Please take into consideration that I am not a specialist of plate tectonics, just a paleontologist.
Although this cycle is often nicknamed the Wilson cycle (probably because of Wilson, 1966), the idea that supercontinent formed cyclically every 440Ma was advanced by Worsley et al. 1984 (see review on the subject by Nance & Murphy 2013).
The mechanism they hypothesize for the breakup of the supercontinent is the mantle heat flow accumulating below the supercontinent while the formation of the supercontinents are bound by the cooling effect on the density of the oceanic lithosphere (see also Nance et al. 1988): so basically, heat accumulate below the insulating supercontinent until it causes it to break up, thus creating rifts and a new oceanic lithosphere, which, with age, cool down and thus become more dense making it more prone to be subducted by the continents (if I understood correctly).
As to "why ca. 450 Ma?" this has probably to do with the cooling speed of the oceanic lithosphere, I would assume.
Another important point: although there are evidences for the existence of a supercontinent breaking-up at 300 Ma (Pangaea), at 750 Ma (Rodinia), at 1.6 Ga (Nuna or Columbia), etc., there are also evidences for an absence of supercontinent at 1.2 Ga (see Pisarevsky et al. 2014), hinting that this cycle is maybe not that regular.
Nance & Murphy, 2013. Origins of the Supercontinent Cycle. Geoscience Frontiers, 4(4): 439-448.
Nance, Worsley & Moody, 1988. The Supercontinent Cycle. Scientific American, 259: 72-79.
Pisarevsky, Wingate, Li, Wang, Tohver & Kirkland, 2014. Age and paleomagnetism of the 1210 Ma Gnowangerup–Fraser dyke swarm, Western Australia, and implications for late Mesoproterozoic paleogeography. Precambrian Research, 246: 1-15.
Wilson, 1966. Did the Atlantic close and then re-open?. Nature, 211: 676-681.
Worsley, Nance & Moody, 1984. Global Tectonics and Eustasy for the past 2 billion years. Marine Geology, 58: 373-400.