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Extending the Algebraic Formalism for Genome Rearrangements to Include Linear Chromosomes
July-Aug. 2013 (vol. 10 no. 4)
pp. 819-831
Pedro Feijao, Inst. of Comput., Univ. of Campinas, Campinas, Brazil
Joao Meidanis, Inst. of Comput., Univ. of Campinas, Campinas, Brazil
Algebraic rearrangement theory, as introduced by Meidanis and Dias, focuses on representing the order in which genes appear in chromosomes, and applies to circular chromosomes only. By shifting our attention to genome adjacencies, we introduce the adjacency algebraic theory, extending the original algebraic theory to linear chromosomes in a very natural way, also allowing the original algebraic distance formula to be used to the general multichromosomal case, with both linear and circular chromosomes. The resulting distance, which we call algebraic distance here, is very similar to, but not quite the same as, double-cut-and-join distance. We present linear time algorithms to compute it and to sort genomes. We show how to compute the rearrangement distance from the adjacency graph, for an easier comparison with other rearrangement distances. A thorough discussion on the relationship between the chromosomal and adjacency representation is also given, and we show how all classic rearrangement operations can be modeled using the algebraic theory.
Index Terms:
genomics,algebra,cellular biophysics,linear time algorithms,algebraic formalism,genome rearrangements,linear chromosomes,algebraic rearrangement theory,genome adjacencies,adjacency algebraic theory,general multichromosomal case,algebraic distance,double-cut-and-join distance,Bioinformatics,Genomics,Biological cells,Extremities,Sorting,IEEE transactions,Computational biology,combinatorial algorithms,Biology and genetics
Citation:
Pedro Feijao, Joao Meidanis, "Extending the Algebraic Formalism for Genome Rearrangements to Include Linear Chromosomes," IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 10, no. 4, pp. 819-831, July-Aug. 2013, doi:10.1109/TCBB.2012.161
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