  In this paper we study the role of topology in DNA gel electrophoresis
experiments via molecular dynamics simulations. The gel is modelled as a 3D
array of obstacles from which half edges are removed at random with probability
p, thereby generating a disordered environment. Changes in the microscopic
structure of the gel are captured by measuring the electrophoretic mobility of
ring polymers moving through the medium, while their linear counterparts
provide a control system as we show they are insensitive to these changes. We
show that ring polymers provide a novel non-invasive way of exploiting topology
to sense microscopic disorder. Finally, we compare the results from the
simulations with an analytical model for the non-equilibrium differential
mobility, and find a striking agreement between simulation and theory
