The distinction between the 
in John opened the door and This key opened the door can initially be made in terms of properties of the SUBJECT; for completeness, similar characterisation of the other complements can be made:
| open | < > | The door opened. |
< ,
> | John opened the door. | |
| <,
> | This key opened the door. | |
<,
 > | The door opened with this key. | |
| <,
,
> | John opened the door with this key. |
The main distinctions are captured; however, the difference between the two inanimate NPs in this key opened the door, and its relatedness to the door opened with this key is still not captured.
Reference: The earliest treatment of selectional frames in distinction to (strict) subcategorisation frames is in:
Chomsky, N. (1965). Aspects of the Theory of Syntax. Cambridgd, Mass.: MIT Press.