Lattice ribbons: A model of double-stranded polymers

We introduce a discrete ribbon model for double-stranded polymers (such as duplex DNA) where the ribbon is constrained to lie on the simple cubic lattice ${\mathbf{Z}}^3$. The ribbon is made up of a sequence of plaquettes and can either be open or closed. We investigate the growth of the number of ribbons as a function of the number of plaquettes and use Monte Carlo methods to estimate the dimensions of the ribbon, the writhe of the backbone and, in the case of orientable closed ribbons, the linking number of the two boundary curves.