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Using graphlet degree vectors to predict atomic displacement parameters in protein structures

ACTA CRYSTALLOGRAPHICA SECTION D-STRUCTURAL BIOLOGY 2023年第12期79卷 1109-1119页

作者： Praznikar, Jure Univ Primorska Fac Math Nat Sci & Informat Technol Glagoljaska 8 Koper Slovenia Inst Jozef Stefan Dept Biochem Mol & Struct Biol Jamova 39 Ljubljana Slovenia

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.

关键词： atomic displacement parameters graphlet degree vectors interatomic contacts macromolecules

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Local and global analysis of macromolecular atomic displacement parameters

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ACTA CRYSTALLOGRAPHICA SECTION D-STRUCTURAL BIOLOGY 2020年第10期76卷 926-937页

作者： Masmaliyeva, Rafiga C. Babai, Kave H. Murshudov, Garib N. Inst Mol Biol & Biotechnol ANAS Baku Azerbaijan RISK Sci Prod Co Baku Azerbaijan MRC Lab Mol Biol Struct Studies Francis Crick Ave Cambridge CB2 0QH England

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.

关键词： refinement validation atomic displacement parameters inverse-gamma mixture model Bayesian statistics ToBvalid

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DebyeFit: a simple tool to obtain an appropriate model of atomic vibrations in solids from atomic displacement parameters obtained at different temperatures

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JOURNAL OF APPLIED CRYSTALLOGRAPHY 2019年第3期52卷 690-692页

作者： Dudka, A. P. Bolotina, N. B. Khrykina, O. N. Russian Acad Sci Fed Sci Res Ctr Crystallog & Photon Shubnikov Inst Crystallog 59 Leninskii Prospekt Moscow 119333 Russia Russian Acad Sci Prokhorov Gen Phys Inst Vavilova 38 Moscow 119991 Russia

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.

关键词： multi-temperature structure analysis atomic displacement parameters Debye and Einstein models temperature-dependent and static atomic displacement parameters

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Optimizing Thermoelectric Properties through Compositional Engineering in Ag-Deficient AgSbTe2 Synthesized by Arc Melting

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ACS APPLIED ELECTRONIC MATERIALS 2024年第5期6卷 2969-2977页

作者： Prado-Gonjal, Jesus Garcia-Calvo, Elena Gainza, Javier Dura, Oscar J. Dejoie, Catherine Nemes, Norbert M. Martinez, Jose Luis Alonso, Jose Antonio Serrano-Sanchez, Federico Univ Complutense Madrid Dept Quim Inorgan E-28040 Madrid Spain CSIC Inst Ciencia Mat Madrid E-28049 Madrid Spain Univ Castilla La Mancha Dept Fis Aplicada E-13071 Ciudad Real Spain European Synchrotron Radiat Facil ESRF F-38000 Grenoble France Univ Complutense Madrid Dept Fis Mat GFMC E-28040 Madrid Spain

Thermoelectric materials offer a promising avenue for energy management, directly converting heat into electrical energy. Among them, AgSbTe(2 )has gained significant attention and continues to be a subject of research at further improving its thermoelectric performance and expanding its practical applications. This study focuses on Ag-deficient Ag(0.7)Sb(1.12)Te(2)and Ag0.7Sb1.12Te1.95Se0.05 materials, examining the impact of compositional engineering within the AgSbTe2 thermoelectric system. These materials have been rapidly synthesized using an arc-melting technique, resulting in the production of dense nanostructured pellets. Detailed analysis through scanning electron microscopy (SEM) reveals the presence of a layered nanostructure, which significantly influences the thermoelectric properties of these materials. Synchrotron X-ray diffraction reveals significant changes in the lattice parameters and atomic displacement parameters (ADPs) that suggest a weakening of bond order in the structure. The thermoelectric characterization highlights the enhanced power factor of Ag-deficient materials that, combined with the low glass-like thermal conductivity, results in a significant improvement in the figure of merit, achieving zT values of 1.25 in Ag(0.7)Sb(1.12)Te(2 )and 1.01 in Ag0.7Sb1.12Te1.95Se0.05 at 750 K.

关键词： thermoelectrics AgSbTe2 arc-melting vacancy compositional engineering synchrotronX-ray diffraction atomic displacement parameters thermoelectric properties

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Algorithms and programs for the shell decomposition of oscillating functions in space

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JOURNAL OF APPLIED CRYSTALLOGRAPHY 2023年第1期56卷 302-311页

作者： Urzhumtseva, Ludmila Lunin, Vladimir Urzhumtsev, Alexandre IBMC Inst Mol & Cellular Biol UPR 9002 CNRS Architecture & Reactivite ARN 15 Rue R Descartes F-67084 Strasbourg France Univ Strasbourg F-67000 Strasbourg France Russian Acad Sci Keldysh Inst Appl Math Inst Math Problems Biol RAS Pushchino 142290 Russia CNRS INSERM UdS Inst Genet & Biol Mol & Cellulaire Ctr Integrat Biol BP 101421 Rue Laurent Fries F-67404 Illkirch Graffenstaden France Univ Lorraine Fac Sci & Technol BP 239 F-54506 Vandoeuvre Les Nancy France

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.

