James,
I don't think that you are re-phrasing me correctly. At least I can
not understand how your statement relates to mine.
You simply have to tell us whether a value of 27.34 read from the last
column of a PDB file means :
(1) B = 27.34 Å^2 , as I (and hopefully some others) think, or
(2) B = 27.34 A^2/(8*pi^2) = 0.346 Å^2 , as you seem to suggest
Once you have settled for one of the two options, you can convert your
B to U and you will get for either choice :
(1) U = 0.346 Å^2
(2) U = 0.00438 Å^2
Even small-molecule crystallographers (who almost always compute and
refine U's) rarely see values as low as U = 0.00438 Å^2.
Cheers
Marc
Quoting James Holton <[log in to unmask]>:
> 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
>
>
>
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