Propagation of phase errors during phase refinement and extension

Abstract

A formalism is developed for estimating phase errors during refinement using non-crystallographic symmetry, solvent flattening or density modification. This formalism, based on a separation of all structure factors into known (best estimate) and unknown (random variable) parts, leads directly to simple expressions for the propagation of phase errors during a refinement process. Phase extension and treatment of unmeasured reflections are readily incorporated into this scheme. The formulation provides a direct method for evaluating the success of a refinement process. This may be useful in cases where examination of the resulting electron density map does not provide a quantitative evaluation of the calculations, such as at low to moderate resolution or when phase extension has been used. It may also provide a basis for designing optimal refinement strategies.