I have been trying to come up with an alternative proof of work allowing arbitrary calculations to be performed instead of hashing.
I blv I have a way to combine blockchain protection with e.g. folding (or any other difficult operation)
In case of proteins, based on a large library of proteins to be folded, in case of any other calculation a (large) library of such calculations.
The idea employs a blockchain just as btc except that the hash of
(transactions in the current block+hash of previous block)
is used to choose a problem from the library. The lowest energy solution (for proteins, or best/only solution for other problems) is sought.
Whoever comes up with lowest local minimum within 10-minute block time gets block reward.
(solution + transactions + hash of previous block)
are hashed together for the next block a-la bitcoin. Faking a block is now similarly difficult.
A bit more detail here
http://telavivmakers.org/index.php/Protein_coin - including way to allow users to design algorithms yet prevent best coder/folder from gaining control.