The electrical current used to move the DNA delivers electrons to the cathode, the negative end from which DNA moves away.
The electrons are taken up by water, resulting in the equation
H2O + 2e- ->
On the other side, the anode, to balance the charges caused by the electrons delivered to the cathode, water loses electrons by the equation
H2O ->
2H+ 1/2 O2 [the oxygen anion loses electrons, forming oxygen gas]
air bubbles form from those gases