There are already several altcoins out there that have implemented exactly what you are describing. For example, Gridcoin mining uses BOINC. SETI@home and Rosetta@home are both BOINC-based projects and there are many others too - i.e. you could also mine gridcoins while solving the calculations required for mathematical modeling or weather prediction. For a full list of BOINC-based projects see:
http://boincstats.com/en/stats/projectStatsInfo
Curecoin is another similar coin that uses Folding@home which is a similar distributed computing project but is not part of BOINC. Foldingcoin is another very similar coin that is built on top of the Counterparty platform.
It should be noted however that the calculations required to actually mine Gridcoin and fold Curecoin (not sure about Foldingcoin) aren't actually the ones that solve protein structure verification. Instead, what happens is that you submit shares to either BOINC projects or Folding@home. Then the miner/folder measures your contribution to these projects and calculates your reward by comparing it with the average contribution of the entire network. Hence the actual "folding" part is still centralized.
On a related note, Primecoin and Riecoin are coins that use the computing power of their networks to solve simple but computationally intensive mathematical problems where all the algorithms and calculations required are actually embedded into the protocol itself in a fully decentralized manner.