Nanosecond structural dynamics of intrinsically disordered ß-casein micelles by neutron spectroscopy.

ß-casein undergoes a reversible endothermic self-association, forming protein micelles of limited size. In its functional state, a single ß-casein monomer is unfolded, which creates a high structural flexibility, which is supposed to play a major role in preventing the precipitation of calcium phosphate particles. We characterize the structural flexibility in terms of nanosecond molecular motions, depending on the temperature by quasielastic neutron scattering. Our major questions are: Does the self-association reduce the chain flexibility? How does the dynamic spectrum of disordered caseins differ from a compactly globular protein? How does the dynamic spectrum of ß-casein in solution differ from that of a protein in hydrated powder states? We report on two relaxation processes on a nanosecond and a sub-nanosecond timescale for ß-casein in solution. Both processes are analyzed by Brownian oscillator model, by which the spring constant can be defined in the isotropic parabolic potential. The slower process, which is analyzed by neutron spin echo, seems a characteristic feature of the unfolded structure. It requires bulk solvent and is not seen in hydrated protein powders. The faster process, which is analyzed by neutron backscattering, has a smaller amplitude and requires hydration water, which is also observed with folded proteins in the hydrated state. The self-association had no significant influence on internal relaxation, and thus, a ß-casein protein monomer flexibility is preserved in the micelle. We derive spring constants of the faster and slower motions of ß-caseins in solution and compared them with those of some proteins in various states (folded or hydrated powder).

Quasielastic neutron scattering studies on couplings of protein and water dynamics in hydrated elastin.

Performing quasielastic neutron scattering measurements and analyzing both elastic and quasielasic contributions, we study protein and water dynamics of hydrated elastin. At low temperatures, hydration-independent methyl group rotation dominates the findings. It is characterized by a Gaussian distribution of activation energies centered at about Em = 0.17 eV. At ∼195 K, coupled protein-water motion sets in. The hydration water shows diffusive motion, which is described by a Gaussian distribution of activation energies with Em = 0.57 eV. This Arrhenius behavior of water diffusion is consistent with previous results for water reorientation, but at variance with a fragile-to-strong crossover at ∼225 K. The hydration-related elastin backbone motion is localized and can be attributed to the cage rattling motion. We speculate that its onset at ∼195 K is related to a secondary glass transition, which occurs when a ß relaxation of the protein has a correlation time of τß âˆ¼ 100 s. Moreover, we show that its temperature-dependent amplitude has a crossover at the regular glass transition Tg = 320 K of hydrated elastin, where the α relaxation of the protein obeys τα ∼ 100 s. By contrast, we do not observe a protein dynamical transition when water dynamics enters the experimental time window at ∼240 K.

Dynamics of water confined in mesoporous magnesium carbonate.

We have measured the dynamics of water confined in a porous magnesium carbonate material, Upsalite®, using the high-resolution neutron backscattering spectrometer SPHERES. We found quasielastic scattering that does not flatten out up to 360 K, which means that the dynamics of water are much slower than in other matrix materials. Specifically, a single Lorentzian line could be fitted to the quasielastic part of the acquired spectra between 220 and 360 K. This, accompanied by an elastic line from dynamically frozen water present at all experimental temperatures, even above the melting point, signaled a significant amount of bound or slow water.

A polymer surfactant corona dynamically replaces water in solvent-free protein liquids and ensures macromolecular flexibility and activity.

The observation of biological activity in solvent-free protein-polymer surfactant hybrids challenges the view of aqueous and nonaqueous solvents being unique promoters of protein dynamics linked to function. Here, we combine elastic incoherent neutron scattering and specific deuterium labeling to separately study protein and polymer motions in solvent-free hybrids. Myoglobin motions within the hybrid are found to closely resemble those of a hydrated protein, and motions of the polymer surfactant coating are similar to those of the hydration water, leading to the conclusion that the polymer surfactant coating plasticizes protein structures in a way similar to hydration water.

Numerically stable form factor of any polygon and polyhedron.

Coordinate-free expressions for the form factors of arbitrary polygons and polyhedra are derived using the divergence theorem and Stokes's theorem. Apparent singularities, all removable, are discussed in detail. Cancellation near the singularities causes a loss of precision that can be avoided by using series expansions. An important application domain is small-angle scattering by nanocrystals.

Multiple Bragg reflection by a thick mosaic crystal. Corrigendum.

An inconsistent approximation in Wuttke [Acta Cryst. (2014), A70, 429-440] is corrected. Section 3.5 on the polar angle random walk is withdrawn.

Multiple Bragg reflection by a thick mosaic crystal. II. Simplified transport equation solved on a grid.

