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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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

The harmonic and anharmonic frequencies of fundamental vibrations in formaldehyde and water were successfully estimated using the B3LYP Kohn-Sham limit. The results obtained with polarization- and correlation-consistent basis sets were fitted with a two-parameter formula. Anharmonic corrections were obtained by a second order perturbation treatment (PT2). We compared the performance of the PT2 scheme on the two title molecules using SCF, MP2 and DFT (BLYP, B3LYP, PBE and B3PW91 functionals) methods combined with polarization consistent pc-n (n = 0, 1, 2, 3, 4) basis sets, Dunning’s basis sets (aug)-cc-pVXZ where X = D, T, Q, 5, 6 and Pople’s basis sets up to 6-311++G(3df,2pd). The influence of SCF convergence level and density grid size on the root mean square of harmonic and anharmonic frequency deviations from experimental values was tested. The wavenumber of formaldehyde CH2 anharmonic asymmetric stretching mode is very sensitive to grid size for large basis sets; this effect is not observed for harmonic modes. BLYP-calculated anharmonic frequencies consistently underestimate observed wavenumbers. On the basis of formaldehyde anharmonic frequencies, we show that increasing the Pople basis set size does not always lead to improved agreement between anharmonic frequencies and experimental values.

FigureSensitivity of water B3LYP calculated harmonic and anharmonic vs(OH) frequencies on selected Pople and polarization consistent basis sets size. The results for pc-n basis sets were fitted with two parameter formula and the CBS(2,3,4) estimated

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The online version of this article (doi:10.1007/s00894-010-0913-3) contains supplementary material, which is available to authorized users.

Poly(ADP-ribose) (pADPr) is a polymer assembled from the enzymatic polymerization of the ADP-ribosyl moiety of NAD by poly(ADP-ribose) polymerases (PARPs). The dynamic turnover of pADPr within the cell is essential for a number of cellular processes including progression through the cell cycle, DNA repair and the maintenance of genomic integrity, and apoptosis. In spite of the considerable advances in the knowledge of the physiological conditions modulated by poly(ADP-ribosyl)ation reactions, and notwithstanding the fact that pADPr can play a role of mediator in a wide spectrum of biological processes, few pADPr binding proteins have been identified so far. In this study, refined in silico prediction of pADPr binding proteins and large-scale mass spectrometry-based proteome analysis of pADPr binding proteins were used to establish a comprehensive repertoire of pADPr-associated proteins. Visualization and modeling of these pADPr-associated proteins in networks not only reflect the widespread involvement of poly(ADP-ribosyl)ation in several pathways but also identify protein targets that could shed new light on the regulatory functions of pADPr in normal physiological conditions as well as after exposure to genotoxic stimuli.

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.

Poly(ADP-ribose) polymerase-1 (PARP-1) has been involved in endothelial cell dysfunction associated with various pathophysiological conditions. The intrinsic mechanism of PARP-1-mediated endothelial cell dysfunction could be related to PARP-1 overactivation, NAD+ consumption and ATP depletion. An alternative way could involve transcription regulation. By using high-density microarrays, we examined early tumor necrosis factor α (TNF-α)-stimulated gene expression profiles in PARP-1+/+ and PARP-1–/– murine heart endothelial cells. TNF-α modulated a significant number of genes in both cell types. We have identified a set of genes whose expression in response to TNF-α is modulated by PARP-1, whereas the expression of others is PARP-1-independent. Up-regulation of several genes involved in the inflammatory response is hampered in the absence of PARP-1. Moreover, NF-κB-dependent transcriptional activation is partially inhibited in PARP-1–/– compared to PARP-1+/+ cells. However, we found that PARP-1 might also silence transcription of several NF-κB target genes. Overall, our results show that PARP-1 is regulating the expression of genes by the endothelial cells both in a positive and a negative fashion, with the final effects depending on the gene. Individual studies of these genes are now necessary to clarify the intrinsic mechanism by which PARP-1 is controlling transcription and thereby finding out different therapeutic approaches involving PARP-1.

Summary

We introduce drive-amplitude-modulation atomic force microscopy as a dynamic mode with outstanding performance in all environments from vacuum to liquids. As with frequency modulation, the new mode follows a feedback scheme with two nested loops: The first keeps the cantilever oscillation amplitude constant by regulating the driving force, and the second uses the driving force as the feedback variable for topography. Additionally, a phase-locked loop can be used as a parallel feedback allowing separation of the conservative and nonconservative interactions. We describe the basis of this mode and present some examples of its performance in three different environments. Drive-amplutide modulation is a very stable, intuitive and easy to use mode that is free of the feedback instability associated with the noncontact-to-contact transition that occurs in the frequency-modulation mode.

