Woops!, yes Randy, I should have written B = 8*pi^2*<u>^2, not
8*pi*<u>^2 in my original response.
Incidentally, the "A factor" of a Lorentzian-distributed atom is 2*pi*w
where "w" is the full-width at half-maximum (FWHM) of the histogram of
displacements.
It is important to remember also that the rms displacement is not the
same as the FWHM of the peak. A Gaussian distribution with rms=1 has a
histogram with FWHM = ~2.35. For example, a carbon atom has a FWHM of
about 0.8 A, which is equivalent to a point atom with a B-factor of ~9
A^2. A carbon atom with a B-factor of 48 A^2 has a FWHM of 2 A.
-James Holton
MAD Scientist
Randy Read wrote:
> Just to clarify what Eleanor is saying:
>
> It was pointed out earlier (by James Holton, if I remember correctly?)
> that only the vibration in the direction parallel to the diffraction
> vector matters. If the mean-squared vibration in that direction is
> 1A^2, then the B-factor will be about 80A^2 (8*Pi^2 to be precise).
>
> However, people tend to think of mean-square displacements in 3D
> space. If the vibration is isotropic, then there is equal vibration
> in the two directions perpendicular to the diffraction vector (which
> don't affect the falloff of the scattering from that atom), and the
> overall mean-square displacement is 3 times the mean-square
> displacement in any one direction. So if you're thinking in terms of
> 3D mean-square displacement, you have to divide by 3 to get the
> displacement parallel to the diffraction vector. In that case, an
> atom with an overall 3D mean-square displacement of 1A^2 has a
> B-factor of about 26A^2 (8*Pi^2/3).
>
> Regards,
>
> Randy Read
>
> On 11 Dec 2008, at 09:39, Eleanor Dodson wrote:
>
>> A small molecule crystallography text would give you the formulation
>> for an ideal case.
>> A rough guide is that a B factor of 80 is equivalent to a mean
>> vibration about the coordinate of 1A
>>
>> But for proteins the B factor becomes the collection bin for all
>> sorts of other errors - unrecognised multiple conformations, , and
>> the restraints used make it harder to interpret.
>>
>> Eleanor
>>
>> Jacob Keller wrote:
>>> Hello Crystallographers,
>>>
>>> does anybody have a good reference dealing with interpretations of
>>> what B-factors (anisotropic or otherwise) really signify? In other
>>> words, a systematic addressing of all of the possible underlying
>>> molecular/crystal/data-collection phenomena which the B-factor
>>> mathematically models?
>>>
>>> Thanks in advance,
>>>
>>> Jacob
>>>
>>> *******************************************
>>> Jacob Pearson Keller
>>> Northwestern University
>>> Medical Scientist Training Program
>>> Dallos Laboratory
>>> F. Searle 1-240
>>> 2240 Campus Drive
>>> Evanston IL 60208
>>> lab: 847.491.2438
>>> cel: 773.608.9185
>>> email: [log in to unmask]
>>> *******************************************
>>>
>
> ------
> Randy J. Read
> Department of Haematology, University of Cambridge
> Cambridge Institute for Medical Research Tel: + 44 1223 336500
> Wellcome Trust/MRC Building Fax: + 44 1223 336827
> Hills Road E-mail: [log in to unmask]
> Cambridge CB2 0XY, U.K.
> www-structmed.cimr.cam.ac.uk
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