Then maybe consider storing an order and a depth value, that will make it easy to do inserts (but it still needs locking as you have to make place for the new node).
Code:
order depth id other data...
1 0 1
2 0 2
3 1 3
4 2 6
5 1 7
6 0 4
7 2 5
There are many ways to store a tree in a database, the hard thing is to find the most effective solution to the situation.
MPTT is great if you're going to traverse the tree, but it isn't great if you just move one level at a time or move things in the tree very frequently.