But FoldingCoin is not that currency, because there is a huge downside in their design: they had to completely give up decentralization, which is the primary innovation and differentiator that block chain-based currencies like Bitcoin bring. Instead, FoldingCoin relies on the Stanford University Folding@home network, on the stats reported by this network, to distribute units of the currency proportionately to the amount of work. This means the Folding@home network could alter the distribution of coins at will, if it is attacked by hackers (likely), or if it operates maliciously (less likely). This means FoldingCoin would be unable to continue operating the day a single entity (the university) decides to stop running the Folding@home network. And so on. All the inconvenients and risks of centralization exist with FoldingCoin.
Trust me, I really wish it would be possible to design a decentralized digital currency built on a protein-folding proof-of-work, but so far nobody has found a way to do this in a decentralized way.
Edit: they openly acknowledge the fact FoldingCoin is not decentralized, see http://foldingcoin.net/fldc-vs-alts/ : "With Counterparty there is no current way of doing decentralized asset creation and issuance"
Edit #2: in theory a decentralized currency based on a protein-folding proof-of-work can exist and would work this way: compute a hash of a block of pending transactions and of the previous block hash (like Bitcoin). Use the resulting hash as a seed to deterministically generate a set of protein-folding problems. Miners try to solve them. Once a sufficient amount of these problems is solved (depending on a "difficulty factor"), broadcast the solutions and the transactions on the network, hence creating a new hash for the next set of protein folding problems. I don't know very much about protein folding, but as I understand the open problems are: (1) how to deterministically generate a set of useful protein-folding problems according to rules that should stay immutable for decades (you can't ask the participants to have to frequently update their mining software because consensus on these rules is hard to change), and (2) how to reduce the size of the solutions data published to the network every block without overflowing it (it is my understanding that protein folding would generate way more than a few hundred kilobytes every 10min which is the current average Bitcoin block size).