EFRESOL: effective resolution of a diffraction data set

Abstract

The resolution of a diffraction data set conveys the details that one expects to distinguish in the Fourier maps calculated with these data. For example, individual atoms in a macromolecular chain cannot be resolved in the maps calculated with 2 Å resolution data sets, while they can be resolved in accurate maps calculated with 1 Å resolution data. However, if a data set is incomplete its high-resolution cutoff becomes less straightforward to interpret. For instance, a Fourier map calculated using a 1 Å resolution data set with many high-resolution reflections missing may rather resemble a map corresponding to 2 Å resolution data. The authors have proposed a method that redefines the traditional notion of data resolution, making it more formal and general. This manuscript presents the corresponding tool, the programEFRESOL. For a data set of an arbitrary completeness, the program calculates its mean, highest and lowest effective resolutions. These values are established through the minimum distance between two point scatterers when their images are still resolved as separate peaks in the Fourier maps calculated with the given data set. Additionally, the program calculates the optical resolution, which is defined as the minimum distance for typical atoms of the structure when they are resolved in a hypothetical synthesis obtained with the given amplitudes and the exact phases if they are known. Both effective and optical resolutions show the `resolving power' of the diffraction data set.

The functional principle of eukaryotic molybdenum insertases

“…The single Cnx1E molybdate anion reported before [20] lies halfway between these newly identified two anions. This discrepancy between the recently published and the current structure is probably due to their different optical resolutions [43] of 2.5 Å and 1.8 Å, respectively, with the low-resolution structure [20] failing to resolve the two molybdate anions. Consistent with this new finding for Cnx1E+Mo, two tungstate anions are also found in the oxo-anion binding pocket of Cnx1E+W (Fig.…”

“… a Effective (d eff ) and corresponding optical (d opt ) resolution of the dataset determined with EFRESOL [43]. b Data completeness for a volume in reciprocal space bounded by an ellipsoid centered on {000} and with the dimensions a= 1/d h00,min , b= 1/d 0k0,min , c= 1/d 00l,min . …”

“… a Effective (d eff ) and corresponding optical (d opt ) resolution of the dataset determined with EFRESOL [43]. …”

The Resolution in X-ray Crystallography and Single-Particle Cryogenic Electron Microscopy

“…In such a form d e f f only accounts for the completeness but not the anisotropy of the data. To overcome this limitation a more complete derivation was suggested [29,33]. In short, d e f f can be defined via comparison of the calculated minimum distance for point scatterers with the theoretical values for the complete dataset [29].…”

Tools for ligand validation inCoot

“…Using the nominal resolution (the R nom presented in the data file) to describe the quality of a data set can be misleading (for example in the case of unusually weak or incomplete data; Weiss, 2001). Measures to address this shortcoming have been published (Urzhumtseva & Urzhumtsev, 2015). Here, a modified value, R eff , was used, taking into account missing data and the standard deviations of the reflection amplitudes (Murshudov, 2016).…”