DebyeFit is a simple tool to calculate the Debye or Einstein characteristic temperature of thermal vibrations in crystals from the equivalent atomic displacement parameters (ADPs) of any atom ...obtained at several temperatures. The ADP values are separated into static and dynamic components to get a best fit to the Debye, Einstein or mixed model. The static term is added to account for possible static disorder. A nonlinear least‐squares technique is used to refine the parameters of the model for sets of ADPs observed in multi‐temperature structural studies. The program provides a good fit between theoretical and observed ADP values.
DebyeFit is a computer program that calculates the Debye/Einstein characteristic temperature of atomic vibrations in solids using equivalent atomic displacement parameters (ADPs) determined at several temperatures. An optimal fit is achieved if ADPs are modeled with both static and dynamic components.
Radiation damage impedes macromolecular diffraction experiments. Alongside the well known effects of global radiation damage, site‐specific radiation damage affects data quality and the veracity of ...biological conclusions on protein mechanism and function. Site‐specific radiation damage follows a relatively predetermined pattern, in that different structural motifs are affected at different dose regimes: in metal‐free proteins, disulfide bonds tend to break first followed by the decarboxylation of aspartic and glutamic acids. Even within these damage motifs the decay does not progress uniformly at equal rates. Within the same protein, radiation‐induced electron density decay of a particular chemical group is faster than for the same group elsewhere in the protein: an effect known as preferential specific damage. Here, BDamage, a new atomic metric, is defined and validated to recognize protein regions susceptible to specific damage and to quantify the damage at these sites. By applying BDamage to a large set of known protein structures in a statistical survey, correlations between the rates of damage and various physicochemical parameters were identified. Results indicate that specific radiation damage is independent of secondary protein structure. Different disulfide bond groups (spiral, hook, and staple) show dissimilar radiation damage susceptibility. There is a consistent positive correlation between specific damage and solvent accessibility.
Uri Shmueli (1928–2023) Brock, Carolyn P.
Acta crystallographica. Section A, Foundations and advances,
July 2023, 2023-Jul-01, 2023-07-01, 20230701, Volume:
79, Issue:
4
Journal Article
Peer reviewed
Open access
Obituary for Uri Shmueli.
Obituary for Uri Shmueli.
In structural biology, atomic displacement parameters, commonly used in the form of B values, describe uncertainties in atomic positions. Their distribution over the structure can provide hints on ...local structural reliability and mobility. A spatial macromolecular model can be represented by a graph whose nodes are atoms and whose edges correspond to all interatomic contacts within a certain distance. Small connected subgraphs, called graphlets, provide information about the wiring of a particular atom. The multiple linear regression approach based on this information aims to predict a distribution of values of isotropic atomic displacement parameters (B values) within a protein structure, given the atomic coordinates and molecular packing. By modeling the dynamic component of atomic uncertainties, this method allows the B values obtained from experimental crystallographic or cryo‐electron microscopy studies to be reproduced relatively well.
The components of the graphlet degree vector, which describes the complexity of the wiring of a given atom, can be used in a multiple linear regression model to predict atomic displacement parameters in protein structures.
This work addresses the problem of the calculation of limited‐resolution maps from an atomic model in cryo‐electron microscopy and in X‐ray and neutron crystallography, including cases where the ...resolution varies from one molecular region to another. Such maps are necessary in real‐space refinement for comparison with the experimental maps. For an appropriate numeric comparison, the calculated maps should reproduce not only the structural features contained in the experimental maps but also the principal map distortions. These model maps can be obtained with no use of Fourier transforms but, similar to density distributions, as a sum of individual atomic contributions. Such contributions, referred to as atomic density images, are atomic densities morphed to reflect distortions of the experimental map, in particular the loss of resolution. They are described by functions composed of a central peak surrounded by Fourier ripples. For practical calculations, atomic images should be cut at some distance. It is shown that to reach a reasonable accuracy such a distance should be significantly larger than the distance customarily applied when calculating density distributions. This is a consequence of the slow rate with which the amplitude of the Fourier ripples decreases. Such a large distance means that at least a few ripples should be included in calculations in order to obtain a map that is sufficiently accurate. Oscillating functions describing these atomic contributions depend, for a given atomic type, on the resolution and on the atomic displacement parameter values. To express both the central peak and the Fourier ripples of the atomic images, these functions are represented by the sums of especially designed terms, each concentrated in a spherical shell and depending analytically on the atomic parameters. In this work, the strength of the dependence of the accuracy of resulting map on the accuracy of the atomic displacement parameters and on the truncation distance, i.e. the number of ripples included in atomic density images, is analyzed. This analysis is completed by practical aspects of the calculation of maps of inhomogeneous resolution. Tests show that the calculation of limited‐resolution maps from an atomic model as a sum of atomic contributions requires a large truncation radius extending beyond the central peak of an atomic image and the first Fourier ripples. The article discusses the practical details of such calculations expressing atomic contributions as analytic functions of the atomic coordinates, the atomic displacement parameters and the local resolution.
