The verbs tie to/tie up and tie down relate to limits put on somebody or something and which make somebody/something unavailable. There are several dictionary examples of these verbs occurrences:
(1) I'm tied to the job while I have mortgage to pay.
(2) She's tied up in the meeting at the moment, but I'll ask her to call you later.
(3) All my money is tied up in property.
(4) I don't want a relationship that ties me down.
My question is are these verbs wholly interchangeable or are there any slight differences of their meanings? Looking into the examples I would suppose that tie down is used when we say about people but not about money. On the other hand, I think of to peposition function as a pointer on a limit and, in my opinion, it doesn't exclude using up or down at once, so can I append up or down to tied in (1)?