Or maybe not?
The sentence in the original question ends with a subordinate clause that does not, by itself, ask a question (“within which we can leverage our existing knowledge”). This is modifying a noun phrase that is part of the question (“set of simple computational rules”). Therefore, this subordinate clause is part of the original question, and should end with a question mark.
Putting all of this together, I would punctuate the sentence like this:
“The question nagging me is, To what extent can we encapsulate all what we observe in nature into a set of simple computational rules, within which we can leverage our existing knowledge?”
No, mate.