ancestor    descendant     depth
1               1            0
1               2            1
1               3            1
1               4            1
2               2            0
3               3            0
4               4            0

INSERT INTO closure_tree_path (ancestor, descendant)
SELECT ancestor, '{$node_id}' FROM closure_tree_path
WHERE descendant = '{$parent_id}'
UNION ALL SELECT '{$node_id}', '{$node_id}';

INSERT INTO closure_tree_path (ancestor, descendant, depth)
SELECT ancestor, '{$node_id}', depth+1 FROM closure_tree_path
WHERE descendant = '{$parent_id}'
UNION ALL SELECT '{$node_id}', '{$node_id}', 0;