Phases can be deduced mathematically from a continuous transform, a la David Sayre’s and others’ work. Compared to a crystallographic pattern, a continuous pattern has huge amounts of information—every pixel (roxel?) would be equivalent to a reflection, so instead of having ~10^4-5 data points you would have, say, 10^8-12, all to define ~10^3-4 atoms. And no b-factors to fit at 100K, since the molecule would not be moving at that temp. Of course this would be totally impossible to actually measure, at least for now (!).
JPK From: CCP4 bulletin board [mailto:CCP4BB@JISCMAIL.AC.UK] On Behalf Of Chen Zhao Sent: Tuesday, January 20, 2015 11:47 PM To: CCP4BB@JISCMAIL.AC.UK Subject: Re: [ccp4bb] A basic question about Fourier Transform Dear Steven, Thank you for your reply! I understand that it is nearly impossible to measure the diffraction of a single molecule, and I am just bringing this up as a thought experiment to help understand the basics in crystallography. But I never thought that some molecules actually allow such measurement because you can burn it over and over again without severe damage. Thanks a lot for this piece of information. But for the phase problem, the difference is that, you can have magnetic lens for the electrons in EM, but you cannot have any lenses for X-ray beam. This is why I am still confused about this point. Thanks a lot again, Chen On Tue, Jan 20, 2015 at 11:21 PM, Steven Chou <stevezc...@gmail.com<mailto:stevezc...@gmail.com>> wrote: I would say you cannot measure the diffraction pattern of a single biological molecule accurately thus far, because biological molecules are not strong scatters and can be damaged easily. For other molecules, actually you can! In high-resolution electron microscopy, the diffraction pattern in the back focal plane is actually the diffraction pattern of a projection of your sample, which is usually composed of one to several hundred biological molecules. For biological molecules, this pattern usually is dampened to almost zero at a resolution between 30A-4A (actual resolution, not theoretical); for some metal compounds, the resolution can reach up to 1 A, or even better. The diffraction pattern in the back focal plane is the Fourier transform (achieved by a convex lens) of the a 2D projection of your sample. If you apply another Fourier transform (using another convex lens) to the diffraction pattern, you can get the 2D image of your sample (which contains both amplitude and phase). That is, in single particle EM (imaging mode), people don't have the phase problem. In diffraction mode (2D electron crystallography), only the diffraction pattern (intensity) is recorded, so they also have the phase problem. HTH, Steven On Tue, Jan 20, 2015 at 10:18 PM, Chen Zhao <c.z...@yale.edu<mailto:c.z...@yale.edu>> wrote: Dear all, I am sorry about this slightly off-topic question. I am now a graduate TA for crystallography course and one student asked me a question that I didn't ask myself before. I don't have enough knowledge to precisely answer this question, so I am seeking for help here. The question is, as I rephrased it, assuming we are able to measure the diffraction pattern of a single molecule with acceptable accuracy and precision (comparable to what we have now for the common crystals), is it better than we measure the diffraction spots from a crystal, given that the spots are just a sampling of the continuous pattern from a single molecule and there is loss of information in the space between the spots that are not sampled by the lattice? Of course this is more of a thought experiment, so we don't need to consider that all measurement is discrete in nature owing to the limitation of the pixel size. I kinda agree with him and I have a feeling that this is related to the sampling theorem. I do appreciate your valuable comments. If this is not true, why? If this is true, what is its effect on electron density? Thank you so much for your attention and your help in advance! Best, Chen -- Steven Chou
