Abstract
Numerical comparison of crystallographic contour maps is used extensively in structure solution and model refinement, analysis and validation. However, traditional metrics such as the map correlation coefficient (map CC, real-space CC or RSCC) sometimes contradict the results of visual assessment of the corresponding maps. This article explains such apparent contradictions and suggests new metrics and tools to compare crystallographic contour maps. The key to the new methods is rank scaling of the Fourier syntheses. The new metrics are complementary to the usual map CC and can be more helpful in map comparison, in particular when only some of their aspects, such as regions of high density, are of interest.
Highlights
Macromolecular crystallography operates with the electron density distribution in crystals
Fourier series contain only a finite set S of terms and are usually calculated on a three-dimensional regular grid Nx  Ny  Nz with the grid nodes described by integer indices n =, P
The question we focus on is how similar are two masks composed of the same number of grid nodes, i.e. covering the same volume of the unit cell
Summary
F(hkl) exp[i’(hkl)]: crystallographic structure factor with indices hkl. Fcalc = Fcalc exp(i’calc): structure factors calculated from an atomic model. Fmodel = Fmodel exp(i’model): structure factors calculated from an atomic model including modelled contribution from bulk solvent and various scales (Afonine et al, 2013). Complete, incomplete: Fourier syntheses calculated with a complete set of structure factors up to a given high-resolution cutoff or with some reflections excluded from this set; both the resolution value and the method used to exclude reflections are described explicitly for particular tests. N: number of grid nodes with the value below the cutoff level in the Fourier synthesis : (n) < ; is given in the same units as . (; ): quantile rank corresponding to the cutoff level for the Fourier synthesis (n). CCr(a, b): rank correlation coefficient between two grid functions. CC(a, b): peak correlation coefficient between two grid functions; selected peaks correspond to the qpeak quantile rank
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