**abstract:**
DNA presents high levels of condensation in all organisms. We are interested in
the problem of DNA packing inside bacteriophage capsids. Bacteriophages are
viruses that infect bacteria. DNA extracted from bacteriophage P4 capsids is
highly knotted. Here use the packing of P4 DNA to motivate a couple of recent
lines of work in our group. First, it is interesting to ask what is the minimal length
of DNA needed to tie a particular knot type. Following on the steps of Y. Diao
and of E.J. Janse van Rensburg, we have characterized both analytically and
numerically the minimum length (also called minimum step number) needed to
form a particular knot in the simple cubic lattice. Second, suppose that we are
dealing with a set of random polygons with the same length and knot type, which
could be the model of some circular DNA with the same topological property. In
general, a simple way of detecting chirality of this knot type is to compute the
mean writhe of the polygons; if the mean writhe is non-zero then the knot is
chiral. Furthermore, we conjecture that the sign of the mean writhe is a
topological invariant of chiral knots. We provide numerical evidence to support
these claims, and we propose a new nomenclature of knots based on the sign of
their expected writhes. This nomenclature can be of particular interest to applied
scientists. This is joint work with Javier Arsuaga, Yuanan Diao, Kai Ishihara,
Juliet Portillo, Rob Scharein, De Witt Sumners and Koya Shimokawa.

Wed 8 Jun, 10:15 - 11:15, Aula Dini

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