Efficient computation of root mean square deviations under rigid transformations

Journal of Computational Chemistry
Anna K HildebrandtAndreas Hildebrandt

Abstract

The computation of root mean square deviations (RMSD) is an important step in many bioinformatics applications. If approached naively, each RMSD computation takes time linear in the number of atoms. In addition, a careful implementation is required to achieve numerical stability, which further increases runtimes. In practice, the structural variations under consideration are often induced by rigid transformations of the protein, or are at least dominated by a rigid component. In this work, we show how RMSD values resulting from rigid transformations can be computed in constant time from the protein's covariance matrix, which can be precomputed in linear time. As a typical application scenario is protein clustering, we will also show how the Ward-distance which is popular in this field can be reduced to RMSD evaluations, yielding a constant time approach for their computation. © 2014 Wiley Periodicals, Inc.

References

Jun 24, 2005·Acta Crystallographica. Section A, Foundations of Crystallography·Douglas L Theobald
Oct 3, 2006·PLoS Computational Biology·Wan Kyu KimMichael Schroeder
Mar 25, 2010·Journal of Proteome Research·Panagiotis L Kastritis, Alexandre M J J Bonvin
Aug 11, 2011·PloS One·Sidhartha ChaudhuryJeffrey J Gray
Dec 27, 2011·Bioinformatics·Tim HarderThomas Hamelryck
Jun 19, 2013·Proteins·Sandor VajdaDima Kozakov

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Citations

Apr 19, 2019·Biomolecules·Christiane B de AraujoEmer S Ferro
Sep 4, 2014·Bioinformatics·Anna Katharina HildebrandtAndreas Hildebrandt

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