title: Effect of knotting on polymer shapes and their enveloping ellipsoids.
abstract: We simulate freely jointed chains to investigate how knotting affects the overall shapes of freely fluctuating circular polymeric chains. To characterize the shapes of knotted polygons, we construct enveloping ellipsoids that minimize volume while containing the entire polygon. The lengths of the three principal axes of the enveloping ellipsoids are used to define universal size and shape descriptors analogous to the squared radius of gyration and the inertial asphericity and prolateness. We observe that polymeric chains forming more complex knots are more spherical and also more prolate than chains forming less complex knots with the same number of edges. We compare the shape measures, determined by the enveloping ellipsoids, with those based on constructing inertial ellipsoids and explain the differences between these two measures of polymer shape.
authors.affiliation: Department of Mathematics, University of California, Santa Barbara, Santa Barbara, California 93106, USA. millett@math.ucsb.edu
authors.forename: Kenneth C
authors.initials: KC
authors.lastname: Millett
authors.forename: Patrick
authors.initials: P
authors.lastname: Plunkett
authors.forename: Michael
authors.initials: M
authors.lastname: Piatek
authors.forename: Eric J
authors.initials: EJ
authors.lastname: Rawdon
authors.forename: Andrzej
authors.initials: A
authors.lastname: Stasiak
mesh_terms: D003198:Computer Simulation; D008958:Models, Molecular; D008968:Molecular Conformation; D011108:Polymers / Q000737:chemistry*
chemical_list: D011108:Polymers