On Friday, 10 November 2017 00:10:22 Keller, Jacob wrote: > Dear Crystallographers, > > I have been considering a thought-experiment of sorts for a while, and wonder > what you will think about it: > > Consider a diffraction data set which contains 62,500 unique reflections from > a 50 x 50 x 50 Angstrom unit cell, with each intensity measured perfectly > with 16-bit depth. (I am not sure what resolution this corresponds to, but it > would be quite high even in p1, I think--probably beyond 1.0 Angstrom?).
Meh. 62500 is < 40^3, so ±20 indices on each axis. 50Å / 20 = 2.5Å, so not quite 2.5Å resolution > Thus, there are 62,500 x 16 bits (125 KB) of information in this alone, and > there is an HKL index associated with each intensity, so that I suppose > contains information as well. One could throw in phases at 16-bit as well, > and get a total of 250 KB for this dataset. > > Now consider an parallel (equivalent?) data set, but this time instead of > reflection intensities you have a real space voxel map of the same 50 x 50 x > 50 unit cell consisting of 125,000 voxels, each of which has a 16-bit > electron density value, and an associated xyz index analogous to the hkl > above. That makes a total of 250 KB, with each voxel a 1 Angstrom cube. It > seems to me this level of graininess would be really hard to interpret, > especially for a static picture of a protein structure. (see attached: top is > a ~1 Ang/pixel down-sampled version of the image below). All that proves is that assigning each 1x1x1 voxel a separate density value is a very inefficient use of information. Adjacent voxels are not independent, and no possible assignment of values will get around the inherent blockiness of the representation. I know! Let's instead of assigning a magnitude per voxel, let's assign a magnitude per something-resolution-sensitive, like a sin wave. Then for each hkl measurement we get one sin wave term. Add up all the sine waves and what do you get? Ta da. A nice map. > Or, if we wanted smaller voxels still, let's say by half, we would have to > reduce the bit depth to 2 bits. But this would still only yield half-Angstrom > voxels, each with only four possible electron density values. > > Is this comparison apt? Off the cuff, I cannot see how a 50 x 50 pixel image > corresponds at all to the way our maps look, especially at around 1 Ang > resolution. Please, if you can shoot down the analogy, do. Aren't Fourier series marvelous? > Assuming that it is apt, however: is this a possible way to see the power of > all of our Bayesian modelling? Could one use our modelling tools on such a > grainy picture and arrive at similar results? > > Are our data sets really this poor in information, and we just model the heck > out of them, as perhaps evidenced by our scarily low data:parameters ratios? > > My underlying motivation in this thought experiment is to illustrate the > richness in information (and poorness of modelling) that one achieves in > fluorescence microscopic imaging. If crystallography is any measure of the > power of modelling, one could really go to town on some of these terabyte 5D > functional data sets we see around here at Janelia (and on YouTube). > > What do you think? > > Jacob Keller > > +++++++++++++++++++++++++++++++++++++++++++++++++ > Jacob Pearson Keller > Research Scientist / Looger Lab > HHMI Janelia Research Campus > 19700 Helix Dr, Ashburn, VA 20147 > (571)209-4000 x3159 > +++++++++++++++++++++++++++++++++++++++++++++++++ > -- Ethan A Merritt, Dept of Biochemistry Biomolecular Structure Center, K-428 Health Sciences Bldg MS 357742, University of Washington, Seattle 98195-7742
