Three-Dimensional Reconstruction of Helical Structures from Small-Angle X-ray Scattering Data

Abstract

Helical particles are of interest because of their similarity to real nanostructures that are formed in processes of self-organization of biopolymers (for example, carrageenans, DNA, etc.). On the other hand, the determination of the structural parameters of such particles from small-angle X-ray scattering data is a complex issue due to the poor conditionality of the inverse problem. This is evident from the practice of using the well-known bead modeling programs. The study considers a modification of the search algorithm in a limited area of space and the behavior of the solutions depending on the parameters of the objective function responsible for the connectivity of the structure, the weight scheme for the scattering intensity curve, and the angular range of the data. The stability of the solutions was statistically assessed using a sequential model search by varying the weights of the penalty terms. The empirical dependences of the optimal values of the search parameters on the parameters of the pair distance distribution curves were determined.