Dear CCP4bbers, As Zbyszek and some others wrote, the explanation of B factors is linked to the mathematical expression of structure factors: the X-ray crystallographer primary data are projections of the reciprocal space. And it's probably better to keep this primary info in PDB files rather than RMS displacements on one hand and to try to make the story short on the other hand: 50 emails on the subject seem to be enough, don't they ?
All the best and have a nice weekend, Philippe Philippe BENAS, Ph.D. ARN UPR 9002 CNRS IBMC Strasbourg 2, Allée Conrad Roentgen F-67084 STRASBOURG cedex +33.3.8841.7109 E-mails: p.be...@ibmc-cnrs.unistra.fr, philippe_be...@yahoo.fr URLs: https://ibmc.cnrs.fr/, https://ibmc.cnrs.fr/laboratoire/arn/ Le samedi 29 mai 2021 à 03:12:39 UTC+2, zbyszek <zbys...@work.swmed.edu> a écrit : B-factors are definitely a measure of uncertainty in variance (square) units. The crystal lattice has multiple occurrence of the atoms that are equivalent by crystal symmetry. They will have the same fractional coordinates within the uncertainty of their position relative to the crystal lattice orientation definition. B-factors are the measure of this uncertainty (variance) in somewhat unusual units (Angstrom squared / (8*pi*pi)). The fact that you can directly measure uncertainty by observing the width of the profile of the atomic distribution (shape of the uncertainty function) does not negate that this function represents uncertainty of atomic position relative to the crystal lattice. As a comment: uncertainty of the centroid of the uncertainty distribution is a second order or recursive uncertainty. As this centroid is deposited as atomic coordinates in pdb files, its uncertainty is a separate subject from the uncertainty (variation) of the atom position in the crystal lattice. Unfortunately theories of uncertainty estimates of uncertainty estimates is more complex and for this reason crystallographers rarely deal productively with uncertainty of the x,y,z coordinates deposited. A second comment: the B-factor really represents the sum of two uncertainties. One is the uncertainty of atom positions in the crystal lattice. The second is our experimental uncertainty about the knowledge of atom position. The first one has a physical interpretation. The second represents our data and analysis, e.g. phasing. For these reasons, saying that the B-factor represents uncertainty estimates is very productive because it is all about uncertainty. Independent uncertainties are convolved with each other to produce a final uncertainty function. In terms of the width squared of that function, it represents the sum of the widths squared of the contributors. In fact this observation is behind the Central Limit Theorem. Zbyszek On 2021-05-28 19:05, James Holton wrote: > I feel I should point out here that B-factors are NOT a measure of > uncertainty. They are a width. This width itself may be uncertain, > as may be the position of the center of the peak, but just because > your peak is broad doesn't mean you don't know where the middle of it > is. > > As for why leave the mean variation squared? I expect it is because > it is supposed to be proportional to temperature. Hence the name > "temperature factor". > > -James Holton > MAD Scientist > > On 5/27/2021 11:09 AM, Gergely Katona wrote: > >> Dear Jonathan, >> >> In 1D sd may be intuitive, but in 3D it is not so much. The square >> root of a symmetric covariance matrix is not universally defined and >> it is not intuitive to me. >> >> Best wishes, >> >> Gergely >> >> Gergely Katona, Professor, Chairman of the Chemistry Program Council >> >> >> Department of Chemistry and Molecular Biology, University of >> Gothenburg >> >> Box 462, 40530 Göteborg, Sweden >> >> Tel: +46-31-786-3959 / M: +46-70-912-3309 / Fax: +46-31-786-3910 >> >> Web: http://katonalab.eu, Email: gergely.kat...@gu.se >> >> From: CCP4 bulletin board <CCP4BB@JISCMAIL.AC.UK> On Behalf Of >> Hughes, Jonathan >> Sent: 27 May, 2021 18:53 >> To: CCP4BB@JISCMAIL.AC.UK >> Subject: [ccp4bb] AW: [ccp4bb] (R)MS >> >> hey! >> >> thank y'all for the informative (and swift!) answers! but, if the B >> factor (as defined) appears in a mathematical formulation, that >> doesn't make it an "appropriate" parameter for mobility/uncertainty. >> wouldn't √B be better, in the same way that, for humans, standard >> deviation (RMSD) is a more appropriate parameter of variability than >> variance? or am i missing something? >> >> cheers >> >> j >> >> Von: Ian Tickle <ianj...@gmail.com> >> Gesendet: Donnerstag, 27. Mai 2021 18:32 >> An: Hughes, Jonathan <jon.hug...@bot3.bio.uni-giessen.de> >> Cc: CCP4BB@JISCMAIL.AC.UK >> Betreff: Re: [ccp4bb] (R)MS >> >> Hi Jonathan >> >> It's historical, it's simply how it appears in the expression for >> the Debye-Waller factor, i.e. exp(-B sin^2(theta)/lambda^2). So it >> must have the same units as lambda^2. >> >> Cheers >> >> -- Ian >> >> On Thu, 27 May 2021 at 13:25, Hughes, Jonathan >> <jon.hug...