Phasingviapure crystallographic least squares: an unexpected feature

2018 ◽  
Vol 74 (2) ◽  
pp. 123-130
Author(s):  
Maria Cristina Burla ◽  
Benedetta Carrozzini ◽  
Giovanni Luca Cascarano ◽  
Carmelo Giacovazzo ◽  
Giampiero Polidori
Keyword(s):  
Least Squares ◽  
Structure Refinement ◽  
Current Model ◽  
Main Tool ◽  
Solution Procedure ◽  
Medium Size ◽  
Density Map ◽  
Electron Density Map ◽  
First Time ◽  
Least Squares Techniques

Crystallographic least-squares techniques, the main tool for crystal structure refinement of small and medium-size molecules, are for the first time used forab initiophasing. It is shown that the chief obstacle to such use, the least-squares severe convergence limits, may be overcome by a multi-solution procedure able to progressively recognize and discard model atoms in false positions and to include in the current model new atoms sufficiently close to correct positions. The applications show that the least-squares procedure is able to solve many small structures without the use of important ancillary tools:e.g.no electron-density map is calculated as a support for the least-squares procedure.

scholarly journals A revisited version of the apo structure of the ligand-binding domain of the human nuclear receptor retinoic X receptor α

2019 ◽  
Vol 75 (2) ◽  
pp. 98-104 ◽  
Author(s):  
Jérôme Eberhardt ◽  
Alastair G. McEwen ◽  
William Bourguet ◽  
Dino Moras ◽  
Annick Dejaegere
Keyword(s):  
Ligand Binding ◽  
Nuclear Receptors ◽  
Binding Domain ◽  
Ligand Binding Domain ◽  
Biophysical Studies ◽  
Density Map ◽  
Α Helix ◽  
Molecular Mode ◽  
Electron Density Map ◽  
First Time

The retinoic X receptor (RXR) plays a crucial role in the superfamily of nuclear receptors (NRs) by acting as an obligatory partner of several nuclear receptors; its role as a transcription factor is thus critical in many signalling pathways, such as metabolism, cell development, differentiation and cellular death. The first published structure of the apo ligand-binding domain (LBD) of RXRα, which is still used as a reference today, contained inaccuracies. In the present work, these inaccuracies were corrected using modern crystallographic tools. The most important correction concerns the presence of a π-bulge in helix H7, which was originally built as a regular α-helix. The presence of several CHAPS molecules, which are visible for the first time in the electron-density map and which stabilize the H1–H3 loop, which contains helix H2, are also revealed. The apo RXR structure has played an essential role in deciphering the molecular mode of action of NR ligands and is still used in numerous biophysical studies. This refined structure should be used preferentially in the future in interpreting experiments as well as for modelling and structural dynamics studies of the apo RXRα LBD.

Refinement of the trial Structure

2010 ◽  
Author(s):  
Jenny Pickworth Glusker ◽  
Kenneth N. Trueblood
Keyword(s):  
Experimental Data ◽  
Least Squares ◽  
Likelihood Methods ◽  
Fourier Methods ◽  
Maximum Likelihood Methods ◽  
Density Map ◽  
Trial Structure ◽  
Phase Angles ◽  
Electron Density Map ◽  
True Structure

When approximate positions have been determined for most, if not all, of the atoms, it is time to begin the refinement of the structure. In this process the atomic parameters are varied systematically so as to give the best possible agreement of the observed structure factor amplitudes (the experimental data) with those calculated for the proposed trial structure. Common refinement techniques involve Fourier syntheses and processes involving least-squares or maximum likelihood methods. Although they have been shown formally to be nearly equivalent—differing chiefly in the weighting attached to the experimental observations—they differ considerably in manipulative details; we shall discuss them separately here. Many successive refinement cycles are usually needed before a structure converges to the stage at which the shifts from cycle to cycle in the parameters being refined are negligible with respect to their estimated errors. When least-squares refinement is used, the equations are, as pointed out below, nonlinear in the parameters being refined, which means that the shifts calculated for these parameters are only approximate, as long as the structure is significantly different from the “correct” one. With Fourier refinement methods, the adjustments in the parameters are at best only approximate anyway; final parameter adjustments are now almost always made by least squares, at least for structures not involving macromolecules. As indicated earlier (Chapters 8 and 9, especially Figure 9.8 and the accompanying discussion), Fourier methods are commonly used to locate a portion of the structure after some of the atoms have been found—that is, after at least a partial trial structure has been identified. Initially, only one or a few atoms may have been found, or maybe an appreciable fraction of the structure is now known. Once approximate positions for at least some of the atoms in the structure are known, the phase angles can be calculated. Then an approximate electron-density map calculated with observed structure amplitudes and computed phase angles will contain a blend of the true structure (from the structure amplitudes) with the trial structure (from the calculated phases).

