12 research outputs found
Gyration radius of a circular polymer under a topological constraint with excluded volume
It is nontrivial whether the average size of a ring polymer should become
smaller or larger under a topological constraint.
Making use of some knot invariants, we evaluate numerically the mean square
radius of gyration for ring polymers having a fixed knot type, where the ring
polymers are given by self-avoiding polygons consisting of freely-jointed hard
cylinders. We obtain plots of the gyration radius versus the number of
polygonal nodes for the trivial, trefoil and figure-eight knots. We discuss
possible asymptotic behaviors of the gyration radius under the topological
constraint. In the asymptotic limit, the size of a ring polymer with a given
knot is larger than that of no topological constraint when the polymer is thin,
and the effective expansion becomes weak when the polymer is thick enough.Comment: 12pages,3figure
Micromechanics of Single Supercoiled DNA Molecules
Abstract. The theory of the mechanical response of single DNA molecules un-der stretching and twisting stresses is reviewed. Using established results for the the semiflexible polymer including the effect of torsional stress, and for the free energy of plectonemic supercoils, a theory of coexisting plectonemic and extended DNA is con-structed and shown to produce phenomena observed experimentally. Analytical results for DNA extension and torque are presented, and effects of anharmonicities in the plec-tonemic free energy are described. An application of the theory to the problem of torsional-stress-induced cruciform extrusion is also discussed. Key words. DNA, molecular biology, statistical mechanics, polymer physics. AMS(MOS) subject classifications. 82D60, 92C05, 92C40