Theory of small-angle scattering from particles in solution

Small-angle scattering (SAS) is a very useful method in biochemistry, providing information on molecular masses, shapes and interactions in solution (see Comment G2.1).

Dilute solutions of identical particles

In order to have an observable signal in X-ray or neutron SAS a solution of the order of 100 μl containing a few milligrams per millilitre of macromolecule is required – corresponding to about 1015 particles for a 50 kDa protein at 1 mg ml−1 (we note that 1 mg ml−1, the usual unit in biochemistry is in fact equal to 1 g l−1, the unit more conveniently used in equations).

We first consider solution conditions such that the particles do not influence each other, i.e. the position and orientation of each particle is totally independent of that of the others. This is the infinite dilution condition, for which we say there is no interparticle interference. In practice, it is achieved at different, low, concentrations for different macromolecules and solvents. For example, the condition may well be satisfied for a given protein at a few milligrams per millilitre, in a neutral pH buffer, but tRNA molecules, which are highly charged at pH 7 in low-salt buffer, interact with each other even at these concentrations, and it might not be possible to reach the infinite dilution condition without increasing the solvent salt concentration.