465378 Lattice Models, Polymers and DNA Topology

Monday, November 14, 2016: 2:06 PM
Yosemite B (Hilton San Francisco Union Square)
Chris Soteros, Mathematics and Statistics, University of Saskatchewan, Saskatoon, SK, Canada

The standard Statistical Mechanics models for linear and ring polymers in dilute solution are respectively the self-avoiding walk (SAW) and self-avoiding polygon (SAP) lattice models. For a SAP model, a ring polymer configuration is represented by a random polygon on a lattice such as the simple cubic lattice, and under good solvent conditions, each equal-length polygon is considered to be an equally likely configuration. These models have the advantages that the excluded volume property is easily incorporated and that combinatorial and asymptotic analysis is possible; they have proved to be very useful for understanding critical phenomena, such as phase transitions, for polymer systems. At the same time, despite the simplicity of the models, there are many challenging questions that remain open about them. In this talk, I will review progress made regarding using SAP models to address questions about the entanglement complexity (knotting and linking) of polymer systems. The work has been motivated in part by experimental studies of: (i) enzyme action on DNA, where observed knot and link frequencies characterize the action of the enzyme, and (ii) DNA confined to viral capsids, where observed knot frequencies characterize how the DNA is packed in the capsid.

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See more of this Session: In Honor of Carol Hall I (Invited Talks)
See more of this Group/Topical: Engineering Sciences and Fundamentals