Dorothy Buck

Gated rotation mechanism of site-specific recombination by ϕC31 integrase

Integrases, such as that of the Streptomyces temperate bacteriophage ϕC31, promote site-specific recombination between DNA sequences in the bacteriophage and bacterial genomes to integrate or excise the phage DNA. ϕC31 integrase belongs to the serine recombinase family, a large group of structurally related enzymes with diverse biological functions. It has been proposed that serine integrases use a “subunit rotation” mechanism to exchange DNA strands after double-strand DNA cleavage at the two recombining att sites, and that many rounds of subunit rotation can occur before the strands are religated. We have analyzed the mechanism of ϕC31 integrase-mediated recombination in a topologically constrained experimental system using hybrid “phes” recombination sites, each of which comprises a ϕC31 att site positioned adjacent to a regulatory sequence recognized by Tn3 resolvase. The topologies of reaction products from circular substrates containing two phes sites support a right-handed subunit rotation mechanism for catalysis of both integrative and excisive recombination. Strand exchange usually terminates after a single round of 180° rotation. However, multiple processive “360° rotation” rounds of strand exchange can be observed, if the recombining sites have nonidentical base pairs at their centers. We propose that a regulatory “gating” mechanism normally blocks multiple rounds of strand exchange and triggers product release after a single round.

Connect sum of lens spaces surgeries: application to Hin recombination

We extend the tangle model, originally developed by Ernst and Sumners [ 18 ], to include composite knots. We show that, for any prime tangle, there are no rational tangle attachments of distance greater than one that first yield a 4-plat and then a connected sum of 4-plats. This is done by studying the corresponding Dehn filling problem via double branched covers. In particular, we build on results on exceptional Dehn fillings at maximal distance to show that if Dehn filling on an irreducible manifold gives a lens space and then a connect sum of lens spaces, the distance between the slopes must be one. We then apply our results to the action of the Hin recombinase on mutated sites. In particular, after solving the tangle equations for processive recombination, we use our work to give a complete set of solutions to the tangle equations modelling distributive recombination.

A topological characterization of knots and links arising from site-specific recombination

We develop a topological model of knots and links arising from a single (or multiple processive) round(s) of recombination starting with an unknot, unlink, or (2, m)-torus knot or link substrate. We show that all knotted or linked products fall into a single family, and prove that the size of this family grows linearly with the cube of the minimum number of crossings. Additionally, we prove that the only possible nontrivial products of an unknot substrate are (2, m)-torus knots and links and those knots and links which consist of two non-adjacent rows of crossings. (In the special case where one row contains only two crossings, these are the well-known twist knots and links.) In the (common) case of (2, m)-torus knot or link substrates whose products have minimal crossing number m + 1, we prove that the types of products are tightly prescribed, and use this to examine previously uncharacterized experimental data. Finally, we illustrate how the model can help determine the sequence of products in multiple rounds of processive recombination.

CLASSIFICATION OF TANGLE SOLUTIONS FOR INTEGRASES, A PROTEIN FAMILY THAT CHANGES DNA TOPOLOGY

A generic integrase protein, when acting on circular DNA, often changes the DNA topology by transforming unknotted circles into torus knots and links. Two systems of tangle equations — corresponding to two possible orientations of two DNA subsequences — arise when modelling this transformation. With no a priori assumptions on the constituent tangles, we utilize Dehn surgery arguments to completely classify the tangle solutions for each of the two systems. A key step is to combine work of our previous paper [10] with recent results of Kronheimer, Mrowka, Ozsvath and Szabo [39] and work of Ernst [23] to show a certain prime tangle must in fact be a Montesinos tangle. These tangle solutions are divided into three classes, common to both systems, plus a fourth class for one system that contains the sole Montesinos tangle. We discuss the possible biological implications of our classification, and of this novel solution.

Predicting Knot and Catenane Type of Products of Site-Specific Recombination on Twist Knot Substrates

Site-specific recombination on supercoiled circular DNA molecules can yield a variety of knots and catenanes. Twist knots are some of the most common conformations of these products, and they can act as substrates for further rounds of site-specific recombination. They are also one of the simplest families of knots and catenanes. Yet, our systematic understanding of their implication in DNA and important cellular processes such as site-specific recombination is very limited. Here, we present a topological model of site-specific recombination characterizing all possible products of this reaction on twist knot substrates, extending the previous work of Buck and Flapan. We illustrate how to use our model to examine previously uncharacterized experimental data. We also show how our model can help determine the sequence of products in multiple rounds of processive recombination and distinguish between products of processive and distributive recombinations. This model studies generic site-specific recombination on arbitrary twist knot substrates, a subject for which there is limited global understanding. We also provide a systematic method of applying our model to a variety of different recombination systems.

Coherent band pathways between knots and links

We categorise coherent band (aka nullification) pathways between knots and 2-component links. Additionally, we characterise the minimal coherent band pathways (with intermediates) between any two knots or 2-component links with small crossing number. We demonstrate these band surgeries for knots and links with small crossing number. We apply these results to place lower bounds on the minimum number of recombinant events separating DNA configurations, restrict the recombination pathways and determine chirality and/or orientation of the resulting recombinant DNA molecules.

Characterization of knots and links arising from site-specific recombination on twist knots

We develop a model characterizing all possible knots and links arising from recombination starting with a twist knot substrate, extending the previous work of Buck and Flapan. We show that all knot or link products fall into three well-understood families of knots and links, and prove that given a positive integer n, the number of product knots and links with minimal crossing number equal to n grows proportionally to n5. In the (common) case of twist knot substrates whose products have minimal crossing number one more than the substrate, we prove that the types of products are tightly prescribed. Finally, we give two simple examples to illustrate how this model can help determine previously uncharacterized experimental data.

Band surgeries and crossing changes between fibered links

We characterize cutting arcs on fiber surfaces that produce new fiber surfaces, and the changes in monodromy resulting from such cuts. As a corollary, we characterize band surgeries between fibered links and introduce an operation called Generalized Hopf banding. We further characterize generalized crossing changes between fibered links, and the resulting changes in monodromy.

Taxonomy of DNA Conformations within Complex Nucleoprotein Assemblies

Here we discuss the paradigms both for modelling complex nucleoprotein assemblies as rational tangles, and the associated enzymatic action as rational subtangle replacement. We harness the correspondence between specific curves on the boundary of a rational tangle and on the boundary of its branched double cover to classify rational tangles of distance d ≥ 2 from a given rational tangle, in turn limiting the underlying DNA geometry.

Two convergent pathways of DNA knotting in replicating DNA molecules as revealed by θ-curve analysis

Abstract During DNA replication in living cells some DNA knots are inadvertently produced by DNA topoisomerases facilitating progression of replication forks. The types of DNA knots formed are conditioned by the 3D organization of replicating DNA molecules. Therefore, by characterizing formed DNA knots it is possible to infer the 3D arrangement of replicating DNA molecules. This topological inference method is highly developed for knotted DNA circles. However, partially replicated DNA molecules have the form of θ-curves. In this article, we use mathematical formalism of θ-curves to characterize the full possibilities of how knotting can occur during replication of DNA molecules in vivo. To do this, we reanalyze earlier experimental studies of knotted, partially replicated DNA molecules and the previously proposed pathway of their formation. We propose a general model of knotting in replication intermediates, and demonstrate that there is an additional, equally important, parallel knotting pathway that also explains how DNA topoisomerases can produce experimentally observed knotted θ-curves. Interestingly, both pathways require intertwining of freshly replicated sister duplexes (precatenanes).