A maximum entropy derivation of the integrated direct methods–isomorphous replacement or integrated direct methods–anomalous scattering probability distributions

Abstract

It is shown that taking the appropriate terms from a series expansion of the Shannon-Jaynes entropy of a density map subject to intensity constraints gives the standard direct methods structure factor probability distribution functions. The use of two maps, one to represent a native structure, the other to represent either heavy atoms or the number density of anomalous scatterers, and the application of a similar expansion to the total entropy of both maps rapidly gives either the integrated direct methods-single isomorphous replacement or the integrated direct methods-anomalous scattering probability densities.