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