Least-Squares Methods and Their Use in Charge Density Analysis

1997 ◽  
Author(s):  
Philip Coppens
Keyword(s):  
Crystal Structure ◽  
Charge Density ◽  
Least Squares ◽  
Structure Refinement ◽  
Error Function ◽  
Crystal Structure Refinement ◽  
Fourier Techniques ◽  
Density Analysis ◽  
Least Squares Techniques

The number of reflection intensities measured in a crystallographic experiment is large, and commonly exceeds the number of parameters to be determined. It was first realized by Hughes (1941) that such an overdetermination is ideally suited for the application of the least-squares methods of Gauss (see, e.g., Whittaker and Robinson 1967), in which an error function S, defined as the sum of the squares of discrepancies between observation and calculation, is minimized by adjustment of the parameters of the observational equations. As least-squares methods are computationally convenient, they have largely replaced Fourier techniques in crystal structure refinement. In addition to the positional and thermal parameters of the atoms, least-squares procedures are used to determine the scale of the data, and parameters such as mosaic spread or particle size, which influence the intensities through multiple-beam effects (Becker and Coppens 1974a, b, 1975). It is not an exaggeration to say that modern crystallography is, to a large extent, made possible by the use of least-squares methods. Similarly, least-squares techniques play a central role in the charge density analysis with the scattering formalisms described in the previous chapter. The following description follows closely the treatment given by Hamilton (1964).

scholarly journals Dispersal and colonization risk of the Walnut Twig Beetle, Pityophthorus juglandis, in southern Europe

2021 ◽  
Author(s):  
Matteo Marchioro ◽  
Massimo Faccoli
Keyword(s):  
Spatiotemporal Data ◽  
Medium Size ◽  
Dispersal Capacity ◽  
Factors Affecting ◽  
Geosmithia Morbida ◽  
Ne Italy ◽  
Pityophthorus Juglandis ◽  
Southwestern Usa ◽  
Walnut Twig Beetle ◽  
First Time

AbstractThe Walnut Twig Beetle (WTB), Pityophthorus juglandis Blackman, is a small bark beetle native to Mexico and Southwestern USA recorded for the first time in Europe (NE Italy) in 2013. WTB attacks walnut (Juglans spp.) and wingnut trees (Pterocarya spp.) and is the vector of Geosmithia morbida Kolarík et al., a pathogen causing the thousand cankers disease (TCD). WTB and TCD represent a serious threat for walnut orchards in Europe. Spatiotemporal data of the WTB-TCD infestations recorded from an 8-year-long (2013–2020) monitoring conducted in 106 walnut orchards of NE Italy were used to develop a model in order to analyze: (i) the effective dispersal capacity of WTB, (ii) the factors affecting dispersal and (iii) the colonization risk of healthy walnut orchards. We registered a mean annual dispersal of 9.4 km, with peaks of about 40 km. Pest dispersal is affected by distance of suitable hosts from the nearest infested site, number of walnut orchards in the surroundings (both infested and healthy), orchard size and walnut species in the orchard. Using the model, it was also possible to calculate the colonization risk of a specific walnut orchard according to its characteristics showing, for instance, that a medium-size (5,000 trees) black walnut orchard located at 25 km from the nearest infested orchard has an infestation risk of about 50% of probability.

