Effect of interaction shape on the condensed toroid of the semiflexible chain

Abstract

We investigate how different microscopic interactions between semiflexible chain segments can qualitatively alter the physical properties of the condensed toroid. We propose a general form of the Hamiltonian of the toroid and discuss its analytic properties. For different interactions, the theory predicts different scaling behaviors of the mean toroidal and cross sectional radii, rc and rcross, as functions of the contour length L: (rc, rcross) ∼ L (Nc), with = (1 5, 2 5) for the van der Waals-type, = (- 1 3, 2 3) for the Coulomb-type, and = (-1,1) for the delta-function-type attractions in the asymptotic limit. For the toroids with finite winding number Nc =100-400, we find ≃0 for the Yukawa interaction with screening parameter κ=0.5-1.0 and =0.1-0.13 for the van der Waals-type interactions. These findings could provide a possible explanation for the experimentally well known observation ≃0 of the condensed DNA toroids. Conformational transitions are also discussed. © 2008 American Institute of Physics.