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  • 1
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 55 (1999), S. 464-468 
    ISSN: 1399-0047
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Real-space targets and molecular-dynamics search protocols have been combined to improve the convergence of macromolecular atomic refinement. This was accomplished by providing a local real-space target function for the molecular-dynamics program X-PLOR. With poor isomorphous replacement experimental phases, molecular dynamics does not improve real-space refinement. However, with high-quality anomalous diffraction phases convergence is improved at the start of refinement, and torsion-angle real-space molecular dynamics performs better than other available least-squares or maximum-likelihood methods in real or reciprocal space. It is shown that the improvements result from an optimization method that can escape local minima and from a reduction of overfitting through the implicit use of phases and through use of a local refinement in which errors in remote parts of the structure cannot be mutually compensating.
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  • 2
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 56 (2000), S. 1316-1323 
    ISSN: 1399-0047
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Until modelling is complete, macromolecular structures are refined in the absence of a model for some of the atoms in the crystal. Techniques for defining positional probability distributions of atoms, and using them to model the missing part of a macromolecular crystal structure and the bulk solvent, are described. The starting information may consist of either a tentative structural model for the missing atoms or an electron-density map. During structure completion and refinement, the use of probability distributions enables the retention of low-resolution phase information while avoiding premature commitment to uncertain higher resolution features. Homographic exponential modelling is proposed as a flexible, compact and robust parametrization that proves to be superior to a traditional Fourier expansion in approximating a model protein envelope. The homographic exponential model also has potential applications to ab initio phasing of Fourier amplitudes associated with macromolecular envelopes.
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  • 3
    ISSN: 1399-0047
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Native data, anomalous data at three wavelengths and an independent peak-wavelength data set for SeMet-substituted protein have been collected from cryoprotected crystals of the TrpRS–adenylate product (TAM) complex to a resolution limit of 1.7 Å. Independent phase sets were developed using SHARP and improved by solvent flipping with SOLOMON using molecular envelopes derived from experimental densities for, respectively, peak-wavelength SAD data from four different crystals, MAD data and their M(S)IRAS combinations with native data. Hendrickson–Lattman phase-probability coefficients from each phase set were used in BUSTER to drive maximum-likelihood refinements of well defined parts of the previously refined room-temperature 2.9 Å structure. Maximum-entropy completion followed by manual rebuilding was then used to generate a model for the missing segments, bound ligand and solvent molecules. Surprisingly, peak-wavelength SAD experiments produced the smallest phase errors relative to the refined structures. Selenomethionylated models deviate from one another by 0.25 Å and from the native model by 0.38 Å, but all have r.m.s. deviations of ∼1.0 Å from the 2.9 Å model. Difference Fourier calculations between amplitudes from the 300 K experiment and the new amplitudes at 100 K using 1.7 Å model phases show no significant structural changes arising from temperature variation or addition of cryoprotectant. The main differences between low- and high-resolution structures arise from correcting side-chain rotamers in the core of the protein as well as on the surface. These changes improve various structure-validation criteria.
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  • 4
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 54 (1998), S. 391-399 
    ISSN: 1399-0047
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Several real-space indices and temperature factors are compared with respect to their correlation with atomic positional error and their ability to indicate atoms and residues with the worst of subtle errors. The best index, rED, is a correlation coefficient between model and map electron densities, similar to one proposed earlier, but incorporating two improvements. Firstly, resolution is accounted for explicitly by calculating the model electron density by Fourier transformation of resolution-truncated scattering factors. Secondly, the deviation between model and map electron densities is assigned to neighboring atoms according to their contribution to the electron density of each grid point. With maps of various qualities, rED is the single index with best correlation to atomic error with grouped or individual atoms, and it is the most reliable indicator of poor residues. With poorer omit maps, imprecision of individual atoms is best diagnosed by a combination of low rED or high B factor. With the improved methods, 60–70% of the least precise atoms can detected in a fully refined structure. Similarly, 40–80% of the least precise atoms of an unrefined model can be detected by comparison with an isomorphous replacement map. This is useful in assessing and improving the quality of a model, but not sufficient to confidently validate all atoms of a structure at sub-atomic resolution.
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  • 5
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 55 (1999), S. 219-224 
    ISSN: 1399-0047
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Improvements in free R cross-validation are based on changed scaling procedures and the use, in map calculation, of estimates of the validation amplitudes which are independent of the actual observed values. The deleterious effects of the omitted test data are mitigated by reduction of the test-set size, which is made possible by constraining test and working sets to share the same scaling coefficients, thereby reducing the degrees of freedom and the dependence of free R on data selection. Further improvements come with use of a modified free R factor, R^{\rm free}_{T_{A}}. Instead of omitting the validation reflections from map calculation, their amplitudes are replaced by the average of resolution peers that is (nearly) independent of the actual cross-validation amplitudes. The improvements are relevant to model building, phase refinement by density modification and especially to real-space refinement. Although for real data at about 3 Å resolution, free R factors of about 0.25 are affected little, the precision of the structure is improved by about 0.1 Å. Tests with simulated data show that with good agreement between observed and calculated amplitudes (as in very high resolution studies or simulated refinement tests), free R factors can be improved by factors greater than two.
