Title:  Mathematical methods to study DNA packing in bacterial viruses
Abstract:  The three dimensional organization of genomes is a key player in multiple biological processes including the genome packaging and release in viruses. The genome of some viruses, such as bacteriophages, is a double stranded DNA (dsDNA) molecule that is stored inside a viral protein capsid at a very high concentration and osmotic pressure. The organization of the viral genome under these extreme physical conditions is believed to be liquid crystalline but remains to be properly described. A general picture of this organization has been given by cryoelectron microscopy (cryoEM) studies that show a series of concentric layers near the surface of the viral capsid followed by a disordered arrangement of DNA fibers near the center of the capsid. In this talk I will present results from three different mathematical approaches to study the problem of dsDNA packing in bacteriophages. The first approach complements the cryoEM observations and uses the formation of knots inside viral capsids as a probe for DNA packing. These results suggest that DNA knots are highly likely upon confinement and that the DNA molecule is chirally organized inside the viral capsid. The second approach aims at identifying the possible sources of the chiral organization of the genome and employs methods from random knotting and brownian dynamics and suggest that the DNA packing motor can account for the suggested chirality of the genome. The third approach uses continuum mechanics models to rigorously describe cryoEM observations as the minima of a liquid crystalline phase. The emergent picture of these approaches suggest that DNA is in a chirally organized liquid crystalline phase in which knots may are the defects of the DNA liquid crystal.