Abstract
The adjacency graph is a structure used to model genomes in several rearrangement distance problems. In particular, most studies use properties of a maximum cycle packing of this graph to develop bounds and algorithms for rearrangement distance problems, such as the reversal distance, the reversal and transposition distance, and the double cut and join distance. When each genome has no repeated genes, there exists only one cycle packing for the graph. However, when each genome may have repeated genes, the problem of finding a maximum cycle packing for the adjacency graph (adjacency graph packing) is NP-hard. In this work, we develop a randomized greedy heuristic and a genetic algorithm heuristic for the adjacency graph packing problem for genomes with repeated genes and unequal gene content. We also propose new algorithms with simple implementation and good practical performance for reversal distance and reversal and transposition distance in genomes without repeated genes, which we combine with the heuristics to find solutions for the problems with repeated genes. We present experimental results and compare the application of these heuristics with the application of the MSOAR framework in rearrangement distance problems. Lastly, we apply our genetic algorithm heuristic to real genomic data to validate its practical use.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Notes
Illustration created using treeio R package (Wang et al. 2020).
References
Alexandrino, A.O., Oliveira, A.R., Dias, U., Dias, Z.: Genome rearrangement distance with reversals, transpositions, and indels. J. Comput. Biol. 28(3), 235–247 (2021)
Alexandrino, A.O., Oliveira, A.R., Dias, U., Dias, Z.: Labeled cycle graph for transposition and indel distance. J. Comput. Biol. 29(03), 243–256 (2022)
Bafna, V., Pevzner, P.A.: Genome rearrangements and sorting by reversals. SIAM J. Comput. 25(2), 272–289 (1996)
Bafna, V., Pevzner, P.A.: Sorting by transpositions. SIAM J. Discrete Math. 11(2), 224–240 (1998)
Bergeron, A., Mixtacki, J., Stoye, J.: A unifying view of genome rearrangements. In: International Workshop on Algorithms in Bioinformatics, pp. 163–173 (2006). Springer, Berlin
Bohnenkämper, L., Braga, M.D.V., Doerr, D., Stoye, J.: Computing the rearrangement distance of natural genomes. J. Comput. Biol. 28(4), 410–431 (2021)
Braga, M.D., Willing, E., Stoye, J.: Double cut and join with insertions and deletions. J. Comput. Biol. 18(9), 1167–1184 (2011)
Brito, K.L., Alexandrino, A.O., Oliveira, A.R., Dias, U., Dias, Z.: Reversals and transpositions distance with proportion restriction. J. Bioinform. Comput. Biol. 19(04), 2150013 (2021)
Chen, X., Zheng, J., Fu, Z., Nan, P., Zhong, Y., Lonardi, S., Jiang, T.: Assignment of orthologous genes via genome rearrangement. IEEE/ACM Trans. Comput. Biol. Bioinf. 2(4), 302–315 (2005)
Christie, D.A.: Genome Rearrangement Problems. Ph.D. thesis, Department of Computing Science, University of Glasgow (1998)
Fu, Z., Chen, X., Vacic, V., Nan, P., Zhong, Y., Jiang, T.: MSOAR: a high-throughput ortholog assignment system based on genome rearrangement. J. Comput. Biol. 14(9), 1160–1175 (2007)
Garczarek, L., Guyet, U., Doré, H., Farrant, G.K., Hoebeke, M., Brillet-Guéguen, L., Bisch, A., Ferrieux, M., Siltanen, J., Corre, E., et al.: Cyanorak v2. 1: a scalable information system dedicated to the visualization and expert curation of marine and brackish picocyanobacteria genomes. Nucleic Acids Res. 49, 1 (2020)
Hannenhalli, S., Pevzner, P.A.: Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals. J. ACM 46(1), 1–27 (1999)
Kahn, C., Raphael, B.: Analysis of segmental duplications via duplication distance. Bioinformatics 24(16), 133–138 (2008)
Makarenkov, V., Leclerc, B.: Circular orders of tree metrics, and their uses for the reconstruction and fitting of phylogenetic trees. In: DIMACS Series in Discrete Mathematics and Theoretical Computer Science, pp. 183–208 (1997)
Mitchell, M.: Introduction to Genetic Algorithms. Springer, Cambridge (2008)
Oliveira, A.R., Brito, K.L., Alexandrino, A.O., Siqueira, G., Dias, U., Dias, Z.: Rearrangement distance problems: an updated survey. ACM Comput. Surv. 56(8) (2024)
Oliveira, A.R., Brito, K.L., Dias, U., Dias, Z.: On the complexity of sorting by reversals and transpositions problems. J. Comput. Biol. 26, 1223–1229 (2019)
Penny, D., Hendy, M.: The use of tree comparison metrics. Syst. Zool. 34(1), 75–82 (1985)
Pinheiro, P.O., Alexandrino, A.O., Oliveira, A.R., de Souza, C.C., Dias, Z.: Heuristics for breakpoint graph decomposition with applications in genome rearrangement problems. In: Proceedings of the 13th Brazilian Symposium on Bioinformatics (BSB’2020), pp. 129–140 (2020)
Radcliffe, A.J., Scott, A.D., Wilmer, E.L.: Reversals and transpositions over finite alphabets. SIAM J. Discrete Math. 19(1), 224–244 (2005)
Shao, M., Lin, Y., Moret, B.M.: An exact algorithm to compute the double-cut-and-join distance for genomes with duplicate genes. J. Comput. Biol. 22(5), 425–435 (2015)
Siqueira, G., Oliveira, A.R., Alexandrino, A.O., Dias, Z.: Heuristics for cycle packing of adjacency graphs for genomes with repeated genes. In: Proceedings of the 14th Brazilian Symposium on Bioinformatics (BSB’2021), pp. 93–105 (2021)
Walter, M.E.M.T., Dias, Z., Meidanis, J.: Reversal and transposition distance of linear chromosomes. In: Proceedings of the 5th International Symposium on String Processing and Information Retrieval (SPIRE’1998), pp. 96–102. IEEE Computer Society, Los Alamitos, CA, USA (1998)
Wang, L.-G., Lam, T.T.-Y., Xu, S., Dai, Z., Zhou, L., Feng, T., Guo, P., Dunn, C.W., Jones, B.R., Bradley, T., et al.: Treeio: an R package for phylogenetic tree input and output with richly annotated and associated data. Mol. Biol. Evol. 37(2), 599–603 (2020)
Willing, E., Stoye, J., Braga, M.: Computing the inversion-indel distance. IEEE/ACM Trans. Comput. Biol. Bioinf. 18(6), 2314–2326 (2021)
Zhai, S., Zhang, P., Zhu, D., Tong, W., Xu, Y., Lin, G.: An approximation algorithm for genome sorting by reversals to recover all adjacencies. J. Comb. Optim. 37(4), 1170–1190 (2019)
Acknowledgements
This work was supported by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior—Brasil (CAPES)—Finance Code 001 and the São Paulo Research Foundation, FAPESP (Grants 2013/08293-7, 2015/11937-9, 2021/13824-8, and 2022/13555-0).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors have no relevant financial or non-financial interests to disclose.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
A preliminary version of this work appeared in the 14th Brazilian Symposium on Bioinformatics (BSB’2021) (Siqueira et al. 2021).
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Siqueira, G., Oliveira, A.R., Alexandrino, A.O. et al. Assignment of orthologous genes in unbalanced genomes using cycle packing of adjacency graphs. J Heuristics 30, 269–289 (2024). https://doi.org/10.1007/s10732-024-09528-z
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10732-024-09528-z