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  • 6
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 55 (1999), S. 835-845 
    ISSN: 1399-0047
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Arginine kinase (AK), a homologue of creatine kinase, catalyses the reversible transfer of a phosphoryl group between a guanidino phosphate and ADP. The family of phosphagen kinases eluded structure determination for over 25 years until an inactive form creatine kinase (CK) structure was determined [Fritz-Wolf et al. (1996). Nature (London), 381, 341–345]. The structure determination of the active-form transition-state complex was non-trivial, owing to the distant relatedness and domain reorientation of AK compared with CK. Phases from a molecular-replacement solution of the large domain, supplemented by single isomorphous replacement and inter-crystal averaging, did not reveal interpretable electron density for the small domain. Reciprocal-space refinement of the initial model (Rfree = 0.54) by any of the commonly used methods, including post facto application of maximum-likelihood methods, led to overfitting without significant improvement of the partial initial model. By contrast, in the local real-space refinements which proved successful, the interdependence of atoms is limited to immediate neighbors, and atomic positions are not influenced by errors or omissions in remote parts of the structure. Modest improvement was possible without overfitting, and this was critical to the calculation of improved phases. Phases were refined and extended from 4.0 to 2.5 Å resolution by Fourier inversion of omit maps, combination with isomorphous replacement phases and averaging between crystal forms, after several batches of real- and reciprocal-space atomic refinement. The final structure refinement, against a 1.86 Å cryo data set yielded a high-quality model with R = 0.196 and Rfree = 0.224.
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  • 7
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 34 (2001), S. 480-483 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: Planarity and similarity restraints are described using a unified framework for the computation layout. In both cases, the gradient and Hessian of the restraint residual with respect to atomic coordinates are derived. All computed quantities (residual, gradient, Hessian, normal and distance to the plane for planarity restraints, rotation and translation in the case of similarity) can be obtained directly, without iterative procedure.
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  • 8
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 56 (2000), S. 1003-1010 
    ISSN: 1600-5740
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: In the compound [C6H6O2]3C60, hydroquinone (C6H6O2) forms a three-dimensional hydrogen-bonded network enclosing roughly spherical cages with point symmetry \overline 3m and a diameter of 13.2 Å at 100 K. Although C60 fits tightly into these cages, it shows threefold orientational disorder, the molecular site symmetry being 2/m. The disorder has been studied with single-crystal Mo Kα X-ray data at four temperatures, 100, 200, 293 and 373 K. In the refinement, C60 was restrained to the icosahedral molecular symmetry m\overline {35} and to rigid-body translational and librational displacements including third- and fourth-order cumulants to account for curvilinear atomic movements, R(|F|) = 3.2–4.7%. At 100 K, bond lengths in C60 refine to the expected values 1.450 (1) and 1.388 (1) Å. The ratio of these values increases with increasing temperature, but the radius of the molecule remains constant at 3.537 (2) Å. The r.m.s. libration amplitudes of C60 are relatively small (5.5° at 373 K) and the probability function of orientations of C60 inside the cage shows large values only at the refined positions, indicating that the energy barrier of reorientation is large. Refinement of an ordered twinned structure was unsuccessful; the orientations of neighboring C60 appear to be uncorrelated.
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  • 9
    ISSN: 1573-3904
    Keywords: Electrostatic interactions ; Iberiotoxin ; K+ channel blockers ; Leiurotoxin ; Peptide-receptor interaction ; Scorpion toxins
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Summary Ca2+-activated K+ channels consist of a large family of membrane proteins, among which two groups have been characterized by electrophysiological criteria, the small conductance (SK) and the large conductance (BK) Ca2+-activated K+ channels. Scorpion toxins that block K+ channels exhibit a common three-dimensional structure constituted of a short α-helix connected by disulfide bonds to a β-sheet. The leiurotoxin I (LTX1) related toxins interact specifically with the SK channel via basic residues of their α-helix, while the charybdotoxin (ChTX) family recognizes the BK channel with basic residues of their β-sheet. In an attempt to better understand the structure-activity relationships of these toxins and the characteristics of the electrostatic interactions with the receptor site, we investigated the electrostatic potential supported by natural toxins and a synthetic analogue to find out if it may help in understanding the molecular mechanisms involved in this peptide-protein interaction.
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  • 10
    ISSN: 1573-3904
    Keywords: Electrostatic interactions ; Iberiotoxin ; K+channel blockers ; Leiurotoxin ; Peptide-receptor interaction ; Scorpion toxins
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Ca2+-activated K+ channels consist of alarge family of membrane proteins, among which twogroups have been characterized by electrophysiologicalcriteria, the small conductance (SK) and the largeconductance (BK) Ca2+-activated K+channels. Scorpion toxins that block K+ channelsexhibit a common three-dimensional structureconstituted of a short α-helix connected bydisulfide bonds to a β-sheet. The leiurotoxin I(LTX1) related toxins interact specifically with theSK channel via basic residues of their α-helix,while the charybdotoxin (ChTX) family recognizes theBK channel with basic residues of their β-sheet.In an attempt to better understand thestructure–activity relationships of these toxins andthe characteristics of the electrostatic interactionswith the receptor site, we investigated theelectrostatic potential supported by natural toxinsand a synthetic analogue to find out if it may help inunderstanding the molecular mechanisms involved inthis peptide–protein interaction.
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