Tangle Analysis of Xer Recombination Reveals only Three Solutions, all Consistent with a Single Three-dimensional Topological Pathway

Topological gelation of reconnecting polymers

Shuffling of genetic material via reconnection of proximal DNA segments is seen in meiosis and some cancers. In contrast with textbook pictures, reconnections are performed within an entangled environment and can result in knotting or linking, detrimental for cells. By performing Brownian dynamics simulations of reconnecting polymers under confinement, modeling the genome in vivo, we find a topological transition between a gas or liquid of unlinked rings and a gel-like structure with a large number of polydisperse linked rings. This transition can be triggered by increasing polymer stiffness or confinement. Our results suggest ways to design future topological materials, such as DNA-based gels involving recombinase proteins.

DNA recombination is a ubiquitous process that ensures genetic diversity. Contrary to textbook pictures, DNA recombination, as well as generic DNA translocations, occurs in a confined and highly entangled environment. Inspired by this observation, here, we investigate a solution of semiflexible polymer rings undergoing generic cutting and reconnection operations under spherical confinement. Our setup may be realized using engineered DNA in the presence of recombinase proteins or by considering micelle-like components able to form living (or reversibly breakable) polymer rings. We find that in such systems, there is a topological gelation transition, which can be triggered by increasing either the stiffness or the concentration of the rings. Flexible or dilute polymers break into an ensemble of short, unlinked, and segregated rings, whereas sufficiently stiff or dense polymers self-assemble into a network of long, linked, and mixed loops, many of which are knotted. We predict that the two phases should behave qualitatively differently in elution experiments monitoring the escape dynamics from a permeabilized container. Besides shedding some light on the biophysics and topology of genomes undergoing DNA reconnection in vivo, our findings could be leveraged in vitro to design polymeric complex fluids—e.g., DNA-based complex fluids or living polymer networks—with desired topologies.

Topological and physical links in soft matter systems

Linking, or multicomponent topological entanglement, is ubiquitous in soft matter systems, from mixtures of polymers and DNA filaments packedin vivoto interlocked line defects in liquid crystals and intertwined synthetic molecules. Yet, it is only relatively recently that theoretical and experimental advancements have made it possible to probe such entanglements and elucidate their impact on the physical properties of the systems. Here, we review the state-of-the-art of this rapidly expanding subject and organize it as follows. First, we present the main concepts and notions, from topological linking to physical linking and then consider the salient manifestations of molecular linking, from synthetic to biological ones. We next cover the main physical models addressing mutual entanglements in mixtures of polymers, both linear and circular. Finally, we consider liquid crystals, fluids and other non-filamentous systems where topological or physical entanglements are observed in defect or flux lines. We conclude with a perspective on open challenges.

A topological analysis of difference topology experiments of condensin with topoisomerase II

An experimental technique called difference topology combined with the mathematics of tangle analysis has been used to unveil the structure of DNA bound by the Mu transpososome. However, difference topology experiments can be difficult and time consuming. We discuss a modification that greatly simplifies this experimental technique. This simple experiment involves using a topoisomerase to trap DNA crossings bound by a protein complex and then running a gel to determine the crossing number of the knotted product(s). We develop the mathematics needed to analyze the results and apply these results to model the topology of DNA bound by 13S condensin and by the condensin MukB.

Pathways of DNA unlinking: A story of stepwise simplification

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.

Plasmid stability analysis based on a new theoretical model employing stochastic simulations

Here, we present a simple theoretical model to study plasmid stability, based on one input parameter which is the copy number of plasmids present in a host cell. The Monte Carlo approach was used to analyze random fluctuations affecting plasmid replication and segregation leading to gradual reduction in the plasmid population within the host cell. This model was employed to investigate maintenance of pEC156 derivatives, a high-copy number ColE1-type Escherichia coli plasmid that carries an EcoVIII restriction-modification system. Plasmid stability was examined in selected Escherichia coli strains (MG1655, wild-type; MG1655 pcnB, and hyper-recombinogenic JC8679 sbcA). We have compared the experimental data concerning plasmid maintenance with the simulations and found that the theoretical stability patterns exhibited an excellent agreement with those empirically tested. In our simulations, we have investigated the influence of replication fails (α parameter) and uneven partition as a consequence of multimer resolution fails (δ parameter), and the post-segregation killing factor (β parameter). All of these factors act at the same time and affect plasmid inheritance at different levels. In case of pEC156-derivatives we concluded that multimerization is a major determinant of plasmid stability. Our data indicate that even small changes in the fidelity of segregation can have serious effects on plasmid stability. Use of the proposed mathematical model can provide a valuable description of plasmid maintenance, as well as enable prediction of the probability of the plasmid loss.

