My guess is that are a form of spring steel. (Piano wire might substitute) I also guess that the are there to firm up the seat a bit and make the whole thing work as a system.
Kind of like the cord clamped from spring to spring. Push on one spring and the one next to it moves a little also.
How is the seat cover compared to the oem, right stiched in the right places etc? Are the midalions oem or repo?