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Theoretically and Practically Faster Algorithms for Protein Structure Alignment

Authors Masahito Tsukahara , Tetsuo Shibuya

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Subject Classification

ACM Subject Classification
  • Theory of computation → Approximation algorithms analysis
  • Applied computing → Molecular structural biology
Keywords
  • Structural Bioinformatics
  • Pairwise Alignment
  • Exact Algorithm
  • Approximation Algorithm
  • Computational Geometry

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Abstract

Identifying shared substructures in 3D protein models is essential for structural bioinformatics. This task can be modeled as a sequential Largest Common Point-set (LCP) problem under the bottleneck distance. We propose a new O(n^13 log n)-time exact algorithm for this problem, which improves upon the previous best-known complexity of O(n^14), where n is the maximum size of the two input structures. Since these theoretical bounds are practically too large, an O(n⁷ log n)-time approximation algorithm with solution-size guarantees has been proposed; however, it remains too time-consuming for practical applications. Thus, we also propose a new filtering technique to enhance the approximation algorithm without increasing the theoretical time complexity or losing the solution-size guarantees. Experiments with PDB data show that our technique achieves over a 24-fold speedup at n = 130. While the previous algorithm required 3.80 hours on average for n = 130 in our experiments, making it difficult to test larger structures, our algorithm can process n = 200 in only 2.33 hours on average.

Cite As Get BibTex

Masahito Tsukahara and Tetsuo Shibuya. Theoretically and Practically Faster Algorithms for Protein Structure Alignment. In 26th International Conference on Algorithms for Bioinformatics (WABI 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 390, pp. 7:1-7:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.WABI.2026.7

Author Details

Masahito Tsukahara
  • Human Genome Center, The Institute of Medical Science, The University of Tokyo, Japan
  • Department of Computer Science, Graduate School of Information Science and Technology, The University of Tokyo, Japan
Tetsuo Shibuya
  • Human Genome Center, The Institute of Medical Science, The University of Tokyo, Japan

Funding

This work was partially supported by KAKENHI Grant Numbers 23K28035.

