I propose this as a thought experiment: Nature has solved this. How? Some lines of reasoning:
#1: The quantum interactions of electrons that are the basis for chemical bonds behave in ways our computers and intuition are incapable of simulating
#2 It's a matter of degree, not kind, and nature is more sophisticated than our computers, reasoning and thought processes.
#3 Nature is magic, whatever you define that to be
#4 When stipulating the degrees of freedom involved (ie from dihedral angles), the possibility of additional information we haven't discovered is being overlooked. Is there a recipe or algorithm that could help?
#5 Proteins don't fold in isolation. We know some proteins need chaperone proteins to fold, for instance. Others form part of a complex. The problem can't be solved in the general case just based on the sequence of the protein you want to know the structure of. That's also a problem experimentally -- we don't know if the structure of a crystalized protein is really the biologically meaningful form.
I'd go with #1. Especially considering that there are quantum approaches to protein folding.
But nature hasn't really "solved" the problem, it is just doing its thing, but the way it does things is completely different from what our computers do.
It is like trying to reproduce a guitar sound using a synthesizer. A guitar solves to problem of sounding like a guitar, but it doesn't mean it is more sophisticated than a synthesizer, in fact, a synthesizer can do much more, it is just that the process by which the guitar makes sounds are hard to simulate.
Could be! Are you thinking thermodynamic fluctuations from surrounding water molecules jostling things around into many combinations? In this view, do you think the final protein would be found by chance, or through intermediate assemblies?
#1: The quantum interactions of electrons that are the basis for chemical bonds behave in ways our computers and intuition are incapable of simulating
#2 It's a matter of degree, not kind, and nature is more sophisticated than our computers, reasoning and thought processes.
#3 Nature is magic, whatever you define that to be
#4 When stipulating the degrees of freedom involved (ie from dihedral angles), the possibility of additional information we haven't discovered is being overlooked. Is there a recipe or algorithm that could help?