Kenneth C. Millett1, Eric J. Rawdon2, Vy T. Tran3, and Andrzej Stasiak4
1Department of Mathematics, University of California Santa Barbara, California 93106, USA
2Department of Mathematics, University of St. Thomas, Saint Paul, Minnesota 55105, USA
3Department of Physics, Washington University, Saint Louis, Missouri 63130, USA
4Center for Integrative Genomics, Faculty of Biology and Medicine, University of Lausanne, CH 1015, Switzerland
(Received 12 July 2010; accepted 9 September 2010; published online 20 October 2010)
Abstract
Using numerical simulations we investigate shapes of random equilateral open and closed chains, one of the simplest models of freely fluctuating polymers in a solution. We are interested in the 3D density distribution of the modeled polymers where the polymers have been aligned with respect to their three principal axes of inertia. This type of approach was pioneered by Theodorou and Suter in 1985. While individual configurations of the modeled polymers are almost always nonsymmetric, the approach of Theodorou and Suter results in cumulative shapes that are highly symmetric. By taking advantage of asymmetries within the individual configurations, we modify the procedure of aligning independent configurations in a way that shows their asymmetry. This approach reveals, for example, that the 3D density distribution for linear polymers has a bean shape predicted theoretically by Kuhn. The symmetry-breaking approach reveals complementary information to the traditional, symmetrical, 3D density distributions originally introduced by Theodorou and Suter.
© 2010 American Institute of Physics