Uncle broke American heart (7)
I believe the answer is:
nucleus
'heart' is the definition.
(I've seen this before)
'uncle broke american' is the wordplay.
'broke' is an anagram indicator.
'american' becomes 'US' (United States).
'uncle' anagrammed gives 'nucle'.
'nucle'+'us'='NUCLEUS'
(Other definitions for nucleus that I've seen before include "Tiny factor" , "hard core" , "basis for development" , "Core, centre" , "Central mass of a cell" .)