Approximate expression for the dynamic structure factor in the Lieb-Liniger model

Recently, Imambekov and Glazman [Phys. Rev. Lett. 100, 206805 (2008)] showed that the dynamic structure factor (DSF) of the 1D Bose gas demonstrates power-law behaviour along the limiting dispersion curve of the collective modes and calculated the corresponding exponents exactly. Combining these recent results with a previously obtained strong-coupling expansion we present an interpolation formula for the DSF of the 1D Bose gas. The obtained expression is further consistent with exact low energy exponents from Luttinger liquid theory and shows nice agreement with recent numerical results.Comment: 4 pages, 3 figure

Rapid self-assembly of α-synuclein observed by in situ atomic force microscopy

Self-assembly of α−synuclein resulting in protein aggregates of diverse morphology has been implicated in the pathogenesis of Parkinson’s disease and other neurodegenerative disorders known as synucleinopathies. Apart from its biomedical relevance, this aggregation process is representative of the interconversion of an unfolded protein into nanostructures with typical amyloid features. We have used in situ tapping mode atomic force microscopy (AFM) to continuously monitor the self-assembly of wild-type α-synuclein, its disease-related mutants A30P and A53T, and the C-terminally truncated variant α-synuclein(1-108). Different aggregation modes were observed depending on experimental conditions, i.e. pH, protein concentration, polyamine concentration, temperature and the supporting substrate. At pH 7.5, in the absence of the biogenic polyamines spermidine or spermine, elongated sheets 1.1(±0.2)nm in height and presumably representing individual β-sheet structures, were formed on mica substrates within a few minutes. Their orientation was directed by the crystalline substructure of the substrate. In contrast, sheet formation was not observed with hydrophobic highly oriented pyrolytic graphite (HOPG) substrates, suggesting that negatively charged surfaces promote α-synuclein self-assembly. In the presence of spermidine or spermine 5.9(±1.0) nm high spheroidal structures were preferentially formed, sharing characteristics with similar structures previously reported for several amyloidogenic proteins and linked to neurotoxicity. Alpha-synuclein spheroid formation depended critically on polyamine binding to the Cterminus, revealing a promoting effect of the C-terminus on α-synuclein assembly in the bound state. In rare cases, fibril growth from spheroids or preformed aggregates was observed. At pH 5.0, fibrils were formed initially and incorporated into amorphous aggregates in the course of the aggregation process, providing evidence for the potential of amyloid fibril surfaces to act as nucleation sites in amorphous aggregation. This study provides a direct insight into different modes of α-synuclein self-assembly and identifies key factors modulating the aggregation process

Large magneto-thermal effect and the spin-phonon coupling in a parent insulating cuprate Pr_{1.3}La_{0.7}CuO_4

The magnetic-field (H) dependence of the thermal conductivity \kappa of Pr_{1.3}La_{0.7}CuO_4 is found to show a pronounced minimum for in-plane fields at low temperature, which is best attributed to the scattering of phonons by free spins that are seen by a Schottky-type specific heat and a Curie-Weiss susceptibility. Besides pointing to a strong spin-phonon coupling in cuprates, the present result demonstrates that the H-dependence of the phonon heat transport should not be naively neglected when discussing the \kappa(H) behavior of cuprates, since the Schottky anomaly is ubiquitously found in cuprates at any doping.Comment: 6 pages, 4 figures, accepted for publication in Phys. Rev.

