Dorothy Elizabeth Buck

Journal Article Physics Reports · July 18, 2024 The last years have witnessed remarkable advances in our understanding of the emergence and consequences of topological constraints in biological and soft matter. Examples are abundant in relation to (bio)polymeric systems and range from the characterizati ... Full text Cite

Double branched covers of knotoids

Journal Article Communications in Analysis and Geometry · January 1, 2022 By using double branched covers, we prove that there is a 1-1 correspondence between the set of knotoids in S2, up to orientation reversion and rotation, and knots with a strong inversion, up to conjugacy. This correspondence allows us to study knotoids th ... Full text Cite

Integrating transposable elements in the 3D genome

Journal Article Mobile DNA · February 4, 2020 Chromosome organisation is increasingly recognised as an essential component of genome regulation, cell fate and cell health. Within the realm of transposable elements (TEs) however, the spatial information of how genomes are folded is still only rarely in ... Full text Cite

Grid diagrams as tools to investigate knot spaces and topoisomerase-mediated simplification of DNA topology.

Journal Article Science advances · February 2020 Grid diagrams with their relatively simple mathematical formalism provide a convenient way to generate and model projections of various knots. It has been an open question whether these 2D diagrams can be used to model a complex 3D process such as the topo ... Full text Cite

Knotting of replication intermediates is narrowly restricted

Conference Contemporary Mathematics · January 1, 2020 The fundamental biological process of DNA replication contains several potential topological pitfalls. These, if not properly managed, lead to cell death. The enzymes (topoisomerases) responsible for averting these topological death warrants can inadverten ... Full text Cite

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

Journal Article Nucleic acids research · September 2018 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. Therefo ... Full text Cite

Erratum to: Toroidal embeddings of abstractly planar graphs are knotted or linked (Journal of Mathematical Chemistry, (2015), 53, 8, (1772-1790), 10.1007/s10910-015-0519-1)

Journal Article Journal of Mathematical Chemistry · October 1, 2017 Unfortunately, the grant funding information was missed in the original publication. It has been corrected with this erratum. The second author was partially supported by EPSRC Grants EP/G039585/1 and EP/H031367/1, and the Leverhulme Trust Grant RP2013-K-0 ... Full text Cite

Band surgeries and crossing changes between fibered links

Journal Article Journal of the London Mathematical Society · October 1, 2016 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 b ... Full text Cite

Some knots in S¹ × S² with lens space surgeries

Journal Article Communications in Analysis and Geometry · January 1, 2016 We propose a classification of knots in S1 × S2 that admit a longitudinal surgery to a lens space. Any lens space obtainable by longitudinal surgery on some knot in S1 × S2 may be obtained from a Berge-Gabai knot in a Heegaard solid torus of S1 × S2, as ob ... Full text Cite

Drawing in mathematics from inverse vision to the liberation of form

Journal Article Leonardo · October 25, 2015 The literature on art and mathematics has focused largely on how geometric forms have influenced artists and on the use of computer visualization in mathematics. The authors consider a fundamental but undiscussed connection between mathematics and art: the ... Full text Cite

Toroidal embeddings of abstractly planar graphs are knotted or linked

Journal Article Journal of Mathematical Chemistry · September 13, 2015 We give explicit deformations of embeddings of abstractly planar graphs that lie on the standard torus $$T^2 \subset \mathbb {R}^3$$T2⊂R3 and that contain neither a nontrivial knot nor a nonsplit link into the plane. It follows that ravels do not embed on ... Full text Cite

Genus ranges of 4-regular rigid vertex graphs

Journal Article Electronic Journal of Combinatorics · September 4, 2015 A rigid vertex of a graph is one that has a prescribed cyclic order of its incident edges. We study orientable genus ranges of 4-regular rigid vertex graphs. The (orientable) genus range is a set of genera values over all orientable surfaces into which a g ... Full text Cite

