Marc SCHILTZ wrote:
Hi James
I must confess that I do not understand your point. If you read a
value from the last column of a PDB file, say 27.34, then this really
means :
B = 27.34 Å^2
for this atom. And, since B=8*pi^2*U, it also means that this atom's
mean square atomic displacement is U = 0.346 Å^2.
It does NOT mean :
B = 27.34 Born = 27.34 A^2/(8*pi^2) = 27.34/(8*pi^2) A^2 = 0.346 Å^2
as you seem to suggest.
Marc,
Allow me to re-phrase your argument in a slightly different way:
If we replace the definition B=8*pi^2*U, with the easier-to-write C =
100*M, then your above statement becomes:
It does NOT mean :
C = 27.34 millimeters^2 = 27.34 centimeter^2/100 = 27.34/100
centimeter^2 = 0.2734 centimeter^2
Why is this not true?
If it was like this, the mean square atomic displacement of this atom
would be U = 0.00438 Å^2 (which would enable one to do ultra-high
resolution studies).
I feel I should also point out that B = 0 is not all that different from
B = 2 (U = 0.03 A^2) if you are trying to do ultra-high resolution
studies. This is because the form factor of carbon and other light
atoms are essentially Gaussians with full-width at half-max (FWHM) ~0.8
A (you can plot the form factors listed in ITC Vol C to verify this),
and "blurring" atoms with a B factor of 2 Borns increases this width to
only ~0.9 A. This is because the real-space "blurring kernel" of a B
factor is a Gaussian function with FWHM = sqrt(B*log(2))/pi Angstrom.
The root-mean-square RMS width of this real-space blurring function is
sqrt(B/8*pi^2) Angstrom, or sqrt(U) Angstrom. This is the real-space
"size" of a B factor Gaussian, and I, for one, find this a much more
intuitive way to think about B factors. I note, however, that the
real-space manifestation of the B factor is an object that can be
measured in units of Angstrom with no funny scale factors. It is only
in "reciprocal space" (which is really angle space) that we see all
these factors of pi popping up.
More on that when I find my copy of James...
-James Holton
MAD Scientist
