The Gastropods have taken over the planet of Jaconda and intend to cause a massive explosion to spread the eggs over the universe.  In order to do this, the leader of the Gastropods, Mestor, kidnaps two Earth child geniuses, Romelus and Remus to work on the equations to allow this to happen, meanwhile, Hugo Lang of Interplanetary Pursuit, is sent off to attempt a rescue.  The Doctor and Peri become involved following a problematic regeneration, and aid Professor Edgeworth, the former leader of Jaconda, who is actually a Time Lord, Azmael, to save the universe.