Coherent band pathways between knots and links

Journal Article Journal of Knot Theory and its Ramifications · February 25, 2015 We categorize coherent band (aka nullification) pathways between knots and 2-component links. Additionally, we characterize the minimal coherent band pathways (with intermediates) between any two knots or 2-component links with small crossing number. We de ... Full text Cite

Reactions mediated by topoisomerases and other enzymes: Modelling localised DNA transformations

Chapter · January 1, 2014 Many proteins cleave and reseal DNA molecules in precisely orchestrated ways. Modelling these reactions has often relied on the axis of the DNA double helix being circular, so these cut-and-seal mechanisms can be tracked by corresponding changes in the kno ... Full text Cite

The classification of rational subtangle replacements between rational tangles

Journal Article Algebraic and Geometric Topology · April 30, 2013 A natural generalization of a crossing change is a rational subtangle replacement (RSR). We characterize the fundamental situation of the rational tangles obtained from a given rational tangle via RSR, building on work of Berge and Gabai, and determine the ... Full text Cite

Topological aspects of DNA function and protein folding.

Journal Article Biochemical Society transactions · April 2013 The Topological Aspects of DNA Function and Protein Folding international meeting provided an interdisciplinary forum for biological scientists, physicists and mathematicians to discuss recent developments in the application of topology to the study of DNA ... Full text Cite

Pretzel knots with unknotting number one

Journal Article Communications in Analysis and Geometry · January 1, 2013 We provide a partial classification of the 3-strand pretzel knots K = P(p, q, r) with unknotting number one. Following the classification by Kobayashi and Scharlemann-Thompson for all parameters odd, we treat the remaining families with r even. We discover ... Full text Cite

Gated rotation mechanism of site-specific recombination by ϕC31 integrase.

Journal Article Proceedings of the National Academy of Sciences of the United States of America · November 2012 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 recom ... Full text Cite

Phylogenetic inference for function-valued traits: speech sound evolution.

Journal Article Trends in ecology & evolution · March 2012 Phylogenetic models have recently been proposed for data that are best represented as a mathematical function (i.e. function valued). Such methods can be used to model the change over time in function-based descriptions of various data of interest to evolu ... Full text Cite

Predicting knot and catenane type of products of site-specific recombination on twist knot substrates.

Journal Article Journal of molecular biology · August 2011 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 recomb ... Full text Cite

Connect sum of lens spaces surgeries: Application to Hin recombination

Journal Article Mathematical Proceedings of the Cambridge Philosophical Society · May 1, 2011 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 ... Full text Cite

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

Journal Article Journal of Physics A: Mathematical and Theoretical · January 28, 2011 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 ... Full text Cite

Taxonomy of DNA conformations within complex nucleoprotein assemblies

Conference Progress of Theoretical Physics Supplement · January 1, 2011 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 rationa ... Full text Cite

Predicting knot or catenane type of site-specific recombination products.

Journal Article Journal of molecular biology · December 2007 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 toru ... Full text Cite

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

Journal Article Journal of Physics A: Mathematical and Theoretical · October 12, 2007 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 sing ... Full text Cite

Classification of tangle solutions for integrases, a protein family that changes DNA topology

Journal Article Journal of Knot Theory and its Ramifications · October 1, 2007 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 - ar ... Full text Cite

Tangle solutions for a family of DNA-rearranging proteins

Journal Article Mathematical Proceedings of the Cambridge Philosophical Society · July 1, 2005 We study two systems of tangle equations that arise when modeling the action of the Integrase family of proteins on DNA. These two systems - direct and inverted repeats - correspond to two different possibilities for the initial DNA sequence. We present on ... Full text Cite

Geometry of site alignment during int family recombination: antiparallel synapsis by the Flp recombinase.

Journal Article Journal of molecular biology · May 2000 The Flp site-specific recombinase functions in the copy number amplification of the yeast 2 microm plasmid. The recombination reaction is catalyzed by four monomers of Flp bound to two separate, but identical, recombination sites (FRT sites) and occurs in ... Full text Cite