  The elasticity of DNA catenanes, i.e. multiply linked DNA rings, is
investigated using the Gauss invariant as a minimal model for topology
conservation. An effective elastic free energy as a function of the distance
$R$ between segments located on different rings is obtained. An anharmonic part
at large distances, growing as $R^{4}$, if $R\gg R_{G}$ ($R_{G}$ being the
radius of gyration of a random walk ring) is found, while for $R\ll R_{G}$ the
interaction is strongly repulsive. Treating the attractive interaction as the
dominant one, distribution functions for the distance between segments located
on different rings for several linking numbers are derived which are in
qualitative agreement with distributions functions obtained experimentally from
electron micrographs of DNA catenanes (S. D. Levene et al., Biophys.J. 69, 277,
1995).