An Overview of Tyrosine Site-specific Recombination: From an Flp Perspective

Tyrosine site-specific recombinases (YRs) are widely distributed among prokaryotes and their viruses, and were thought to be confined to the budding yeast lineage among eukaryotes. However, YR-harboring retrotransposons (the DIRS and PAT families) and DNA transposons (Cryptons) have been identified in a variety of eukaryotes. The YRs utilize a common chemical mechanism, analogous to that of type IB topoisomerases, to bring about a plethora of genetic rearrangements with important physiological consequences in their respective biological contexts. A subset of the tyrosine recombinases has provided model systems for analyzing the chemical mechanisms and conformational features of the recombination reaction using chemical, biochemical, topological, structural, and single molecule-biophysical approaches. YRs with simple reaction requirements have been utilized to bring about programmed DNA rearrangements for addressing fundamental questions in developmental biology. They have also been employed to trace the topological features of DNA within high-order DNA interactions established by protein machines. The directed evolution of altered specificity YRs, combined with their spatially and temporally regulated expression, heralds their emergence as vital tools in genome engineering projects with wide-ranging biotechnological and medical applications.

Xer Site-Specific Recombination: Promoting Vertical and Horizontal Transmission of Genetic Information

Two related tyrosine recombinases, XerC and XerD, are encoded in the genome of most bacteria where they serve to resolve dimers of circular chromosomes by the addition of a crossover at a specific site, dif. From a structural and biochemical point of view they belong to the Cre resolvase family of tyrosine recombinases. Correspondingly, they are exploited for the resolution of multimers of numerous plasmids. In addition, they are exploited by mobile DNA elements to integrate into the genome of their host. Exploitation of Xer is likely to be advantageous to mobile elements because the conservation of the Xer recombinases and of the sequence of their chromosomal target should permit a quite easy extension of their host range. However, it requires means to overcome the cellular mechanisms that normally restrict recombination to dif sites harbored by a chromosome dimer and, in the case of integrative mobile elements, to convert dedicated tyrosine resolvases into integrases.

Resolution of Multimeric Forms of Circular Plasmids and Chromosomes

One of the disadvantages of circular plasmids and chromosomes is their high sensitivity to rearrangements caused by homologous recombination. Odd numbers of crossing-over occurring during or after replication of a circular replicon result in the formation of a dimeric molecule in which the two copies of the replicon are fused. If they are not converted back to monomers, the dimers of replicons may fail to correctly segregate at the time of cell division. Resolution of multimeric forms of circular plasmids and chromosomes is mediated by site-specific recombination, and the enzymes that catalyze this type of reaction fall into two families of proteins: the serine and tyrosine recombinase families. Here we give an overview of the variety of site-specific resolution systems found on circular plasmids and chromosomes.

Organization of DNA partners and strand exchange mechanisms during Flp site-specific recombination analyzed by difference topology, single molecule FRET and single molecule TPM

Flp site-specific recombination between two target sites (FRTs) harboring non-homology within the strand exchange region does not yield stable recombinant products. In negatively supercoiled plasmids containing head-to-tail sites, the reaction produces a series of knots with odd-numbered crossings. When the sites are in head-to-head orientation, the knot products contain even-numbered crossings. Both types of knots retain parental DNA configuration. By carrying out Flp recombination after first assembling the topologically well defined Tn3 resolvase synapse, it is possible to determine whether these knots arise by a processive or a dissociative mechanism. The nearly exclusive products from head-to-head and head-to-tail oriented "non-homologous" FRT partners are a 4-noded knot and a 5-noded knot, respectively. The corresponding products from a pair of native (homologous) FRT sites are a 3-noded knot and a 4-noded catenane, respectively. These results are consistent with non-homology-induced two rounds of dissociative recombination by Flp, the first to generate reciprocal recombinants containing non-complementary base pairs and the second to produce parental molecules with restored base pairing. Single molecule fluorescence resonance energy transfer (smFRET) analysis of geometrically restricted FRTs, together with single molecule tethered particle motion (smTPM) assays of unconstrained FRTs, suggests that the sites are preferentially synapsed in an anti-parallel fashion. This selectivity in synapse geometry occurs prior to the chemical steps of recombination, signifying early commitment to a productive reaction path. The cumulative topological, smFRET and smTPM results have implications for the relative orientation of DNA partners and the directionality of strand exchange during recombination mediated by tyrosine site-specific recombinases.

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

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.

The topology of plasmid-monomerizing Xer site-specific recombination

Xer site-specific recombination at cer and psi converts bacterial plasmid multimers into monomers so that they can be efficiently segregated to both daughter cells at cell division. Recombination is catalysed by the XerC and XerD recombinases acting at ~30 bp core sites, and is regulated by the action of accessory proteins bound to accessory DNA sequences adjacent to the core sites. Recombination normally occurs only between sites in direct repeat in a negatively supercoiled circular DNA molecule, and yields two circular products linked together in a right-handed four-node catenane with antiparallel sites. These and other topological results are explained by a model in which the accessory DNA sequences are interwrapped around the accessory proteins, trapping three negative supercoils so that strand exchange by the XerC and XerD yields the observed four-node catenane.

