Re: [ccp4bb] R pim and Rmeans
Hi Frank, of course R_pim is just one number and it may not be discriminatory enough to decide when to stop including images. But I can say from my own experience that R_pim will not drop forever. I have seen data sets with R_pim values of 0.5% to 2.0 A or better resolution, but never R_pim values significantly smaller than that (even with the redundancy approaching 100). You may try this out yourself. I bet you that R_pim will eventually go up again after a few revolutions when radiation damage kicks in. The real question in my opinion is, when is the deviation from the 1/(N-1) drop such, that you would want to stop including more images. Cheers, Manfred. * * *Dr. Manfred S. Weiss * * * * Team Leader * * * * EMBL Hamburg OutstationFon: +49-40-89902-170 * * c/o DESY, Notkestr. 85 Fax: +49-40-89902-149 * * D-22603 Hamburg Email: [EMAIL PROTECTED] * * GERMANY Web: www.embl-hamburg.de/~msweiss/ * * * On Tue, 9 Dec 2008, Frank von Delft wrote: Hi Manfred thanks a lot for your comments, since they raise some interesting points. R_pim should give the precision of the averaged measurement, hence the name. It will decrease with increasing data redundancy, obviously. The decrease will be proportional to the square root of the redundancy if only statistical errors or counting errors are present. If other things happen, such as for instance radiation damage, then you are introducing systematic errors, which will lead to either R_pim decreasing less than it should, or R_pim even increasing. This raises an important issue. As more and more images keep being added to a data set, could one decide at some point, when to add any further images? This really is the point: in these days of fast data collection, I assume that most people collect more frames than necessary for completeness. At least, I always do. So the question is no longer is this data good enough -- that you can test quickly enough with downstream programs. Rather, it is, how many of the frames that I have should I include, so that you don't have to run the same combination of downstream programs for 20 combinations of frames. Radiation damage is the key, innit. Sure, I can pat myself on the shoulder by downweighting everything by 1/1-N -- so after 15 revolutions of tetragonal crystal that'll give a brilliant Rpim, but the crystal will be a cinder and the data presumably crap. But it's the intermediate zone (1-2x completeness) where I need help, but I don't see how Rpim is discriminatory enough. phx.
Re: [ccp4bb] R pim and Rmeans
There are useful plots from scala showing various measures v frame number. I usually look at those and do some hand waving to decide where the increasing R_xs indicate you are measuring nothing, or measuring something different from the first frames because of radiation damage Eleanor Frank von Delft wrote: Hi Manfred thanks a lot for your comments, since they raise some interesting points. R_pim should give the precision of the averaged measurement, hence the name. It will decrease with increasing data redundancy, obviously. The decrease will be proportional to the square root of the redundancy if only statistical errors or counting errors are present. If other things happen, such as for instance radiation damage, then you are introducing systematic errors, which will lead to either R_pim decreasing less than it should, or R_pim even increasing. This raises an important issue. As more and more images keep being added to a data set, could one decide at some point, when to add any further images? This really is the point: in these days of fast data collection, I assume that most people collect more frames than necessary for completeness. At least, I always do. So the question is no longer is this data good enough -- that you can test quickly enough with downstream programs. Rather, it is, how many of the frames that I have should I include, so that you don't have to run the same combination of downstream programs for 20 combinations of frames. Radiation damage is the key, innit. Sure, I can pat myself on the shoulder by downweighting everything by 1/1-N -- so after 15 revolutions of tetragonal crystal that'll give a brilliant Rpim, but the crystal will be a cinder and the data presumably crap. But it's the intermediate zone (1-2x completeness) where I need help, but I don't see how Rpim is discriminatory enough. phx.
