圆形基因组上的重排事件
Rearrangement Events on Circular Genomes
摘要：
基因组重排模型的早期文献将计算进化距离的问题视为一个固有的组合问题。特别是，注意使用将一个基因组转化为另一个基因组所需的最少事件数来估计距离。事后看来，这种方法类似于早期从DNA序列推断系统发育树的方法，如最大简约法--两者都是由真实距离使进化变化最小化的原则所激励的，如果这一原则真实反映了现实，那么两者都是有效的。最近的文献考虑统计模型下的基因组重排，继续与基于DNA的方法并行;这里的目标是使用基于模型的方法（例如最大似然技术）来计算距离估计，该距离估计包含大量的重排路径，可以将一个基因组转化为另一个。至关重要的是，这种方法需要决定一组可行的重排事件，在本文中，我们专注于表征动机良好的模型签署，单染色体的圆形基因组，其中区域的数量保持固定。由于重排通常是用排列来数学描述的，我们将代表重排的排列集合分离出来，这些排列在生物学上是合理的，例如倒位和易位。我们为这些重排提供了精确的数学表达式，然后在应用它们时用基因组中的一组切割来描述它们。我们直接比较削减断点，并使用这个概念来计算不同的重排行动，适用于给定数量的削减。最后，我们提供了一些重排模型的例子，并讨论了一些问题时出现的定义合理的模型。
英文摘要：
Early literature on genome rearrangement modelling views the problem of computing evolutionary distances as an inherently combinatorial one. In particular, attention was given to estimating distances using the minimum number of events required to transform one genome into another. In hindsight, this approach is analogous to early methods for inferring phylogenetic trees from DNA sequences such as maximum parsimony -- both are motivated by the principle that the true distance minimises evolutionary change, and both are effective if this principle is a true reflection of reality. Recent literature considers genome rearrangement under statistical models, continuing this parallel with DNA-based methods; the goal here is to use model-based methods (for example maximum likelihood techniques) to compute distance estimates that incorporate the large number of rearrangement paths that can transform one genome into another. Crucially, this approach requires one to decide upon a set of feasible rearrangement events and, in this paper, we focus on characterising well-motivated models for signed, uni-chromosomal circular genomes, where the number of regions remains fixed. Since rearrangements are often mathematically described using permutations, we isolate the sets of permutations representing rearrangements that are biologically reasonable in this context, for example inversions and translocations. We provide precise mathematical expressions for these rearrangements, and then describe them in terms of the set of cuts made in the genome when they are applied. We directly compare cuts to breakpoints, and use this concept to count the distinct rearrangement actions which apply a given number of cuts. Finally, we provide some examples of rearrangement models, and include a discussion of some questions that arise when defining plausible models.
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