The Residue interaction energy bonus is a comparison of the residues in your protein versus those of a large set of native proteins.
We take a subset of score terms that have to do with residue-to-residue interactions and give each residue a combined score. We see how well your amino acid stacks up against others of the same type in the set of native proteins we scored. We do this across the entire protein and determine a bonus or penalty.
This will give penalties when residues are not contributing at a proper level. In essence, is this residue pulling its weight based on what we have seen it capable of doing on average.
If you are in-game and have a penalty, you can expand the bonuses list and click on "Show" to see which residues are contributing most to your penalty. The larger/darker the red (default color) circles the more of an influence that residue is having.
Let me know if any of this wasn't clear of if you have questions at all. I'll try and answer or find the right person to answer them.
There's a bug currently where the game will say "All bonuses gained, no conditions" even if you have a penalty.