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A Custom Bio-Inspired Algorithm for the Molecular Distance Geometry Problem

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Intelligent Systems (BRACIS 2023)

Abstract

Protein structure allows for an understanding of its function and enables the evaluation of possible interactions with other proteins. The molecular distance geometry problem (MDGP) regards determining a molecule’s three-dimensional (3D) structure based on the known distances between some pairs of atoms. An important application consists in finding 3D protein arrangements through data obtained by nuclear magnetic resonance (NMR). This work presents a study concerning the discretized version of the MDGP and the viability of employing genetic algorithms (GAs) to look for optimal solutions. We present computational results for input instances whose sizes varied from 10 to \(10^3\) atoms. The results obtained show that approaches to solving the discrete version of the MDGP based on GAs are promising.

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Notes

  1. 1.

    Instance set is publicly available in: https://bit.ly/3d0ezzo.

  2. 2.

    The set of instances is available in https://www.rcsb.org/.

References

  1. Berman, H.M., et al.: The protein data bank. Nucleic Acids Res. 28(1), 235–242 (2000)

    Article  Google Scholar 

  2. Biswas, P., Toh, K.C., Ye, Y.: A distributed SDP approach for large-scale noisy anchor-free graph realization with applications to molecular conformation. SIAM J. Sci. Comput. 30(3), 1251–1277 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  3. Carneiro, S., Souza, M., Filho, N., Tarrataca, L., Rosa, J., Assis, L.: Algoritmo genético aplicado ao problema da geometria de distâncias moleculares. In: Anais do LII Simpósio Brasileiro de Pesquisa Operacional (2020)

    Google Scholar 

  4. Creighton, T.E.: Proteins: Structures and Molecular Properties. Macmillan (1993)

    Google Scholar 

  5. Cucuringu, M., Singer, A., Cowburn, D.: Eigenvector synchronization, graph rigidity and the molecule problem. Inf. Infer. J. IMA 1(1), 21–67 (2012)

    MathSciNet  MATH  Google Scholar 

  6. Dong, Q., Wu, Z.: A linear-time algorithm for solving the molecular distance geometry problem with exact inter-atomic distances. J. Global Optim. 22(1), 365–375 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  7. Goldberg, D.E.: Genetic Algorithms in Search. Optimization, and Machine Learning (1989)

    Google Scholar 

  8. Goncalves, D.S., Lavor, C., Liberti, L., Souza, M.: A new algorithm for the \(^k\)dmdgp subclass of distance geometry problems (2020)

    Google Scholar 

  9. Gong, Y.J., et al.: Distributed evolutionary algorithms and their models: a survey of the state-of-the-art. Appl. Soft Comput. 34, 286–300 (2015)

    Article  Google Scholar 

  10. Hendrickson, B.: The molecule problem: exploiting structure in global optimization. SIAM J. Optim. 5(4), 835–857 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  11. Lavor, C., Liberti, L., Maculan, N., Mucherino, A.: The discretizable molecular distance geometry problem. Comput. Optim. Appl. 52(1), 115–146 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  12. Leung, N.H.Z., Toh, K.C.: An SDP-based divide-and-conquer algorithm for large-scale noisy anchor-free graph realization. SIAM J. Sci. Comput. 31(6), 4351–4372 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  13. Liberti, L., Lavor, C., Maculan, N., Marinelli, F.: Double variable neighbourhood search with smoothing for the molecular distance geometry problem. J. Global Optim. 43(2–3), 207–218 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  14. Liberti, L., Lavor, C., Mucherino, A.: The discretizable molecular distance geometry problem seems easier on proteins. In: Mucherino, A., Lavor, C., Liberti, L., Maculan, N. (eds.) Distance Geometry, pp. 47–60. Springer, New York (2013). https://doi.org/10.1007/978-1-4614-5128-0_3

