At the end of Children of Dune we find out from Ghanima that Leto runs and runs and runs as the only way to temporarily relieve his horror and grief at the fact that he's giving up any chance of romantic love or having his own family to undergo a millenia-long body horror transformation.
Then in God Emperor Leto is physically no longer able to run. But Siona, descendant of Ghanima, when we first meet her, is running.
















