Biophys J, June 1998, p. 2760-2775, Vol. 74, No. 6

Low-Resolution Structures of Proteins in Solution Retrieved from X-Ray Scattering with a Genetic Algorithm

 ^*Centro de Investigaciones Biológicas, C.S.I.C. Velázquez 144, 28006 Madrid, Spain;  ^#Departamento de Bioquímica y Biología Molecular I, Facultad de C.C. Químicas, U.C.M. Ciudad Universitaria s/n, 28040 Madrid, Spain;  ^§Laboratorium voor Chemische en Biologische Dynamica, Celestijnenlaan 200D Katholieke Universiteit Leuven, B-3001 Leuven, Belgium;  ^¶Daresbury Laboratory, Warrington WA4 4AD, England

Small-angle x-ray solution scattering (SAXS) is analyzed with a new method to retrieve convergent model structures that fit the scattering profiles. An arbitrary hexagonal packing of several hundred beads containing the problem object is defined. Instead of attempting to compute the Debye formula for all of the possible mass distributions, a genetic 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 resolution is increased by reducing the bead radius together with the search space in successive cycles of refinement. The method has been tested with protein SAXS (0.001 < S < 0.06 Å¹) calculated from x-ray crystal structures, adding noise to the profiles. The models obtained closely approach the volumes and radii of gyration of the known structures, and faithfully reproduce the dimensions and shape of each of them. This includes finding the active site cavity of lysozyme, the bilobed structure of -crystallin, two domains connected by a stalk in b2-crystallin, and the horseshoe shape of pancreatic ribonuclease inhibitor. The low-resolution solution structure of lysozyme has been directly modeled from its experimental SAXS profile (0.003 < S < 0.03 Å¹). The model describes lysozyme size and shape to the resolution of the measurement. The method may be applied to other proteins, to the analysis of domain movements, to the comparison of solution and crystal structures, as well as to large macromolecular assemblies.

Biophys J, June 1998, p. 2760-2775, Vol. 74, No. 6
© 1998 by the Biophysical Society   0006-3495/98/06/2760/16  $2.00

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