Hi, It is enough to have Ų as unit to express uncertainty in 3D, but one can express it with a single number only in a very specific case when the atom is isotropic. Few atoms have a naturally isotropic distribution around their mean position in very high resolution protein crystal structures. The anisotropic atoms can be described by a 3x3 matrix, where each row and column is associated with the uncertainty in a specific spatial direction. The matrix elements are the product of the uncertainty in these directions. The diagonal elements will be the square of uncertainty in the same direction and they should be always positive, the off-diagonal combination of directions are covariances (+,0 or -). In the end, every element will have a unit distance*distance and the matrix will be symmetric. We cannot just take the square root of the matrix elements and expect something meaningful, if for no other reason the problem with negative covariances. To calculate the square root on the matrix itself one has to diagonalize it first. The height of a person in your example sounds easy to define, but the mathematical formalism will not decide that for me. I can also define height as the longest cord of a person or the maximum elevation of a car mechanic under a car. Through diagonalization one can at least extract some interesting, intuitive, principal directions. The final product, the sqrt(matrix), is not more intuitive to me. To convert it to something intuitive I would have to diagonalize square rooted matrix again. So shall we make an exception for the special, isotropic description? Or use general principles for isotropic and anisotropic treatments?
About what B-factors are, I like to think about them as necessary model parameters. Computational biologists also use them for benchmarking their molecular dynamics models. They are also reproducible to the extent that one can identify specific atoms just based on their anisotropic tensor from independent structure determinations in the same crystal form. They are of course not immune to errors and variation. I also wonder how we can represent model parameter variation in the best way. I admire NMR spectroscopists’ approach to deposit multiple samples from a structural distribution. One could reproduce their conclusions without assuming any sort of error model from these samples. In crystallography, we have more and more distributions to deal with because we are swimming in data. It is easy to sample/resample data sets from the same or different crystals (SFX for example). Which can lead to many replicates of structural models. I cannot really motivate to create multiple PDB entries for these replicates, it is not good for to reader to try to understand which PDB codes belong to which group of samples. Maybe it works for up to 10 structures, but how about a 100? Is it possible to deposit crystal structures as a chain of model/data pairs under the same entry? It is possible to just make a tarball and deposit in alternative services such as Zenodo, but it would be a pity to completely bypass the PDB. I can think of more compact description of structural distributions, for example mean positions and mean B-factors of atoms with their associated covariance matrices, analogously how MD trajectories can be described as average structures and covariance matrices. I think the assumption of independent variations per atoms is too strong in many cases and does not give an accurate picture of uncertainty. 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: [email protected] From: CCP4 bulletin board <[email protected]> On Behalf Of Hughes, Jonathan Sent: 28 May, 2021 14:49 To: [email protected] Subject: [ccp4bb] AW: [ccp4bb] AW: [ccp4bb] AW: [ccp4bb] (R)MS hi ian, yes, that aspect was in my mind, a bit, but i wanted to keep it simple. my point wasn't really how the "uncertainty" parameter is derived but rather its units. i can imagine that uncertainty in 3D could be expressed in ų (without helping the naïve user much) or in Å (which to me at least seems useful), but Ų (i.e. the B factor) seems neither logical nor helpful in this context, irrespective of its utility elsewhere. if you just see the B factor as a number, ok, you can do the √ in your head, but if it's visualized as in pymol/putty larger uncertainties become exaggerated – which is another word for "misrepresented". cheers j Von: Ian Tickle <[email protected]<mailto:[email protected]>> Gesendet: Freitag, 28. Mai 2021 12:10 An: Hughes, Jonathan <[email protected]<mailto:[email protected]>> Cc: [email protected]<mailto:[email protected]> Betreff: Re: [ccp4bb] AW: [ccp4bb] AW: [ccp4bb] (R)MS Hi Jonathan On Thu, 27 May 2021 at 18:34, Hughes, Jonathan <[email protected]<mailto:[email protected]>> wrote: "B = 8π2<u2> where u is the r.m.s. displacement of a scattering center, and <...> denotes time averaging" Neither of those statements is necessarily correct: u is the _instantaneous_ displacement which of course is constantly changing (on a timescale of the order of femtoseconds) and cannot be measured. So u2 is the squared instantaneous displacement, <u2> is the mean-squared displacement, and so the root-mean-squared displacement (which of course is amenable to measurement) is sqrt(<u2>), not the same thing at all as u. Incidentally, the 8π2 constant factor comes from Fourier-transforming the Debye-Waller factor expression I mentioned earlier. Also for crystals at least, the averaging is not only over time, it's over all unit cells, i.e. the displacements are not only thermal in origin but also due to spatial static disorder (instantaneous differences between unit cells). it would seem to me that we would be able to interpret things MUCH more easily with u rather than anything derived from u². So then I think what you mean is sqrt(<u2>) rather than <u2>, which seems not unreasonable. Cheers -- Ian ________________________________ 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 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/
