The Nucleus was the control centre of the Swarm. It was a microscopic creature akin to a virus with a crustacean-like appearance. In 5000, the Nucleus took control of the Fourth Doctor's brain, but was stopped by the Doctor "not thinking". It escaped through his tear ducts and was enlarged to human size by the TARDIS' relative dimensional stabiliser. When it tried hatching a hive of its Swarm on Titan Base, the Doctor ignited Titan's atmosphere, destroying the base along with the Nucleus. (TV: The Invisible Enemy)
The Swarm remained dormant in the TARDIS' computer until the Doctor's seventh incarnation. Shortly afterwards, the Doctor returned to Titan Base in the company of Ace and Hector Thomas in 4920. The TARDIS had been commandeered by Hector, who had fallen under the control of the Swarm. It ensured its own creation by returning to the Bi-Al Foundation, where it mutated from the Saturnian plague.
While in 4920, the Nucleus cloned itself and uploaded its mind to the Bi-Al Foundation computer. It then used the TARDIS to travel forward in time to the 52nd century, by which time the centre had become a Hypernet relay station. Using the TARDIS' Relative Dimensional Stabiliser and the power of the Hypernet, it intended to recreate itself and become corporeal. However, it was defeated by the Doctor, Ace and Hector. (AUDIO: Revenge of the Swarm)