Pathways of DNA unlinking: A story of stepwise simplification

Abstract

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.

Recent advances on the non-coherent band surgery model for site-specific recombination

“…The same research group later showed that the XerCD-dif -FtsK enzymatic complex could unlink replication links tied in vivo in E. coli cells deficient in the decatenase topoIV [33]. Several groups of authors, including our own, studied mathematically the mechanism and pathways of DNA unlinking by site-specific recombination [12,13,83,85]. In [83] we showed that at least 2m steps are needed to unlink a replication link of type T (2, 2n) with one recombination site in each component in the orientation indicated in Figure 3.…”

“…Each reconnection represented a non-coherent banding. The implementation was adapted from our published work in [85] (see Section 5.3 for more details). Table 1.…”

“…Here we use BFACF, a well-known Markov Chain Monte Carlo algorithm, to uniformly sample random conformations of knotted self-avoiding polygons (SAPs) in the simple cubic lattice Z 3 (reviewed in [63]). Using Recombo, our own software package, we algorithmically identify binding sites, perform recombination and identify the resulting product knots [85]. A robust statistical analysis of the resulting transition probability networks gives us insight into the quantitative behavior of topological simplification via recombination.…”

Distance one lens space fillings and band surgery on the trefoil knot

“…It is often convenient to isotope L 1 and L 2 so that a coherent or non-coherent band surgery can be expressed as the replacement of a rational (0) tangle by an (∞) or (±1/n) tangle ( Figure 9). When n is small, these tangles have special relevance in biology (see for example [69,71,70,64,67]). For example, in the context of DNA recombination, the local reconnection sites correspond to the core regions of the recombination sites, i.e.…”

“…If the linking number is instead −n/2, Corollary 1.2 follows from the characterization of coherent band surgeries between T (2, n) torus links and certain two-bridge knots in [21,Theorem 3.1]. While both coherent and non-coherent band surgeries have biological relevance, more attention in the literature has been paid to the coherent band surgery model (see for example [37,21,64,38,13,14,67]). This is due in part to the relative difficulty in working with non-orientable surfaces, as is the case with non-coherent band surgery on knots.…”