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1.  Superspace description of wagnerite-group minerals (Mg,Fe,Mn)2(PO4)(F,OH) 
A unified superspace model, based on average triplite structure, for the description of different modulation periodicities of wagnerite and related phases
Reinvestigation of more than 40 samples of minerals belonging to the wagnerite group (Mg, Fe, Mn)2(PO4)(F,OH) from diverse geological environments worldwide, using single-crystal X-ray diffraction analysis, showed that most crystals have incommensurate structures and, as such, are not adequately described with known polytype models (2b), (3b), (5b), (7b) and (9b). Therefore, we present here a unified superspace model for the structural description of periodically and aperiodically modulated wagnerite with the (3+1)-dimensional superspace group C2/c(0β0)s0 based on the average triplite structure with cell parameters a ≃ 12.8, b ≃ 6.4, c ≃ 9.6 Å, β ≃ 117° and the modulation vectors q = β b*. The superspace approach provides a way of simple modelling of the positional and occupational modulation of Mg/Fe and F/OH in wagnerite. This allows direct comparison of crystal properties.
PMCID: PMC3970752  PMID: 24675594
wagnerite; modulated structure; superspace; unified model; triplite
2.  Equivalence of superspace groups 
The standard settings of (3 + d)-dimensional superspace groups are determined for a series of modulated compounds, especially concentrating on d = 2 and 3. The coordinate transformation in superspace is discussed in view of its implications in physical space.
An algorithm is presented which determines the equivalence of two settings of a (3 + d)-dimensional superspace group (d = 1, 2, 3). The algorithm has been implemented as a web tool on , providing the transformation of any user-given superspace group to the standard setting of this superspace group in . It is shown how the standard setting of a superspace group can be directly obtained by an appropriate transformation of the external-space lattice vectors (the basic structure unit cell) and a transformation of the internal-space lattice vectors (new modulation wavevectors are linear combinations of old modulation wavevectors plus a three-dimensional reciprocal-lattice vector). The need for non-standard settings in some cases and the desirability of employing standard settings of superspace groups in other cases are illustrated by an analysis of the symmetries of a series of compounds, comparing published and standard settings and the transformations between them. A compilation is provided of standard settings of compounds with two- and three-dimensional modulations. The problem of settings of superspace groups is discussed for incommensurate composite crystals and for chiral superspace groups.
PMCID: PMC3553647  PMID: 23250064
symmetry; superspace groups; two-dimensionally modulated crystals; three-dimensionally modulated crystals
3.  Topological properties of hydrogen bonds and covalent bonds from charge densities obtained by the maximum entropy method (MEM) 
The maximum-entropy charge densities of six amino acids and peptides reveal systematic dependencies of the properties at bond critical points on bond lengths. MEM densities demonstrate that low-order multipoles (l max = 1) and isotropic atomic displacement parameters for H atoms in the multipole model are insufficient for capturing all the features of charge densities in hydrogen bonds.
Charge densities have been determined by the Maximum Entropy Method (MEM) from the high-resolution, low-temperature (T ≃ 20 K) X-ray diffraction data of six different crystals of amino acids and peptides. A comparison of dynamic deformation densities of the MEM with static and dynamic deformation densities of multipole models shows that the MEM may lead to a better description of the electron density in hydrogen bonds in cases where the multipole model has been restricted to isotropic displacement parameters and low-order multipoles (l max = 1) for the H atoms. Topological properties at bond critical points (BCPs) are found to depend systematically on the bond length, but with different functions for covalent C—C, C—N and C—O bonds, and for hydrogen bonds together with covalent C—H and N—H bonds. Similar dependencies are known for AIM properties derived from static multipole densities. The ratio of potential and kinetic energy densities |V(BCP)|/G(BCP) is successfully used for a classification of hydrogen bonds according to their distance d(H⋯O) between the H atom and the acceptor atom. The classification based on MEM densities coincides with the usual classification of hydrogen bonds as strong, intermediate and weak [Jeffrey (1997) ▶. An Introduction to Hydrogen Bonding. Oxford University Press]. MEM and procrystal densities lead to similar values of the densities at the BCPs of hydrogen bonds, but differences are shown to prevail, such that it is found that only the true charge density, represented by MEM densities, the multipole model or some other method can lead to the correct characterization of chemical bonding. Our results do not confirm suggestions in the literature that the promolecule density might be sufficient for a characterization of hydrogen bonds.
PMCID: PMC2749645  PMID: 19767685
topological properties; hydrogen bonding; maximum entropy method; charge densities; peptides; amino acids
4.  Atomic modeling of cryo-electron microscopy reconstructions – Joint refinement of model and imaging parameters 
Journal of structural biology  2013;182(1):10-21.
