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.
Where there is profit there is competition. As a miner years ago, i was able to produce a lot of bitcoins with my GPU setup. When the ASICs came out i tried to compete, but simply did not have the capital. But other people did. And it wasnt just one person, it was a few big companies that did this.
So no longer is the individual able to mine BTC, its now a profession. So if this happened to FLDC, that wouldnt really be a bad thing, because if it is to happen, then that would mean FLDC has gained enough value for someone to pour money into being the top folder. So then the economy of FLDC would be where the general public has the interest and the Folders would simply be a profession.
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.