LOW-RESOLUTION STRUCTURES OF PROTEINS IN SOLUTION RETRIEVED FROM X-RAY-SCATTERING WITH A GENETIC ALGORITHM

Small-angle x-ray solution scattering (SAXS) is analyzed with a new me thod to retrieve convergent model structures that fit the scattering p rofiles. An arbitrary hexagonal packing of several hundred beads conta ining the problem object is defined. Instead of attempting to compute the Debye formula for all of the possible mass distributions, a geneti c algorithm is employed that efficiently searches the configurational space and evolves best-fit bead models. Models from different runs of the algorithm have similar or identical structures. The modeling resol ution is increased by reducing the bead radius together with the searc h space in successive cycles of refinement. The method has been tested with protein SAXS (0.001 < S < 0.06 Angstrom(-1)) calculated from x-r ay crystal structures, adding noise to the profiles. The models obtain ed closely approach the volumes and radii of gyration of the known str uctures, and faithfully reproduce the dimensions and shape of each of them. This includes finding the active site cavity of lysozyme, the bi lobed structure of gamma-crystallin, two domains connected by a stalk in beta b2-crystallin, and the horseshoe shape of pancreatic ribonucle ase inhibitor. The low-resolution solution structure of lysozyme has b een directly modeled from its experimental SAXS profile (0.003 < S < 0 .03 Angstrom(-1)). The model describes lysozyme size and shape to the resolution of the measurement. The method may be applied to other prot eins, to the analysis of domain movements, to the comparison of soluti on and crystal structures, as well as to large macromolecular assembli es.