When refining the fit of component atomic structures into electron microscopic reconstructions, use of a resolution-dependent atomic density function makes it possible to jointly optimize the atomic model and imaging parameters of the microscope. Atomic density is calculated by one-dimensional Fourier transform of atomic form factors convoluted with a microscope envelope correction and a low-pass filter, allowing refinement of imaging parameters such as resolution, by optimizing the agreement of calculated and experimental maps. A similar approach allows refinement of atomic displacement parameters, providing indications of molecular flexibility even at low resolution. A modest improvement in atomic coordinates is possible following optimization of these additional parameters. Methods have been implemented in a Python program that can be used in stand-alone mode for rigid-group refinement, or embedded in other optimizers for flexible refinement with stereochemical restraints. The approach is demonstrated with refinements of virus and chaperonin structures at resolutions of 9 through 4.5 Å, representing regimes where rigid-group and fully flexible parameterizations are appropriate. Through comparisons to known crystal structures, flexible fitting by RSRef is shown to be an improvement relative to other methods and to generate models with all-atom rms accuracies of 1.5–2.5 Å at resolutions of 4.5–6 Å.
PMCID: PMC3662558  PMID: 23376441
Fitting; Optimization; Structure; Resolution; Restraint; B-factor; Flexibility
5.  REFMAC5 for the refinement of macromolecular crystal structures 
The general principles behind the macromolecular crystal structure refinement program REFMAC5 are described.
This paper describes various components of the macromolecular crystallographic refinement program REFMAC5, which is distributed as part of the CCP4 suite. REFMAC5 utilizes different likelihood functions depending on the diffraction data employed (amplitudes or intensities), the presence of twinning and the availability of SAD/SIRAS experimental diffraction data. To ensure chemical and structural integrity of the refined model, REFMAC5 offers several classes of restraints and choices of model parameterization. Reliable models at resolutions at least as low as 4 Å can be achieved thanks to low-resolution refinement tools such as secondary-structure restraints, restraints to known homologous structures, automatic global and local NCS restraints, ‘jelly-body’ restraints and the use of novel long-range restraints on atomic displacement parameters (ADPs) based on the Kullback–Leibler divergence. REFMAC5 additionally offers TLS parameterization and, when high-resolution data are available, fast refinement of anisotropic ADPs. Refinement in the presence of twinning is performed in a fully automated fashion. REFMAC5 is a flexible and highly optimized refinement package that is ideally suited for refinement across the entire resolution spectrum encountered in macromolecular crystallography.
PMCID: PMC3069751  PMID: 21460454
REFMAC5; refinement
6.  Atomic resolution studies of carbonic anhydrase II 
The structure of human carbonic anhydrase II has been solved with a sulfonamide inhibitor at 0.9 Å resolution. Structural variation and flexibility is seen on the surface of the protein and is consistent with the anisotropic ADPs obtained from refinement. Comparison with 13 other atomic resolution carbonic anhydrase structures shows that surface variation exists even in these highly ordered isomorphous crystals.
Carbonic anhydrase has been well studied structurally and functionally owing to its importance in respiration. A large number of X-ray crystallographic structures of carbonic anhydrase and its inhibitor complexes have been determined, some at atomic resolution. Structure determination of a sulfonamide-containing inhibitor complex has been carried out and the structure was refined at 0.9 Å resolution with anisotropic atomic displacement parameters to an R value of 0.141. The structure is similar to those of other carbonic anhydrase complexes, with the inhibitor providing a fourth nonprotein ligand to the active-site zinc. Comparison of this structure with 13 other atomic resolution (higher than 1.25 Å) isomorphous carbonic anhydrase structures provides a view of the structural similarity and variability in a series of crystal structures. At the center of the protein the structures superpose very well. The metal complexes superpose (with only two exceptions) with standard deviations of 0.01 Å in some zinc–protein and zinc–ligand bond lengths. In contrast, regions of structural variability are found on the protein surface, possibly owing to flexibility and disorder in the individual structures, differences in the chemical and crystalline environments or the different approaches used by different investigators to model weak or complicated electron-density maps. These findings suggest that care must be taken in interpreting structural details on protein surfaces on the basis of individual X-ray structures, even if atomic resolution data are available.
PMCID: PMC2865367  PMID: 20445237
carbonic anhydrase; structure comparison; metalloproteins; atomic resolution
Methodological consequences of population heterogeneity for the sequential logit model in studies of education transitions are now well understood. There are two main mechanisms by which heterogeneity may cause biases to parameter estimates in sequential logit models: outcome incommensurability and population incommensurability. These methodological problems are intrinsic to the substantive research question and thus are not easily remediable with better statistical models. All statistical solutions require extra information in the form of additional data or additional assumptions. In some settings, the researcher may explicitly introduce a form of heterogeneity into the sequential logit model and then evaluate the model. In other settings, the researcher may wish to stay with the conventional sequential logit model and interpret the results descriptively.
