Protein folding is driven by the amino acid side-chains. One of the main driving forces in protein folding is how the amino acids react to water. This basically depends on whether they are made solely of C and H, or whether they have O, N or S in as well. CH ones are hydrophobic, oily, and have hysterics if they get wet; polar ones with O/N/S in are quite happy to go for a swim and share electrons with the surrounding water. In the cell or the lab, proteins fold in a watery (aqueous) environment, so all the hydrophobic AAs try to hide in the centre of the protein, away from the scary wet stuff, while all the hydrophilic ones try to get to the outside.
The other
cringe: at oversimplification, but I don't want to post whole modules here) force in driving protein folding is how the other amino acids in the protein react to each other. This is lots of fun; the -vely charged ones attract the +vely charged ones, and repel the other -ve ones; the big bulky ones can push others out of the way; Cys can form a disulphide bridge (a pair of Cysteines drop their Hs and the Ss bond to each other), etc. Anyway, that drives them into coils, sheets and folds, and those into complexe arrangements which make the overall structure.
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Whoo, back to the examples I mentioned in the paragraph above the Genetics spoiler. Normal haemoglobin (ok, the final molecule is a set of four, ignore that for now) is a chain of hundreds of amino acids; in sickle-cell anaemia, a one-base substitution occurs (one base of the gene is swapped for another): the coding for Glu is changed to Val - and this leaves a hydrophobic patch on the outside of the molecule, which causes trouble. The haemoglobins start sticking together at the hydrophobic patch, making long spikes which draw the red blood cells out long and bent. All of the problems from sickle-cell anaemia result from that one-codon change: one codon changes one amino acid, which changes one protein, which changes one type of cell, which causes trouble.
Prions are an interesting species - misfolded proteins that not only don't work properly, but they go and cause trouble as well. Worse than larger louts! Really evil prions can turn other proteins into prions as well, and thus cause even more trouble. BSE/mad cow disease, scrapie and vCJD are caused by prions. I'm afraid I don't actually know that much about them, but I can find out if anyone wants more.
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Ump. Back to the opening subject - normally protein structures are solved with Xray Crystallography; however, we're doing the number-crunching for something else. What I think
blush: haven't read their site in detail) F@H is doing, is modelling the interactions between the amino acids in the protein, and between the amino acids and the surrounding environment, to work out how they'll all move and end up. The computer models the size, electronic properties, shape, flexibility, hydrophobicity etc of each thing in in the bit of protein it's modelling, and sees what happens with a particular set. Because these things are so small, things happen pretty darn fast - that's why the site talks about nanoseconds and picoseconds while each WorkUnit takes hours: there's a lot of stuff to keep in mind. HOW they do the folding is important as well as just the end result; if you can model the steps it goes through from start to finish, then you know more about what to do if things go wrong. (See prions waffling.)
However, this method does not take account of anything that happens afterwards - and many proteins have "post-translational modifications": once they've been synthesised, they get extras such as metal ions, sugars, prosthetic groups eg haem, etc. This is quite important; 30-40% of proteins contain one or more metal ions, for example. The difference between what we think bits of the proteins are, and what they actually are, could be tremendous. So, ultimately, we may depend on Xray crystallography or other laboratory-based techniques to study protein accurate structures in detail.
The more the merrier!
Nice science Spam Soph.. i could follow it 
