Well, it depends what you define as "verifiability". True, the minimum free energy structure doesn't have a 1:1 correspondence with the actual biological structure, but similar systems have used energy as a decent ranking metric (google Foldit), and it's "the best we've got" as far as a concrete, verifiable calculation. Furthermore, computation of the free energy is far simpler than other possible metrics, whether homology-based (does this look like an evolutionarily related structure), domain-specific (does this have an appropriate # of helices, sheets, turns), etc. Thus, we can make do with free energy as a check for PoW, and I wager that the expansion of computer power for such a project will outweigh the negatives of not relying on other forms of verification.
/technical rant
Yes, I've seen Foldit (I was one of the first bunch of people who used it upon release).
That'd be nice, because it'd be really easy for me to doctor without any focus on structure. An accurate free energy calculation is also pretty computationally intensive as compared to a metric like Z-score or RMSD, which can be run in way less than a second.
You can reward them based on finding some local minima based on the structure that incorporates Z-score/RMSD as well as free energy, but I could also probably doctor that pretty easily and it actually poorly reflects on overall computational work.
In either case, you definitely need someone to verify the solutions afterwards --> centralization of the coin distribution is absolutely necessary (especially as the work needs to come from a central organization!).
The easiest thing to do is just to run a backend on the miner's computer that gives them administrative control, even if only on a VM, and then they can tell exactly what code is being executed.
The bounty system that I proposed in the other thread allows for these other metrics to be slowly incorporated in the evolution of this coin (i.e. accept structures of protein XYZ only if mean C-alpha distances to reference homology structure is less than 2A.) But that will come in a future version.
That's a really, really bad idea [2A confinement for C-alphas] and will result in a lot of not so useful structures. Z-score would be a way better metric for that. This is all based on the assumption as well that you're just looking for a structure closest to what the actual structure achieved through X-ray crystallography would be if you could get it. There are a lot of other important problems, such as dynamic ligand-receptor interactions over a time course. Ideally any PoW system should not be pigeon-holed by a single problem but adaptive to multiple problems.
Anyway, seems like a neat idea, not sure how you'll really implement it without administrative control of your nodes, would like to be interested but already have IRL research projects spanning multiple labs (and also here on bitcointalk).