Objective Criteria for Estimation of Initial Parameters for the Modeling of Micelle and Liposome Structures from Small-Angle X-ray Scattering Data

The structures of hydrophobic membrane proteins are studied using matrices, which serve as models of cell membranes and are formed by the appropriate amphiphilic molecules, e.g., by surfactant or lipid molecules. To study the structure of a protein incorporated into an artificial membrane, first of all it is necessary to determine the structure of the membrane. The ELLLIP and ELLMIC algorithms were previously developed to address this issue by small-angle X-ray scattering. These algorithms allow the construction of models of ellipsoidal vesicles based on the atomic structure of a lipid or surfactant monomer. However, the results of modeling depend, to a large extent, on the subjective assessment of the initial values of the structural parameters of the matrices and may be wrong due to the ambiguity in the solution of such problems. Here, we present an independent approach to the determination of the initial sizes of model membranes for their subsequent structural modeling, which is based on the analysis of the pair-distance distribution functions derived directly from the small-angle X-ray scattering curve.