Re: [ccp4bb] R pim and Rmeans
Hi Frank, maybe this is an opportunity to state that there is indeed a way to assess radiation damage by looking at an R-factor plot, but that R-factor is R_d [1], not R_pim. The formula and some explanation is in the CCP4 wiki at http://strucbio.biologie.uni-konstanz.de/ccp4wiki/index.php/R-factors#measuring_radiation_damage best, Kay [1] Diederichs, K. (2006) Some aspects of quantitative analysis and correction of radiation damage. Acta Cryst D62, 96-101 Frank von Delft schrieb: Hi Manfred thanks a lot for your comments, since they raise some interesting points. R_pim should give the precision of the averaged measurement, hence the name. It will decrease with increasing data redundancy, obviously. The decrease will be proportional to the square root of the redundancy if only statistical errors or counting errors are present. If other things happen, such as for instance radiation damage, then you are introducing systematic errors, which will lead to either R_pim decreasing less than it should, or R_pim even increasing. This raises an important issue. As more and more images keep being added to a data set, could one decide at some point, when to add any further images? This really is the point: in these days of fast data collection, I assume that most people collect more frames than necessary for completeness. At least, I always do. So the question is no longer is this data good enough -- that you can test quickly enough with downstream programs. Rather, it is, how many of the frames that I have should I include, so that you don't have to run the same combination of downstream programs for 20 combinations of frames. Radiation damage is the key, innit. Sure, I can pat myself on the shoulder by downweighting everything by 1/1-N -- so after 15 revolutions of tetragonal crystal that'll give a brilliant Rpim, but the crystal will be a cinder and the data presumably crap. But it's the intermediate zone (1-2x completeness) where I need help, but I don't see how Rpim is discriminatory enough. phx. -- Kay Diederichshttp://strucbio.biologie.uni-konstanz.de email: [EMAIL PROTECTED]Tel +49 7531 88 4049 Fax 3183 Fachbereich Biologie, Universität Konstanz, Box M647, D-78457 Konstanz This e-mail is digitally signed. If your e-mail client does not have the necessary capabilities, just ignore the attached signature smime.p7s. smime.p7s Description: S/MIME Cryptographic Signature
Re: [ccp4bb] refmac 5.5.0068 error
Dear Michael, ARP/wARP should recognise this refmac version with no problem. Before typing './install.sh' just do 'refmac5 -i' to check that refmac is executed fine and CCP4 environment is setup. If the problem remains please get back to us with details on the ARP/wARP version number and computer operating system. Best regards, Victor Michael Jackson wrote: hello, Thank you for the reply about the refmac 5.5.0066 error. I downloaded refmac 5.5.0068 but there appears to be a problem for ARPwARP to recognise the version. I reinstalled ARPwARP and the install shell script freezes when it looks for the refmac file.
[ccp4bb] plate survey
Hi Community, I would like to do a little survey on popular 2-3 drop per 96 well plates, and the pros and cons of these plates. I know that the new Cornings, the MRC and the Intelliplates are used often in the labs I visit (we use 2 drop MRC plates mostly). Perhaps you can comment on optical quality, robot handling (picking up, dispensing), performance (cracking!), ease of harvesting crystals etc. Please reply directly to me at [EMAIL PROTECTED] [EMAIL PROTECTED] or * [EMAIL PROTECTED] [EMAIL PROTECTED], I will post a summary. Flip
Re: [ccp4bb] Summary - torsion angle restraints in REFMAC
