There have been several design puzzles now with the Core Exists filter, but we've never really explained how it works or why it's there. This post is meant to explain a bit about the filter and how you can use it to improve your score in design puzzles.
As you know, a protein is made up of a long chain of amino acids, but the chain folds up into a globular, compact shape. One of the main forces that drives folding is the burial of hydrophobic residues. Since the protein is surrounded by water, the only way to hide the hydrophobic residues is to fold them into the center of the protein and shield them from water with polar residues. This is why the most stable proteins have well-packed cores with lots of buried hydrophobics.
When designing a protein, we want to make sure that it has a well-packed core of hydrophobic residues to stabilize the fold. The "Core Exists" filter calculates the solvent-accessible surface area of each residue to determine which residues are buried and which residues are exposed to water. Then it checks that the number of buried residues meets some threshold (usually 30% of the total number of residues). Additional buried residues get a score bonus, but any fewer than the threshold and your protein will get a penalty. If a protein does not pass the filter, the Show checkbox will highlight residues that are not buried—you should try to pack more of these into the core of your protein.
Note that, in puzzles with multiple chains, residues at the interface between chains are counted as buried. So, while individual chains should have their own cores, large well-packed interfaces will also contribute to the filter score.
Hope this helps—we've been seeing some great designs from these puzzles! If you have a question, please leave a comment below.