Reconstruction of protein form with X-ray solution scattering and a genetic algorithm

We have reconstructed, from experimental similar to 2 nm resolution X-ray solution scattering profiles, the corresponding shapes and sizes of myoglobin, troponin C, spermadhesin PSP-I/PSP-II, chymotrypsinogen A, superoxide dismutase, ovalbumin, tubulin, nitrite reductase, catalase, the structural change of troponin C upon dissociation of the two high affinity Ca2+, and the solution model structure of a tandem pair of fibronectin type III cytoplasmic domains of integrin alpha 6 beta 4 before determination of its crystal structure. To this purpose we have designed a new genetic algorithm which gradually explores a discrete search space and evolves convergent models made of several hundred beads (down to 0.3 nm radius) best fitting the scattering profile upon Debye calculation, without geometrical constraints or penalty for loose beads. This is a procedure of effective numerical transformation of the one-dimensional scattering profiles into three-dimensional model structures. The number of beads in models is correlated with the protein molecular mass (with one exception). The shape and approximate dimensions of each protein have been retrieved by a set of ten solution models, essentially superimposable with the available crystal structures. (C) 2000 Academic Press.