On the Ligand tab (upper left of web page), at left you'll see PDB (model coordinates) and PDB (ideal coordinates). The Ideal coords really are idealized, including a very different torsion between the two ring systems in this ligand. The Model coords seem correct (one of the two in the asymmetric unit was chosen, on some basis), but, again a Hmm?, the Bfactors of the Model coords were all reset to 10.00. Dave -Original Message- From: Artem Evdokimov [mailto:[EMAIL PROTECTED] Sent: Tuesday, December 09, 2008 9:36 PM To: Borhani, David; CCP4BB@JISCMAIL.AC.UK Subject: RE: [ccp4bb] Summary - torsion angle restraints in REFMAC Interestingly, in the interactive 3D applet view of the ligand from the PDB the two are perfectly in plane, whereas in the protein viewer the two groups are clearly out of plane. I assume that this means that the coordinates for the 3D ligand view are re-computed internally and are not representative of what's actually in the PDB. Hmm? Artem -Original Message- From: CCP4 bulletin board [mailto:[EMAIL PROTECTED] On Behalf Of Borhani, David Sent: Tuesday, December 09, 2008 9:25 PM To: CCP4BB@JISCMAIL.AC.UK Subject: Re: [ccp4bb] Summary - torsion angle restraints in REFMAC RE: Ian's and Eckhard's wise suggestion to deposit non-standard parameters used to refine ligands: I have had some ligands where the 1 8 peri-substituents (amino methyl groups) on a 6/6 fused aromatic ring (deazapteridine derivatives) were very clearly out of the plane. It took extensive fiddling with the refmac dictionary to get the torsion planarity restraints relaxed enough so that these two atoms were allowed to move into the very clear difference density waiting for them, even with 1.1 A data! See http://www.rcsb.org/pdb/explore.do?structureId=1KMS and http://www.rcsb.org/pdb/explore.do?structureId=1KMV for examples; paper is here: http://www.ncbi.nlm.nih.gov/pubmed/12096917 I thought I had deposited the refmac library file, but now I cannot find it on the PDB web site. Maybe I'm not looking in the right place, but if you click, in the ligand (LII) area, on ligand structure view, then (at left) Component definition (CIF), you can find this: http://www.rcsb.org/pdb/files/ligand/LII.cif. BUT, THIS IS NOT MY FILE! Rather, some auto-generated file (probably wrong; definitely doesn't have my relaxed parameters). Similarly, for http://www.rcsb.org/pdb/explore.do?structureId=2C2S (http://www.ncbi.nlm.nih.gov/pubmed/17569517), with a rather strange carborane ligand, I *distinctly* remember depositing the library file, because the EBI deposition software got completely tied in knots trying to interpret the deposited coords. Again, no files to be found on the PDB. http://www.rcsb.org/pdb/files/ligand/34B.cif is again not my file, but an auto-generated one (probably wrong, given the trouble the EBI s/w had). Hoping some folks at EBI/RCSB monitor the CCP4BB, Dave David Borhani, Ph.D. D. E. Shaw Research, LLC 120 West Forty-Fifth Street, 39th Floor New York, NY 10036 [EMAIL PROTECTED] 212-478-0698 http://www.deshawresearch.com
Re: [ccp4bb] Restrictions in ccp4-6.1 ?
The current value of maxbat in scala_/parameters.fh is 5000 Mind you, according to CVS this was increased from 1000 to 5000 in 1999! sortmtz and reindex also have MBATCH=5000. There's no restriction in the library itself. Cheers Martyn -Original Message- From: CCP4 bulletin board on behalf of Mueller, Juergen-Joachim Sent: Tue 12/9/2008 7:28 AM To: CCP4BB@JISCMAIL.AC.UK Subject: [ccp4bb] Restrictions in ccp4-6.1 ? Dear developers, I wonder if the restrictions for MBATCH=1000 in CCP4-v6.0.2 and for scala (maxbat=1000,maxpmr=2000,maxmat=1000, maxrun=3) hold also in V6.1? Otherwise I cannot use the precompiled versions and have to recompile!? Thank you, Jürgen
[ccp4bb] generating omit maps
Hi Everyone, Can anyone tell me a relatively easy way to generate an omit density map for a ligand? I know that CNS can do this, but I was wondering if there's a CCP4 related program to generate omit maps. Thanks, Kathleen
Re: [ccp4bb] generating omit maps
Subject: generating omit maps From: Kathleen Frey [EMAIL PROTECTED] Reply-To: Kathleen Frey [EMAIL PROTECTED] Date: Wed, 10 Dec 2008 10:30:47 -0500 Hi Everyone, Can anyone tell me a relatively easy way to generate an omit density map for a ligand? I know that CNS can do this, but I was wondering if there's a CCP4 related program to generate omit maps. Thanks, Kathleen Hi Kathleen, Not CCP4, I know, but this can be done very easily in PHENIX: http://www.phenix-online.org/documentation/autobuild.htm#anch159 HTH, Luca Luca Jovine, Ph.D. Group Leader, Protein Crystallography Unit Karolinska Institutet Department of Biosciences and Nutrition Hälsovägen 7, SE-141 57 Huddinge, Sweden Voice: +46.(0)8.6083-301 FAX: +46.(0)8.6089-290 E-mail: [EMAIL PROTECTED] W3: http://jovinelab.org
Re: [ccp4bb] generating omit maps
