Simulation of the shape of chaperonins using the small-angle x-ray scattering curves and torus form factor

The inverse scattering problem has been solved for protein complexes whose surfaces can be described by a set of the simplest doubly connected surfaces in the uniform approximation (a scattering potential inside the molecule is a constant). Solutions of two proteins-well-known GroEL bacterial chaperonin and poor-studied bacteriophage chaperonin, which is a product of 146 gene (gp146)-were taken for the experiment. The shapes of protein complexes have been efficiently reconstructed from the experimental scattering curves. The shell method, the method of the rotation of amino acid sequences with the use of the form factor of an amino acid, and the method of seeking the model parameters of a protein complex with the preliminarily obtained form factor of the model have been used to reconstruct the shape of these particles.