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Re: [ccp4bb]: B factors



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On Friday 13 December 2002 18:45, Edward Berry wrote:

> 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. 

Actually, in this equation mu (usually "u") refers to the component of the 
displacement in the direction parallel to the diffraction vector (i.e. 
perpendicular to the corresponding Bragg planes).  If we assume isotropic 
thermal motion, then there will be similar displacement in three orthogonal 
directions, so to get the radial rms displacement in any direction we have to 
multiply by the square root of 3.  The result is that a radial rms 
displacement of 1A comes at an isotropic B-factor of about 26A^2, not 79.

By the way, this is frequently in error (or at least poorly explained) in 
textbooks, so I don't mean this as criticism of Edward Berry.

-- 

Randy J. Read
Department of Haematology, University of Cambridge
Cambridge Institute for Medical Research      Tel: + 44 1223 336500
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