as a small variation on this, I would first finish the protein, and then include ligands, working from larger to smaller (ATP = citrate = glycerol = sulphates = waters). Sometimes several waters (from automated solvent building) in place of a bona fide ligand (or a glycerol for example) refine eerily well and give reasonable maps... Mark J. van Raaij Dpto de Bioquímica, Facultad de Farmacia Universidad de Santiago 15782 Santiago de Compostela Spain http://web.usc.es/~vanraaij/ On 10 Dec 2008, at 16:41, Mischa Machius wrote: Kathleen - The easiest way is to simply remove the ligand from the coordinates and refine for a few cycles. Whether that is particularly meaningful is another question. Better would be to remove the ligand coordinates, shake the remaining coordinates (i.e., randomly displace them by a small amount), and then refine. Even better, perhaps, would be to calculate a simulated-annealing omit map, but AFAIK, you can't use CCP4 for that. IMHO, the best option is to not include the ligand in the model-building and refinement processes until all of the protein(s), solvent molecules, etc. have been properly modeled. I personally tend to include ligands only at the very end of the modeling/refinement process, unless there is really no ambiguity. This strategy will minimize any model bias from the ligand, and it will give you an omit map by default (until you actually include the ligand). Best - MM Mischa Machius, PhD Associate Professor Department of Biochemistry UT Southwestern Medical Center at Dallas 5323 Harry Hines Blvd.; ND10.214A Dallas, TX 75390-8816; U.S.A. Tel: +1 214 645 6381 Fax: +1 214 645 6353 On Dec 10, 2008, at 9:30 AM, Kathleen Frey wrote: Hi Everyone, Can anyone tell me a relatively easy way to generate an omit density map for a ligand? I know that CNS can do this, but I was wondering if there's a CCP4 related program to generate omit maps. Thanks, Kathleen
Re: [ccp4bb] generating omit maps
On Dec 10, 2008, at 9:52 AM, Mark J. van Raaij wrote: as a small variation on this, I would first finish the protein, and then include ligands, working from larger to smaller (ATP = citrate = glycerol = sulphates = waters). Sometimes several waters (from automated solvent building) in place of a bona fide ligand (or a glycerol for example) refine eerily well and give reasonable maps... Automated solvent building that includes automatic refinement should probably be banned ;) I usually add solvent molecules before adding ligands. For one, the electron density usually improves when adding solvent, so that the interpretation of the ligands becomes easier. I would recommend to check every single solvent molecule, i.e., never use automatic solvent- modeling and refinement (!) routines blindly. Make sure to remove those solvent molecules that have clearly been placed into ligand density before doing the actual refinement. Another potential problem may have to be taken into consideration as well: depending on the resolution, it can happen that protein side chains are being moved into ligand density if it is not occupied by some atoms. In such cases, I use a mixed strategy derived from the approaches described in my first post. Best - MM On 10 Dec 2008, at 16:41, Mischa Machius wrote: Kathleen - The easiest way is to simply remove the ligand from the coordinates and refine for a few cycles. Whether that is particularly meaningful is another question. Better would be to remove the ligand coordinates, shake the remaining coordinates (i.e., randomly displace them by a small amount), and then refine. Even better, perhaps, would be to calculate a simulated-annealing omit map, but AFAIK, you can't use CCP4 for that. IMHO, the best option is to not include the ligand in the model-building and refinement processes until all of the protein(s), solvent molecules, etc. have been properly modeled. I personally tend to include ligands only at the very end of the modeling/refinement process, unless there is really no ambiguity. This strategy will minimize any model bias from the ligand, and it will give you an omit map by default (until you actually include the ligand). Best - MM Mischa Machius, PhD Associate Professor Department of Biochemistry UT Southwestern Medical Center at Dallas 5323 Harry Hines Blvd.; ND10.214A Dallas, TX 75390-8816; U.S.A. Tel: +1 214 645 6381 Fax: +1 214 645 6353 On Dec 10, 2008, at 9:30 AM, Kathleen Frey wrote: Hi Everyone, Can anyone tell me a relatively easy way to generate an omit density map for a ligand? I know that CNS can do this, but I was wondering if there's a CCP4 related program to generate omit maps. Thanks, Kathleen
