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RMSD and Symmetry
Evangelos A Coutsias1, Michael J Wester2
1Department of Applied Mathematics and Statistics and Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, New York 11794.
Journal of Computational Chemistry
|March 5, 2019
Summary
This study introduces a novel algorithm for efficiently calculating the root-mean-square deviation (RMSD) between molecular structures, improving upon existing methods for structural comparison and alignment.
Area of Science:
- Computational Biology
- Structural Bioinformatics
- Numerical Algorithms
Background:
- Comparing biomolecular or solid body structures commonly involves minimizing root-mean-square deviation (RMSD).
- Existing algorithms may not be optimal in terms of computational efficiency or handling complex symmetries.
Purpose of the Study:
- To present a new, robust numerical algorithm for computing RMSD between molecular structures.
- To provide an efficient method for calculating mutual RMSDs within a list of molecules and associated rotation matrices.
- To address and resolve issues related to symmetry in structural alignment and superposition.
Main Methods:
- Development of a novel numerical algorithm for RMSD computation.
- Implementation of methods to handle molecular symmetry, including geometric degeneracy and alternative alignments.
- Calculation of RMSD gradients and rotation matrices.
Main Results:
- The new algorithm computes RMSD and rotation matrices in a minimal number of operations compared to previous methods.
- The algorithm effectively addresses problems of symmetry, including degenerate superpositions.
- A software package, frmsd, has been developed and is freely available.
Conclusions:
- The presented algorithm offers a more efficient and robust approach to structural comparison using RMSD.
- The handling of symmetry issues provides more accurate and comprehensive structural alignments.
- The freely available software facilitates broader application in biomolecular structure analysis.
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