Model carbyne vs ideal and DNA catenanes

The structure and stability of two-component carbyne catenanes, viewed as model compounds for DNA catenanes, have been estimated by molecular mechanics (MM) calculations. The carbyne catenane molecules studied were composed from interwined cyclic molecules constituted solely from carbon atoms bonded by alternating single and triple bonds. The total number of carbon atoms in molecules studied was set to 60, and the complementary sizes of the catenane components varied. The component cycles were entangled by 2, 4, ..., 11 crossings. For the catenanes with the number of crossings equal to six and seven more than one catenane topological type was considered. The calculated MM strain energy of carbyne catenanes was correlated with the averaged crossing number and length-to-diameter ratio of ideal catenanes as well as the electrophoretic mobility and sedimentation coefficient of DNA catenanes. To observe these correlations, for each topological type of carbyne catenane, it was necessary to find the proportion of the sizes of the two catenane components at which the MM strain energy is the lowest. Then, the values of these energies were correlated with characteristics of ideal and real DNA catenanes. The fits are significant and nonlinear.