FtsK-dependent XerCD-dif recombination unlinks replication catenanes in a stepwise manner Koya Shimokawaa, Kai Ishiharab, Ian Graingec, David J. Sherrattd, and Mariel Vazqueze,1 aDepartment of Mathematics, Saitama University, Saitama 380-8570, Japan; bFaculty of Education, Yamaguchi University, Yamaguchi 753-8512, Japan; cSchool of Environmental and Life Sciences, University of Newcastle, Callaghan, NSW 2308, Australia; dDepartment of Biochemistry, University of Oxford, Oxford OX1 3QU, United Kingdom; and eDepartment of Mathematics, San Francisco State University, San Francisco, CA 94132 Edited by De Witt Sumners, Florida State University, Tallahassee, FL, and accepted by the Editorial Board October 17, 2013 (received for review May 10, 2013) In Escherichia coli, complete unlinking of newly replicated sister In E. coli, XerCD-dif recombination plays an essential role in chromosomes is required to ensure their proper segregation at cell chromosome dimer resolution (reviewed in ref. 7). Furthermore, division. Whereas replication links are removed primarily by top- when coupled with FtsK, XerCD recombination at dif sites can oisomerase IV, XerC/XerD-dif site-specific recombination can me- unlink 2m-cats produced in vitro by λ-Integrase (3). These results diate sister chromosome unlinking in Topoisomerase IV-deficient suggested a potential in vivo role for XerCD–FtsK recombination, cells. This reaction is activated at the division septum by the DNA which was then hypothesized to work with TopoIV to unlink translocase FtsK, which coordinates the last stages of chromosome DNA links produced by DNA replication. To test this hypothe- segregation with cell division. It has been proposed that, after being sis, a pair of supercoiled linked plasmids, each with one dif site, activated by FtsK, XerC/XerD-dif recombination removes DNA links was produced in vivo by replication in TopoIV-deficient cells, in a stepwise manner. Here, we provide a mathematically rigorous and these were then incubated in vitro with XerCD–FtsK50C (4). characterization of this topological mechanism of DNA unlinking. The ATP-dependent reaction efficiently produced unlinked cir- We show that stepwise unlinking is the only possible pathway that cles. The ATP dependence of the reaction is likely twofold: firstly strictly reduces the complexity of the substrates at each step. Finally, the DNA translocase activity of FtsK relies upon ATP hydrolysis we propose a topological mechanism for this unlinking reaction. for movement, and in the absence of translocation there is no stimulation of recombination. Secondly, the energy from ATP APPLIED DNA topology | tangle method | Xer recombination | band surgery | hydrolysis is also used to align the two recombining dif sites so MATHEMATICS topology simplification that subsequent recombination produces the observed stepwise reduction in complexity. In addition to right-handed (RH) torus he Escherichia coli chromosome is a 4.6-Mbp circular double- links with parallel sites and with 2–14 crossings, unknotted Tstranded (ds) DNA duplex, in which the two DNA strands dimers and a few dimeric knots were also observed. The exper- are wrapped around each other ∼420,000 times. During repli- imental data suggested a stepwise reaction where crossings are cation, DNA gyrase acts to remove the majority of these strand removed one at a time, iteratively converting links into knots, crossings, but those that remain result in two circular sister into links, until two free circles are obtained (Fig. 1). A control – BIOCHEMISTRY molecules that are nontrivially linked. This creates the topolog- experiment demonstrated that XerCD FtsK50C recombination ical problem of separating the two linked sister chromosomes to could convert knotted dimers (RH torus knots with two directly ensure proper segregation at the time of cell division. Unlinking repeated dif sites) to free circles. Separate experiments showed of replication links in E. coli is largely achieved by Topoisomerase that chromosome unlinking in E. coli can be accomplished in fi IV (TopoIV), a type II topoisomerase (1, 2). However, Ip et al. vivo by multiple rounds of XerCD-dif or Cre-loxP site-speci c demonstrated that XerC/XerD-dif (XerCD-dif) site-specific re- combination, coupled with action of the translocase FtsK, could Significance resolve linked plasmid substrates in vitro and hypothesized that this system could work alongside, yet independently of, TopoIV Newly replicated circular chromosomes are topologically linked. during in vivo unlinking of replicative catenanes in the bacterial XerC/XerD-dif (XerCD-dif)–FtsK recombination acts in the repli- chromosome (3). Grainge et al. then demonstrated that in- cation termination region of the Escherichia coli chromosome to creased site-specific recombination could indeed compensate for remove links introduced during homologous recombination and a loss of TopoIV activity in unlinking chromosomes in vivo (4). replication, whereas Topoisomerase IV removes replication links When the activity of TopoIV is blocked, the