Re: [ccp4bb] generating omit maps
Let me also follow up on this point. I also agree that the ligand should be added very late in the refinement/model-building procedure. I also encourage people in my group to create a subdirectory BEFORE_LIGANDS into which they put the current PDB and map (or mtz) files prior to adding the ligand. Putting it into a separate directory avoids accidentally deleting it if you tidy up your modeling files at some later state. Come publication time, include in your manuscript the map generated at this stage prior to inclusion of the ligand. It is sometimes not as pretty but it gives the reader a honest view of your ligand density. Cheers, Andy -- Andrew M. Gulick, Ph.D. --- (716) 898-8619 Hauptman-Woodward Institute 700 Ellicott St Buffalo, NY 14203 --- Hauptman-Woodward Institute Dept. of Structural Biology, SUNY at Buffalo http://www.hwi.buffalo.edu/Faculty/Gulick/Gulick.html http://labs.hwi.buffalo.edu/gulick On 12/10/08 10:41 AM, Mischa Machius [EMAIL PROTECTED] wrote: Kathleen - The easiest way is to simply remove the ligand from the coordinates and refine for a few cycles. Whether that is particularly meaningful is another question. Better would be to remove the ligand coordinates, shake the remaining coordinates (i.e., randomly displace them by a small amount), and then refine. Even better, perhaps, would be to calculate a simulated-annealing omit map, but AFAIK, you can't use CCP4 for that. IMHO, the best option is to not include the ligand in the model-building and refinement processes until all of the protein(s), solvent molecules, etc. have been properly modeled. I personally tend to include ligands only at the very end of the modeling/refinement process, unless there is really no ambiguity. This strategy will minimize any model bias from the ligand, and it will give you an omit map by default (until you actually include the ligand). Best - MM -- -- Mischa Machius, PhD Associate Professor Department of Biochemistry UT Southwestern Medical Center at Dallas 5323 Harry Hines Blvd.; ND10.214A Dallas, TX 75390-8816; U.S.A. Tel: +1 214 645 6381 Fax: +1 214 645 6353 On Dec 10, 2008, at 9:30 AM, Kathleen Frey wrote: Hi Everyone, Can anyone tell me a relatively easy way to generate an omit density map for a ligand? I know that CNS can do this, but I was wondering if there's a CCP4 related program to generate omit maps. Thanks, Kathleen
Re: [ccp4bb] generating omit maps
Kathleen - The easiest way is to simply remove the ligand from the coordinates and refine for a few cycles. Whether that is particularly meaningful is another question. Better would be to remove the ligand coordinates, shake the remaining coordinates (i.e., randomly displace them by a small amount), and then refine. Even better, perhaps, would be to calculate a simulated-annealing omit map, but AFAIK, you can't use CCP4 for that. IMHO, the best option is to not include the ligand in the model-building and refinement processes until all of the protein(s), solvent molecules, etc. have been properly modeled. I personally tend to include ligands only at the very end of the modeling/refinement process, unless there is really no ambiguity. This strategy will minimize any model bias from the ligand, and it will give you an omit map by default (until you actually include the ligand). Best - MM Mischa Machius, PhD Associate Professor Department of Biochemistry UT Southwestern Medical Center at Dallas 5323 Harry Hines Blvd.; ND10.214A Dallas, TX 75390-8816; U.S.A. Tel: +1 214 645 6381 Fax: +1 214 645 6353 On Dec 10, 2008, at 9:30 AM, Kathleen Frey wrote: Hi Everyone, Can anyone tell me a relatively easy way to generate an omit density map for a ligand? I know that CNS can do this, but I was wondering if there's a CCP4 related program to generate omit maps. Thanks, Kathleen
Re: [ccp4bb] R pim and Rmeans
