Chapter 8: Structure and Dynamics of Supercoiled DNA Knots and Catenanes

Circular DNA molecules in vivo form catenanes and knots during such processes as replication or recombination. In addition, DNA molecules are often subjected to a torsional tension, which results in their supercoiling. The interplay between catenation, knotting and supercoiling leads to unexpected conformational changes of entire DNA molecules, and this has interesting physical and biological consequences. We show in this chapter how modelling DNA as a semi-flexible ribbon can be applied to get information about the molecular conformation of DNA molecules with complex topologies. In particular, our results highlight the importance of the chirality of knots and catenanes in the structural changes induced by DNA supercoiling. For example, strongly linked right-handed toroidal DNA catenanes undergo a specific folding that can be reversed by the introduction of negative supercoiling in each chain, or the shape of negatively supercoiled DNA trefoil knots depends on their chirality. In each case, we perform dynamical simulations including hydrodynamics, to investigate the consequences of these structural changes on the sedimentation and gel electrophoretic behaviour of the modelled knotted and catenated DNA molecules.