Small-angle scattering: a view on the properties, structures and structural changes of biological macromolecules in solution

A self-contained presentation of the main concepts and methods for interpretation of X-ray and neutron-scattering patterns of biological macromolecules in solution, including a reminder of the basics of X-ray and neutron scattering and a brief overview of relevant aspects of modern instrumentation, is given. For monodisperse solutions the experimental data yield the scattering intensity of the macromolecules, which depends on the contrast between the solvent and the particles as well as on their shape and internal scattering density fluctuations, and the structure factor, which is related to the interactions between macromolecules. After a brief analysis of the information content of the scattering intensity, the two main approaches for modelling the shape and/or structure of macromolecules and the global minimization schemes used in the calculations are presented. The first approach is based, in its more advanced version, on the spherical harmonics approximation and relies on few parameters, whereas the second one uses bead models with thousands of parameters. Extensions of bead modelling can be used to model domain structure and missing parts in high-resolution structures. Methods for computing the scattering patterns from atomic models including the contribution of the hydration shell are discussed and examples are given, which also illustrate that significant differences sometimes exist between crystal and solution structures. These differences are in some cases explainable in terms of rigid-body motions of parts of the structures, Results of two extensive studies - on ribosomes and on the allosteric protein aspartate transcarbamoylase - illustrate the application of the various methods. The unique bridge between equilibrium structures and thermodynamic or kinetic aspects provided by scattering techniques is illustrated by modelling of intermolecular interactions, including crystallization, based on an analysis of the structure factor and recent time-resolved work on assembly and protein folding.