Accurate anharmonic experimental vibrational frequencies for water clusters consisting of 2-5 water molecules have been predicted based on comparing different methods with MP2/aug-cc-pVTZ calculated and experimental anharmonic frequencies. The combination of using HF/6-31G* scaled frequencies for intramolecular modes and anharmonic frequencies for intermolecular modes gives excellent agreement with experiment for the water dimer and trimer, and are as good as the expensive anharmonic MP2 calculations. The water trimer, the cyclic Ci and S4 tetramers, and the cyclic pentamer all have unique peaks in the infrared spectrum between 500 and 800 cm-1 and between 3400 and 3700 cm-1. Under the right experimental conditions these different clusters can be uniquely identified using high resolution IR spectroscopy.

The impact of image pattern recognition on accessing large databases of medical images has recently been explored, and content-based image retrieval (CBIR) in medical applications (IRMA) is researched. At the present, however, the impact of image retrieval on diagnosis is limited, and practical applications are scarce. One reason is the lack of suitable mechanisms for query refinement, in particular, the ability to (1) restore previous session states, (2) combine individual queries by Boolean operators, and (3) provide continuous-valued query refinement. This paper presents a powerful user interface for CBIR that provides all three mechanisms for extended query refinement. The various mechanisms of man–machine interaction during a retrieval session are grouped into four classes: (1) output modules, (2) parameter modules, (3) transaction modules, and (4) process modules, all of which are controlled by a detailed query logging. The query logging is linked to a relational database. Nested loops for interaction provide a maximum of flexibility within a minimum of complexity, as the entire data flow is still controlled within a single Web page. Our approach is implemented to support various modalities, orientations, and body regions using global features that model gray scale, texture, structure, and global shape characteristics. The resulting extended query refinement has a significant impact for medical CBIR applications.

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.

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.

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.

The standard molar enthalpy of combustion (ΔcHom) and formation (ΔfHom) of quaternary ammonium tetrachlorozincate [n-CnH2n+1N(CH3)3]2ZnCl4 have been determined for the hydrocarbon chain length from even number 8 to 18 of carbon atoms (n) by an oxygen-bomb combustion calorimeter. The results indicated that the values of ΔcHom increased and ΔfHom decreased with increasing chain length and showed a linear dependence on the number of carbon atoms, which were caused by that the order and rigidity of the hydrocarbon chain decreased with increasing the carbon atoms. The linear regression equations are -ΔcHom =1440.50n +3730.67 and -ΔfHom = −85.32n + 1688.22.

The convergence properties of the absolute single-molecule configurational entropy and the correction terms used to estimate it are investigated using microsecond molecular dynamics simulation of a peptide test system and an improved methodology. The results are compared with previous applications for systems of diverse chemical nature. It is shown that (i) the effect of anharmonicity is small, (ii) the effect of pairwise correlation is typically large, and (iii) the latter affects to a larger extent the entropy estimate of thermodynamic states characterized by a higher motional correlation. The causes of such deviations from a quasi-harmonic behavior are explained. This improved approach provides entropies also for molecular systems undergoing conformational transitions and characterized by highly frustrated energy surfaces, thus not limited to systems sampling a single quasi-harmonic basin. Overall, this study emphasizes the need for extensive phase-space sampling in order to obtain a reliable estimation of entropic contributions.

Concentration gradients inside cells are involved in key processes such as cell division and morphogenesis. Here we show that a model of the enzymatic step catalized by phosphofructokinase (PFK), a step which is responsible for the appearance of homogeneous oscillations in the glycolytic pathway, displays Turing patterns with an intrinsic length-scale that is smaller than a typical cell size. All the parameter values are fully consistent with classic experiments on glycolytic oscillations and equal diffusion coefficients are assumed for ATP and ADP. We identify the enzyme concentration and the glycolytic flux as the possible regulators of the pattern. To the best of our knowledge, this is the first closed example of Turing pattern formation in a model of a vital step of the cell metabolism, with a built-in mechanism for changing the diffusion length of the reactants, and with parameter values that are compatible with experiments. Turing patterns inside cells could provide a check-point that combines mechanical and biochemical information to trigger events during the cell division process.