In the morning at the Simons Center for Data Analysis, Brian Weitzner (JHU) gave a nice talk about determining structures of antibodies, and predicting structures of new or novel antibodies for drug design and so on. I learned many things in the talk, one of which is that there are only 100,000 known protein structures. That might sound like a big number, but compare it to the number of known protein sequences!. Another thing I learned is that it is often possible to get a good guess at a structure for a (part of a) protein by looking at the (known) structures of similar sequences. The cool thing is that they (the large community or communities) have developed very good “energy functions” or scores for ranking (and thus optimizing) conformations; these are obviously approximations to the real physics, but seem to work extremely well.
In the rest of my research day, I batted around issues with diffraction microscopy, ptycography, and cryo-electron microscopy imaging with Leslie Greengard. We talked about a very non-trivial issue for the first two, which is that there can be very different functions with identical squared-moduli of their Fourier transforms, or at least we think there must be. There sure are in one dimension. What about in three dimensions? We talked about an exciting prospect for the latter, which is that the cryo-EM problem is very similar to an old idea I had of deprojecting all galaxy images ever taken. “Cryo-EM for galaxies!”