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Extending the Algebraic Formalism for Genome Rearrangements to Include Linear Chromosomes

机译:扩展基因组重排的代数形式主义以包括线性染色体

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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.
机译:由Meidanis和Dias提出的代数重排理论着重于代表基因在染色体中出现的顺序,并且仅适用于圆形染色体。通过将注意力转移到基因组邻接上,我们引入了邻接代数理论,以一种非常自然的方式将原始代数理论扩展到线性染色体,还允许将原始代数距离公式用于线性和圆形的一般多染色体情况染色体。所得的距离在这里我们称为代数距离,与双切并联接距离非常相似,但并不完全相同。我们提出了线性时间算法来对其进行计算和对基因组进行排序。我们展示了如何从邻接图计算重排距离,以便与其他重排距离进行比较。还详细讨论了染色体和邻接表示之间的关系,我们展示了如何使用代数理论对所有经典重排操作进行建模。

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