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Analytical symmetry detection in protein assemblies. II. Dihedral and Cubic symmetries

Guillaume Pagès 1 Sergei Grudinin 1
1 NANO-D - Algorithms for Modeling and Simulation of Nanosystems
Inria Grenoble - Rhône-Alpes, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology, LJK - Laboratoire Jean Kuntzmann
Abstract : Protein assemblies are often symmetric, as this organization has many advantages compared to individual proteins. Complex protein structures thus very often possess high-order symmetries. Detection and analysis of these symmetries has been a challenging problem and no efficient algorithms have been developed so far. This paper presents the extension of our cyclic symmetry detection method for higher-order symmetries with multiple symmetry axes. These include dihedral and cubic, i.e., tetrahedral, octahedral, and icosa-hedral, groups. Our method assesses the quality of a particular symmetry group and also determines all of its symmetry axes with a machine precision. The method comprises discrete and continuous optimization steps and is applicable to assemblies with multiple chains in the asymmetric subunits or to those with pseudo-symmetry. We implemented the method in C++ and exhaustively tested it on all 51,358 symmetrical assemblies from the Protein Data Bank (PDB). It allowed us to study structural organization of symmetrical assemblies solved by X-ray crystallography, and also to assess the symmetry annotation in the PDB. For example, in 1.6% of the cases we detected a higher symmetry group compared to the PDB annotation, and we also detected several cases with incorrect annotation. The method is available at The graphical user interface of the method built for the SAMSON platform is available at
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Submitted on : Friday, June 15, 2018 - 12:18:32 PM
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Guillaume Pagès, Sergei Grudinin. Analytical symmetry detection in protein assemblies. II. Dihedral and Cubic symmetries. Journal of Structural Biology, Elsevier, 2018, 203 (3), pp.185-194. ⟨10.1016/j.jsb.2018.05.005⟩. ⟨hal-01816449⟩



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