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

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 http://team.inria.fr/nano-d/software/ananas. The graphical user interface of the method built for the SAMSON platform is available at http://samson-connect.net.

Mots clés: Point-Group Symmetry; Cubic Groups; Group Theory; Discrete Optimization; Protein Structure; Continuous Optimization

Domaines: Bio-informatique [q-bio.QM]; Biochimie, Biologie Moléculaire

Guillaume Pagès, Sergei Grudinin. Analytical symmetry detection in protein assemblies. II. Dihedral and Cubic symmetries. Journal of Structural Biology, 2018, 203 (3), pp.185-194. ⟨10.1016/j.jsb.2018.05.005⟩. ⟨hal-01816449⟩