PMCID: PMC3203205  PMID: 22043133
8.  To B or not to B: a question of resolution? 
A simple rule of thumb based on resolution is not adequate to identify the best treatment of atomic displacements in macromolecular structural models. The choice to use isotropic B factors, anisotropic B factors, TLS models or some combination of the three should be validated through statistical analysis of the model refinement.
In choosing and refining any crystallographic structural model, there is tension between the desire to extract the most detailed information possible and the necessity to describe no more than what is justified by the observed data. A more complex model is not necessarily a better model. Thus, it is important to validate the choice of parameters as well as validating their refined values. One recurring task is to choose the best model for describing the displacement of each atom about its mean position. At atomic resolution one has the option of devoting six model parameters (a ‘thermal ellipsoid’) to describe the displacement of each atom. At medium resolution one typically devotes at most one model parameter per atom to describe the same thing (a ‘B factor’). At very low resolution one cannot justify the use of even one parameter per atom. Furthermore, this aspect of the structure may be described better by an explicit model of bulk displacements, the most common of which is the translation/libration/screw (TLS) formalism, rather than by assigning some number of para­meters to each atom individually. One can sidestep this choice between atomic displacement parameters and TLS descriptions by including both treatments in the same model, but this is not always statistically justifiable. The choice of which treatment is best for a particular structure refinement at a particular resolution can be guided by general considerations of the ratio of model parameters to the number of observations and by specific statistics such as the Hamilton R-­factor ratio test.
PMCID: PMC3322606  PMID: 22505267
atomic displacements; B factors; TLS models; model parameters
9.  Processing incommensurately modulated protein diffraction data with Eval15 
Data processing of an incommensurately modulated profilin–actin crystal is described.
Recent challenges in biological X-ray crystallography include the processing of modulated diffraction data. A modulated crystal has lost its three-dimensional translational symmetry but retains long-range order that can be restored by refining a periodic modulation function. The presence of a crystal modulation is indicated by an X-ray diffraction pattern with periodic main reflections flanked by off-lattice satellite reflections. While the periodic main reflections can easily be indexed using three reciprocal-lattice vectors a*, b*, c*, the satellite reflections have a non-integral relationship to the main lattice and require a q vector for indexing. While methods for the processing of diffraction intensities from modulated small-molecule crystals are well developed, they have not been applied in protein crystallography. A recipe is presented here for processing incommensurately modulated data from a macromolecular crystal using the Eval program suite. The diffraction data are from an incommensurately modulated crystal of profilin–actin with single-order satellites parallel to b*. The steps taken in this report can be used as a guide for protein crystallographers when encountering crystal modulations. To our knowledge, this is the first report of the processing of data from an incommensurately modulated macromolecular crystal.
PMCID: PMC3121298  PMID: 21697601
modulation; incommensurate; Eval15; profilin–actin
10.  Functional Energetic Landscape in the Allosteric Regulation of Muscle Pyruvate Kinase I. Calorimetric Study 
Biochemistry  2009;48(40):9448-9455.
Rabbit muscle pyruvate kinase (RMPK) is an important allosteric enzyme of the glycolytic pathway catalyzing a transfer of the phosphate from phosphoenolpyruvate (PEP) to ADP. The energetic landscape of the allosteric regulatory mechanism of RMPK was characterized by isothermal titration calorimetry (ITC) in the temperature range from 4°C to 45°C. ITC data for RMPK binding to substrates PEP and ADP, for the allosteric inhibitor Phe, as well as for combination of ADP and Phe were globally analyzed. The thermodynamic parameters characterizing the linked-multiple- equilibria system were extracted. Four novel insights were uncovered 1. The binding preference of ADP for either the T- or R-state is temperature dependent; namely, more favorably to the T- and R-state at high and low temperature, respectively. This cross over of affinity towards R and T-state implies that ADP plays a complex role in modulating the allosteric behavior of RMPK. Depending on the temperature, binding of ADP can regulate RMPK activity by favoring the enzyme to either the R- or T-state. 2. The binding of Phe is negatively coupled to that of ADP i.e. Phe and ADP prefer not to bind to the same subunit of RMPK. 3. The release or absorption of protons linked to the various equilibria is specific to the particular reaction. As a consequence, pH will exert a complex effect on these linked equilibria resulting in proton being an allosteric regulatory ligand of RMPK. 4. The R↔T equilibrium is accompanied by a significant ΔCp rendering RMPK most sensitive to temperature under physiological conditions. During muscle activity, both pH and temperature fluctuations are known to happen; thus, results of this study are physiologically relevant.
