There are certainly some issues here, and I am not sure I can give you a definitive answer. Your second link is to a page on liquid state theory, and I believe the term structure factor is used slightly differently there.
For a start, I think the form factor is considered separately, so that the structure factor is purely for distance distributions irrespective of particle type (as in your quote). In contrast, the form factor is part of the structure factor used in crystallography, so different atom types are automatically included.
As I understand it, the SAXS curve is an intensity curve. Thus the FT would give you distances, as in the Patterson function of crystallography. This is then what they call the "distance distribution function". It is clearly related in some way to the pair distribution function of liquid state theory, but I don't think it is quite the same.
My hunch would be that (3) and (4) are the same (with the caveats listed by Sjors and Richard). Differential scattering (of X-rays or electrons) by different particle types must be included in both the EM volume and the SAXS curve, so I don't think that can be an issue. There may be some issues with appropriate normalisation?
I guess the more practical approach is to just try it! crysol should give you a SAXS curve from an atomic model. You can make an EM volume from that atomic model, and then follow your procedure.
HTH
Martyn
*
* Dr. Martyn Winn
* STFC Daresbury Laboratory, Daresbury, Warrington, WA4 4AD, U.K.
* Tel: +44 1925 603455 (DL) or +44 1235 567865 (RcaH)
* E-mail: [log in to unmask] Skype: martyn.winn
*
> -----Original Message-----
> From: Collaborative Computational Project in Electron cryo-Microscopy
> [mailto:[log in to unmask]] On Behalf Of Ardan Patwardhan
> Sent: 31 October 2013 10:59
> To: [log in to unmask]
> Subject: Re: [ccpem] Correspondance between rotationally averaged power
> spectrum and SAXS curve
>
> Dear Sjors and Richard
>
> Many thanks for your replies.
>
> There is still one thing that I am unclear about:
> To calculate the radially averaged power spectrum
> 1) Take the 3D density map and Fourier transform (FT) it
> 2) Convert 3D FT to 3D power spectrum (PS)
> 3) Radially average 3D PS to obtain 1D PS
>
> According to what I understand of SAXS
> (http://en.wikipedia.org/wiki/Biological_small-angle_scattering but
> also other sources): 4) the SAX scattering 1D curve is the FT of the
> "distance distribution function". I understand that the FT of the
> "distance distribution function"
> (http://en.wikipedia.org/wiki/Radial_distribution_function#The_structur
> e_fac
> tor) under the assumption that "all particles are identical" is a
> structure factor function.
>
> So for biological macromolecules, if we account for a) CTF, MTF
> effects etc and b) the fact that the scattering cross sections will be
> different for EM and X-rays, should we expect (3) and (4) to be the
> same? Is the "all particles are identical" assumption valid even for
> ribosomes and viruses where protein + DNA/RNA is present?
>
> Many thanks best wishes
>
> -----Original Message-----
> From: RICHARD HENDERSON [mailto:[log in to unmask]]
> Sent: 30 October 2013 19:20
> To: Ardan Patwardhan; [log in to unmask]
> Subject: Re: [ccpem] Correspondance between rotationally averaged power
> spectrum and SAXS curve
>
> Ardan,
>
> Not identical, but definitely similar. The scattering cross-sections
> are different for X-rays and electrons. Electron scattering is also
> very sensitive to bonding (electron cloud radius) whereas X-ray
> scattering is proportional to Z with a simpler form-factor.
>
> However, to the extent that C = N = O and hydrogen scatters less for
> electrons and X-rays, they are similar.
>
> Richard
>
> On 30/10/2013 18:09, Ardan Patwardhan wrote:
> > Dear all
> >
> > I was wondering if anyone could point me to a reference on the
> > following
> > question:
> >
> > Is the rotationally averaged power spectrum of a 3DEM reconstruction
> > (in the absence of CTF effects etc) expected to be identical to a
> > small angle X-ray scattering (SAXS) curve?
> >
> > Many thanks and best wishes
> >
> > Ardan Patwardhan
> >
> > European Bioinformatics Institute (EMBL-EBI) European Molecular
> > Biology Laboratory
> >
> > Wellcome Trust Genome Campus
> >
> > Hinxton, Cambridge CB10 1SD, UK
> > Tel: +44 1223 492649
> >
>
> --
> Richard Henderson
> MRC Laboratory of Molecular Biology
> Francis Crick Avenue
> Cambridge Biomedical Campus
> Cambridge CB2 0QH, U.K.
> tel: +44-(0)1223-267065
> fax: +44-(0)1223-268300
> web: http://www2.mrc-lmb.cam.ac.uk/groups/rh15/
>
>
> -----
>
> From Sjors:
> Hi Ardan,
>
> No. Differences may for example arise from different MTFs of the
> detectors used in the EM and X-ray experiments (or other envelope-
> affecting factors).
>
> Sjors
>
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> 10/30/13
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