A new method is suggested for the calculation of maps of limited and eventually inhomogeneous resolution as an analytic function of all atomic parameters, including local resolution. Practical details of map calculation are discussed.
Real‐space refinement of atomic models in macromolecular crystallography and cryo‐electron microscopy fits a model to a map obtained with experimental data. To do so, the atomic model is converted ...into a map of limited resolution and then this map is compared quantitatively with the experimental one. For an appropriate comparison, the atomic contributions comprising the model map should reflect the resolution of the experimental map and the atomic displacement parameter (ADP) values. Such contributions are spherically symmetric oscillating functions, different for chemically different kinds of atoms, different ADPs and different resolution values, and their derivatives with respect to atomic parameters rule the model refinement. For given parameter values, every contribution may be calculated numerically using two Fourier transforms, which is highly time consuming and makes calculation of the respective derivatives problematic. Alternatively, for an atom of each required type its contribution can be expressed in an analytical form as a sum of specially designed terms. Each term is different from zero essentially inside a spherical shell, and changing the ADP value does not change its form but rather changes the value of one of its arguments. In general, these terms become a convenient tool for the decomposition of oscillating spherically symmetric functions. This work describes the algorithms and respective software, named dec3D, to carry out such a shell decomposition for density contributions of different kinds of atoms and ions.
Algorithms and software have been developed to decompose spherically symmetric oscillating functions in space into a sum of specially designed shell functions. Such decomposition allows the analytical expression of a resolution‐limited atomic image as a function of the atomic coordinates, isotropic disorder parameter and local resolution associated with the atom.
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.
Macromolecular atomic B‐value distributions have been modelled using a mixture of shifted inverse‐gamma distributions. B‐value and resolution‐dependent local ADP differences have also been applied for the validation of heavy atoms and ligands.
The crystal structure of type I clathrate Ba8Al16Ge30 prepared by arc melting in argon atmosphere has been studied by using a neutron powder diffractometer from 10 to 900 K. We found that the site ...preferences in the host structure were relevant to the guest atom features, which agrees with a previous report. Data were analyzed using two models for the Ba atom position in the larger cage (Ba2): an on-center 6d-site model and an off-center 24k-site one. The Maximum Entropy Method (MEM) results agree well with the 24k model and the shape of the nuclear density distribution of Ba2 atom evolves with increasing temperature.
The single-crystal structures of YbB12, TmB12, and LuB12 were studied in the temperature range of 88–293 K, those of HoB12 and ErB12 – in the range of 88–500 K using high-resolution X-ray diffraction ...data in order to correlate the structure changes with the changes in the physical properties of the dodecaborides under study. The lattice deformations caused by the cooperative Jahn – Teller effect were studied. A method is proposed for approximating the temperature dependences of atomic displacement parameters (ADPs) from lattice sites using the extended Debye or Einstein models. The break points in the temperature dependences of ADPs in combination with nonmonotonic changes in the lattice parameters near the critical temperatures Tc indicate phase transformations revealed from diffraction data. The lattice instability and the rearrangement of the phonon spectrum near Tc are accompanied by the observed changes in the physical characteristics. A sensitive structural diagnostic tool was created to detect implicit phase transitions, quantum critical points and quantum instabilities of various nature that lead to the appearance of anomalies in the physical properties of crystals.
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•The crystal lattices of the studied dodecaborides are slightly distorted by the Jahn-Teller effect.•The temperature dependences of the atomic displacement parameters (ADPs) from the lattice sites are approximated by the extended Debye or Einstein models.•A sensitive structural diagnostics tool is created to detect ‘hidden’ phase transitions associated with nonmonotonic changes in the physical properties of crystals.
Radiation damage remains one of the major limitations to accurate structure determination in protein crystallography (PX). Despite the use of cryo‐cooling techniques, it is highly probable that a ...number of the structures deposited in the Protein Data Bank (PDB) have suffered substantial radiation damage as a result of the high flux densities of third generation synchrotron X‐ray sources. Whereas the effects of global damage upon diffraction pattern reflection intensities are readily detectable, traditionally the (earlier onset) site‐specific structural changes induced by radiation damage have proven difficult to identify within individual PX structures. More recently, however, development of the BDamage metric has helped to address this problem. BDamage is a quantitative, per‐atom metric identifies potential sites of specific damage by comparing the atomic B‐factor values of atoms that occupy a similar local packing density environment in the structure. Building upon this past work, this article presents a program, RABDAM, to calculate the BDamage metric for all selected atoms within any standard‐format PDB or mmCIF file. RABDAM provides several useful outputs to assess the extent of damage suffered by an input PX structure. This free and open‐source software will allow assessment and improvement of the quality of PX structures both previously and newly deposited in the PDB.
A program to measure the extent of specific radiation damage suffered by an individual protein crystal structure, suitable for running on any standard‐format PDB or mmCIF file, is presented.
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