EMBL Hamburg Biological
Small Angle Scattering

Form and structure factors, interactions, modelling

Jan Skov Pedersen

Aarhus University, Denmark

The lecture will deal with the classical modeling approach for analysis of small-angle scattering data. In the first part, analytical models are considered, and in a second part, effects of inter-particle interactions are described.

An overview over the form factors of various simple geometrical objects like spheres, ellipsoids, cylinders, discs etc will be given. A few examples are treated in greater detail. In addition, the form factors of polymer models with many internal degrees of freedoms are given, also with a few examples treated in detail. It will be described how one can use of Monte Carlo simulations for generating form factors of complex structures for which an analytical calculation is not possible. The method is ideally suited for polymer-like systems with many degrees of freedom as the MC method can be used for obtaining ensemble-average form factors. The MC method can also be used for rigid structures for generating points that represent the components of the structure, so that the form factor can be obtained using these points via the Debye equation. The examples of the latter include modelling of ISCOM vaccine particles that have a structure of a perforated membrane, and the structure of solubilized membrane proteins.

In the last part of the lectures, the effects of inter-particle interactions are discussed. The main analytical results will be given for spherical particles and polymer-like particles; approximations valid for particles with some anisotropy are also described.

Throughout the lectures, examples of applications to experimental data are included.


  • J. Skov Pedersen (1997) Analysis of Small-angle Scattering Data from Polymeric and Colloidal Systems: Modelling and Least-squares Fitting. Advances in Colloid and Interface Science 70, 171-201.
  • J. Skov Pedersen (2002) Monte Carlo Simulation Techniques Applied in the Analysis of Small-Angle Scattering Data from Colloids and Polymer Systems. Editors: Peter Lindner and Thomas Zemb. Neutrons, X-Rays and Light, 381-389. Elsevier.
  • J. Skov Pedersen (2002) Modelling of Small-Angle Scattering Data from Colloids and Polymer Systems. Editors: Peter Lindner and Thomas Zemb. Neutrons, X-Rays and Light, 391-420. Elsevier.
  • K.K. Andersen, C.L.P. Oliveira, K.L. Larsen, F.M. Poulsen, T.H. Callisen, P. Westh, J. Skov Pedersen, D.E. Otzen (2009) The Role of Decorated SDS Micelles in Sub-CMC Protein Denaturation and Association. Journal of Molecular Biology, 391(1), 207-226.
  • J. Skov Pedersen ; C.L.P. Oliveira. H.B Hubschmann, L. Arelth, S. Manniche, N. Kirkby, H.M. Nielsen (2012). Structure of Immune Stimulating Complex Matrices and Immune Stimulating Complexes in Suspension Determined by Small-Angle X-Ray Scattering. Biophysical Journal 102, 2372-2380.
  • J.D. Kaspersen, C.M. Jessen, B.S. Vad, E.S. Sorensen, K.K. Andersen, M. Glasius, C.L.P. Oliveira, D.E. Otzen, J.S. Pedersen, (2014). Low-Resolution Structures of OmpA-DDM Protein-Detergent Complexes. ChemBioChem 15(14), 2113-2124.

Date/time: Friday, 31 October 2012, 9:00

  Last modified: October 16, 2014

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