Tangle analysis of difference topology experiments: applications to a Mu protein-DNA complex

We develop topological methods for analyzing difference topology experiments involving 3-string tangles. Difference topology is a novel technique used to unveil the structure of stable protein-DNA complexes involving two or more DNA segments. We analyze such experiments for the Mu protein-DNA complex. We characterize the solutions to the corresponding tangle equations by certain knotted graphs. By investigating planarity conditions on these graphs we show that there is a unique biologically relevant solution. That is, we show there is a unique rational tangle solution, which is also the unique solution with small crossing number.Comment: 60 pages, 74 figure

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 like site-specific recombination is very limited. Here we present a topological model of site-specific recombination characterising all possible products of this reaction on twist knot substrates, extending previous work of Buck and Flapan. We illustrate how to use our model to examine previously uncharacterised 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 recombination. 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.Comment: 17 pages, 13 figures. One figure correction. To appear in the Journal of Molecular Biology. See also arXiv:1007.2115v1 math.GT for topological proofs for the model presented her

AN ELEMENTARY PROOF OF THE EFFECT OF 3-MOVE ON THE JONES POLYNOMIAL

A mathematical knot is an embedded circle in R3. A fundamental problem in knot theory is classifying knots up to its numbers of crossing points. Knots are often distinguished by using a knot invariant, a quantity which is the same for equivalent knots. Knot polynomials are one of well known knot invariants. In 2006, J. Przytycki showed the effects of a n move (a local change in a knot diagram) on several knot polynomials. In this paper, the authors review about knot polynomials, especially Jones polynomial, and give an alternative proof to a part of the Przytychi's result for the case n = 3 on the Jones polynomial.ope

Establishing RNA binding proteins as key components of Alzheimer's disease pathophysiology

Aggregation of the microtubule associated protein tau (MAPT) into filamentous neurofibrillary tangles (NFTs) is a defining molecular hallmark of neurodegenerative diseases such as Alzheimer’s disease (AD) and frontotemporal dementia (FTD). Despite the discovery of NFTs decades ago, the molecular mechanisms underpinning their formation and neurotoxicity have remained elusive. Recently, our lab has shown that stress granule (SG) associated RNA binding proteins (RBPs) co-deposit with pathological tau in mouse models and human disease; reduction of the SG associated protein TIA1 also protects against tau-mediated behavioral deficits and degeneration. Here we demonstrate that RBPs facilitate tau pathogenesis and exhibit prominent signs of dysfunction early in disease. By immunoprecipitating pathological tau from the transgenic rTg4510 AD mouse model, we have found that tau associates with many RBPs and ribosomal subunits, and these associations change as tau pathology develops. These RBPs also become increasingly insoluble in tauopathy, consistent with the formation of fibrillar aggregates. We also show by immunohistochemistry that as tau forms mature neurofibrillary tangles, RBPs lose their interaction with tau and aggregate to the periphery of the tangle in mouse and human tissue, suggesting that RBPs contribute to earlier stages of tau aggregation. Seeing this, we sought to determine at what point of tau pathogenesis RBPs become relevant to the disease process. Using the PS19 mouse line, which develops tangle pathology more slowly than the rTg4510, we have found that RBP immunohistochemistry is highly sensitive to tissue fixation methods, that different brain regions have unique localization patterns of canonically nuclear RBPs, and that transgenic tau mice show striking changes in hippocampal RBP regulation very early in tau pathogenesis. This precedes an eventual destabilization and disruption of the nuclear lamina. We further show that overexpression of TIA1 accelerates the somatodendritic accumulation of phosphorylated tau in vivo, and that TIA1 granules co-localize with granules of misfolded tau. Together these findings support the idea that ribonucleoprotein granules contribute significantly to early pathological tau formation and that misregulation of these proteins progresses in tandem with tau pathology. RBPs thus offer promising new therapeutic targets for Alzheimer’s disease and related tauopathies

3D visualization software to analyze topological outcomes of topoisomerase reactions.

The action of various DNA topoisomerases frequently results in characteristic changes in DNA topology. Important information for understanding mechanistic details of action of these topoisomerases can be provided by investigating the knot types resulting from topoisomerase action on circular DNA forming a particular knot type. Depending on the topological bias of a given topoisomerase reaction, one observes different subsets of knotted products. To establish the character of topological bias, one needs to be aware of all possible topological outcomes of intersegmental passages occurring within a given knot type. However, it is not trivial to systematically enumerate topological outcomes of strand passage from a given knot type. We present here a 3D visualization software (TopoICE-X in KnotPlot) that incorporates topological analysis methods in order to visualize, for example, knots that can be obtained from a given knot by one intersegmental passage. The software has several other options for the topological analysis of mechanisms of action of various topoisomerases

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 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 $n^5$. 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.Comment: 32 pages, 7 tables, 27 figures, revised: figures re-arranged, and minor corrections. To appear in Journal of Physics