PMCID: PMC2759577  PMID: 19719244
Two state model; global analysis; isothermal heat capacity; multiple equilibria; allostery
11.  The Development of a Portable Hard Disk Encryption/Decryption System with a MEMS Coded Lock 
Sensors (Basel, Switzerland)  2009;9(11):9300-9331.
In this paper, a novel portable hard-disk encryption/decryption system with a MEMS coded lock is presented, which can authenticate the user and provide the key for the AES encryption/decryption module. The portable hard-disk encryption/decryption system is composed of the authentication module, the USB portable hard-disk interface card, the ATA protocol command decoder module, the data encryption/decryption module, the cipher key management module, the MEMS coded lock controlling circuit module, the MEMS coded lock and the hard disk. The ATA protocol circuit, the MEMS control circuit and AES encryption/decryption circuit are designed and realized by FPGA(Field Programmable Gate Array). The MEMS coded lock with two couplers and two groups of counter-meshing-gears (CMGs) are fabricated by a LIGA-like process and precision engineering method. The whole prototype was fabricated and tested. The test results show that the user's password could be correctly discriminated by the MEMS coded lock, and the AES encryption module could get the key from the MEMS coded lock. Moreover, the data in the hard-disk could be encrypted or decrypted, and the read-write speed of the dataflow could reach 17 MB/s in Ultra DMA mode.
PMCID: PMC3260643  PMID: 22291566
portable hard disk encryption/decryption system; MEMS coded lock; FPGA
12.  A Transition Path Ensemble Study Reveals a Linchpin Role for Mg2+ during Rate-Limiting ADP Release from Protein Kinase A† 
Biochemistry  2009;48(48):11532-11545.
Protein kinases are key regulators of diverse signaling networks critical for growth and development. Protein kinase A (PKA) is an important kinase prototype that phosphorylates protein targets at Ser and Thr residues by converting ATP to ADP. Mg2+ ions play a crucial role in regulating phosphoryl transfer and can limit overall enzyme turnover by affecting ADP release. However, the mechanism by which Mg2+ participates in ADP release is poorly understood. Here we use a novel transition path ensemble technique, the harmonic Fourier beads method, to explore the atomic and energetic details of the Mg2+-dependent ADP binding and release. Our studies demonstrate that adenine-driven ADP binding to PKA creates three ion-binding sites at the ADP/PKA interface that are absent otherwise. Two of these sites bind the previously characterized Mg2+ ions, whereas the third site binds a monovalent cation with high affinity. This third site can bind the P-3 residue of substrate proteins and may serve as a reporter of the active site occupation. Binding of Mg2+ ions restricts mobility of the Gly-rich loop that closes over the active site. We find that simultaneous release of ADP with Mg2+ ions from the active site is unfeasible. Thus, we conclude that Mg2+ ions act as a linchpin and that at least one ion must be removed prior to pyrophosphate-driven ADP release. The results of the present study enhance understanding of Mg2+-dependent association of nucleotides with protein kinases.
PMCID: PMC2789581  PMID: 19886670
13.  Bardet-Biedl Syndrome-associated Small GTPase ARL6 (BBS3) Functions at or near the Ciliary Gate and Modulates Wnt Signaling* 
The Journal of Biological Chemistry  2010;285(21):16218-16230.
The expansive family of metazoan ADP-ribosylation factor and ADP-ribosylation factor-like small GTPases is known to play essential roles in modulating membrane trafficking and cytoskeletal functions. Here, we present the crystal structure of ARL6, mutations in which cause Bardet-Biedl syndrome (BBS3), and reveal its unique ring-like localization at the distal end of basal bodies, in proximity to the so-called ciliary gate where vesicles carrying ciliary cargo fuse with the membrane. Overproduction of GDP- or GTP-locked variants of ARL6/BBS3 in vivo influences primary cilium length and abundance. ARL6/BBS3 also modulates Wnt signaling, a signal transduction pathway whose association with cilia in vertebrates is just emerging. Importantly, this signaling function is lost in ARL6 variants containing BBS-associated point mutations. By determining the structure of GTP-bound ARL6/BBS3, coupled with functional assays, we provide a mechanistic explanation for such pathogenic alterations, namely altered nucleotide binding. Our findings therefore establish a previously unknown role for ARL6/BBS3 in mammalian ciliary (dis)assembly and Wnt signaling and provide the first structural information for a BBS protein.
PMCID: PMC2871489  PMID: 20207729
Diseases; Protein/Structure; Centriole; Signal Transduction; Subcellular Organelles; ARL6; BBS3; Bardet-Biedl Syndrome; Cilia; Small GTPase
14.  Experimental Electron Density and Neutron Diffraction Studies on the Polymorphs of Sulfathiazole 
Crystal Growth & Design  2014;14(3):1227-1239.
