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It's magic; it's science; it's beautiful; and it's really complicated.
Protein molecules are the machines that keep our bodies running. As such, they're of great interest to us. But they're too small to see using light-- even the most powerful electron microscopes can only see them as blobs.
Nuclear Magnetic Resonance is a type of spectroscopy... we hit the proteins with radio waves while they're in a strong magnetic field, and we listen to how they respond. It's similar to ringing a carillon, and deducing the structure of the bells from the sound. We listen very carefully, with sensitive coils, and reconstruct the characteristics of the molecule using complex software on modern computers.
Here's an example of a 2-dimensional spectrum from one of the proteins being studied here at Vanderbilt.
The peaks you see represent individual atoms in a protein- actually the interactions between specific atoms. We use the positions of the peaks and their sizes to determine the distances between the atoms, and then put together a model that fits those constraints.
Some day, when I've learned enough about the details of NMR, I'm going to write a book called "NMR for dummies", and it will explain the whole thing in terms that a 9th grader could understand. It won't be too rigorous, I'm afraid, but it'll get the point across, for those of us who want to understand the idea, and are not masters of mathematics.
Meanwhile, I'm at the point where I'm looking for a version of that book, myself. So far, the best I've come across on the web is Joseph Hornak's NMR tutorial. I'm very impressed with the work he's put into this. It rivals Gale Rhodes' page on Xray crystallography, but it's not quite perfect, either. I also recently found a brief intro by Rzepa, and also an interesting one by Keith Brown, . If you've come across something better, please let me know!