Gel electrophoresis can be used to separate nicked circular DNA molecules of equal length
but forming different knot types. At low electric fields, complex knots drift faster than
simpler knots. However, at high electric field the opposite is the case and simpler knots
migrate faster than more complex knots. Using Monte Carlo simulations we investigate the
reasons of this reversal of relative order of electrophoretic mobility of DNA molecules
forming different knot types. We observe that at high electric fields the simulated knotted
molecules tend to hang over the gel fibres and require passing over a substantial energy
barrier to slip over the impeding gel fibre. At low electric field the interactions of
drifting molecules with the gel fibres are weak and there are no significant energy
barriers that oppose the detachment of knotted molecules from transverse gel fibres.