Particle shape reconstruction by Small-Angle Scattering. Integration of Group Theory and Maxinmum Entropy to multipole expansion method

The reconstruction of the shape of biological macromolecules in solution from small-angle scattering data is an important task for understanding the structure-function relationship. In the last few decades, the multipole expansion method was used to attack this problem. Here we present an improvement of the existing techniques by including the advantages of the group theory and maximum entropy. To show the capability of this method, pseudoexperimental scattering curves have been simulated and analyzed. Six different particle shapes have been considered: sphere, cylinder, cone, double cone, ellipsoid and cube. The results obtained by the proposed procedure gave an excellent agreement between the original and reconstructed shapes. The method is quite general, and can be applied to systems of different kinds.