Yup, there is that. It doesn't help make the decision, though, of how much to include. And the other problem is it requires higher redundancy than I usually have when living on the edge of completeness vs death. (It's not multiplicity-weighted, is it?) (It's other problem is that it is hidden in the currently least user-friendly program in crystallography -- as powerful as the algorithm undoubtedly is; I argue that by definition a user-unfriendly program cannot be considered powerful. But I digress. And provoke... and don my flame-shield.) phx. Kay Diederichs wrote: Hi Frank, maybe this is an opportunity to state that there is indeed a way to assess radiation damage by looking at an R-factor plot, but that R-factor is R_d [1], not R_pim. The formula and some explanation is in the CCP4 wiki at http://strucbio.biologie.uni-konstanz.de/ccp4wiki/index.php/R-factors#measuring_radiation_damage best, Kay [1] Diederichs, K. (2006) Some aspects of quantitative analysis and correction of radiation damage. Acta Cryst D62, 96-101 Frank von Delft schrieb: Hi Manfred thanks a lot for your comments, since they raise some interesting points. R_pim should give the precision of the averaged measurement, hence the name. It will decrease with increasing data redundancy, obviously. The decrease will be proportional to the square root of the redundancy if only statistical errors or counting errors are present. If other things happen, such as for instance radiation damage, then you are introducing systematic errors, which will lead to either R_pim decreasing less than it should, or R_pim even increasing. This raises an important issue. As more and more images keep being added to a data set, could one decide at some point, when to add any further images? This really is the point: in these days of fast data collection, I assume that most people collect more frames than necessary for completeness. At least, I always do. So the question is no longer is this data good enough -- that you can test quickly enough with downstream programs. Rather, it is, how many of the frames that I have should I include, so that you don't have to run the same combination of downstream programs for 20 combinations of frames. Radiation damage is the key, innit. Sure, I can pat myself on the shoulder by downweighting everything by 1/1-N -- so after 15 revolutions of tetragonal crystal that'll give a brilliant Rpim, but the crystal will be a cinder and the data presumably crap. But it's the intermediate zone (1-2x completeness) where I need help, but I don't see how Rpim is discriminatory enough. phx.
[ccp4bb] definition of I Sigma I
Hi, does anyone have a definition of I Sigma I please. Any definitions that i have found are not very informative for novices. thanks andy
Re: [ccp4bb] definition of I Sigma I
Hi - I Sigma I means nothing. I/sigma(I) is the average intensity of a group of reflections divided by the average standard deviation (sigma) of the same group of reflections. Usually its reported per resolution shell, groups of reflections within thin shells of resolution. I/sigma(I) is the intensity divided by the standard deviation (sigma) of a reflection, averaged for a group of reflections. Its also usually reported per resolution shell, groups of reflections within thin shells of resolution. Both report signal over noise, and in many (most?) publications its unclear which one is reported. They are similar but not the same. Hope this helps. A. On 10 Dec 2008, at 23:14, ANDY DODDS wrote: Hi, does anyone have a definition of I Sigma I please. Any definitions that i have found are not very informative for novices. thanks andy
[ccp4bb] Ref for B-factor Underlying Phenomenon
Hello Crystallographers, does anybody have a good reference dealing with interpretations of what B-factors (anisotropic or otherwise) really signify? In other words, a systematic addressing of all of the possible underlying molecular/crystal/data-collection phenomena which the B-factor mathematically models? Thanks in advance, Jacob *** Jacob Pearson Keller Northwestern University Medical Scientist Training Program Dallos Laboratory F. Searle 1-240 2240 Campus Drive Evanston IL 60208 lab: 847.491.2438 cel: 773.608.9185 email: [EMAIL PROTECTED] ***
[ccp4bb] Summary: Modeling residues with very poor density
