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

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) approximately Lnu(Nc), with nu=(1/5,2/5) for the van der Waals-type, nu=(-1/3,2/3) for the Coulomb-type, and nu=(-1,1) for the delta-function-type attractions in the asymptotic limit. For the toroids with finite winding number Nc=100-400, we find nu approximately 0 for the Yukawa interaction with screening parameter kappa=0.5-1.0 and nu=0.1-0.13 for the van der Waals-type interactions. These findings could provide a possible explanation for the experimentally well known observation nu approximately 0 of the condensed DNA toroids. Conformational transitions are also discussed.