Sum rules for atomic form factors and total x‐ray scattering intensities

Time-resolved small- and wide-angle X-ray scattering (SAXS and WAXS) methods probe the structural dynamics of proteins in solution. Although technologically advanced, these methods are in many cases limited by data interpretation. The calculation of X-ray scattering profiles is computationally demanding and poses a bottleneck for all SAXS/WAXS-assisted structural refinement and, in particular, for the analysis of time-resolved data. A way of speeding up these calculations is to represent biomolecules as collections of coarse-grained scatterers. Here, such coarse-graining schemes are presented and discussed and their accuracies examined. It is demonstrated that scattering factors coincident with the popular MARTINI coarse-graining scheme produce reliable difference scattering in the range 0 < q < 0.75 Å−1. The findings are promising for future attempts at X-ray scattering data analysis, and may help to bridge the gap between time-resolved experiments and their interpretation.

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X-Ray Scattering Form Factors with Relativistic Wave Functions

Physical Review ◽

10.1103/physrev.146.43 ◽

1966 ◽

Vol 146 (1) ◽

pp. 43-46 ◽

Cited By ~ 1

Author(s):

D. Chattarji ◽

N. V. V. J. Swamy

Keyword(s):

Form Factors ◽

Wave Functions ◽

Relativistic Wave ◽

X Ray ◽

X Ray Scattering ◽

Ray Scattering

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Interference Effects in Neutron and X Ray Scattering

Canadian Journal of Physics ◽

10.1139/p74-298 ◽

1974 ◽

Vol 52 (22) ◽

pp. 2281-2298 ◽

Cited By ~ 48

Author(s):

H. R. Glyde

Keyword(s):

Phonon Scattering ◽

Sum Rules ◽

Waller Factor ◽

Interference Term ◽

Scattering Intensity ◽

X Ray ◽

X Ray Scattering ◽

Debye Waller Factor ◽

The One ◽

Ray Scattering

The properties of interference between the one and multiphonon contributions to the dynamic and static scattering functions, S(Q, ω) and S(Q), first considered by Ambegaokar et al., are discussed in detail for b.c.c 3He and 4He for comparison with recent neutron and proposed X ray scattering experiments. Calculations of interference for Na and of the Debye temperature appropriate to the Debye–Waller factor in b.c.c 3He are also presented. In all cases the on shell interference term which alters the one phonon scattering intensity is found to be more important than the off shell term which alters the one phonon line shape. This is characteristic of systems in which anharmonic effects produce a large phonon frequency shift but in which the phonon lifetimes remain long. The difficulty in establishing the one phonon sum rules experimentally in the presence of interference is emphasized. As noted by Horner, existing unusual variations of scattering intensity observed in solid 4He can be satisfactorily explained by taking account of interference and this difficulty without introducing an anomolous Debye–Waller factor. Comparisons with liquid 4He suggest a similar difficulty in establishing the sum rules there.

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Study of the internal structure of polymer micelles by anomalous small-angle X-ray scattering at two edges

Journal of Applied Crystallography ◽

10.1107/s0021889813022450 ◽

2013 ◽

Vol 46 (5) ◽

pp. 1407-1413 ◽

Cited By ~ 5

Author(s):

Megumi Sakou ◽

Atsuro Takechi ◽

Shin-ichi Murakami ◽

Kazuo Sakurai ◽

Isamu Akiba

Keyword(s):

Spatial Distribution ◽

Form Factor ◽

Small Angle ◽

Form Factors ◽

Solid Sphere ◽

Hydrophobic Core ◽

X Ray ◽

The Core ◽

X Ray Scattering ◽

Ray Scattering

Anomalous small-angle X-ray scattering with two marker elements was applied to the structural analysis of poly(4-vinylphenol rubidium salt)-block-poly(4-bromostyrene) (RbPVPh-b-PBrS) micelles, where Br and Rb were the markers for the hydrophobic core and the hydrated corona, respectively. By using two different markers for the hydrophobic core and the hydrated corona, the form factors of the core and corona were extracted separately from the scattering profile of the whole RbPVPh-b-PBrS micelles. The form factor of the hydrophobic core (the spatial distribution of Br) revealed that the core was regarded as a solid sphere with a smooth surface and a radius of 47 nm. Conversely, the form factor of the spatial distribution of Rb+indicated that the shell of the RbPVPh-b-PBrS micelles was 15 nm thick.

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