FtsK-dependent XerCD- dif recombination unlinks replication catenanes in a stepwise manner

Abstract

In Escherichia coli, complete unlinking of newly replicated sister chromosomes is required to ensure their proper segregation at cell division. Whereas replication links are removed primarily by topoisomerase IV, XerC/XerD-dif site-specific recombination can mediate sister chromosome unlinking in Topoisomerase IV-deficient cells. This reaction is activated at the division septum by the DNA translocase FtsK, which coordinates the last stages of chromosome segregation with cell division. It has been proposed that, after being activated by FtsK, XerC/XerD-dif recombination removes DNA links in a stepwise manner. Here, we provide a mathematically rigorous characterization of this topological mechanism of DNA unlinking. We show that stepwise unlinking is the only possible pathway that strictly reduces the complexity of the substrates at each step. Finally, we propose a topological mechanism for this unlinking reaction.DNA topology | tangle method | Xer recombination | band surgery | topology simplification T he Escherichia coli chromosome is a 4.6-Mbp circular doublestranded (ds) DNA duplex, in which the two DNA strands are wrapped around each other ∼420,000 times. During replication, DNA gyrase acts to remove the majority of these strand crossings, but those that remain result in two circular sister molecules that are nontrivially linked. This creates the topological problem of separating the two linked sister chromosomes to ensure proper segregation at the time of cell division. Unlinking of replication links in E. coli is largely achieved by Topoisomerase IV (TopoIV), a type II topoisomerase (1, 2). However, Ip et al. demonstrated that XerC/XerD-dif (XerCD-dif) site-specific recombination, coupled with action of the translocase FtsK, could resolve linked plasmid substrates in vitro and hypothesized that this system could work alongside, yet independently of, TopoIV during in vivo unlinking of replicative catenanes in the bacterial chromosome (3). Grainge et al. then demonstrated that increased site-specific recombination could indeed compensate for a loss of TopoIV activity in unlinking chromosomes in vivo (4). When the activity of TopoIV is blocked, the result is cell lethality. We here propose a mathematically rigorous analysis to describe the pathway and mechanisms of unlinking of replication links by XerCD-FtsK. This work places a fundamental biological process within a mathematical context.Site-specific recombination is a process of breakage and reunion at two specific dsDNA duplexes (the recombination sites). When the DNA substrate consists of circular DNA molecules, the recombination sites may occur in a single DNA circle or in separate circles. Two sites are in direct repeat if they are in the same orientation on one DNA circle (Fig. 1). The relative orientation of the sites is harder to characterize when the two sites are on separate DNA circles. In the case of simple torus links with 2m crossings (also called 2m-catenanes, or 2m-cats) for an integer m > 1, the sites are said to be in parallel or antipara...

Assembly, translocation, and activation of XerCD- dif recombination by FtsK translocase analyzed in real-time by FRET and two-color tethered fluorophore motion

“…This suggestion is consistent with the previous result that the formation of the XerCD-dif synapsis is independent of FtsK C (24). FtsK can resolve catenated chromosomes produced by replication (41). We have previously suggested that FtsK may facilitate this decatenation by remaining in the vicinity of XerCD-dif after the activation of recombination and activating multiple rounds of recombination (12,24).…”

On the derivation of the HOMFLYPT polynomial invariant for fluid knots

“…Remarkably, a similar reconnection pattern (which brings the trefoil knot to the Hopf link, the unknot and the unlink of two smaller unknotted loops) is also shown to characterize DNA recombination: quite remarkably, a mathematically rigorous characterization of the topological mechanism of DNA unlinking is shown to be the only possible pathway that strictly reduces complexity by stepwise unlinking (Shimokawa et al 2013). The mathematics behind this proof suggests that it would be equally applicable to flux tube reconnections.…”

Mathematical validation of a biological model for unlinking replication catenanes by recombination

“…An intriguing problem is how proteins that are much smaller than the large DNA molecules on which they act manage to resolve topological exigencies rather than exacerbate them. In their recent work, Shimokawa et al address a particular aspect of this problem (2).…”

“…The proof of theorem 2 is based on a classic invariant called the "signature," which for a link L is the difference between the number of positive and negative eigenvalues of a matrix associated to the surface bounded by L. Shimokawa et al (2) show that the absolute value of the signature for any link L, jσ(L)j, is at most c(L) − 1, where c(L) is the crossing number of L. The authors further show that (2m)-torus links and (2m − 1)-torus knots are special in that they realize the equality, jIσ(L)j = c(L) -1. Finally, by combining their tangle model for XerCD action with a theorem from knot theory (7), the authors establish that the signature of the product goes down by, at most, one for a single round of enzyme action.…”

“…A (4)-torus catenane with appropriately oriented XerCD target sites may be easily constructed using topological tricks familiar to recombination biochemists. Now that Shimokawa et al (2) have provided the mathematical expectations for the action of FtsK-XerCD on this topologically unique substrate (Fig. 1), biologists would be remiss not to put them to an experimental test.…”