University of Campinas, Campinas.
University of Campinas, Campinas and Scylla Bioinformatics, Brazil.
IEEE/ACM Trans Comput Biol Bioinform. 2013 Jul-Aug;10(4):819-31. doi: 10.1109/TCBB.2012.161.
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.
代数重排理论由 Meidanis 和 Dias 引入，专注于表示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相邻关系上，我们引入了相邻代数理论，以非常自然的方式将原始代数理论扩展到线性染色体，同时也允许原始代数距离公式用于一般的多染色体情况，包括线性和圆形染色体。我们在这里称之为代数距离的这个距离非常类似于，但不完全等同于双切割和连接距离。我们提出了线性时间算法来计算它并对基因组进行排序。我们展示了如何从邻接图计算重排距离，以便更容易与其他重排距离进行比较。还对染色体和邻接表示之间的关系进行了深入讨论，并展示了如何使用代数理论来模拟所有经典的重排操作。
