Our Jo has said that the trio have the three major magical cores in their wands, so I presume that means that they represent the three sides of a 'complete' magical person.
Ron- Unicorn tail
Hermione- Dragon heart string
Harry- Pheonix feather (Fawkes's)

I've pondered on this ''V has Harry's blood' and 'Dumb has a gleam in his eye' because of it' thing and I think it MIGHT have something to do with a 'life debt'. I mean we were introduced to Wizard Life Debt fleetinfly with Petigrew and then reminded of it with the Unbreakable Oath, but it hasn't been explained that well; it habgs there as a potential story line...???