It's true that proteins don't have to be in their global minima function, but they do if you want them to stick around for a long time and not cause problems (see: Creutzfeld-Jakob disease, Alzheimer's, Parkinson's, etc.). There was some research a while back that took the question of: what sort of molecule would have it's global minimum conformation also be the quickest to fold to? (Unfortunately, I don't have the citation handy...) The result they came up with was something that looked an awful lot like proteins.
I'm curious:
-- How long would they stay around for?
-- What sorts of problems? Would you need a lot of "bad" proteins to cause problems or just a few?
What I'm trying to get at is wondering if nature uses very good heuristic/approximate/probabilistic algorithm. I.e. if there is an algorithm that almost always works and having a few proteins that aren't at global minima isn't an issue and they dissipate very quickly, then observation would make it look like nature is solving the problem exactly even if its not.
Alternatively, the proteins we find in nature might be more tractable than the general problem described in all its mathematical glory (i.e. the inputs might be restricted to some subset of the input space which is solvable very quickly).
That depends on the thermodynamics. Specifically, it depends on the depth of the local minimum and the energy in the system. With some random chance, a protein can get out of a local minimum and fold into a different conformation. If nature is depending on the fold not changing, this could be a problem.
What sorts of problems? Would you need a lot of "bad" proteins to cause problems or just a few?
Again, it depends. In general, unfolded proteins are a bad thing. They are also a fairly common thing to find in cells, and cells have a specific "unfolded protein response" that kicks into gear if there are too many. Too many unfolded proteins literally "gum up the works".
For prions, tau (in Alzheimer's), and others, the story is a bit different. In these cases, the presence of even a few improperly folded proteins can catalyze further misfolding.
Alternatively, the proteins we find in nature might be more tractable than the general problem described in all its mathematical glory
This is almost certainly the case, but more tractable != not intractable. Solving the problem also requires clever solutions and a better understanding of physics. If your curious, I did my Ph.D. preliminary exam on one example (modern methods of handling side-chain entropy, including belief propagation techniques). The LaTeX source is at: http://github.com/jballanc/prelim/
They are also a fairly common thing to find in cells
Interesting. You mean totally unfolded or not folded correctly (i.e. proteins that haven't started the process or proteins that went through it and got to the wrong state)?
Also, does this mean that "nature has solved this problem" aren't true? I.e. "nature" doesn't get it right all the time, just often enough that we're generally okay?
In biology, there's little difference between "totally unfolded" and "not folded correctly". (In fact, there's been some research indicating that there may not be such a thing as "totally unfolded"; i.e. that all proteins have some structure all the time.) There are two ways that you get proteins improperly folded. The first is that this is how they are made. In bacteria that number is only ~10%, but in eukaryotes (i.e. Humans), that number can be as high as ~50%. These proteins need help from other proteins to fold correctly. The other way you get unfolded proteins is by stress. Usually it's either heat stress or oxidative stress that causes proteins to unfold (not surprisingly, the proteins which help other proteins fold are often called "heat-shock proteins").
As for wether or not "nature has solved this problem", well...of course it has. We're here right? I think the thing to remember is that evolution is not, strictly speaking, an optimization process. Rather, it is a "just good enough" process. For example, a dolphin has more efficient lungs than you, an eagle has better eyes than you, almost everything that walks the earth is faster and stronger than you, and you're actually rather poorly built for walking upright (a reason most of us will suffer lower back pain as we age), but none of that matters. For the niche that humans occupy, their large brains are sufficient to beat out all competitors, and yet chances are that some day something will come around with an even better brain and push us out.
