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

Pagès, Guillaume; Grudinin, Sergei

doi:10.1016/j.jsb.2018.05.005

Cited by 17 publications

(15 citation statements)

References 22 publications

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“…Our initial approach consisted in projecting the centers of mass of the different subunits on the plane orthogonal to the principal eigenvector of the inertia matrix of the assembly, and then reordering the subunits according to this projection. During the second part of this work [26], we developed a much more general and robust method that automatically determines the permutations between the subunits for each rotation operator in a certain symmetry group including cyclic, dihedral and cubic cases.…”

Section: Working With Molecular Assembliesmentioning

confidence: 99%

“…This perception is based on a robust determination of permutations between the assembly subunits corresponding to each rotation operator within the symmetry group. All the relevant details including the discrete optimization approach for the identification of the permutations are described in the second part of this work, which is specifically devoted to high-order symmetries with multiple symmetry axes [26].…”

Section: Computational Detailsmentioning

confidence: 99%

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Analytical symmetry detection in protein assemblies. I. Cyclic symmetries

Pagès

Kinzina

Grudinin

2018

Journal of Structural Biology

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Symmetry in protein, and, more generally, in macromolecular assemblies is a key point to understand their structure, stability and function. Many symmetrical assemblies are currently present in the Protein Data Bank (PDB) and some of them are among the largest solved structures, thus an efficient computational method is needed for the exhaustive analysis of these. The cyclic symmetry groups represent the most common assemblies in the PDB. These are also the building blocks for higher-order symmetries. This paper presents a mathematical formulation to find the position and the orientation of the symmetry axis in a cyclic symmetrical protein assembly, and also to assess the quality of this symmetry. Our method can also detect symmetries in partial assemblies. We provide an efficient C++ implementation of the method and demonstrate its efficiency on several examples including partial assemblies and pseudo symmetries. We also compare the method with two other published techniques and show that it is significantly faster on all the tested examples. Our method produces results with a machine precision, its cost function is solely based on 3D Euclidean geometry, and most of the operations are performed analytically. The method is available athttp://team.inria.fr/nano-d/software/ananas. The graphical user interface of the method built for the SAMSON platform is available athttp://samson-connect.net.

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Section: Working With Molecular Assembliesmentioning

confidence: 99%

Section: Computational Detailsmentioning

confidence: 99%

Analytical symmetry detection in protein assemblies. I. Cyclic symmetries

Pagès

Kinzina

Grudinin

2018

Journal of Structural Biology

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“…Over the years, efforts have been made to define and quantify protein symmetry levels using various methods based on quaternary-structure-alignment algorithms [9][10][11][12][13][14][15][16][17][18][19]. These methods involve superposing one peptide on another, and estimating their alignment by root mean square deviation (RMSD) of matching α-carbons, or by a related scoring formula.…”

Section: Introductionmentioning

confidence: 99%

Side chain flexibility and the symmetry of protein homodimers

Shalit

Tuvi-Arad

2020

PLoS ONE

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A comprehensive analysis of crystallographic data of 565 high-resolution protein homodimers comprised of over 250,000 residues suggests that amino acids form two groups that differ in their tendency to distort or symmetrize the structure of protein homodimers. Residues of the first group tend to distort the protein homodimer and generally have long or polar side chains. These include: Lys, Gln, Glu, Arg, Asn, Met, Ser, Thr and Asp. Residues of the second group contribute to protein symmetry and are generally characterized by short or aromatic side chains. These include: Ile, Pro, His, Val, Cys, Leu, Trp, Tyr, Phe, Ala and Gly. The distributions of the continuous symmetry measures of the proteins and the continuous chirality measures of their building blocks highlight the role of side chain geometry and the interplay between entropy and symmetry in dictating the conformational flexibility of proteins.

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“…The problem of detecting structural and, more specifically, symmetrical repetitions in protein assemblies can be formulated very well and was demonstrated to have efficient solutions [7,8]. On the other hand, identification of proteins with tandem repeats is a more difficult problem with a looser formulation [9,10,11].…”

Section: Introductionmentioning

confidence: 99%

DeepSymmetry: using 3D convolutional networks for identification of tandem repeats and internal symmetries in protein structures

Pagès

Grudinin

2019

Bioinformatics

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Motivation: Thanks to the recent advances in structural biology, nowadays three-dimensional structures of various proteins are solved on a routine basis. A large portion of these contain structural repetitions or internal symmetries. To understand the evolution mechanisms of these proteins and how structural repetitions affect the protein function, we need to be able to detect such proteins very robustly. As deep learning is particularly suited to deal with spatially organized data, we applied it to the detection of proteins with structural repetitions. Results: We present DeepSymmetry, a versatile method based on three-dimensional (3D) convolutional networks that detects structural repetitions in proteins and their density maps. Our method is designed to identify tandem repeat proteins, proteins with internal symmetries, symmetries in the raw density maps, their symmetry order, and also the corresponding symmetry axes. Detection of symmetry axes is based on learning six-dimensional Veronese mappings of 3D vectors, and the median angular error of axis determination is less than one degree. We demonstrate the capabilities of our method on benchmarks with tandem repeated proteins and also with symmetrical assemblies. For example, we have discovered over 10,000 putative tandem repeat proteins that are not currently present in the RepeatsDB database. Availability: The method is available at https://team.inria.fr/nano-d/software/deepsymmetry. It consists of a C++ executable that transforms molecular structures into volumetric density maps, and a Python code based on the TensorFlow framework for applying the DeepSymmetry model to these maps.

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

Cited by 17 publications

References 22 publications

Analytical symmetry detection in protein assemblies. I. Cyclic symmetries

Analytical symmetry detection in protein assemblies. I. Cyclic symmetries

Side chain flexibility and the symmetry of protein homodimers

DeepSymmetry: using 3D convolutional networks for identification of tandem repeats and internal symmetries in protein structures

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