The generalized Darwin-Hamilton equations [Wuttke (2014). Acta Cryst. A70, 429-440] describe multiple Bragg reflection from a thick, ideally imperfect crystal. These equations are simplified by making full use of energy conservation, and it is demonstrated that the conventional two-ray Darwin-Hamilton equations are obtained as a first-order approximation. Then an efficient numeric solution method is presented, based on a transfer matrix for discretized directional distribution functions and on spectral collocation in the depth coordinate. Example solutions illustrate the orientational spread of multiply reflected rays and the distortion of rocking curves, especially if the detector only covers a finite solid angle.

BornAgain: software for simulating and fitting grazing-incidence small-angle scattering.

BornAgain is a free and open-source multi-platform software framework for simulating and fitting X-ray and neutron reflectometry, off-specular scattering, and grazing-incidence small-angle scattering (GISAS). This paper concentrates on GISAS. Support for reflectometry and off-specular scattering has been added more recently, is still under intense development and will be described in a later publication. BornAgain supports neutron polarization and magnetic scattering. Users can define sample and instrument models through Python scripting. A large subset of the functionality is also available through a graphical user interface. This paper describes the software in terms of the realized non-functional and functional requirements. The web site https://www.bornagainproject.org/ provides further documentation.

Hyperfine interaction in cobalt by high-resolution neutron spectroscopy.

We have investigated the ferromagnetic phase transition of elemental Co by high-resolution neutron backscattering spectroscopy. We monitored the splitting of the nuclear levels by the hyperfine field at the Co nucleus. The energy of this hyperfine splitting is identified as the order parameter of the ferromagnetic phase transition. By measuring the temperature dependence of the energy we determined the critical exponent [Formula: see text] and the ferromagnetic Curie temperature of [Formula: see text] K. The present result of the critical exponent agrees better with the predicted value (0.367) of the three-dimensional Heisenberg model than that determined previously by nuclear magnetic resonance.

Substrate Locking Promotes Dimer-Dimer Docking of an Enzyme Antibiotic Target.

Protein dynamics manifested through structural flexibility play a central role in the function of biological molecules. Here we explore the substrate-mediated change in protein flexibility of an antibiotic target enzyme, Clostridium botulinum dihydrodipicolinate synthase. We demonstrate that the substrate, pyruvate, stabilizes the more active dimer-of-dimers or tetrameric form. Surprisingly, there is little difference between the crystal structures of apo and substrate-bound enzyme, suggesting protein dynamics may be important. Neutron and small-angle X-ray scattering experiments were used to probe substrate-induced dynamics on the sub-second timescale, but no significant changes were observed. We therefore developed a simple technique, coined protein dynamics-mass spectrometry (ProD-MS), which enables measurement of time-dependent alkylation of cysteine residues. ProD-MS together with X-ray crystallography and analytical ultracentrifugation analyses indicates that pyruvate locks the conformation of the dimer that promotes docking to the more active tetrameric form, offering insight into ligand-mediated stabilization of multimeric enzymes.

Crossover from localized to diffusive water dynamics in carbon nanohorns: A comprehensive quasielastic neutron-scattering analysis.

Incoherent neutron scattering by water confined in carbon nanohorns was measured with the backscattering spectrometer SPHERES and analyzed in exemplary breadth and depth. Quasielastic spectra admit δ-plus-Kohlrausch fits over a wide q and T range. From the q and T dependence of fitted amplitudes and relaxation times, however, it becomes clear that the fits do not represent a uniform physical process, but that there is a crossover from localized motion at low T to diffusive α relaxation at high T. The crossover temperature of about 210 to 230 K increases with decreasing wave number, which is incompatible with a thermodynamic strong-fragile transition. Extrapolated diffusion coefficients D(T) indicate that water motion is at room temperature about 2.5 times slower than in the bulk; in the supercooled state this factor becomes smaller. At even higher temperatures, where the α spectrum is essentially flat, a few percentages of the total scattering go into a Lorentzian with a width of about 1.6µeV, probably due to functional groups on the surface of the nanohorns.

Translational diffusion of hydration water correlates with functional motions in folded and intrinsically disordered proteins.

Hydration water is the natural matrix of biological macromolecules and is essential for their activity in cells. The coupling between water and protein dynamics has been intensively studied, yet it remains controversial. Here we combine protein perdeuteration, neutron scattering and molecular dynamics simulations to explore the nature of hydration water motions at temperatures between 200 and 300 K, across the so-called protein dynamical transition, in the intrinsically disordered human protein tau and the globular maltose binding protein. Quasi-elastic broadening is fitted with a model of translating, rotating and immobile water molecules. In both experiment and simulation, the translational component markedly increases at the protein dynamical transition (around 240 K), regardless of whether the protein is intrinsically disordered or folded. Thus, we generalize the notion that the translational diffusion of water molecules on a protein surface promotes the large-amplitude motions of proteins that are required for their biological activity.

