Stolz Robert, Yoshida Masaaki, Brasher Reuben, Flanner Michelle, Ishihara Kai, Sherratt David J, Shimokawa Koya, Vazquez Mariel
Department of Microbiology and Molecular Genetics, University of California Davis, Davis, USA.
Department of Mathematics, Saitama University, Saitama, Japan.
Sci Rep. 2017 Sep 29;7(1):12420. doi: 10.1038/s41598-017-12172-2.
In Escherichia coli DNA replication yields interlinked chromosomes. Controlling topological changes associated with replication and returning the newly replicated chromosomes to an unlinked monomeric state is essential to cell survival. In the absence of the topoisomerase topoIV, the site-specific recombination complex XerCD- dif-FtsK can remove replication links by local reconnection. We previously showed mathematically that there is a unique minimal pathway of unlinking replication links by reconnection while stepwise reducing the topological complexity. However, the possibility that reconnection preserves or increases topological complexity is biologically plausible. In this case, are there other unlinking pathways? Which is the most probable? We consider these questions in an analytical and numerical study of minimal unlinking pathways. We use a Markov Chain Monte Carlo algorithm with Multiple Markov Chain sampling to model local reconnection on 491 different substrate topologies, 166 knots and 325 links, and distinguish between pathways connecting a total of 881 different topologies. We conclude that the minimal pathway of unlinking replication links that was found under more stringent assumptions is the most probable. We also present exact results on unlinking a 6-crossing replication link. These results point to a general process of topology simplification by local reconnection, with applications going beyond DNA.
在大肠杆菌中，DNA复制会产生相互连接的染色体。控制与复制相关的拓扑变化并使新复制的染色体恢复到未连接的单体状态对于细胞存活至关重要。在缺乏拓扑异构酶topoIV的情况下，位点特异性重组复合物XerCD-dif-FtsK可以通过局部重新连接来消除复制连接。我们之前通过数学证明，在逐步降低拓扑复杂性的同时，通过重新连接来解开复制连接存在一条独特的最小途径。然而，重新连接保留或增加拓扑复杂性在生物学上是合理的。在这种情况下，是否存在其他解开连接的途径？哪一条是最有可能的？我们在对最小解开连接途径的分析和数值研究中考虑这些问题。我们使用具有多个马尔可夫链采样的马尔可夫链蒙特卡罗算法，对491种不同的底物拓扑结构、166个纽结和325个连接进行局部重新连接建模，并区分连接总共881种不同拓扑结构的途径。我们得出结论，在更严格假设下发现的解开复制连接的最小途径是最有可能的。我们还给出了解开一个6交叉复制连接的精确结果。这些结果指向了一个通过局部重新连接进行拓扑简化的一般过程，其应用超出了DNA领域。
