I spoke briefly with Vijay Pande about this in 2011. Folding does have a lot of the right properties for a good proof-of-work system, the main exception being that the solution must be unique to the input. It may be possible to achieve this by embedding information into sets of constraints, as long as any particular set of constraints can be shown to be isoenergetic. Or perhaps by expanding the problem by adding more atoms in a way that embeds information about the inputs. Also, the solutions would be quite large. But I think he was more interested with my experience writing molecular dynamics code than blockchain, and rescinded the RA offer after this conversation, so I haven’t thought about it much since then.

Reconsidering (briefly) now, I think it can be done.