The NeXus data format.

NeXus is an effort by an international group of scientists to define a common data exchange and archival format for neutron, X-ray and muon experiments. NeXus is built on top of the scientific data format HDF5 and adds domain-specific rules for organizing data within HDF5 files, in addition to a dictionary of well defined domain-specific field names. The NeXus data format has two purposes. First, it defines a format that can serve as a container for all relevant data associated with a beamline. This is a very important use case. Second, it defines standards in the form of application definitions for the exchange of data between applications. NeXus provides structures for raw experimental data as well as for processed data.

Brillouin-scattering study of propylene carbonate: an evaluation of phenomenological and mode coupling analyses.

Brillouin-scattering spectra of the molecular glass-forming material propylene carbonate (PC) in the temperature range 140 K to 350 K were analyzed using both the phenomenological Cole-Davidson memory function and a hybrid memory function consisting of the Cole-Davidson function plus a power-law term representing the critical decay part of the fast beta relaxation. The spectra were also analyzed using the extended two-correlator schematic mode-coupling theory (MCT) model recently employed by Götze and Voigtmann to analyze depolarized light backscattering, dielectric, and neutron-scattering spectra of PC [Phys. Rev. E 61, 4133 (2000)]. We assess the ability of the phenomenological and MCT fits, each with three free fitting parameters, to simultaneously describe the spectra and give reasonable values for the alpha-relaxation time tau(alpha).

Multiple Bragg reflection by a thick mosaic crystal.

Symmetric Bragg-case reflections from a thick, ideally imperfect, crystal slab are studied mostly by analytical means. The scattering transfer function of a thin mosaic layer is derived and brought into a form that allows for analytical approximations or easy quadrature. The Darwin-Hamilton equations are generalized, lifting the restriction of wavevectors to a two-dimensional scattering plane. A multireflection expansion shows that wavevector diffusion can be studied independently of the real-space coordinate. Combining analytical arguments and Monte Carlo simulations, multiple Bragg reflections are found to result in a minor correction of the reflected intensity, a moderate broadening of the reflected azimuth angle distribution, a considerable modification of the polar angle distribution, and a noticeable shift and distortion of rocking curves.

Simulation-guided optimization of small-angle analyzer geometry in the neutron backscattering spectrometer SPHERES.

The resolution of neutron backscattering spectrometers deteriorates at small scattering angles where analyzers deviate from exact backscattering. By reducing the azimuth angle range of the analyzers, the resolution can be improved with little loss of peak intensity. Measurements at the spectrometer SPHERES are in excellent agreement with simulations, which proves the dominance of geometric effects.

Comment on "Elastic incoherent neutron scattering operating by varying instrumental energy resolution: Principle, simulations, and experiments of the resolution elastic neutron scattering (RENS)" [Rev. Sci. Instrum. 82, 105115 (2011)].

In a recent contribution to this journal, Magazù, Migliardo, and Benedetto suggest to determine relaxation times from inflection points in the elastic neutron scattering intensity as function of (1) resolution time or (2) temperature. Method (1) can be generalized into a scaling law. Method (2) is only approximately valid; its application to protein data does not back a wavenumber-independent dynamic transition.

SPHERES, Jülich's high-flux neutron backscattering spectrometer at FRM II.

SPHERES is a third-generation neutron backscattering spectrometer, located at the 20 MW German neutron source FRM II and operated by the Jülich Centre for Neutron Science. It offers an energy resolution (fwhm) better than 0.65 µeV, a dynamic range of ± 31 µeV, and a signal-to-noise ratio of up to 1750:1.

Hydrogen release from sodium alanate observed by time-resolved neutron backscattering.

Innermolecular motion in Na(3)AlH(6) gives rise to a Lorentzian spectrum with a wavenumber-independent width of about 1  µeV at 180 °C, which is probably due to the rotation of AlH(6) tetrahedra. There is no such quasielastic line in NaAlH(4) or NaH. Based on this finding, time-resolved measurements on the neutron backscattering spectrometer SPHERES were used to monitor the decomposition kinetics of sodium alanate, [Formula: see text] NaH. Both reaction steps were found to be accelerated by autocatalysis, most likely at the surfaces of Na(3)AlH(6) and NaH crystallites.