Dependence of α-synuclein aggregate morphology on solution conditions

α-Synuclein is the major component of Lewy bodies and Lewy neurites, which are granular and filamentous protein inclusions that are the defining pathological features of several neurodegenerative conditions such as Parkinson's disease. Fibrillar aggregates formed from α-synuclein in vitro resemble brain-derived material, but the role of such aggregates in the etiology of Parkinson's disease and their relation to the toxic molecular species remain unclear. In this study, we investigated the effects of pH and salt concentration on the in vitro assembly of human wild-type α-synuclein, particularly with regard to aggregation rate and aggregate morphology. Aggregates formed at pH 7.0 and pH 6.0 in the absence of NaCl and MgCl, were fibrillar; the pH 6.0 fibrils displayed a helical twist, as clearly evident by scanning force and electron microscopy. Incubations at pH 7.0 remained transparent during the process of aggregation and exhibited strong thioflavin-T and weak 8-anilino-1-naphthalene-sulfonate (ANS) binding; furthermore, they were efficient in seeding fibrillization of fresh solutions. In contrast, incubating α-synuclein at low pH (pH 4.0 or pH 5.0) resulted in the rapid formation of turbid suspensions characterized by strong ANS binding, reduced thioflavin-T binding and reduced seeding efficiency. At pH 4.0, fibril formation was abrogated; instead, very large aggregates (dimensions similar to100 mum) of amorphous appearance were visible by light microscopy. As with acidic conditions, addition of 0.2 M NaCl or 10 mM MgCl, to pH 7.0 incubations led to a shorter aggregation lag time and formation of large, amorphous aggregates. These results demonstrate that the morphology of α-synuclein aggregates is highly sensitive to solution conditions, implying that the fibrillar state does not necessarily represent the predominant or most functionally significant aggregated state under physiological conditions. (C) 2002 Elsevier Science Ltd. All rights reserved

Skew-Unfolding the Skorokhod Reflection of a Continuous Semimartingale

The Skorokhod reflection of a continuous semimartingale is unfolded, in a possibly skewed manner, into another continuous semimartingale on an enlarged probability space according to the excursion-theoretic methodology of Prokaj (2009). This is done in terms of a skew version of the Tanaka equation, whose properties are studied in some detail. The result is used to construct a system of two diffusive particles with rank-based characteristics and skew-elastic collisions. Unfoldings of conventional reflections are also discussed, as are examples involving skew Brownian Motions and skew Bessel processes.Comment: 20 pages. typos corrected, added a remark after Proposition 2.3, simplified the last part of Example 2.

Structural characterization of copper(II) binding to α-Synuclein: Insights into the bioinorganic chemistry of Parkinson's disease

The aggregation of α -synuclein (AS) is characteristic of Parkinson’s disease and other neurodegenerative synucleinopathies. We demonstrate here that Cu(II) ions are effective in accelerating AS aggregation at physiologically relevant concentrations without altering the resultant fibrillar structures. By using numerous spectroscopic techniques (absorption, CD, EPR, and NMR), we have located the primary binding for Cu(II) to a specific site in the N terminus, involving His-50 as the anchoring residue and other nitrogen oxygen donor atoms in a square planar or distorted tetragonal geometry. The carboxylate-rich C terminus, originally thought to drive copper binding, is able to coordinate a second Cu(II) equivalent, albeit with a 300-fold reduced affinity. The NMR analysis of AS–Cu(II) complexes reveals the existence of conformational restrictions in the native state of the protein. The metallobiology of Cu(II) in Parkinson’s disease is discussed by a comparative analysis with other Cu(II)-binding proteins involved in neurodegenerative disorders

Dynamic and static density-density correlations in the one-dimensional Bose gas: exact results and approximations

We discuss approximate formulas for the dynamic structure factor of the one-dimensional Bose gas in the Lieb-Liniger model that appear to be applicable over a wide range of the relevant parameters such as the interaction strength, frequency, and wavenumber. The suggested approximations are consistent with the exact results known in limiting cases. In particular, we encompass exact edge exponents as well as Luttinger liquid and perturbation theoretic results. We further discuss derived approximations for the static structure factor and the pair distribution function g(x). The approximate expressions show excellent agreement with numerical results based on the algebraic Bethe ansatz.Comment: 8 pages, 6 figure

Theory of superfluidity and drag force in the one-dimensional Bose gas

The one-dimensional Bose gas is an unusual superfluid. In contrast to higher spatial dimensions, the existence of non-classical rotational inertia is not directly linked to the dissipationless motion of infinitesimal impurities. Recently, experimental tests with ultracold atoms have begun and quantitative predictions for the drag force experienced by moving obstacles have become available. This topical review discusses the drag force obtained from linear response theory in relation to Landau's criterion of superfluidity. Based upon improved analytical and numerical understanding of the dynamical structure factor, results for different obstacle potentials are obtained, including single impurities, optical lattices and random potentials generated from speckle patterns. The dynamical breakdown of superfluidity in random potentials is discussed in relation to Anderson localization and the predicted superfluid-insulator transition in these systems.Comment: 17 pages, 12 figures, mini-review prepared for the special issue of Frontiers of Physics "Recent Progresses on Quantum Dynamics of Ultracold Atoms and Future Quantum Technologies", edited by Profs. Lee, Ueda, and Drummon