@bot3.bio.uni-giessen.de> wrote: >> >> o yes! but maybe the crystal people could explain to me why the B >> factor is the variance (with units of Ų) rather than the standard >> deviation (i.e. RMS, with units of Å) when, to my simple mind, the >> latter would seem be the more appropriate description of variability >> in space? >> >> cheers >> >> jon >> >> Von: CCP4 bulletin board <CCP4BB@JISCMAIL.AC.UK> Im Auftrag von >> Pearce, N.M. (Nick) >> Gesendet: Donnerstag, 27. Mai 2021 12:38 >> An: CCP4BB@JISCMAIL.AC.UK >> Betreff: Re: [ccp4bb] Analysis of NMR ensembles >> >> If you want something comparable to B-factors don’t forget to put >> the MSF in the B-factor column, not the RMSF. Will change the >> scaling of the tube radius considerably! >> >> Nick >> >> On 27 May 2021, at 11:16, Harry Powell - CCP4BB >> <0000193323b1e616-dmarc-requ...@jiscmail.ac.uk> wrote: >> >> Cool… >> >> Purely for visualisation this does look like the approved CCP4 way - >> >> >> <Screen Shot 2021-05-27 at 10.13.59.png> >> >> Harry >> >> On 27 May 2021, at 10:01, Stuart McNicholas >> <000019a0c5f649e5-dmarc-requ...@jiscmail.ac.uk> wrote: >> >> Drawing style (right menu in display table) -> Worm scaled by -> >> Worm >> scaled by NMR variability >> >> in ccp4mg? >> >> This changes the size of the worm but not the colour. >> >> On Thu, 27 May 2021 at 09:56, Harry Powell - CCP4BB >> <0000193323b1e616-dmarc-requ...@jiscmail.ac.uk> wrote: >> >> Anyway, thanks to all those who answered my original question - >> especially >> >> Tristan: Chimerax (+ his attached script) >> Michal, Scott: Theseus >> (https://theobald.brandeis.edu/theseus/ [1]) >> Bernhard: Molmol (https://pubmed.ncbi.nlm.nih.gov/8744573/ >> [2] ) >> Rasmus CYRANGE (http://www.bpc.uni-frankfurt.de/cyrange.html >> [3]) and https://www.ccpn.ac.uk/ [4] (of course…) >> Andrew (uwmn - not sure if this is buildable on a modern box) >> Smita: PyMol (not sure if I’m allowed to say that on >> ccp4bb…) >> >> or I could script it and use Gesamt or Superpose for the >> superposition if I wanted to stay in the ccp4 universe and had the >> time to spare ;-) >> >> Harry >> >> > ######################################################################## >> >> To unsubscribe from the CCP4BB list, click the following link: >> https://www.jiscmail.ac.uk/cgi-bin/WA-JISC.exe?SUBED1=CCP4BB&A=1 [5] >> >> This message was issued to members of www.jiscmail.ac.uk/CCP4BB [6], >> a mailing list hosted by www.jiscmail.ac.uk [7], terms & conditions >> are available at https://www.jiscmail.ac.uk/policyandsecurity/ [8] >> >> > ######################################################################## >> >> To unsubscribe from the CCP4BB list, click the following link: >> https://www.jiscmail.ac.uk/cgi-bin/WA-JISC.exe?SUBED1=CCP4BB&A=1 [5] >> >> This message was issued to members of www.jiscmail.ac.uk/CCP4BB [6], >> a mailing list hosted by www.jiscmail.ac.uk [7], terms & conditions >> are available at https://www.jiscmail.ac.uk/policyandsecurity/ [8] > > ------------------------- > > To unsubscribe from the CCP4BB list, click the following link: > https://www.jiscmail.ac.uk/cgi-bin/WA-JISC.exe?SUBED1=CCP4BB&A=1 [5] > > ------------------------- > > To unsubscribe from the CCP4BB list, click the following link: > https://www.jiscmail.ac.uk/cgi-bin/WA-JISC.exe?SUBED1=CCP4BB&A=1 [5] > > ------------------------- > > To unsubscribe from the CCP4BB list, click the following link: > https://www.jiscmail.ac.uk/cgi-bin/WA-JISC.exe?SUBED1=CCP4BB&A=1 [5] > > ------------------------- > > To unsubscribe from the CCP4BB list, click the following link: > https://www.jiscmail.ac.uk/cgi-bin/WA-JISC.exe?SUBED1=CCP4BB&A=1 > > ------------------------- > > To unsubscribe from the CCP4BB list, click the following link: > https://www.jiscmail.ac.uk/cgi-bin/WA-JISC.exe?SUBED1=CCP4BB&A=1 > > ------------------------- > > To unsubscribe from the CCP4BB list, click the following link: > https://www.jiscmail.ac.uk/cgi-bin/WA-JISC.exe?SUBED1=CCP4BB&A=1 > > Links: > ------ > [1] https://theobald.brandeis.edu/theseus/ > [2] https://pubmed.ncbi.nlm.nih.gov/8744573/ > [3] http://www.bpc.uni-frankfurt.de/cyrange.html > [4] https://www.ccpn.ac.uk/ > [5] > https://www.jiscmail.ac.uk/cgi-bin/WA-JISC.exe?SUBED1=CCP4BB&A=1 > [6] http://www.jiscmail.ac.uk/CCP4BB > [7] http://www.jiscmail.ac.uk > [8] https://www.jiscmail.ac.uk/policyandsecurity/ ######################################################################## To unsubscribe from the CCP4BB list, click the following link: https://www.jiscmail.ac.uk/cgi-bin/WA-JISC.exe?SUBED1=CCP4BB&A=1 This message was issued to members of www.jiscmail.ac.uk/CCP4BB, a mailing list hosted by www.jiscmail.ac.uk, terms & conditions are available at https://www.jiscmail.ac.uk/policyandsecurity/ ######################################################################## To unsubscribe from the CCP4BB list, click the following link: https://www.jiscmail.ac.uk/cgi-bin/WA-JISC.exe?SUBED1=CCP4BB&A=1 This message was issued to members of www.jiscmail.ac.uk/CCP4BB, a mailing list hosted by www.jiscmail.ac.uk, terms & conditions are available at https://www.jiscmail.ac.uk/policyandsecurity/
