Applications of topology to study DNA and chromosomes

Our group is interested in applications of knot theory to understand the three dimensional organization of the genome in different organisms. We are also interested in the applications of computational homology to analyze genomic data.

Our current main interests are:

- DNA Packing in Bacteriophages.
- Minicircle Organization in kDNA Networks of Trypanosomes
- The Geometry and Topology of Chromatin During Interphase
- Applications of Computational Homology to the Analysis of Copy Number Changes in Breast Cancer


DNA packing in bacteriophages. NSF funded research (DMS-0920887)


Double stranded (Ds) DNA viruses such as bacteriophages, adenoviruses and herpesviruses keep their genome in a spherical protein container called a capsid. The radius of the capsid is at least two orders of magnitude smaller than the length of the viral genome. This implies that once the DNA is packed inside the capsid it is subjected to strong bending and repulsive interactions (due to its rigidity and negative charge). Little is currently understood about the biophysical properties of the DNA molecule under these extreme conditions. In our group we use bacteriophage P4 to investigate such properties.

Bacteriophages, viruses that propagate in bacteria, are commonly used to study DNA packing and folding in other dsDNA viruses because they have similar morphology and share similar assembly pathways. A number of models have been proposed to explain the folding of the DNA molecule inside the bacteriophage capsid. However these models provide only a very general description of the trajectory of the DNA. This lack of understanding is reflected in the inability of current DNA folding models to predict the finding that DNA molecules abruptly extracted from bacteriophage P4 are knotted (i.e. are circles which cannot be laid flat on a plane without self-intersecting).

In our work, we have experimentally shown that P4 knots preserve information about the folding of the DNA inside the capsid and about the physical properties of the DNA itself. We are currently developing a model of DNA folding which improves on the models now available by incorporating biophysical properties that account for and allow for the reproduction of the knotted structures observed in P4. The long-term goal of this work is to provide a novel quantitative description of the process of DNA packing and folding inside dsDNA viruses that is consistent with the topological information observed in P4 and with other published data.

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Minicircle Organization in kDNA Networks of Trypanosomes (Selected by the NSF for the NSF highlights 2011)


Trypanosomes and leishmania, two trypanosomatid parasites, are protozoa which cause fatal diseases such as sleeping sickness, Chagas disease and Leishmaniasis. Although they have a significant impact on the health and economies of many third world countries, these diseases continue to be catalogued as “neglected” by the World Health Organization. A distinctive feature of trypanosomatid parasites is that their mitochondrial DNA, known as kinetoplast DNA, is organized into thousands of minicircles and a few dozen maxicircles. Furthermore, minicircles in these organisms are topologically linked, forming a gigantic network in which the minicircles are interlocked in a chainmail-like structure) The topological structure of the minicircles is of great significance both because it is species-specific and because it is a promising target for the development of drugs. However, the biophysical factors that led to the formation of the network during evolution remain poorly understood, along with its topological properties. We have introduced the Square Lattice Minicircle model to model how these networks grow and fond that the formation of a network, assuming condensation, reaches a density of minicircles at which percolation occurs.

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The Geometry and Topology of Chromatin During Interphase. NIH funded research (RO1-GM109457)


Previously supported by NIH grant 2S06GM52588
During interphase chromosomes are confined to sub-nuclear regions called chromosome territories. The position of these territories has been associated with a number of biological processes such as cell differentiation and are believed to have a very important role in cancer and other human diseases.

We are developing statistical methods that interrogate mFISH or SKY data for chromosome clustering (i.e. for deviations from randomness in the relative positions of chromosomes). Our approach is based on the hypothesis that chromosomes that are in close proximity form radiation induced chromosome aberrations more often than those that are far apart (known as the proximity effect hypothesis). When applying these methods to human lymphocytes we find two sets of chromosomes that are on average closer to each other than what randomness would predict these are: {1,16,17,19,22}and {13,14,15,21,22} (Cornforth et al. 2002, Arsuaga et al. 2004, Vives et al. 2005). We have recently investigated the topology of the interface between chromosome territories assuming that the chromatin follows the trajectory of a random walk. We have found that the probability that two territories are topologically linked grows as 1-O(1/sqrt(nm)) where n and m correspond to the lenght of the polygons.

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Applications of Computational Homology to the Analysis of Copy Number Changes in Breast Cancer. NSF funded project. Grant number 1217324


Previously funded by RIMI program. Grant number 2P20MD000544.
Breast cancer is a very heterogeneous disease that in the US affects 200,000 people per year. It is clinically classified according to certain parameters such as Stage and grade. In addition, molecular phenotyping has allowed the categorization of tumors using expression of surrogate markers of Estrogen and Progesterone Receptors (ER) and (PR) and of the gene ERBB2 (also known as HER2). Most microarrays studies focus on finding specific genes that are either amplified or deleted and whose expression is correspondinly changed. We use computational homology to test for differences in the copy number (and gene expression) topography of each chromosomes. Therefore we interrogate not to single probes/genes but to combinations of nearby probes using techniques from algebraic homology.

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