This is a terrible idea for several reasons, the chief of which is the fact that the difficulty of protein folding simulations is not easily predicted. One consequence of this is that if someone were to develop a more efficient algorithm for protein folding, they could easily dominate the mining market and pull off a 51% attack. You could argue that this might have a positive societal impact, but it would also probably destroy the foldingcoin network.

The reason Bitcoin (and most/all other good proof-of-work systems) use repeated application of a cryptographic hash is that it's A) very predictable how long finding a solution will take (on average) and B) unlikely that someone will destroy the proof-of-work system by inventing a more efficient method of calculating the hash.