Detection of translational noncrystallographic symmetry in Patterson functions.

Iracema Caballero,Airlie J Mccoy,Randy J Read,Massimo D Sammito,Pavel V Afonine,Isabel Usón

doi:10.1107/s2059798320016836

Abstract

Detection of translational noncrystallographic symmetry (TNCS) can be critical for success in crystallographic phasing, particularly when molecular-replacement models are poor or anomalous phasing information is weak. If the correct TNCS is detected then expected intensity factors for each reflection can be refined, so that the maximum-likelihood functions underlying molecular replacement and single-wavelength anomalous dispersion use appropriate structure-factor normalization and variance terms. Here, an analysis of a curated database of protein structures from the Protein Data Bank to investigate how TNCS manifests in the Patterson function is described. These studies informed an algorithm for the detection of TNCS, which includes a method for detecting the number of vectors involved in any commensurate modulation (the TNCS order). The algorithm generates a ranked list of possible TNCS associations in the asymmetric unit for exploration during structure solution.

Highlights

Translational noncrystallographic symmetry (TNCS) arises when the asymmetric unit contains components that are oriented in the same way and can be superimposed by a translation that does not correspond to any symmetry operation in the space group
The modulations of the intensities arise because the contribution to a structure factor of molecules related by translational noncrystallographic symmetry (TNCS) have the same amplitudes but have relative phases determined by the projection of the translation vector on the diffraction vector
The planes affected by intensity modulation are perpendicular to the translation vectors between copies related by TNCS (TNCS vectors)

Summary

Introduction

Translational noncrystallographic symmetry (TNCS) arises when the asymmetric unit contains components that are oriented in (nearly) the same way and can be superimposed by a translation that does not correspond to any symmetry operation in the space group. The modulations of the intensities arise because the contribution to a structure factor of molecules related by TNCS have the same (or similar) amplitudes but have relative phases determined by the projection of the translation vector on the diffraction vector As a result, they interfere constructively for some reflections and destructively for others, so that there is a systematic modulation of the sum of their contributions. For this reason, in addition to the TNCS vector it is necessary to estimate any small rotational differences in their orientations (TNCS rotations) and the size of random coordinate differences (TNCS r.m.s.d.) caused by conformational differences (Read et al, 2013) in order to correctly account for TNCS modulation (Fig. 1)

Methods

Results

Conclusion