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Exact solution for minimization of root mean square deviation with G-RMSD to determine molecular similarity


Nabika, Tomohiro; Iwata, Satoru; Satoh, Hiroko (2024). Exact solution for minimization of root mean square deviation with G-RMSD to determine molecular similarity. Bulletin of the Chemical Society of Japan, 97(4):uoae037.

Abstract

Generalized root mean square deviation (G-RMSD) is an optimization method for three-dimensional molecular similarity determination. It calculates the minimum value of RMSD among all the possible one-to-one matchings between the atoms and positions of the molecules. The first paper on G-RMSD introduced two approaches called alternating optimization (AO) and tangent space relaxation (TSR) methods, which give local optimum solutions. We propose here a new method of G-RMSD using a branch-and-bound method (BnB) on isometric transformations, called IsometryOpt, which is mathematically proven to give an exact G-RMSD index, i.e. this method can reach the global optimum solution. The performance of IsometryOpt was compared to AO and TSR, as well as the MatchFastOpt method. IsometryOpt shows better performance than MatchFastOpt for molecules with the same number of atoms. AO and TSR fail to reach exact values in some cases. We also have developed two improved methods to search for all possible matches of a substructure in one or more molecules. One is called IsometrySearch, which uses BnB on isometric transformations. The other is a variant version of MatchFPT, called MatchFPT-delta. Computer experiments indicate that MatchFPT-delta performs better than MatchFPT and IsometrySearch.

Abstract

Generalized root mean square deviation (G-RMSD) is an optimization method for three-dimensional molecular similarity determination. It calculates the minimum value of RMSD among all the possible one-to-one matchings between the atoms and positions of the molecules. The first paper on G-RMSD introduced two approaches called alternating optimization (AO) and tangent space relaxation (TSR) methods, which give local optimum solutions. We propose here a new method of G-RMSD using a branch-and-bound method (BnB) on isometric transformations, called IsometryOpt, which is mathematically proven to give an exact G-RMSD index, i.e. this method can reach the global optimum solution. The performance of IsometryOpt was compared to AO and TSR, as well as the MatchFastOpt method. IsometryOpt shows better performance than MatchFastOpt for molecules with the same number of atoms. AO and TSR fail to reach exact values in some cases. We also have developed two improved methods to search for all possible matches of a substructure in one or more molecules. One is called IsometrySearch, which uses BnB on isometric transformations. The other is a variant version of MatchFPT, called MatchFPT-delta. Computer experiments indicate that MatchFPT-delta performs better than MatchFPT and IsometrySearch.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Department of Chemistry
Dewey Decimal Classification:540 Chemistry
Scopus Subject Areas:Physical Sciences > General Chemistry
Language:English
Date:28 March 2024
Deposited On:09 May 2024 10:15
Last Modified:30 Jun 2024 01:41
Publisher:Chemical Society of Japan
ISSN:0009-2673
OA Status:Hybrid
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1093/bulcsj/uoae037
Project Information:
  • : FunderJSPS
  • : Grant ID
  • : Project Title
  • Content: Published Version
  • Language: English
  • Licence: Creative Commons: Attribution 4.0 International (CC BY 4.0)