Supplementary Materials

References

  1. Tatsuya Akutsu. Protein structure alignment using dynamic programing and iterative improvement. IEICE Transactions on Information, E79-D(12):1629-1636, 1996. URL: https://globals.ieice.org/en_transactions/information/10.1587/e79-d_12_1629/_p.
  2. Christoph Ambühl, Samarjit Chakraborty, and Bernd Gärtner. Computing largest common point sets under approximate congruence. In Mike S. Paterson, editor, Algorithms - ESA 2000, pages 52-64. Springer Berlin Heidelberg, 2000. URL: https://doi.org/10.1007/3-540-45253-2_6.
  3. K. S. Arun, T. S. Huang, and S. D. Blostein. Least-squares fitting of two 3-d point sets. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-9(5):698-700, 1987. URL: https://doi.org/10.1109/TPAMI.1987.4767965.
  4. Saugata Basu, Richard Pollack, and Marie-Françoise Roy. Algorithms in Real Algebraic Geometry, volume 10 of Algorithms and Computation in Mathematics. Springer, 2 edition, 2006. URL: https://doi.org/10.1007/3-540-33099-2.
  5. Rudolf Bayer. Symmetric binary b-trees: Data structure and maintenance algorithms. Acta Informatica, 1(4):290-306, December 1972. URL: https://doi.org/10.1007/BF00289509.
  6. Helen M. Berman, John Westbrook, Zukang Feng, Gary Gilliland, T. N. Bhat, Helge Weissig, Ilya N. Shindyalov, and Philip E. Bourne. The protein data bank. Nucleic Acids Research, 28(1):235-242, January 2000. URL: https://doi.org/10.1093/nar/28.1.235.
  7. Nathalie S. Boutonnet, Marianne J. Rooman, Maria-Elena Ochagavia, Jean Richelle, and Shoshana J. Wodak. Optimal protein structure alignments by multiple linkage clustering: application to distantly related proteins. Protein Engineering, Design and Selection, 8(7):647-662, July 1995. URL: https://doi.org/10.1093/protein/8.7.647.
  8. Samarjit Chakraborty and Somenath Biswas. Approximation algorithms for 3-d common substructure identification in drug and protein molecules. In Frank Dehne, Jörg-Rüdiger Sack, Arvind Gupta, and Roberto Tamassia, editors, Algorithms and Data Structures, pages 253-264. Springer Berlin Heidelberg, 1999. URL: https://doi.org/10.1007/3-540-48447-7_26.
  9. Vicky Choi and Navin Goyal. A combinatorial shape matching algorithm for rigid protein docking. In Suleyman Cenk Sahinalp, S. Muthukrishnan, and Ugur Dogrusoz, editors, Combinatorial Pattern Matching, pages 285-296, Berlin, Heidelberg, 2004. Springer Berlin Heidelberg. URL: https://doi.org/10.1007/978-3-540-27801-6_21.
  10. Vicky Choi and Navin Goyal. An efficient approximation algorithm for point pattern matching under noise. In José R. Correa, Alejandro Hevia, and Marcos Kiwi, editors, LATIN 2006: Theoretical Informatics, pages 298-310. Springer Berlin Heidelberg, 2006. URL: https://doi.org/10.1007/11682462_30.
  11. Lars Holm, Christos Ouzounis, Chris Sander, Georg Tuparev, and Gert Vriend. A database of protein structure families with common folding motifs. Protein Science, 1(12):1691-1698, 1992. URL: https://doi.org/10.1002/pro.5560011217.
  12. Shuai Cheng Li, Dongbo Bu, Jinbo Xu, and Ming Li. Finding largest well-predicted subset of protein structure models. In Paolo Ferragina and Gad M. Landau, editors, Combinatorial Pattern Matching, pages 44-55, Berlin, Heidelberg, 2008. Springer Berlin Heidelberg. URL: https://doi.org/10.1007/978-3-540-69068-9_7.
  13. Shuai Cheng Li, Dongbo Bu, Jinbo Xu, and Ming Li. Finding nearly optimal gdt scores. Journal of Computational Biology, 18(5):693-704, 2011. URL: https://doi.org/10.1089/cmb.2010.0123.
  14. Shuai Cheng Li and Yen Kaow Ng. On protein structure alignment under distance constraint. Theoretical Computer Science, 412(32):4187-4199, 2011. Algorithms and Computation. URL: https://doi.org/10.1016/j.tcs.2010.11.045.
  15. John Moult, Krzysztof Fidelis, Andriy Kryshtafovych, Burkhard Rost, and Anna Tramontano. Critical assessment of methods of protein structure prediction - round viii. Proteins, 77(Suppl 9):1-4, 2009. URL: https://doi.org/10.1002/prot.22589.
  16. John Moult, Jan T. Pedersen, Richard Judson, and Krzysztof Fidelis. A large-scale experiment to assess protein structure prediction methods. Proteins: Structure, Function, and Bioinformatics, 23(3):ii-iv, 1995. URL: https://doi.org/10.1002/prot.340230303.
  17. Aleksandar Poleksic. On complexity of protein structure alignment problem under distance constraint. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 9(2):511-516, 2012. URL: https://doi.org/10.1109/TCBB.2011.133.
  18. Masahito Tsukahara and Tetsuo Shibuya. ProteinStructureAlignmentPlus. Software, URL: https://github.com/masat03110/ProteinStructureAlignmentPlus (visited on 2026-08-10).
    Software Heritage Logo archived version
  19. Masahito Tsukahara and Tetsuo Shibuya. Efficient and accurate approximation algorithms for protein structure alignment. In Bioinformatics Research and Applications: 21st International Symposium, ISBRA 2025, Helsinki, Finland, August 3–5, 2025, Proceedings, Part I, pages 122-134, Berlin, Heidelberg, 2025. Springer-Verlag. URL: https://doi.org/10.1007/978-981-95-0698-9_11.
  20. Gert Vriend and Chris Sander. Detection of common three-dimensional substructures in proteins. Proteins, 11(1):52-58, 1991. URL: https://doi.org/10.1002/prot.340110107.
  21. Jinbo Xu, Feng Jiao, and Bonnie Berger. A parameterized algorithm for protein structure alignment. Journal of Computational Biology, 14(5):564-577, 2007. PMID: 17683261. URL: https://doi.org/10.1089/cmb.2007.R003.
  22. Rongqing Yuan, Jing Zhang, Andriy Kryshtafovych, R. Dustin Schaeffer, Jian Zhou, Qian Cong, and Nick V. Grishin. Casp16 protein monomer structure prediction assessment. Proteins: Structure, Function, and Bioinformatics, 94(1):86-105, 2026. URL: https://doi.org/10.1002/prot.70031.
  23. A. Zemla, C. Venclovas, J. Moult, and K. Fidelis. Processing and analysis of casp3 protein structure predictions. Proteins, 37(Suppl 3):22-29, 1999. URL: https://doi.org/10.1002/(sici)1097-0134(1999)37:3+<22::aid-prot5>3.3.co;2-n.
  24. Adam Zemla. Lga: a method for finding 3d similarities in protein structures. Nucleic Acids Research, 31(13):3370-3374, July 2003. URL: https://doi.org/10.1093/nar/gkg571.
  25. Yang Zhang and Jeffrey Skolnick. Scoring function for automated assessment of protein structure template quality. Proteins: Structure, Function, and Bioinformatics, 57(4):702-710, 2004. URL: https://doi.org/10.1002/prot.20264.
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