Improved algorithms for quantifying the near symmetry of proteins: Complete side chains analysis

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Symmetry of proteins, an important source of their elegant structure and unique functions, is not as perfect as it may seem. In the framework of continuous symmetry, in which symmetry is no longer a binary yes/no property, such imperfections can be quantified and used as a global descriptor of the three-dimensional structure. We pre- sent an improved algorithm for calculating the continuous symmetry measure for proteins that takes into account their complete set of atoms including all side chains. Our method takes advantage of the protein sequence and the division into peptides in order to improve the accuracy and efficiency of the calculation over previous methods. The Hungarian algorithm is applied to solve the assignment problem and find the permutation that defines the symmetry operation. Analysis of the symmetry of several sets of protein homomers, with various degrees of rotational symme- try is presented. The new methodology lays the foundations for accurate, efficient and reliable large scale symmetry analysis of protein structure and can be used as a collective variable that describes changes of the protein geometry along various processes, both at the backbone level and for the complete protein structure.

Original languageEnglish
Article number39
JournalJournal of Cheminformatics
Issue number1
StatePublished - 2019

Bibliographical note

Funding Information:
Supported by the Israel Science Foundation (Grant 411/15).

Publisher Copyright:
© The Author(s) 2019. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver ( applies to the data made available in this article, unless otherwise stated.


  • Chirality
  • Hungarian algorithm
  • Molecular descriptors
  • Permutations
  • Protein structure
  • RMSD
  • Side chains
  • Symmetry


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