There is a relatively instructive figure to what Colin describes available from the gallery: http://www.ruppweb.org/garland/gallery/Ch9/pages/Biomolecular_Crystallography_Fig_9-05_PART1.htm For B=10, at 2.5 cutoff, ripples expected; for B=100 and 2.5 A, no ripples expected.
One can also generate what Colin says using the FT calculator on my web site: Calculate first SFs with a Metal and a C and low B-factors, but cut the resolution at 2.5 or so. http://www.ruppweb.org/cgi-bin/webfac.exe?cell=20&anode=Cu&resolution=2.5&E1=C&x1=0.1&N1=1.0&B1=5.0&E2=FE&x2=0.7&N2=1.0&B2=5.0&A1=No&OUTFILE=webfac.phs&anoweb=GoGoGo ! Then generate the FT on a fine grid (for esthetics, not information conservation - see Shannon) and observe the big ripples. http://www.ruppweb.org/cgi-bin/webmap.exe?grid=100&resolution=2.5&INFILE=webfac.phs&anoweb=GoGoGo ! (you need to select unique file names or the webserver will overwrite simultaneous submissions) An extreme case of ripples is in the Uranium atom figure. They look similar but not as excessive around real heavy atoms or even Se. http://www.ruppweb.org/garland/gallery/Ch10/pages/Biomolecular_Crystallography_Fig_10-10.htm BR On Thu, Jul 7, 2011 at 2:17 AM, Colin Nave <colin.n...@diamond.ac.uk> wrote: > Dear Thierry (and others) > > Perhaps a bit confusing to say "a sharp feature such as an heavy atom". > Heavy atoms are, well, heavy (lots of electrons) rather than sharp. Any > ripples around them in a Fourier truncated map could swamp the lighter atoms > nearby. > > If Zbyszek's criteria A (and his other criteria apply), there will be no > sharp cut off in the data and no significant ripples. If the data had a > sharp cut off like a box function (an extreme case), each atom would have > ripples around it like a sinc (sin(x)/x) function. > > This is (or at least used to be) a problem in small molecule > crystallography if the data did not gradually fade to zero at the resolution > of the calculation. > > I am sure this is just rewording what you are saying! > Regards > Colin > > PS Following Nicholas's suggestion, it would be interesting to compare > maximum entropy and Fourier maps particularly at different resolution cut > offs. > > > > > -----Original Message----- > > From: CCP4 bulletin board [mailto:CCP4BB@JISCMAIL.AC.UK] On Behalf Of > > Fischmann, Thierry > > Sent: 06 July 2011 18:59 > > To: CCP4BB@JISCMAIL.AC.UK > > Subject: Re: [ccp4bb] How to evaluate Fourier transform ripples > > > > Dear Zbyszek > > > > Wouldn't ripples be the results of calculating maps with truncated > > Fourier summations (unavoidably), and, consequently, be more obvious > > around a sharp feature such as an heavy atom metal center? > > > > The mathematic basis can be found here: > > http://en.wikipedia.org/wiki/Gibbs_phenomenon > > > > With best regards, > > > > Thierry > > > > Note: sent a 2nd time as it seems that it did not reach the BB the > > first > > time. Apologies if the message reaches you twice. > > > > -----Original Message----- > > From: CCP4 bulletin board [mailto:CCP4BB@JISCMAIL.AC.UK] On Behalf Of > > Zbyszek Otwinowski > > Sent: Wednesday, July 06, 2011 1:19 PM > > To: CCP4BB@JISCMAIL.AC.UK > > Subject: Re: [ccp4bb] How to evaluate Fourier transform ripples > > > > The question about Fourier transformation ripples has a straightforward > > answer in a fairly typical situation: > > A) data are collected to the resolution limit of diffraction, > > B) phases are uniform in quality across the resolution range, which is > > equivalent to R-free being uniform with respect to resolution within a > > factor of 2 or so, > > C) maps are not sharpened. > > > > The ripples originate from not including unobserved structure factors. > > The > > intensity of diffraction decreases rapidly past the measurability > > limit, > > so, in the above situation, the unobserved diffraction contributes very > > little. Consequently, the answer is that typically one should not see > > ripples. > > Ripples should not be confused with the effect of electron density maps > > being smoothed by vibrations and other forms of disorder. > > > > Zbyszek Otwinowski > > > > > > > > Dear All, Hi. I was asked in a manuscript revision to discuss > > > about the possible effects of Fourier transformation ripples on the > > > crystallographic results. Specifically, the reviewers question > > whether > > > ripples may affect on the electron density around heavy metal center > > which > > > has a Mo-S-As connection. From which angle or in which way this > > problem > > > should be addressed most convincingly ? Thank you for any > > > suggestion.Best,Conan > > > > > > Zbyszek Otwinowski > > UT Southwestern Medical Center at Dallas > > 5323 Harry Hines Blvd. > > Dallas, TX 75390-8816 > > Tel. 214-645-6385 > > Fax. 214-645-6353 > > Notice: This e-mail message, together with any attachments, contains > > information of Merck & Co., Inc. (One Merck Drive, Whitehouse Station, > > New Jersey, USA 08889), and/or its affiliates Direct contact > > information > > for affiliates is available at > > http://www.merck.com/contact/contacts.html) that may be confidential, > > proprietary copyrighted and/or legally privileged. It is intended > > solely > > for the use of the individual or entity named on this message. If you > > are > > not the intended recipient, and have received this message in error, > > please notify us immediately by reply e-mail and then delete it from > > your system. > -- ----------------------------------------------------------------- Bernhard Rupp (Hofkristallrat a. 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