σ²_R, a reciprocal-space measure of the quality of macromolecular electron-density maps

A reciprocal-space measure of the quality of macromolecular crystallographic phases based on the variance of the local roughness of the map is presented. It has previously been shown that the presence of distinct regions of solvent and protein in macromolecular crystals leads to a high value of the standard deviation of local r.m.s. electron density and that this can in turn be used as a reliable measure of the quality of macromolecular electron-density maps [Terwilliger & Berendzen (1999a ▶). Acta Cryst. D55, 501–505]. Here, it is demonstrated that a similar measure, θ_R², the variance of the local roughness of the electron density, can be calculated in reciprocal space. The formulation is suitable for rapid evaluation of macromolecular crystallographic phases, for phase improvement and for ab initio phasing procedures