I have a queen platform bed that I am setting up with larger slats so that I do not need a center support or post. There will be just a mattress laid directly on the slats, no box spring. Together we weigh 400 lbs. The slats will be supported by the side rails only. What size and orientation of lumber do I need to use so that it will not sag (at all!) in the middle with no center rail or legs in the middle of the bed? Are 2x4s laid flat okay for this? Or do they need to stand vertically? Or do I need bigger lumber like 2x6s? How far apart should they be? Wood will be regular yellow southern pine lumber from a lumber yard.