scholarly journals Local and global analysis of macromolecular Atomic Displacement Parameters

2020 ◽  
Author(s):  
Rafiqa C Masmaliyeva ◽  
Kaveh H Babai ◽  
Garib N Murshudov
Keyword(s):  
Gamma Distribution ◽  
Global Analysis ◽  
Atomic Displacement ◽  
B Value ◽  
Local Analysis ◽  
Inverse Gamma Distribution ◽  
Inverse Gamma ◽  
Expectation Maximisation ◽  
Atomic Displacement Parameters ◽  
Global And Local

AbstractThis paper describes the global and local analyses of Atomic Displacement Parameters (ADP) of macromolecules solved and refined using X-ray crystallography method. It is shown that the distribution of ADPs follows the (mixture of) Shifted Inverse Gamma distribution(s). The parameters of the mixture of SIGDs are estimated using Expectation/Maximisation methods. In addition, a method for resolution and individual ADP dependent local analysis of neighbouring atoms has been designed. This method facilitates the detection of the mismodelled atoms and indicates potential identity of heavy metal atoms. It also helps in detecting of disordered and/or wrongly modelled ligands. Both global and local analyses can be used to detect errors in atomic structures thus helping in (re)building, refinement and validation of macromolecular structures. It can also serve as an additional validation tool during data deposition to the PDB.SynopsisMacromolecular atomic B value distributions have been modelled using a mixture of Shifted Inverse Gamma Distribution. Also, B value and resolution dependent local ADP differences have been applied for validation of heavy atoms and ligands.

scholarly journals Local and global analysis of macromolecular atomic displacement parameters

2020 ◽  
Vol 76 (10) ◽  
pp. 926-937
Author(s):  
Rafiga C. Masmaliyeva ◽  
Kave H. Babai ◽  
Garib N. Murshudov
Keyword(s):  
Global Analysis ◽  
Expectation Maximization Algorithm ◽  
Atomic Displacement ◽  
Local Analysis ◽  
X Ray Crystallography ◽  
Inverse Gamma ◽  
Metal Atoms ◽  
Atomic Displacement Parameters ◽  
Global And Local ◽  
Validation Tool

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.

scholarly journals Variance Adaptive Shrinkage (vash): Flexible Empirical Bayes estimation of variances

2016 ◽  
Author(s):  
Mengyin Lu ◽  
Matthew Stephens
Keyword(s):  
Gamma Distribution ◽  
Empirical Bayes ◽  
Variance Estimation ◽  
R Package ◽  
Bayes Estimation ◽  
Inverse Gamma Distribution ◽  
Inverse Gamma ◽  
Tissues Expression ◽  
Flexible Model ◽  
Better Than

AbstractMotivationWe consider the problem of estimating variances on a large number of “similar” units, when there are relatively few observations on each unit. This problem is important in genomics, for example, where it is often desired to estimate variances for thousands of genes (or some other genomic unit) from just a few measurements on each. A common approach to this problem is to use an Empirical Bayes (EB) method that assumes the variances among genes follow an inverse-gamma distribution. Here we describe a more flexible EB method, whose main assumption is that the distribution of the variances (or, as an alternative, the precisions) is unimodal.ResultsWe show that this more flexible assumption provides competitive performance with existing methods when the variances truly come from an inverse-gamma distribution, and can outperform them when the distribution of the variances is more complex. In analyses of several human gene expression datasets from the Genotype Tissues Expression (GTEx) consortium, we find that our more flexible model often fits the data appreciably better than the single inverse gamma distribution. At the same time we find that, for variance estimation, the differences between methods is often small, suggesting that the simpler methods will often suffice in practice.AvailabilityOur methods are implemented in an R package vashr available from http://github.com/mengyin/vashr.

Sign in / Sign up

Export Citation Format

Share Document