SAXS

When calculating a scattering profile using crysol a number of radii and volumes are used and reported. I'm trying to figure out what they are and how they are used in the calculation of the scattering profile.

here I did a test with a random PDB file:

Code: Select all

 C R Y S O L    Version 2.8.3  -- 04/10/12
 
 
 -- Program  started  at   26-Apr-2017   09:37:34--
 
 --------  Real space resolution and grid  -------- 
 
  Maximum order of harmonics ............................ : 15
  Order of Fibonacci grid ............................... : 17
  Total number of directions ............................ : 2585
 
 ------------  Reciprocal space grid  -------------
 
   in s = 4*pi*sin(theta)/lambda [1/angstrom] 
  Maximum scattering angle .............................. : 0.5000
  Number of angular points .............................. : 51
 
 --- Structural parameters (sizes in angstroms) --- 
 
 PDB file name .......................................... : linoleic.pdb
  Number of atoms read .................................. : 52
 Geometric Center:    8.037    0.749    7.158
  Number of carbons read ................................ : 18
  Number of oxygens read ................................ : 2
  Number of hydrogen atoms read ......................... : 32
 Center of the excess electron density: 29.071  2.364 -3.368
 Electron   Rg   :  6.408       Envelope   Rg      :  6.730    
 Shape      Rg   :  6.260       Envelope  volume   :  603.1    
 Shell    volume :  1328.       Envelope  surface  :  259.6    
 Shell      Rg   :  8.503       Envelope  radius   :  11.29    
 Shell    width  :  3.000       Envelope  diameter :  22.12    
 Molecular Weight:  280.4       Dry volume         :  339.9    
 Displaced volume:  478.3       Average atomic rad.:  1.300    
 
 -- No data fitting, parameters entered manually --
 
 Solvent density ........................................ : 0.3340
 Contrast of the solvation shell ........................ : 3.000e-2
 Average atomic radius .................................. : 1.300
 Excluded Volume ........................................ : 478.3
 Average atomic volume .................................. : 9.198
 Radius of gyration from atomic structure ............... : 8.988
 Average electron density ............................... : 0.3261
  
 ----------------  Output files  ------------------
  
 Intensities    saved to file linoleic00.int
 Net amplitudes saved to file linoleic00.alm
 
  C R Y S O L    Version 2.8.3  -- 04/10/12 ----  terminated at   26-Apr-2017   09:37:34--

Crysol reports a "dry volume", is that simply the volume of the individual atoms and atomic groups (Ie the sum of Vj in the original crysol paper)? And when fitting, is this value influenced by the choice of Ra?

When fitting to an experimental curve, crysol fits a volume (in addition to Ra), is this what is displayed as "Excluded Volume" in the above?
Finally there is also something called "Displaced volume" which in the current case is the same as the "Excluded volume", but it is not clear for me what this volume is or how its used (if it is used at all).

I suspect that the reported "Excluded volume" is used to calculate the scattering profile of the excluded solvent (see viewtopic.php?f=11&t=2214):

I(s) = <|Aa(s) - (V/V0)*p0*Ac(s)+dp*Ab(s)|^2>omega

where V is the "Excluded volume" (which may be adjusted to fit the data). If i'm correct, Is the "Dry volume" then V0?

When calculating (not fitting to data) a scattering curve, is the parameter Ra set to the average atomic radius?

I hope you can help shed some light on these parameters.

Dry volume is simply computed from the molecular weight
as V=1.21*MW where MW is in Dalton and V is in A^3.

Displaced volume is the sum of the Van-der-Waals volumes of individual atomic groups,
(i.e. it serves as V0 in formula).

Excluded volume is the adjusted value (V in the formula, in prediction mode it is therefore equal to V0)

In prediction mode Ra is set to the average radius of atomic group.

Tank you very much

Dear ATSAS team,

You write "Displaced volume is the sum of the Van-der-Waals volumes of individual atomic groups,
(i.e. it serves as V0 in formula)"

But the Crysol article (1995) lists volumes from (1) Fraser et al. (1978) and from International Tables of X-ray Crystallography (1968). Are these volumes not used in the current version of Crysol (and Cryson)? In that case, why did you chose to use Wan-der-Waals volumes instead?
I understand why you don't use the values from International Tables anymore, since these are volumes in solid-state crystals, and thus probably a non-optimal approximation for the effective atomic volumes in proteins. However, the volumes from Fraser et al. seemed to be a good choice.

/Andreas

Fraser et al. (1978) lists observed volumes for just four atoms.
The present version of Crysol supports 108 atom and atomic groups (e.g. CH)
whose Wan-der-Waals volumes seem to work well.

Please note that the formfactors are still computed from Gaussian spheres, not solid spheres

SAXS

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