result is cell le- only. Based on gel mobility patterns of the products of recombi- thality. We here propose a mathematically rigorous analysis to nation, a stepwise unlinking pathway has been proposed. Here, describe the pathway and mechanisms of unlinking of replication we present a rigorous mathematical validation of this model, a links by XerCD–FtsK. This work places a fundamental biological significant advance over prior biological approaches. We show process within a mathematical context. definitively that there is a unique shortest pathway of unlinking Site-specific recombination is a process of breakage and re- by XerCD-dif–FtsK that strictly reduces the complexity of the union at two specific dsDNA duplexes (the recombination sites). links at every step. We delineate the mechanism of action of When the DNA substrate consists of circular DNA molecules, the enzymes at each step along this pathway and provide a 3D the recombination sites may occur in a single DNA circle or in interpretation of the results. separate circles. Two sites are in direct repeat if they are in the Author contributions: K.S., D.J.S., and M.V. designed research; K.S., K.I., and M.V. per- same orientation on one DNA circle (Fig. 1). The relative ori- formed research; K.S., K.I., I.G., D.J.S., and M.V. contributed new reagents/analytic tools; entation of the sites is harder to characterize when the two sites K.S., K.I., I.G., D.J.S., and M.V. analyzed data; and K.S., I.G., D.J.S., and M.V. wrote the are on separate DNA circles. In the case of simple torus links paper. with 2m crossings (also called 2m-catenanes, or 2m-cats) for an The authors declare no conflict of interest. integer m > 1, the sites are said to be in parallel or antiparallel This article is a PNAS Direct Submission. D.W.S. is a guest editor invited by the Editorial Board. orientation with respect to each other (Fig. 1). Site-specific re- Freely available online through the PNAS open access option. combination occurs in two steps (5, 6): first, the recombination 1To whom correspondence should be addressed. E-mail: [email protected]. sites are brought together (synapsis); second, each site is cleaved This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. and the DNA ends are exchanged, then rejoined. 1073/pnas.1308450110/-/DCSupplemental. www.pnas.org/cgi/doi/10.1073/pnas.1308450110 PNAS Early Edition | 1of6 Downloaded by guest on September 28, 2021 dimensional topology, one can show that the tangles involved are all rational (14, 15, 21). Therefore, all solutions to the XerCD– psi system of equations can be computed using tangle calculus. There are only three solutions consistent with the experimental data (15). It was further shown that these solutions can be seen as different projections of the same three-dimensional (3D) ob- ject, and a unique topological mechanism for XerCD at psi was Fig. 1. Proposed stepwise unlinking by XerCD-dif–FtsK recombination: Parallel proposed that incorporated all three solutions (15). RH 2m-cats [e.g., T(2,6)p] are converted to RH torus knots [e.g., T(2,5)] with In Grainge et al. (4), several systems of tangle equations were directly repeated sites; such knots are converted to RH cats, and so on, proposed for the pathway taking replication links to two open iteratively, until the reaction stops at two open circles. (In ref. 4, RH torus circles (the unlink). Tangle calculus was used to solve each sys- links with parallel sites and up to 14 crossings, also called parallel 2m-cats tem. For example, all possible systems of two equations con- and denoted by T(2,2m)p, were used as substrates of Xer recombination.) verting a RH 6-cat with parallel sites into a knotted product with five or fewer crossings were considered. Using tangle calculus, recombination. The reactions required DNA translocation by only three biologically meaningful solutions were found, all of which produced the RH 5-crossing torus knot with directly re- FtsK. Overexpression of FtsK50C in TopoIV-deficient cells was sufficient to drive the topology simplification. Furthermore, in peated sites. The authors proposed that the three solutions are fl vivo XerCD activation by actively translocating FtsK is essential equivalent by 3D rigid motion (i.e., the three solutions re ect to effectively unlink replication links (4). In the absence of FtsK, different views of the same 3D shape). This study concluded that the stepwise unlinking pathway of Fig. 1 is the most likely pathway an active XerCD complex may produce complicated DNA knots – and links, with a small yield of unlinks (8). Whereas Xer site-specific of XerCD FtsK recombination when acting on 2m-cats, and recombination on DNA plasmids in vitro has been well-characterized posited a stepwise mechanism of action. at a local biochemical level, the mechanism of Xer-mediated DNA The mathematical study in ref. 4 assumed that solutions to the tangle equations were rational, sums of rational tangles, or closely unlinking in vivo remains unclear, and is extremely technically fi difficult to address experimentally.