Solving crystal structures
One of my roommates is a chemist; a conversation about cooking somehow wandered into an introduction to the problem of solving crystal structures. Apparently, to determine the structures of proteins (such as DNA), chemists first find a way to generate large, pure amounts of the protein, and then find a way to crystallize it. Then, using data from single crystal X-ray diffraction, they solve for the structure of the crystal. For several reasons this is the hardest part of the process: large proteins yield small crystals in general, which means you can’t collect as much diffraction data, and there’s always some distortion in the data due to imperfections in the lattice structure and whatnot.
This struck me as a noisy tomography problem, and got me thinking of maybe looking into it as a research avenue. My roommate tells me that solving crystal structures is currently something of a black art, involving years of intuition-building experience and patient collection and refinement of data. He says this is a problem that has resisted the efforts of some of the greatest minds of science, so while searching for an algorithm to directly solve the problem is overly ambitious, an algorithm that somehow reduces the effort would surely be a welcome gift to structural biologists. Supposedly Caltech offers a self-contained course in X-ray diffraction and introductory structure solving, so after he gets back to me on the details and whether it’s offered this fall, I might end up switching out one of my math classes for that course.