Abstract
This paper describes the global and local analysis of atomic displacement parameters (ADPs) of macromolecules in X-ray crystallography. The distribution of ADPs is shown to follow the shifted inverse-gamma distribution or a mixture of these distributions. The mixture parameters are estimated using the expectation-maximization algorithm. In addition, a method for the resolution- and individual ADP-dependent local analysis of neighbouring atoms has been designed. This method facilitates the detection of mismodelled atoms, heavy-metal atoms and disordered and/or incorrectly modelled ligands. Both global and local analyses can be used to detect errors in atomic models, thus helping in the (re)building, refinement and validation of macromolecular structures. This method can also serve as an additional validation tool during PDB deposition.
Highlights
The ever-increasing numbers of macromolecular structures solved by crystallographic and cryoEM methods, and deposited in the PDB (Berman et al, 2000; Lawson et al, 2016), require statistically robust and automatic tools for refinement (Sheldrick, 2008; Adams et al, 2010; Global Phasing, 1997; Murshudov et al, 2011), validation (Read et al, 2011) and deposition (Adams et al, 2019)
We model multimodal atomic displacement parameters (ADPs) distributions as a mixture of SIGDs, which can potentially be used further to identify mismodelled and/or structurally compact regions
Many macromolecular structures in the PDB solved by X-ray crystallography show multimodal distributions of ADPs
Summary
The ever-increasing numbers of macromolecular structures solved by crystallographic and cryoEM methods, and deposited in the PDB (Berman et al, 2000; Lawson et al, 2016), require statistically robust and automatic tools for refinement (Sheldrick, 2008; Adams et al, 2010; Global Phasing, 1997; Murshudov et al, 2011), validation (Read et al, 2011) and deposition (Adams et al, 2019). It can be expected that (i) if atoms are placed in incorrect positions, during refinement their B values will increase dramatically to reflect the absence of the density, as the signal-to-noise ratio in these regions is close or equal to zero, and (ii) if two or more domains/subunits have different intermolecular and/or crystal contacts, they will have different ADPs reflecting their mobility, reducing the signal-to-noise ratio and making the interpretation of such regions very difficult In both cases there will be multiple modes of ADP distribution, and correspondingly the signal-to-noise ratio will be different. This idea is used to calculate the differences between ADPs as well as the potential adjustment of occupancies to make the ADPs of neighbouring atoms similar
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