What is the puzzle that is currently available that has the highest possible score?
It doesn't really matter. Scores are based on ranks, and they're all worth 100 global points right now.
Aside from that, looks like "Beginner Puzzle (<150): Staphylococcus Aureus Electron Density" has higher scores.
... and the date (before after New Chapter = Jan 2014).
The biggest score I'v seen before New Chapter is 22379 pts here:
It's a dimer of 234 residues, which makes it 468 residues (score is 8000 + a certain amount of points per residue).
It does not mean that bigger puzzles always yield higher points. This one is 611 residues and the higher score (of a very limited number of players) reached 21227 pts:
But may be it had higher potential. Too late to take this chalenge now.
The biggest score per residue is 49 in this puzzle:
It's a 'small' tetramer of 40 residues (total 160).
Usually, small puzzles tend to have higher points per residue (segment).
After New Chapter, there was some changes (also bonus and malus in filters) and same puzzles tend to score lower.
We do not have enough experience now with this in order to give an idea.
The 611 big one is currently 17809 (still in competition).
If you want to have the all fame higher in New Chapter, just try this one (you can try until 2017):