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

The price for simplicity of the linear genetic code is the inevitably large size of genomes and the attendant DNA entanglements. Circular chromosomes, or closed circular chromosome domains, are prone to knotting and catenation by a variety of DNA transactions. Knots in DNA pose road blocks to replication and transcription and increase the frequency of genetic rearrangements (1). Topoisomerases, enzymes that remove obstructive DNA crossings, play a crucial role in the duplication, decoding, and dissemination of biological information. 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). Perhaps no other life process better illustrates the intricacies and pageantry of DNA topology than replication. The intertwined nature of the double helix, the inherent negative supercoiling of DNA in vivo, the build-up of counterbalancing negatively and positively supercoiled domains on either side of the replisome, the propensity for knotting within replication bubbles, and the formation of “precatenanes” (interwound daughter duplexes) by diffusion of supercoils across the replication fork contribute to a veritable topological extravaganza (3). The net result is that the products of replication of a circular chromosome are interlinked circles (catenanes) that need to be unlinked for faithful segregation (Fig. 1). In Escherichia coli, this task is accomplished by the type II topoisomerase Topo IV by breaking and joining double strands, and transporting one double-stranded DNA segment through another in the process (Fig. 1). Unlinking of a different sort, the resolution of a dimer of the E. coli chromosome formed by homologous recombination back into monomers, is performed by the XerCD site-specific recombinase assisted by FtsK, an ATP hydrolyzing motor protein that translocates along DNA. Quite surprisingly, the FtsK–XerCD system is able to mimic Topo IV in unlinking two catenated DNA circles in vitro or catenated sister chromosomes in vivo (4, 5). A plausible scheme, consistent with experimental results, is the simplification of topology in steps of one by the repeated action of the recombinase (Fig. 1). This explanation, based on the in vitro results, relies on the implicit faith that the electrophoretic migration of individual DNA bands reveals their true topological character. In reality, this need not be so. Furthermore, alternative—if somewhat less elegant—routes for unlinking cannot be ruled out. Shimokawa et al. (2) have now provided a mathematical validation of the biologists’ intuitive model for unlinking catalyzed by FtsK–XerCD. The method the authors use is tangle analysis, which has been successfully applied to deduce strand exchange mechanisms catalyzed by site-specific recombinases (6). In a simplified view, a tangle is a 3D ball containing two strings, representing segments of a DNA molecule, connected to four points on the sphere (NE, NW, SE, and SW in a geographical sense, in Fig. 2). The strings may cross each other in a variety of ways. Three negative supercoil crossings from a circular plasmid substrate trapped by the interaction between a recombinase and its target sites are shown in Fig. 2. This “topological filter” will then dictate the topology of the recombinant product resulting from strand exchange. In their present work (2), Shimokawa et al. extend the tangle method to the unlinking reaction, under the assumption that each recombination step reduces the topological complexity of the substrate. Their analysis reveals a unique shortest pathway for accomplishing this end. Based on tangle analysis and theorems from classic knot theory, the authors propose a specific 3D representation of the FtsK–XerCD recombination synapse. Rigid body rotation of the synapse provides three possible tangle solutions, signifying a