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The construction of three-dimensional models of protein macromolecules is a serious challenge due to the possible ambiguity of solving the inverse problem of reconstructing a three-dimensional structure from a one-dimensional small-angle scattering profile. The target function of this task can have several local minima, which leads to the dependence of the solution on the initial values of the model parameters and on the method of finding the global minimum. The problem of creating structural models is also complicated by averaging the scattering pattern over all orientations of particles in space and by the size and shape distribution of scattering objects in the case of polydispersity and/or polymorphism. In this study, the issue of ambiguity in solving inverse problems and restoring the three-dimensional structure of a protein is considered using the structure of the ectodomain of an insulin receptor-related receptor (ectoIRR) in solution as an example. The paper presents a consistent approach to solving this problem, starting from the determination of general structural parameters and  ab initio  reconstruction of shape to modeling by rigid bodies (using molecular tectonics), hybrid methods, and analysis of scattering profiles by singular vector decomposition.

biochemistry (moscow). supplement. series a, membrane and cell biology

The Ambiguity Issue in Solving Inverse Problems of Small-Angle Scattering: A Consistent Approach Using an Insulin Receptor-Related Receptor as an Example. Methods for Interpreting SAXS Data