Oh, I didn't notice you used 4x4 before. I used L 2x4 in the corners, so you shouldn't worry about that.
I would consider a backing on it though, if you plan on using a wave maker, for a few $ it will give you some insurance against the side to side motion. I know you used ties on the corners, and will be dressing it as well. A backing would also help keep moisture from your drywall and keep light spilling out the edges on the wall of you light a refugium at night.
What are you thinking of for hardware?