Folding is, or at least, should be amenable to a proof-of-work function. I'm studying molecular biology, so I can give more background.
Basically, folding is PoW in that:
1. It's difficult to find a configuration that is "better" then the best so far. By "best", I am referring to the
minimum free energy, or a similar score system, where the atoms in the protein are in a most energetically favorable state. That is analogous to "difficulty" - If difficulty increases, then the free energy criteria required to satisfy the "folded" criteria is smaller. This problem is difficult because of the vast configuration space of possible positions for each of the protein residues (something on the order of 3^300), otherwise known as
Levinthal's paradox.
2. It's relatively simple to compute the free energy of the system. (More difficult than a hash, but much simpler than trying to find the minimum free energy structure).
3. If someone manages to "cheat" (find a structure with a good MFE in substantially less time than the rest), well that's called a scientific breakthrough. And that someone gets rewarded with a lot of coins. Probably the most direct incentivizing of R&D possible.
Check out
http://en.wikipedia.org/wiki/Foldit some time. Interesting concept.
1 & 2 sounds good, but the current folding projects contain some thousand atoms (or proteins, don't remember right now) place them in a 3d space ... we are talking about some mb here i would say way to much for a blockchain! bitcoin exists since 2009 and needs something like 8 gb currently, on average a bitcoin block is not more than 10k or so (arverage! currently more like 150)
3 would be great
(but unlikely)
what about an attacker who simply takes all available atoms and throws them into a space search with heuristics? he may come up with a solution that has low energy but is unrealistic due to some folding rules. or is it really that "simple"?
A PDB (structure) is ~500kB. DOn't know if that's too big or small, but for 10000, that is 5GB, less w/ compressing (compression ratio ~ 5:1 with 7-zip). Of course for additional structures beyond the initial set, this will increase further, don't know how much.
No, folding is not that simple. Side chain residues only fit in certain ways; otherwise the sterics will blow the thing apart. MFE also takes into account bond lengths, charge, torsion and dihedral angles, hydrophobicity, all the way to to things like implicit solvation models (which folding@home uses a simplified version of).
That said, you mention a valid concern that proteins may adopt "low energy" configs that are unrealistic. This mainly applies for very dynamic proteins, proteins that form multi-subunit complexes, transmembrane proteins, etc which all require special "rules" to fold properly, but this is kinda beyond my expertise here. To alleviate that, careful selection of the initial set of proteins that are stable, have reasonable dynamics, etc. will be required (by people smarter than me). The bounty system that I proposed can help if scientists can specify specific criteria, that can be checked easily (e.g. must have 2 alpha helices, Ser273 must not be in hydrophobic core, etc). This is complicated though, so I don't expect to see this in the first iteration of the client.
http://www.ncbi.nlm.nih.gov/protein/YP_005795070.1 - the bottommost part with a lot of random letters is the actual sequence; the other stuff is identifying information that is useful generally and also for certain domain-based/homology-based folding algorithms (too complicated to discuss here).)
What does it mean?
You simply take this string and start folding? Is there no other protein or something?
That string describes the amino acid residues on the protein (i.e. L = leucine, E = glutamic acid, etc). Any mediocre biologist has these memorized. See
http://bioinformatics.istge.it/bcd/Curric/PrwAli/_18604_tabular513.gif . A protein is made up of a string of these, terminated by a NH3 (N-terminal side) and a COOH (C-terminal side). Other codes can be used to denote post-translation modifications (beyond the scope of this forum).
As for a real project, I'm far too busy (medical school + graduate school) to seriously program anything, but I'm willing to look at code / give advice / refer to people smarter than me for further advice.