Has it something to do with word: 来由? I mean 来由 is a "reason, a cause". So whenever you put Object(Obj) inside this "parenthesis" 由Obj来 you emphasise the cause of the action? or smth?
So as I think as an example:
"由我来..."
Literally: "From me comes something"
So the meaning of 由Obj来 is "up to" or "It's up to (it/her/him) to do something"