Current theoretical models fail to predict the topological complexity of the human genome.

Understanding the folding of the human genome is a key challenge of modern structural biology. The emergence of chromatin conformation capture assays (e.g.

Free-energy calculations for semi-flexible macromolecules: applications to DNA knotting and looping.

We present a method to obtain numerically accurate values of configurational free energies of semiflexible macromolecular systems, based on the technique of thermodynamic integration combined with normal-mode analysis of a reference system subject to harmonic constraints. Compared with previous free-energy calculations that depend on a reference state, our approach introduces two innovations, namely, the use of internal coordinates to constrain the reference states and the ability to freely select these reference states. As a consequence, it is possible to explore systems that undergo substantially larger fluctuations than those considered in previous calculations, including semiflexible biopolymers having arbitrary ratios of contour length L to persistence length P.

New biologically motivated knot table.

The knot nomenclature in common use, summarized in Rolfsen's knot table [Rolfsen (1990) Knots and Links, American Mathematical Society], was not originally designed to distinguish between mirror images. This ambiguity is particularly inconvenient when studying knotted biopolymers such as DNA and proteins, since their chirality is often significant. In the present article, we propose a biologically meaningful knot table where a representative of a chiral pair is chosen on the basis of its mean writhe.

On the mean and variance of the writhe of random polygons.

We here address two problems concerning the writhe of random polygons. First, we study the behavior of the mean writhe as a function length. Second, we study the variance of the writhe.

Modeling of chromosome intermingling by partially overlapping uniform random polygons.

During the early phase of the cell cycle the eukaryotic genome is organized into chromosome territories. The geometry of the interface between any two chromosomes remains a matter of debate and may have important functional consequences. The Interchromosomal Network model (introduced by Branco and Pombo) proposes that territories intermingle along their periphery.

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.

Accessibility and occlusion of biopolymers, ray tracing of radiating tubes, and the temperature of a tangle.

We introduce a measure of complexity, an energy, for any conformation of filaments. It is the occlusion, the portion hidden when viewed from an arbitrary exterior point. By inverting we get the exposure, a first approximation of the accessibility of the filaments.

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

Unlabelled: 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.

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.