Determining the topology of stable protein–DNA complexes

Difference topology is an experimental technique that can be used to unveil the topological structure adopted by two or more DNA segments in a stable protein–DNA complex. Difference topology has also been used to detect intermediates in a reaction pathway and to investigate the role of DNA supercoiling. In the present article, we review difference topology as applied to the Mu transpososome. The tools discussed can be applied to any stable nucleoprotein complex.

Predicting knot or catenane type of site-specific recombination products

Site-specific recombination on supercoiled circular DNA yields a variety of knotted or catenated products. Here, we present a topological model of this process and characterize all possible products of the most common substrates: unknots, unlinks, and torus knots and catenanes. This model tightly prescribes the knot or catenane type of previously uncharacterized data. We also discuss how the model helps to distinguish products of distributive recombination and, in some cases, determine the order of processive recombination products.

Coloring the Mu transpososome

Background

Tangle analysis has been applied successfully to study proteins which bind two segments of DNA and can knot and link circular DNA. We show how tangle analysis can be extended to model any stable protein-DNA complex.

Results

We discuss a computational method for finding the topological conformation of DNA bound within a protein complex. We use an elementary invariant from knot theory called colorability to encode and search for possible DNA conformations. We apply this method to analyze the experimental results of Pathania, Jayaram, and Harshey (Cell 2002). We show that the only topological DNA conformation bound by Mu transposase which is biologically likely is the five crossing solution found by Pathania et al (although other possibilities are discussed).

Conclusion

Our algorithm can be used to analyze the results of the experimental technique described in Pathania et al in order to determine the topological conformation of DNA bound within a stable protein-DNA complex.

TopoICE-R: 3D visualization modeling the topology of DNA recombination

TopoICE-R is a three-dimensional visualization and manipulation software for solving 2-string tangle equations and can be used to model the topology of DNA bound by proteins such as recombinases and topoisomerases.

AVAILABILITY

This software, manual and example files are available at www.knotplot.com/download for Linux, Windows and Mac.

Communication between accessory factors and the Cre recombinase at hybrid psi-loxP sites

By placing loxP adjacent to the accessory sequences from the Xer/psi multimer resolution system, we have imposed topological selectivity and specificity on Cre/loxP recombination. In this hybrid recombination system, the Xer accessory protein PepA binds to psi accessory sequences, interwraps them, and brings the loxP sites together such that the product of recombination is a four-node catenane. Here, we investigate communication between PepA and Cre by varying the distance between loxP and the accessory sequences, and by altering the orientation of loxP. The yield of four-node catenane and the efficiency of recombination in the presence of PepA varied with the helical phase of loxP with respect to the accessory sequences. When the orientation of loxP was reversed, or when half a helical turn was added between the accessory sequences and loxP, PepA reversed the preferred order of strand exchange by Cre at loxP. The results imply that PepA and the accessory sequences define precisely the geometry of the synapse formed by the loxP sites, and that this overcomes the innate preference of Cre to initiate recombination on the bottom strand of loxP. Further analysis of our results demonstrates that PepA can stimulate strand exchange by Cre in two distinct synaptic complexes, with the C-terminal domains of Cre facing either towards or away from PepA. Thus, no specific PepA-recombinase interaction is required, and correct juxtaposition of the loxP sites is sufficient to activate Cre in this system.

DNA topology and geometry in Flp and Cre recombination

The Flp recombinase of yeast and the Cre recombinase of bacteriophage P1 both belong to the lambda-integrase (Int) family of site-specific recombinases. These recombination systems recognize recombination-target sequences that consist of two 13bp inverted repeats flanking a 6 or 8bp spacer sequence. Recombination reactions involve particular geometric and topological relationships between DNA target sites at synapsis, which we investigate using nicked-circular DNA molecules. Examination of the tertiary structure of synaptic complexes formed on nicked plasmid DNAs by atomic-force microscopy, in conjunction with detailed topological analysis using the mathematics of tangles, shows that only a limited number of recombination-site topologies are consistent with the global structures of plasmids bearing directly and inversely repeated sites. The tangle solutions imply that there is significant distortion of the Holliday-junction intermediate relative to the planar structure of the four-way DNA junction present in the Flp and Cre co-crystal structures. Based on simulations of nucleoprotein structures that connect the two-dimensional tangle solutions with three-dimensional models of the complexes, we propose a recombination mechanism in which the synaptic intermediate is characterized by a non-planar, possibly near-tetrahedral, Holliday-junction intermediate. Only modest conformational changes within this structure are needed to form the symmetric, planar DNA junction, which may be characteristic of shorter-lived intermediates along the recombination pathway.