Knot Energy, Complexity, and Mobility of Knotted Polymers
F Vargas-Lara and AM Hassan and ML Mansfield and JF Douglas, SCIENTIFIC REPORTS, 7, 13374 (2017).
The Coulomb energy E-C is defined by the energy required to charge a conductive object and scales inversely to the self-capacity C, a basic measure of object size and shape. It is known that C is minimized for a sphere for all objects having the same volume, and that C increases as the symmetry of an object is reduced at fixed volume. Mathematically similar energy functionals have been related to the average knot crossing number < m >, a natural measure of knot complexity and, correspondingly, we find E-C to be directly related to < m > of knotted DNA. To establish this relation, we employ molecular dynamics simulations to generate knotted polymeric configurations having different length and stiffness, and minimum knot crossing number values m for a wide class of knot types relevant to the real DNA. We then compute E-C for all these knotted polymers using the program ZENO and find that the average Coulomb energy < E-C > is directly proportional to < m >. Finally, we calculate estimates of the ratio of the hydrodynamic radius, radius of gyration, and the intrinsic viscosity of semi-flexible knotted polymers in comparison to the linear polymeric chains since these ratios should be useful in characterizing knotted polymers experimentally.
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