加权基因组距离很难对易位比例施加限制
Weighted genomic distance can hardly impose a bound on the proportion of transpositions
摘要：
两个基因组之间的基因组距离，即，在比较基因组学研究中，将一个基因组转化为另一个基因组所需的最小数量的基因组重排通常被用作基因组进化接近性的量度。然而，在包括具有显著不同“功率”的重排的模型中，例如反转（其是“弱”且最频繁的重排）和易位（其更“功率”但罕见），基因组距离通常对应于具有大比例易位的转化，这在生物学上是不适当的。加权基因组距离是一种传统的方法，通过分配相对权重α > 1来限制易位的比例。许多先前的研究解决了使用α \leq 2计算加权基因组距离的问题。利用环形基因组上的多断点重排模型，该模型同时捕获反转（建模为2-断点）和易位（建模为3-断点），我们证明了对于α \in（1，2]），最小权重变换可能完全由易位组成，这意味着相应的加权基因组距离实际上并没有达到限制易位比例的目的。我们进一步证明了对于α \in（1，2），最小权变换不依赖于α在这个区间的特定选择.我们给出了一个完整的特征，这样的转换，并表明，他们符合的转换，在同一时间具有最短的长度，使最小数量的基因组中的断裂。我们的结果也提供了一个理论基础的经验观察，对于α < 2，在最小重量的转换，换位优于反转。
英文摘要：
Genomic distance between two genomes, i.e., the smallest number of genome rearrangements required to transform one genome into the other, is often used as a measure of evolutionary closeness of the genomes in comparative genomics studies. However, in models that include rearrangements of significantly different "power" such as reversals (that are "weak" and most frequent rearrangements) and transpositions (that are more "powerful" but rare), the genomic distance typically corresponds to a transformation with a large proportion of transpositions, which is not biologically adequate. Weighted genomic distance is a traditional approach to bounding the proportion of transpositions by assigning them a relative weight α > 1. A number of previous studies addressed the problem of computing weighted genomic distance with α \leq 2. Employing the model of multi-break rearrangements on circular genomes, that captures both reversals (modelled as 2-breaks) and transpositions (modelled as 3-breaks), we prove that for α \in (1,2], a minimum-weight transformation may entirely consist of transpositions, implying that the corresponding weighted genomic distance does not actually achieve its purpose of bounding the proportion of transpositions. We further prove that for α \in (1,2), the minimum-weight transformations do not depend on a particular choice of α from this interval. We give a complete characterization of such transformations and show that they coincide with the transformations that at the same time have the shortest length and make the smallest number of breakages in the genomes. Our results also provide a theoretical foundation for the empirical observation that for α < 2, transpositions are favored over reversals in the minimum-weight transformations.
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