High resolution X-ray diffraction data on forms I–IV of sulfathiazole and neutron diffraction data on forms II–IV have been collected at 100 K and analyzed using the Atoms in Molecules topological approach. The molecular thermal motion as judged by the anisotropic displacement parameters (adp’s) is very similar in all four forms. The adp of the thiazole sulfur atom had the greatest amplitude perpendicular to the five-membered ring, and analysis of the temperature dependence of the adps indicates that this is due to genuine thermal motion rather than a concealed disorder. A minor disorder (∼1–2%) is evident for forms I and II, but a statistical analysis reveals no deleterious effect on the derived multipole populations. The topological analysis reveals an intramolecular S–O···S interaction, which is consistently present in all experimental topologies. Analysis of the gas-phase conformation of the molecule indicates two low-energy theoretical conformers, one of which possesses the same intramolecular S–O···S interaction observed in the experimental studies and the other an S–O···H–N intermolecular interaction. These two interactions appear responsible for “locking” the molecular conformation. The lattice energies of the various polymorphs computed from the experimental multipole populations are highly dependent on the exact refinement model. They are similar in magnitude to theoretically derived lattice energies, but the relatively high estimated errors mean that this method is insufficiently accurate to allow a definitive stability order for the sulfathiazole polymorphs at 0 K to be determined.
High resolution X-ray diffraction data on sulfathiazole (forms I−IV) and neutron diffraction data have been used to analyze the polymorphic electron density using Quantum Theory of Atoms in Molecules. Two low-energy theoretical conformers are found in the gas phase, one of which possesses an S−O···S interaction (a) and the other an S−O···H−N (b) intermolecular interaction. These interactions appear responsible for “locking” the molecular conformation.
PMCID: PMC3963452  PMID: 24672285
15.  Modulating Accidental Fermi Resonance: What a Difference a Neutron Makes 
Vibrational reporters have shown significant promise as sensitive probes of local environments in proteins and nucleic acids. The utility of two potential vibrational probes, the cyanate and azide groups in phenyl cyanate and 3-azidopyridine, respectively, has been hindered by accidental Fermi resonance. Anharmonic coupling, between the fundamental –OCN or –N3 asymmetric stretch vibration with a near resonant combination band, results in an extremely broad and complex absorption profile for each of these probes. A total of eight phenyl cyanate and six 3-azidopyridine isotopomers were synthesized and studied. Isotopic editing effectively modulated the accidental Fermi resonance — the absorption profiles of several isotopomers were greatly simplified while others remained complex. The origins of the observed profiles are discussed. Addition of a single neutron to the middle atom of the oscillator converted the absorption profile to essentially a single band resulting from either the cyanate or azide asymmetric stretch vibration.
PMCID: PMC3137378  PMID: 21769311
Phenyl Cyanate; 3-Azidopyridine; IR spectroscopy; Isotopic editing; Anharmonic Coupling; Vibrational Probes
16.  Estimation of formamide harmonic and anharmonic modes in the Kohn-Sham limit using the polarization consistent basis sets 
Journal of Molecular Modeling  2011;17(9):2265-2274.
Formamide harmonic and anharmonic frequencies of fundamental vibrations in the gas phase and in several solvents were successfully estimated in the B3LYP Kohn-Sham complete basis set limit (KS CBS). CBS results were obtained by extrapolating a power function (two-parameter formula) to the results calculated with polarization-consistent basis sets. Anharmonic corrections using the second order perturbation treatment (PT2) and hybrid B3LYP functional combined with polarization consistent pc-n (n = 0, 1, 2, 3, 4) and several Pople’s basis sets were analyzed for all fundamental formamide vibrational modes in the gas phase and solution. Solvent effects were modeled within a PCM method. The anharmonic frequency of diagnostic amide vibration C = O in the gas phase and the CCl4 solution calculated with the VPT2 method was significantly closer to experimental data than the corresponding harmonic frequency. Both harmonic and anharmonic frequencies of C = O stretching mode decreased linearly with solvent polarity, expressed by relative environment permittivity (ε) ratio (ε − 1)/(2ε + 1). However, an unphysical behavior of solvent dependence of some low frequency anharmonic amide modes of formamide (e.g., CN stretch, NH2 scissoring, and NH2 in plane bend) was observed, probably due to the presence of severe anharmonicity and Fermi resonance.