  15. Liberti, L., Lavor, C., Mucherino, A., Maculan, N.: Molecular distance geometry methods: from continuous to discrete. Int. Trans. Oper. Res. 18(1), 33–51 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  16. Maculan Filho, N., Lavor, C.C., de Souza, M.F., Alves, R.: Álgebra e Geometria no Cálculo de Estrutura Molecular. Colóquio Brasileiro de Matemática, IMPA (2017)

    Google Scholar 

  17. Moré, J.J., Wu, Z.: Global continuation for distance geometry problems. SIAM J. Optim. 7(3), 814–836 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  18. Moré, J.J., Wu, Z.: Distance geometry optimization for protein structures. J. Global Optim. 15(3), 219–234 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  19. Mucherino, A., Lavor, C., Liberti, L.: The discretizable distance geometry problem. Optim. Lett. 6(8), 1671–1686 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  20. Mucherino, A., Lavor, C., Liberti, L.: Exploiting symmetry properties of the discretizable molecular distance geometry problem. J. Bioinform. Comput. Biol. 10(03), 1242009 (2012)

    Article  MATH  Google Scholar 

  21. Mucherino, A., Liberti, L., Lavor, C.: MD-jeep: an implementation of a branch and prune algorithm for distance geometry problems. In: Fukuda, K., Hoeven, J., Joswig, M., Takayama, N. (eds.) ICMS 2010. LNCS, vol. 6327, pp. 186–197. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15582-6_34

    Chapter  Google Scholar 

  22. Mulati, M.H., Constantino, A.A., da Silva, A.F.: Otimização por colônia de formigas. In: Lopes, H.S., de Abreu Rodrigues, L.C., Steiner, M.T.A. (eds.) Meta-Heurísticas em Pesquisa Operacional, 1 edn., Chap. 4, pp. 53–68. Omnipax, Curitiba, PR (2013)

    Google Scholar 

  23. Nobile, M.S., Citrolo, A.G., Cazzaniga, P., Besozzi, D., Mauri, G.: A memetic hybrid method for the molecular distance geometry problem with incomplete information. In: 2014 IEEE Congress on Evolutionary Computation (CEC), pp. 1014–1021. IEEE (2014)

    Google Scholar 

  24. Schlick, T.: Molecular Modeling and Simulation: An Interdisciplinary Guide: An Interdisciplinary Guide, vol. 21. Springer, New York (2010). https://doi.org/10.1007/978-1-4419-6351-2

  25. Sit, A., Wu, Z.: Solving a generalized distance geometry problem for protein structure determination. Bull. Math. Biol. 73(12), 2809–2836 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  26. Souza, M., Gonçalves, D.S., Carvalho, L.M., Lavor, C., Liberti, L.: A new algorithm for a class of distance geometry problems. In: 18th Cologne-Twente Workshop on Graphs and Combinatorial Optimization (2020)

    Google Scholar 

  27. Yang, X.S.: Engineering Optimization: An Introduction with Metaheuristic Applications. Wiley (2010)

    Google Scholar 

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Acknowledgements

Douglas O. Cardoso acknowledges the financial support by the Foundation for Science and Technology (Fundação para a Ciência e a Tecnologia, FCT) through grant UIDB/05567/2020, and by the European Social Fund and programs Centro 2020 and Portugal 2020 through project CENTRO-04-3559-FSE-000158.

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Correspondence to Laura S. Assis .

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Carneiro, S.R.L., de Souza, M.F., Cardoso, D.O., Tarrataca, L., Assis, L.S. (2023). A Custom Bio-Inspired Algorithm for the Molecular Distance Geometry Problem. In: Naldi, M.C., Bianchi, R.A.C. (eds) Intelligent Systems. BRACIS 2023. Lecture Notes in Computer Science(), vol 14195. Springer, Cham. https://doi.org/10.1007/978-3-031-45368-7_12

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  • DOI: https://doi.org/10.1007/978-3-031-45368-7_12

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