Re: [ccp4bb]: B factors

[Edward Berry <eaberry@lbl.gov>]

***  For details on how to be removed from this list visit the  ***
***          CCP4 home page http://www.ccp4.ac.uk         ***



gina clayton wrote:
...
...
> we (postdocs) are having a discussion in our lab about structures that
> are published with high B factors ( including in the wilson value) along
> the protein backbone and the legitimacy of these structures. We have
> seen several papers that base their arguments on specific amino acid
> interactions and yet the structures have Bfactors 70 + up to even
> 180......A recent one had an average B factor of 68 ( 60 for solvent)
> and wilson  value of 59 at 2.5 angstrom. Perhaps not the worst
> example.....but.....So I guess we would like some advice as to what is
> the current opinion about B factors, resolution and good structures?

I would also be interested in the current opinion(s). Speaking for
myself, I think that 80 or 100 is a very reasonable average atomic B
for structures diffracting to low resolution, and the relative scarcity
of such high B-factors in the PDB is due to questionable practices used
in the past which did not preserve the overall B-factor information
present in the original data.

Plagiarizing my textbook:
The B-factor of an atom is related to its mean square displacement
<mu^2> of the atomic vibration by :
B = 8pi^2<mu^2>

so the root-mean-square displacement mu(rms)
  mu(rms) = sqrt<mu^2> = sqrt(B)/sqrt(8pi^2) =sqrt(B/79)

So roughly speaking with a B-factor of 79 the atom will spend half it's
time inside a sphere of radius 1A, and depending on the distribution
probably most of its time within a radius of 2 A. This degree of
delocalization does not detract much from the electron density in a
3A map, or perhaps a better way of looking at it is that the reason
the crystal only diffracts to 3A is that most of the atoms are
delocalized over a sphere of radius 2-3 A. If you see a 3A structure
with average atomic B-factor in the 20-30 range, you should ask why
the data at 1.5 A wasn't used!

Because of the sqrt dependency on B, the B-factor can go quite a
lot higher without increasing the rms displacement much:

B=79 -> 	1 A* rms deviation
B=100 -> 	10/8.9 = 1.12 A*
B=316 -> 	2 A*.
B=711-> 	3 A*
B=1264 -> 	4 A*
B=1975 -> 	5 A*

Note that the Wilson B-factor should be significantly lower,
as the badly disordered atoms have much less contribution
to the average intensity in the range where the wilson plot
is interpreted- You can be sure those atoms with B=180 don't
contribute much to the falloff between 3.0 and 2.0 A-
they already fell off, dropped out somewhere around 4 or 5 A!
Thus the Wilson B weights the low-B-factor atoms more strongly,
while the average atomic B weights them all equally. Even in
high resolution structures there can be loops and termini that
are poorly ordered, and a high B-factor doesn't mean the atom
isn't there.

Edward (just a wee bit defensive on this topic)