A formula for the average number of knot interlinks caused by type 2 topoisomerase action

During the double-stranded passage that takes place because of the topoisomerase action, a plectonemically interwound DNA often becomes knotted. In this process, a portion of the substrate supercoils are converted into interlinks that contribute to the topology of the knot formed. In this appendix, an approximate formula is derived for the average number of these interlinks in terms of the number of supercoils and branches in the substrate. This will give an indication of the complexity of the average knot obtained. When two regions of DNA come together before passage, the substrate is divided into two domains in essentially the same way as intramolecular recombination divides the substrate into two domains (Boles, T. C., White, J. H., and Cozzarelli, N. R. (1990) J. Mol. Biol. 213, 931-951). Nodes formed between DNA segments from different domains are called interdomainal.