# AMBER Archive (2004)Subject: Re: AMBER: factor used in b-factor calculation

From: Bimo Ario Tejo (bimo7_at_gmx.de)
Date: Wed Mar 10 2004 - 05:02:46 CST

Dear Fabian,

I think (8/3)pi**2 is right if we consider fluctuation as displacements of
atom in any particular direction, i.e. all orthogonal axes x, y, and z.

<r**2> = <x**2> + <y**2> + <z**2> = 3<x**2>

Single direction of B-factor is:

B = 8pi**2<x**2>

So, B-factor of atom in terms of radial displacements is:

B = (8/3)pi**2<r**2)

Cheers,
bimo

> Hi,
>
> i have a question about the b-factor calculation with ptraj. As far as i
> have understood, the b-factor is the atomic fluctuation multiplied by
> (8/3)*pi*pi.
>
> Now, to my confusion, i found on the ptraj homepage the following
> statement:
>
> ... multiplied by 8pi**2 ...
>
> and in the sourcecode of actions.c:
>
> /*
> * B-factors are 8*PI*PI * <r>**2 hence we do not sqrt the
> fluctuations!!!
> */
>
> But some lines above:
>
> bfactor = (8.0/3.0)*PI*PI;
>
> So, i seems that actually the value is calculated with 8/3 and not with
> 8 as stated on the homepage and in the sourcecode. Can someone please
> confirm this?
>
> And second, it would be nice if someone could give me some literature
> references where it is explained, how the 8/3*pi*pi factor was derived.
>
> Bye,
>
> Fabian
>
> --
>
> Fabian Bös
>
> Institute of Technical Biochemistry
> University of Stuttgart / Germany
>
> Phone: +49-711-6857481
> Fax: +49-711-6853196
> Email: fabian.boes_at_itb.uni-stuttgart.de
>
> http://www.itb.uni-stuttgart.de
>
>
>
>
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