Thank you Afonine, Hans, Kumar, Deliang, Mark, Jose, Tim, Eleanor and Ed for sharing your thoughts. Here is a summary of the responses I received- 1. One should try to model residues based on 2Fo-Fc maps contoured at 1.0 sigma level. Structures of mobile regions/loops can sometimes be modeled based on maps carved at 0.5-0.6 sigma, but in such cases extreme care must be taken to avoid modeling based on noise signals and not to omit genuine signals visible in the region. 2. 2Fo-Fc maps contoured below 0.5 sigma and Fo-Fc maps contoured below 1.5 sigma are full of noise signals and hence need to be carefully analyzed. It is advisable to avoid modeling anything based solely on signals seen below the above-mentioned sigma cut offs. Fo-Fc maps sometimes improve significantly after refining the initial model a couple of times. 3. There seems to be disagreement over modeling residues that one can not see in maps and leaving out residues that one can see in maps. Thanks a lot for your responses. AM
Re: [ccp4bb] Ref for B-factor Underlying Phenomenon
The original reference is Debye, P. (1914) Ann. d. Physik 43, 49, which is in German. Waller's paper came later and the forgotten paper wich did the math rigorously was Ott, H. (1935) Ann. d. Physik 23, 169. The best description I have seen in English was in chapter 1 section 3 of: James R. W. (1962) “The Optical Principles of the Diffraction of X-rays: The Crystalline State”, Vol II. Bell Hyman Ltd., London. James is a big book with a lot of math in it, but it is remarkably easy to read. Particularly chapter 1. I highly recommend it. The long and short of the B-factor phenomenon is that the primary effect of corrupting a perfect lattice by moving the atoms away from their ideal positions is a drop in the Bragg intensities and a corresponding increase in background (the elastically-scattered photons that don't go into the spots have to go somewhere). R. W. James shows the math to prove that the falloff of the Bragg intensities with resolution is the Fourier transform of the histogram of atomic displacements. It actually doesn't matter if the displacements in adjacent unit cells are correlated or not. It is only the histogram of displacements from the ideal lattice that is important. If the distribution (histogram) of atomic displacements is Gaussian, then its Fourier transform is also a Gaussian and therefore has the form exp(-B*s^2). Where B = 8*pi*u^2 and u is the displacement of an atom along the scattering vector s (halfway between the incident and diffracted beams). It is interesting that movement of atoms perpendicular to s has absolutely no effect on the Bragg intensity! In this way, anisotropic displacement distributions lead to anisotropic diffraction as the crystal rotates. Waller showed that thermal vibrations (phonons) in simple crystals do indeed produce a Gaussian distribution of atomic displacements, but it is also interesting to note that non-Gaussian atomic displacement distributions cannot be fully described by a B factor. For example, if the atomic displacements have a Lorentzian shape, then the intensity fall-off will be exponential: exp(-A*s) (the Fourier transform of a Lorentzian is an exponential, and vice versa). I THINK this may be the origin of using the letter B, as it is the second term in the Taylor expansion of an arbitrary displacement distribution: exp( ln(K) - A*s -B*s^2 - C*s^3 ...) For Gaussian atomic displacements, all terms except B will be zero. But, I have to admit that Debye's paper doesn't have an equation that looks like this. In fact, even R. W. James doesn't call it B, he calls it M. So, I could be wrong about the origin of B, but I think someone else must have written down the above equation before I did. -James Holton MAD Scientist Jacob Keller wrote: Hello Crystallographers, does anybody have a good reference dealing with interpretations of what B-factors (anisotropic or otherwise) really signify? In other words, a systematic addressing of all of the possible underlying molecular/crystal/data-collection phenomena which the B-factor mathematically models? Thanks in advance, Jacob *** Jacob Pearson Keller Northwestern University Medical Scientist Training Program Dallos Laboratory F. Searle 1-240 2240 Campus Drive Evanston IL 60208 lab: 847.491.2438 cel: 773.608.9185 email: [EMAIL PROTECTED] mailto:[EMAIL PROTECTED] ***
