non-Linear Normal Modes of a protein-DNA complex

Non-Linear Normal Modes of a protein-DNA complex

Test cases

To assessed the method with three types of tests, visual inspection of the motions, the energy and topology comparisons between the linear and non-linear deformations, and the  memory and CPU consumption of our method. There are, generally, three basic types of internal motions that a molecular system may exhibit. These are bending, stretching and twisting and shown below for a coiled-coil water-soluble protein from the cytoplasmic domain of a bacterial chemoreceptor (pdb code 2ch7).

Comparison of linear (A, C, E) and non-linear (B, D, F) motion extrapolations of a coiled coil protein (pdb code 2ch7). Three types of motions are shown, bending (A, B), stretching (C, D), and twisting (E, F). Several snapshots at different deformation amplitudes are superposed to each other. These are colored according to the values of the overall deformation, as measured by the root-mean-square deviation (RMSD). The colorbars show the RMSD with respect to the initial position. The arrows follow the trajectories of individual atoms.

Running time

Total time taken by the NOLB method to compute first 10, 100, and 1,000 normal modes for five molecular structures as a function of their size in a log-log scale. a) Timings for a Linux desktop provided. b) timings for a MacBook laptop provided.


Alexandre Hoffmann & Sergei Grudinin,

Nano-D team, Inria/CNRS Grenoble, France
e-mail: Sergei.Grudinin @


NOLB User Guide (v. 1.1)

NOLB for MacOS (v. 1.9)

NOLB for Linux (v. 1.9, supported GLIBC versions >= 2.10)

Data sets and scripts for structural transitions


GUI will be made available soon at


Usage cases and examples

For the explanation of the main method please see [1]. The way to generate structural ensembles within constant RMSD and applications to flexible docking are shown in [2]. Nonlinear structural transitions including those with iterative reconstruction of the Hessian matrix are explained and assessed in [3]. Elastic network modification using coloured contact maps, called HOPMA (Cyrillic transcript for NORMA), which boosts functional structural transitions and dynamics is given in [4]. We plan to integrate the essence of the HOPMA code inside NOLB, the full package is available at


All rights reserved. The academic version is free.


[1] Alexandre Hoffmann & Sergei Grudinin. NOLB : Non-linear rigid block normal mode analysis method. Journal of Chemical Theory and Computation, 2017, 13 (5), pp.2123-2134. DOI: 10.1021/acs.jctc.7b00197.  BibTex

[2] Emelie Neveu, Petr Popov, Alexandre Hoffmann, Angelo Migliosi, Xavier Besseron, Gregoire Danoy, Pascal Bouvry, Sergei Grudinin. RapidRMSD: Rapid determination of RMSDs corresponding to motions of flexible molecules. Bioinformatics, Oxford University Press (OUP), 2018, 34(16):2757–2765.〈10.1093/bioinformatics/bty160〉 BibTex

[3] Sergei Grudinin, Elodie Laine & Alexandre Hoffmann. Predicting protein functional motions: an old recipe with a new twist. 2020. Biophysical Journal. Volume 118, Issue 10, 19 May 2020, Pages 2513-2525.

[4] Elodie Laine & Sergei Grudinin. HOPMA: Boosting protein functional dynamics with colored contact maps. 2020. BibTex

Other NMA approaches

There is a list of other NMA methods including the following,

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