Dear Zbyszek: Thanks a lot for your good summary. It is very interesting but, do you think there are some references for more detailed description, especially from mathematics point of view about correlating B-factor to the Gaussian probability distribution (the B-factor unit of A^2 is my first doubt as for the probability distribution description)? Thanks again for your efforts!
Best Regards, Hailiang > The B-factor in crystallography represents the convolution (sum) of two > types of uncertainties about the atom (electron cloud) position: > > 1) dispersion of atom positions in crystal lattice > 2) uncertainty of the experimenter's knowledge about the atom position. > > In general, uncertainty needs not to be described by Gaussian function. > However, communicating uncertainty using the second moment of its > distribution is a widely accepted practice, with frequently implied > meaning that it corresponds to a Gaussian probability function. B-factor > is simply a scaled (by 8 times pi squared) second moment of uncertainty > distribution. > > In the previous, long thread, confusion was generated by the additional > assumption that B-factor also corresponds to a Gaussian probability > distribution and not just to a second moment of any probability > distribution. Crystallographic literature often implies the Gaussian > shape, so there is some justification for such an interpretation, where > the more complex probability distribution is represented by the sum of > displaced Gaussians, where the area under each Gaussian component > corresponds to the occupancy of an alternative conformation. > > For data with a typical resolution for macromolecular crystallography, > such multi-Gaussian description of the atom position's uncertainty is not > practical, as it would lead to instability in the refinement and/or > overfitting. Due to this, a simplified description of the atom's position > uncertainty by just the second moment of probability distribution is the > right approach. For this reason, the PDB format is highly suitable for the > description of positional uncertainties, the only difference with other > fields being the unusual form of squaring and then scaling up the standard > uncertainty. As this calculation can be easily inverted, there is no loss > of information. However, in teaching one should probably stress more this > unusual form of presenting the standard deviation. > > A separate issue is the use of restraints on B-factor values, a subject > that probably needs a longer discussion. > > With respect to the previous thread, representing poorly-ordered (so > called 'disordered') side chains by the most likely conformer with > appropriately high B-factors is fully justifiable, and currently is > probably the best solution to a difficult problem. > > Zbyszek Otwinowski > > > >>>> - they all know what B is and how to look for regions of high B >>>> (with, say, pymol) and they know not to make firm conclusions about >>>> H-bonds >>>> to flaming red side chains. >>> >>>But this "knowledge" may be quite wrong. If the flaming red really >>> indicates >>>large vibrational motion then yes, one whould not bet on stable H-bonds. >>>But if the flaming red indicates that a well-ordered sidechain was >>> incorrectly >>>modeled at full occupancy when in fact it is only present at >>> half-occupancy >>>then no, the H-bond could be strong but only present in that >>> half-occupancy >>>conformation. One presumes that the other half-occupancy location >>> (perhaps >>>missing from the model) would have its own H-bonding network. >>> >> >> I beg to differ. If a side chain has 2 or more positions, one should be >> a >> bit careful about making firm conclusions based on only one of those, >> even >> if it isn't clear exactly why one should use caution. Also, isn't the >> isotropic B we fit at "medium" resolution more of a "spherical cow" >> approximation to physical reality anyway? >> >> Phoebe >> >> >> > > > Zbyszek Otwinowski > UT Southwestern Medical Center at Dallas > 5323 Harry Hines Blvd. > Dallas, TX 75390-8816 > Tel. 214-645-6385 > Fax. 214-645-6353 > >
