I think you have to be a little more clear as to what you mean by an "electron density map". If you mean our usual maps that we calculate all the time the Patterson map is just the usual Patterson map. It also repeats to infinity, with the infinitely long Patterson vectors (infinitely high frequency components) being required to create the Bragg peaks. If you mean an electron density map of a single object with finite bounds your Patterson map will also have finite bounds, just with twice the radius.
The Patterson boundary is not a sharp drop-off because there aren't as many long vectors as short ones, but the distribution depends on the exact shape of your object. Once you have a Patterson map that has an isolated edge (no cross-vectors) back calculating the original object is pretty easy. (Miao, et al, Annu. Rev. Phys. Chem. 2008, 59:387-410) Dale Tronrud On 01/13/12 10:54, Jacob Keller wrote: > I am trying to think, then, what would the Patterson map of a > Fourier-transformed electron density map look like? Would you get the > shape/outline of the object, then a sharp drop-off, presumably? Is > this used to orient molecules in single-particle FEL diffraction > experiments? > > JPK > > On Fri, Jan 13, 2012 at 12:33 PM, Dale Tronrud > <[email protected]> wrote: >> >> >> On 01/13/12 09:53, Jacob Keller wrote: >>> No, I meant the non-lattice-convoluted pattern--the pattern arising >>> from the Fourier-transformed electron density map--which would >>> necessarily become more complicated with larger molecular size, as >>> there is more information to encode. I think this will manifest in >>> what James H called a smaller "grain size." >> >> I've been thinking about these matters recently and had a nifty >> insight about exactly this matter. (While this idea is new to me >> I doubt it is new for others.) >> >> The lower limit to the size of the features in one of these >> "scattergrams" is indicated by the scattergram's highest frequency >> Fourier component. Its Fourier transform is the Patterson map. >> While we usually think of the Patterson map as describing interatomic >> vectors, it is also the frequency space for the diffraction pattern. >> For a noncrystalline object the highest frequency component corresponds >> to the longest Patterson vector or, in other words, the diameter of >> the object! The bigger the object, the higher the highest frequency >> of the scattergram, and the smaller its features. >> >> Dale Tronrud >> >>> >>> JPK >>> >>> On Fri, Jan 13, 2012 at 11:41 AM, Yuri Pompeu <[email protected]> wrote: >>>> to echo Tim's question: >>>> If by pattern you mean the position of the spots on the film, I dont think >>>> they would change based on the complexity of the macromolecule being >>>> studied. As far I know it, the position of the spots are dictated by the >>>> reciprocal lattice points >>>> (therefore the real crystal lattice) (no?) >>>> The intensity will, obviously, vary dramatically... >>>> ps. Very interesting (cool) images James!!! >>> >>> >>> > > >