关键词： real-space refinement Fourier ripples oscillating functions shell decomposition Omega function limited-resolution atomic images atomic displacement parameters

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Temperature-dependent crystal structure investigation of 4f hybridized thermoelectric clathrate Ba8-xCexAuySi46-y

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ACTA CRYSTALLOGRAPHICA SECTION B-STRUCTURAL SCIENCE CRYSTAL ENGINEERING AND MATERIALS 2022年第3-1期78卷 359-+页

作者： Sandemann, Jonas Reardon, Hazel Iversen, Bo Brummerstedt Aarhus Univ Ctr Integrated Mat Res Dept Chem DK-8000 Aarhus Denmark Aarhus Univ iNANO DK-8000 Aarhus Denmark

Thermoelectric materials allow for conversion of waste heat into electrical energy, and they represent a green solution for improving our energy efficiency. Inclusion of 4f electrons near the Fermi level may boost the Seebeck coefficient, which is essential for high thermoelectric performance. In this study, Ce was successfully substituted for Ba on the guest atom sites in the type-I clathrate Ba8-xCexAuySi46-y and the material was characterized using high-resolution synchrotron powder X-ray diffraction data measured from 100 K to 1000 K to investigate potential structural implications of the inclusion of a 4f element. The thermal expansion and bonding of the host structure are not affected by the presence of Ce, as seen from the linear coefficient of unit-cell thermal expansion of 7.30 (8) x 10(-6) K-1 and the average host Debye temperature of 404 (7) K determined from the multi-temperature atomic displacement parameters, both of which are similar to values obtained for pure Ba8AuySi46-y. The anisotropic atomic displacement parameters on the guest atom site in the large clathrate cage populated by Ba surprisingly reveals isotropic behavior, which is different from all other clathrates reported in literature, and thus represents a unique host-guest bonding situation.

关键词： thermoelectrics synchrotron powder diffraction atomic displacement parameters Debye and Einstein temperatures clathrates

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Direct calculation of cryo-EM and crystallographic model maps for real-space refinement

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ACTA CRYSTALLOGRAPHICA SECTION D-STRUCTURAL BIOLOGY 2022年第12期78卷 1451-1468页

作者： Urzhumtsev, Alexandre G. Urzhumtseva, Ludmila M. Lunin, Vladimir Y. UdS Inst Genet & Biol Mol & Cellulaire Ctr Integrat Biol CNRSINSERM 1 Rue Laurent FriesBP 10142 F-67404 Illkirch Graffenstaden France Univ Lorraine Fac Sci & Technol BP 239 F-54506 Vandoeuvre Les Nancy France IBMC Inst Mol & Cellular Biol CNRS Architecture & Reactivite ARN UPR 9002 15 Rue R Descartes F-67084 Strasbourg France Univ Strasbourg F-67000 Strasbourg France RAS Keldysh Inst Appl Math Inst Math Problems Biol Pushchino 142290 Russia

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

关键词： real-space refinement map calculation atomic images Fourier ripples truncation distances resolution atomic displacement parameters shell decomposition interference functions

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Uri Shmueli (1928-2023)

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Acta crystallographica. Section A, Foundations and advances 2023年第4期79卷 387-389页

作者： Brock, Carolyn P. Department of Chemistry University of Kentucky Lexington Kentucky 40506-0055 United States

Obituary for Uri Shmueli.

关键词： atomic displacement parameters crystal packing International Tables for Crystallography structure-factor statistics thermal motion

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Structural instability and poorly defined phase transitions in rare-earth dodecaborides RB12 (R=Ho-Lu) at intermediate temperatures

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SOLID STATE SCIENCES 2020年 107卷 106273-106273页

作者： Khrykina, O. N. Dudka, A. P. Bolotina, N. B. Sluchanko, N. E. Shitsevalova, N. Yu Russian Acad Sci Shubnikov Inst Crystallog Fed Sci Res Ctr Crystallog & Photon Moscow 119333 Russia Russian Acad Sci Prokhorov Gen Phys Inst 38 Vavilov Str Moscow 119991 Russia Moscow Inst Phys & Technol 9 Inst Skiy Lane Dolgoprudnyi 141700 Russia Natl Acad Sci Ukraine Frantsevich Inst Problems Mat Sci 3 Krzhyzhanovsky Str UA-03142 Kiev Ukraine

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 T-c T-c indicate phase transformations revealed from diffraction data. The lattice instability and the rearrangement of the phonon spectrum near T-c 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.

关键词： Rare-earth dodecaborides Multi-temperature X-ray diffraction data Lattice distortions atomic displacement parameters Debye & Einstein models Structure Properties

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Error estimates in atom coordinates and B factors in macromolecular crystallography

CURRENT RESEARCH IN STRUCTURAL BIOLOGY

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CURRENT RESEARCH IN STRUCTURAL BIOLOGY 2023年 6卷 100111页

作者： Helliwell, John R. Univ Manchester Dept Chem Manchester M13 9PL England

The overall diffraction precision index (DPI) of a biological macromolecule crystal structure was first described by Cruickshank in 1999. This topical review proceeds from this point and describes the subsequent elaboration of the index to individual atom coordinates. Additional developments were introduced by the availability of a webserver, which provides a transformed PDB entry with individual atom coordinate errors derived from applying the DPI method using the parameters provided by the authors and then subsequently added to the PDB file. This webserver has been extensively used and harnessed in describing non-covalent distance error estimates as well as assessing the significance, or otherwise, of atom movements in a variety of studies. The standard uncertainties on a biological macromolecule's atomic displacement parameters (the 'B factors') has been an entirely different challenge but is obviously important since the crystallographic community has developed the habit of quoting B factors to a false precision in papers. This can convey a false certainty in the dynamics of a structure. A method involving parallelisation of workflows for diffraction image data processing does however offer estimates of the precision of B factors.

关键词： Coordinates atomic displacement parameters B factors Precision estimates

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