The iron content of iron superoxide dismutase: determination by anomalous scattering

1983 ◽  
Vol 218 (1210) ◽  
pp. 119-126 ◽  
Keyword(s):  
Superoxide Dismutase ◽  
Iron Content ◽  
Three Dimensional ◽  
Anomalous Scattering ◽  
Total Iron Content ◽  
Iron Site ◽  
Iron Superoxide Dismutase ◽  
Density Map ◽  
The Difference ◽  
Electron Density Map

The number of iron atoms in the dimeric iron-containing superoxide dismutase from Pseudomonas ovalis and their atomic positions have been determined directly from anomalous scattering measurements on crystals of the native enzyme. To resolve the long-standing question of the total amount of iron per molecule for this class of dismutase, the occupancy of each site was refined against the measured Bijvoet differences. The enzyme is a symmetrical dimer with one iron site in each subunit. The iron position is 9 ņ from the intersubunit interface. The total iron content of the dimer is 1.2±0.2 moles per mole of protein. This is divided between the subunits in the ratio 0.65:0.55; the difference between them is probably not significant. Since each subunit contains, on average, slightly more than half an iron atom we conclude that the normal state of this enzyme is two iron atoms per dimer but that some of the metal is lost during purification of the protein. Although the crystals are obviously a mixture of holo- and apo-enzymes, the 2.9 Å electron density map is uniformly clean, even at the iron site. We conclude that the three-dimensional structures of the iron-bound enzyme and the apoenzyme are identical.

scholarly journals The physics of galaxy evolution with SPICA observations

2019 ◽  
Vol 15 (S359) ◽  
pp. 72-77
Author(s):  
Luigi Spinoglio ◽  
Juan A. Fernández-Ontiveros ◽  
Sabrina Mordini
Keyword(s):  
Galaxy Evolution ◽  
Cosmic Time ◽  
Medium Size ◽  
3 Dimensional ◽  
Cosmic Vision ◽  
Infrared Telescope ◽  
Black Hole Accretion ◽  
Esa Cosmic Vision ◽  
Cluster Cores ◽  
First Time

AbstractThe evolution of galaxies at Cosmic Noon (1 < z < 3) passed through a dust-obscured phase, during which most stars formed and black holes in galactic nuclei started to shine, which cannot be seen in the optical and UV, but it needs rest frame mid-to-far IR spectroscopy to be unveiled. At these frequencies, dust extinction is minimal and a variety of atomic and molecular transitions, tracing most astrophysical domains, occur. The Space Infrared telescope for Cosmology and Astrophysics (SPICA), currently under evaluation for the 5th Medium Size ESA Cosmic Vision Mission, fully redesigned with its 2.5-m mirror cooled down to T < 8K will perform such observations. SPICA will provide for the first time a 3-dimensional spectroscopic view of the hidden side of star formation and black hole accretion in all environments, from voids to cluster cores over 90% of cosmic time. Here we outline what SPICA will do in galaxy evolution studies.

scholarly journals A complicated quasicrystal approximant ∊16 predicted by the strong-reflections approach

2010 ◽  
Vol 66 (1) ◽  
pp. 17-26 ◽  
Author(s):  
Mingrun Li ◽  
Junliang Sun ◽  
Peter Oleynikov ◽  
Sven Hovmöller ◽  
Xiaodong Zou ◽  
...  
Keyword(s):  
Electron Diffraction ◽  
Unit Cell ◽  
Space Groups ◽  
Inverse Fourier Transformation ◽  
Transmission Electron ◽  
Structure Factors ◽  
Precession Electron Diffraction ◽  
Density Map ◽  
Electron Density Map ◽  
Good Agreement

The structure of a complicated quasicrystal approximant ∊16 was predicted from a known and related quasicrystal approximant ∊6 by the strong-reflections approach. Electron-diffraction studies show that in reciprocal space, the positions of the strongest reflections and their intensity distributions are similar for both approximants. By applying the strong-reflections approach, the structure factors of ∊16 were deduced from those of the known ∊6 structure. Owing to the different space groups of the two structures, a shift of the phase origin had to be applied in order to obtain the phases of ∊16. An electron-density map of ∊16 was calculated by inverse Fourier transformation of the structure factors of the 256 strongest reflections. Similar to that of ∊6, the predicted structure of ∊16 contains eight layers in each unit cell, stacked along the b axis. Along the b axis, ∊16 is built by banana-shaped tiles and pentagonal tiles; this structure is confirmed by high-resolution transmission electron microscopy (HRTEM). The simulated precession electron-diffraction (PED) patterns from the structure model are in good agreement with the experimental ones. ∊16 with 153 unique atoms in the unit cell is the most complicated approximant structure ever solved or predicted.

Sign in / Sign up

Export Citation Format

Share Document