Francis Andrew R
Centre for Research in Mathematics, School of Computing, Engineering and Mathematics, University of Western Sydney, Sydney, Australia,
J Math Biol. 2014 Dec;69(6-7):1693-718. doi: 10.1007/s00285-013-0747-6. Epub 2013 Dec 29.
Rearrangements of bacterial chromosomes can be studied mathematically at several levels, most prominently at a local, or sequence level, as well as at a topological level. The biological changes involved locally are inversions, deletions, and transpositions, while topologically they are knotting and catenation. These two modelling approaches share some surprising algebraic features related to braid groups and Coxeter groups. The structural approach that is at the core of algebra has long found applications in sciences such as physics and analytical chemistry, but only in a small number of ways so far in biology. And yet there are examples where an algebraic viewpoint may capture a deeper structure behind biological phenomena. This article discusses a family of biological problems in bacterial genome evolution for which this may be the case, and raises the prospect that the tools developed by algebraists over the last century might provide insight to this area of evolutionary biology.
细菌染色体的重排可以在几个层面上进行数学研究，最显著的是在局部或序列层面，以及拓扑层面。局部涉及的生物学变化是倒位、缺失和转座，而拓扑学上的变化是打结和连环。这两种建模方法具有一些与辫群和考克斯特群相关的惊人代数特征。长期以来，作为代数核心的结构方法在物理和分析化学等科学领域有应用，但迄今为止在生物学中的应用方式较少。然而，有一些例子表明，代数观点可能揭示生物现象背后更深层次的结构。本文讨论了一系列细菌基因组进化中的生物学问题，代数方法可能适用于这些问题，并提出了一个前景，即代数学家在过去一个世纪开发的工具可能为进化生物学的这一领域提供见解。