FigureFormamide harmonic and anharmonic frequencies of fundamental vibrations in the gas phase and in several solvents were successfully estimated in the B3LYP Kohn-Sham complete basis set limit (KS CBS). CBS results were obtained by extrapolating a power function (two-parameter formula) to the results calculated with polarization-consistent basis sets. Anharmonic corrections using the second order perturbation treatment (PT2) and hybrid B3LYP functional combined with polarization consistent pc-n (n = 0, 1, 2, 3, 4) and several Pople’s basis sets were analysed for all fundamental formamide vibrational modes in the gas phase and solution.
Electronic supplementary material
The online version of this article (doi:10.1007/s00894-010-0944-9) contains supplementary material, which is available to authorized users.
PMCID: PMC3168737  PMID: 21267754
Harmonic vibration; Anharmonic vibration; Complete basis set limit; Formamide; Solvent effect
17.  Molecular Mechanism of Allosteric Communication in Hsp70 Revealed by Molecular Dynamics Simulations 
PLoS Computational Biology  2012;8(12):e1002844.
Investigating ligand-regulated allosteric coupling between protein domains is fundamental to understand cell-life regulation. The Hsp70 family of chaperones represents an example of proteins in which ATP binding and hydrolysis at the Nucleotide Binding Domain (NBD) modulate substrate recognition at the Substrate Binding Domain (SBD). Herein, a comparative analysis of an allosteric (Hsp70-DnaK) and a non-allosteric structural homolog (Hsp110-Sse1) of the Hsp70 family is carried out through molecular dynamics simulations, starting from different conformations and ligand-states. Analysis of ligand-dependent modulation of internal fluctuations and local deformation patterns highlights the structural and dynamical changes occurring at residue level upon ATP-ADP exchange, which are connected to the conformational transition between closed and open structures. By identifying the dynamically responsive protein regions and specific cross-domain hydrogen-bonding patterns that differentiate Hsp70 from Hsp110 as a function of the nucleotide, we propose a molecular mechanism for the allosteric signal propagation of the ATP-encoded conformational signal.
Author Summary
Allostery, or the capability of proteins to respond to ligand binding events with a variation in structure or dynamics at a distant site, is a common feature for biomolecular function and regulation in a large number of proteins. Intra-protein connections and inter-residue coordinations underlie allosteric mechanisms and react to binding primarily through a finely tuned modulation of motions and structures at the microscopic scale. Hence, all-atom molecular dynamics simulations are suitable to investigate the molecular basis of allostery. Moreover, understanding intra-protein communication pathways at atomistic resolutions offers unique opportunities in rational drug design. Proteins of the Hsp70 family are allosteric molecular chaperones involved in maintaining cellular protein homeostasis. These proteins are involved in several types of cancer, neurodegenerative diseases, aging and infections and are therefore pharmaceutically relevant targets. In this work we have analyzed, by multiple molecular dynamics simulations, the long-range dynamical and conformational effects of ligands bound to Hsp70, and found relevant differences in comparison to the known non-allosteric structural homolog Hsp110. The resulting model of the mechanism of allosteric propagation offers the opportunity of identifying on-pathway allosteric druggable sites, which we propose could guide rational drug-design efforts targeting Hsp70.
PMCID: PMC3531320  PMID: 23300424
18.  Tetra-n-butyl­ammonium bromide: a redetermination at 150 K addressing the merohedral twinning 
The redetermined, low temperature (150 K), structure of tetra-n-butyl­ammonium bromide, (C4H9)4N+·Br−, has been found to be merohedrally twinned via twin law −1 0 0, 0 − 1 0, 1 0 1. The structure was previously determined, with low precision, no inclusion of H atoms and only the bromide ion refined with anisotropic displacement parameters, by Wang et al. (1995 ▶). Mol. Cryst. Liq. Cryst. Sci. Tech. A, 264, 115–129. The redetermined structure has considerably improved precision in all geometrical parameters, has all non-H atoms refined anisotropically, H atoms included, and is isomorphous with the iodide analogue. The structure is otherwise routine, with the shortest cation to anion contacts being between the bromide anion and the CH atoms close to the ammonium nitro­gen centre at a distance of ca. 2.98–3.11 Å. Each anion makes eight such contacts to four different anions. The n-butyl chains are fully extended, adopting an all-anti conformation with approximate S 4 point symmetry.
PMCID: PMC3201250  PMID: 22058750
19.  Some B eq are more equivalent than others 
B eq is a well defined entity that represents one property, mean-square displacement, of the anisotropic atomic displacement parameter tensor from which it is derived. B eq is not, however, the best estimate of the B factor that would result from isotropic model refinement. A new entity B est is proposed to serve this purpose.
