A program for evaluating the solution scattering from macromolecules with known atomic structure is presented. The program uses multipole expansion for fast calculation of the spherically averaged scattering pattern and takes into account the hydration shell. Given the atomic coordinates (e.g. from the Brookhaven Protein Data Bank) it can either predict the solution scattering curve or fit the experimental scattering curve using only two free parameters, the average displaced solvent volume per atomic group and the contrast of the hydration layer. The program runs on IBM PCs and on the major UNIX platforms. Journal of Applied CrystallographyISSN0021-8898 © 1995

Practical aspects of low‐resolution shape determination in small‐angle scattering studies of biological macromolecules in solution are considered. The shape restoration method using spherical harmonics [Svergun, Volkov, Kozin & Stuhrmann (1996). Acta Cryst. A52, 419–426] is extended to account for deviations from the idealized model and to work directly on raw experimental data sets. An algorithm to restore the structure of homodimeric particles in terms of the shape of the monomer and the separation between the monomers is implemented. Applications of the program to the shape restoration of several proteins, with known and unknown crystal structures, from X‐ray solution‐scattering data are presented.

Solution scattering curves evaluated from the crystal structures of the T and R states of the allosteric enzyme aspartate transcarbamylase from Escherichia coli were compared with the experimental x-ray scattering patterns. Whereas the scattering from the crystal structure of the T state agrees with the experiment, large deviations reflecting a significant difference between the quaternary structures in the crystal and in solution are observed for the R state. The experimental curve of the R state was fitted by rigid body movements of the subunits in the crystal R structure which displace the latter further away from the T structure along the reaction coordinates of the T-->R transition observed in the crystals. Taking the crystal R structure as a-reference, it was found that in solution the distance between the catalytic trimers along the threefold axis is 0.34 nm larger and the trimers are rotated by 11 degrees in opposite directions around the same axis; each of the three regulatory dimers is rotated by 9 degrees around the corresponding twofold axis and displaced by 0.14 nm away from the molecular center along this axis.

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Solution scattering curves evaluated from the crystal structures of the T and R states of the allosteric enzyme aspartate transcarbamylase from Escherichia coli were compared with the experimental x-ray scattering patterns. Whereas the scattering from the crystal structure of the T state agrees with the experiment, large deviations reflecting a significant difference between the quaternary structures in the crystal and in solution are observed for the R state. The experimental curve of the R state was fitted by rigid body movements of the subunits in the crystal R structure which displace the latter further away from the T structure along the reaction coordinates of the T-->R transition observed in the crystals. Taking the crystal R structure as a-reference, it was found that in solution the distance between the catalytic trimers along the threefold axis is 0.34 nm larger and the trimers are rotated by 11 degrees in opposite directions around the same axis; each of the three regulatory dimers is rotated by 9 degrees around the corresponding twofold axis and displaced by 0.14 nm away from the molecular center along this axis.