Plenary Talk
Carla Tesi,
Department of Mathematics, University of Bologna
Mathematical models of entangled macromolecules
The problem of entanglement complexity in polymeric systems is a quite common and relevant issue in physics, chemistry and biology. For instance polymer entanglement in melts and dense solutions is known to affect the rheological and elastic properties of the material. In biology DNA and RNA are quite long macromolecules and often live in restricted (crowded) environments. This gives rise to extremely entangled spatial organization that can dramatically affect elementary cell processes if enzymes as topo-isomerase are inactive. Given that long polymers are highly flexible and in solution, statistical approaches, performed on relatively simple coarse-grained models of the molecule, turn out to be effective. Here I will review some of these approaches by focussing on discrete (on and off lattice) models. In particular I will present some rigorous and numerical results on the topological entanglement (knots and links) of polymers both in free solution and under geometrical and mechanical constraints. Open problems and technical subtleties will be also mentioned during the talk.