Crystallographic structural models for macromolecules have typically included an isotropic displacement parameter B iso for each atom. In cases where the structural model instead includes anisotropic displacement parameters U ij, the derived quantity B eq can be substituted for B iso for many purposes. B eq is not, however, the best predictor of the value B iso that would hypothetically have been obtained by direct refinement of an isotropic model. A new entity B est is proposed that represents an estimate for B iso that minimizes the Kullback–Leibler divergence from a paired anisotropic model. In general B est/B eq < 1, with the difference between the two values becoming larger for atoms that are more anisotropic. Although this difference does not affect direct refinement of either isotropic or anisotropic models, it is relevant to any analysis that compares isotropic and anisotropic models of the same underlying structure. In particular, it may lead to improved selection of multi-group TLS models based on analysis of an initial isotropic refinement.
PMCID: PMC3211245  PMID: 22011466
macromolecular refinement; TLS; anisotropy
20.  Redetermination of tamarugite, NaAl(SO4)2·6H2O 
The crystal structure of tamarugite [sodium aluminium bis­(sulfate) hexa­hydrate] was redetermined from a single crystal from Mina Alcaparossa, near Cerritos Bayos, southwest of Calama, Chile. In contrast to the previous work [Robinson & Fang (1969 ▶). Am. Mineral. 54, 19–30], all non-H atoms were refined with anisotropic displacement parameters and H-atoms were located by difference Fourier methods and refined from X-ray diffraction data. The structure is built up from nearly regular [Al(H2O)6]3+ octa­hedra and infinite double-stranded chains [Na(SO4)2]3− that extend parallel to [001]. The Na+ cation has a strongly distorted octa­hedral coordination by sulfate O atoms [Na—O = 2.2709 (11) – 2.5117 (12) Å], of which five are furnished by the chain-building sulfate group S2O4 and one by the non-bridging sulfate group S1O4. The [Na(SO4)2]3− chain features an unusual centrosymmetric group formed by two NaO6 octa­hedra and two S2O4 tetra­hedra sharing five adjacent edges, one between two NaO6 octa­hedra and two each between the resulting double octa­hedron and two S2O4 tetra­hedra. These groups are then linked into a double-stranded chain via corner-sharing between NaO6 octa­hedra and S2O4 tetra­hedra. The S1O4 group, attached to Na in the terminal position, completes the chains. The [Al(H2O)6]3+ octa­hedron (〈Al—O〉 = 1.885 (11) Å) donates 12 comparatively strong hydrogen bonds (O⋯O = 2.6665 (14) – 2.7971 (15) Å) to the sulfate O atoms of three neighbouring [Na(SO4)2]3− chains, helping to connect them in three dimensions, but with a prevalence parallel to (010), the cleavage plane of the mineral. Compared with the previous work on tamarugite, the bond precision of Al—O bond lengths as an example improved from 0.024 to 0.001 Å.
PMCID: PMC3790334  PMID: 24098156
21.  Structure of mouse ADP-ribosylhydrolase 3 (mARH3) 
The crystal structure of ADP-ribosylhydrolase 3 from M. musculus has been determined and refined to a resolution of 1.8 Å. A detailed comparison with the human orthologue at the protein-sequence level as well as of the three-dimensional architecture is presented.
ADP-ribosylation is a reversible and covalent post-translational modification in which the attachment of ADP-ribose is catalyzed by ADP-ribosyltransferases and the removal of ADP-ribose is catalyzed by ADP-ribosylhydrolases. ADP-ribosylhydrolase 3 from mouse, consisting of 347 amino-acid residues, has been cloned, purified and crystallized. The three-dimensional structure has been resolved at a resolution of 1.8 Å. The structure constitutes a compact all-α-­helical protein with two Mg2+ ions located in the active-site crevice. A structural comparison of mouse ADP-ribosylhydrolase 3 with its human orthologue shows a high degree of structural similarity. Furthermore, four prokaryotic proteins deposited in the PDB could be identified as being structurally related.
PMCID: PMC2374154  PMID: 18323597
ADP-ribosylhydrolase 3
22.  Crystal Structure, SAXS and Kinetic Mechanism of Hyperthermophilic ADP-Dependent Glucokinase from Thermococcus litoralis Reveal a Conserved Mechanism for Catalysis 
PLoS ONE  2013;8(6):e66687.
ADP-dependent glucokinases represent a unique family of kinases that belong to the ribokinase superfamily, being present mainly in hyperthermophilic archaea. For these enzymes there is no agreement about the magnitude of the structural transitions associated with ligand binding and whether they are meaningful to the function of the enzyme. We used the ADP-dependent glucokinase from Termococcus litoralis as a model to investigate the conformational changes observed in X-ray crystallographic structures upon substrate binding and to compare them with those determined in solution in order to understand their interplay with the glucokinase function. Initial velocity studies indicate that catalysis follows a sequential ordered mechanism that correlates with the structural transitions experienced by the enzyme in solution and in the crystal state. The combined data allowed us to resolve the open-closed conformational transition that accounts for the complete reaction cycle and to identify the corresponding clusters of aminoacids residues responsible for it. These results provide molecular bases for a general mechanism conserved across the ADP-dependent kinase family.
PMCID: PMC3688580  PMID: 23818958
23.  The structural basis of muscle contraction. 
The myosin cross-bridge exists in two conformations, which differ in the orientation of a long lever arm. Since the lever arm undergoes a 60 degree rotation between the two conformations, which would lead to a displacement of the myosin filament of about 11 nm, the transition between these two states has been associated with the elementary 'power stroke' of muscle. Moreover, this rotation is coupled with changes in the active site (CLOSED to OPEN), which probably enable phosphate release. The transition CLOSED to OPEN appears to be brought about by actin binding. However, kinetics shows that the binding of myosin to actin is a two-step process which affects both ATP and ADP affinity and vice versa. The structural basis of these effects is only partially explained by the presently known conformers of myosin. Therefore, additional states of the myosin cross-bridge should exist. Indeed, cryoelectron microscopy has revealed other angles of the lever arm induced by ADP binding to a smooth muscle actin-myosin complex.
PMCID: PMC1692754  PMID: 10836495
24.  Mutation Analysis of PobR and PcaU, Closely Related Transcriptional Activators in Acinetobacter† 
Journal of Bacteriology  1998;180(19):5058-5069.
Acinetobacter PobR and PcaU are transcriptional activators that closely resemble each other in primary structure, DNA-binding sites, metabolic modulators, and physiological function. PobR responds to the inducer-metabolite p-hydroxybenzoate and activates transcription of pobA, the structural gene for the enzyme that converts p-hydroxybenzoate to protocatechuate. This compound, differing from p-hydroxybenzoate only in that it contains an additional oxygen atom, binds to PcaU and thereby specifically activates transcription of the full set of genes for protocatechuate catabolism. Particular experimental attention has been paid to PobR and PcaU from Acinetobacter strain ADP1, which exhibits exceptional competence for natural transformation. This trait allowed selection of mutant strains in which pobR function had been impaired by nucleotide substitutions introduced by PCR replication errors. Contrary to expectation, the spectrum of amino acids whose substitution led to loss of function in PobR shows no marked similarity to the spectrum of amino acids conserved by the demand for continued function during evolutionary divergence of PobR, PcaU, and related proteins. Surface plasmon resonance was used to determine the ability of mutant PobR proteins to bind to DNA in the pobA-pobR intergenic region. Deleterious mutations that strongly affect DNA binding all cluster in and around the PobR region that contains a helix-turn-helix motif, whereas mutations causing defects in the central portion of the PobR primary sequence do not seem to have a significant effect on operator binding. PCR-generated mutations allowing PobR to mimic PcaU function invariably caused a T57A amino acid substitution, making the helix-turn-helix sequence of PobR more like that of PcaU. The mutant PobR depended on p-hydroxybenzoate for its activity, but this dependence could be relieved by any of six amino acid substitutions in the center of the PobR primary sequence. Independent mutations allowing PcaU to mimic PobR activity were shown to be G222V amino acid substitutions in the C terminus of the 274-residue protein. Together, the analyses suggest that PobR and PcaU possess a linear domain structure similar to that of LysR transcriptional activators which largely differ in primary structure.
PMCID: PMC107540  PMID: 9748437
25.  Optimized Structure and Vibrational Properties by Error Affected Potential Energy Surfaces 
The precise theoretical determination of the geometrical parameters of molecules at the minima of their potential energy surface and of the corresponding vibrational properties are of fundamental importance for the interpretation of vibrational spectroscopy experiments. Quantum Monte Carlo techniques are correlated electronic structure methods promising for large molecules, which are intrinsically affected by stochastic errors on both energy and force calculations, making the mentioned calculations more challenging with respect to other more traditional quantum chemistry tools. To circumvent this drawback in the present work, we formulate the general problem of evaluating the molecular equilibrium structures, the harmonic frequencies, and the anharmonic coefficients of an error affected potential energy surface. The proposed approach, based on a multidimensional fitting procedure, is illustrated together with a critical evaluation of systematic and statistical errors. We observe that the use of forces instead of energies in the fitting procedure reduces the statistical uncertainty of the vibrational parameters by 1 order of magnitude. Preliminary results based on variational Monte Carlo calculations on the water molecule demonstrate the possibility to evaluate geometrical parameters and harmonic and anharmonic coefficients at this level of theory with an affordable computational cost and a small stochastic uncertainty (<0.07% for geometries and <0.7% for vibrational properties).
PMCID: PMC3787481  PMID: 24093004

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