Crystallization of Adenylylsulfate Reductase from Desulfovibrio gigas: A Strategy Based on Controlled Protein Oligomerization

Adenylylsulfate reductase (adenosine 5′-phosphosulfate reductase, APS reductase or APSR, E.C.1.8.99.2) catalyzes the conversion of APS to sulfite in dissimilatory sulfate reduction. APSR was isolated and purified directly from massive anaerobically grown Desulfovibrio gigas, a strict anaerobe, for structure and function investigation. Oligomerization of APSR to form dimers–α_2β_2, tetramers–α_4β_4, hexamers–α_6β_6, and larger oligomers was observed during purification of the protein. Dynamic light scattering and ultracentrifugation revealed that the addition of adenosine monophosphate (AMP) or adenosine 5′-phosphosulfate (APS) disrupts the oligomerization, indicating that AMP or APS binding to the APSR dissociates the inactive hexamers into functional dimers. Treatment of APSR with β-mercaptoethanol decreased the enzyme size from a hexamer to a dimer, probably by disrupting the disulfide Cys156—Cys162 toward the C-terminus of the β-subunit. Alignment of the APSR sequences from D. gigas and A. fulgidus revealed the largest differences in this region of the β-subunit, with the D. gigas APSR containing 16 additional amino acids with the Cys156—Cys162 disulfide. Studies in a pH gradient showed that the diameter of the APSR decreased progressively with acidic pH. To crystallize the APSR for structure determination, we optimized conditions to generate a homogeneous and stable form of APSR by combining dynamic light scattering, ultracentrifugation, and electron paramagnetic resonance methods to analyze the various oligomeric states of the enzyme in varied environments

Bose-Einstein condensation in an optical lattice: A perturbation approach

We derive closed analytical expressions for the order parameter $\Phi (x)$ and for the chemical potential $\mu$ of a Bose-Einstein Condensate loaded into a harmonically confined, one dimensional optical lattice, for sufficiently weak, repulsive or attractive interaction, and not too strong laser intensities. Our results are compared with exact numerical calculations in order to map out the range of validity of the perturbative analytical approach. We identify parameter values where the optical lattice compensates the interaction-induced nonlinearity, such that the condensate ground state coincides with a simple, single particle harmonic oscillator wave function

Optimal Choices of Reference for a Quasi-local Energy: Spherically Symmetric Spacetimes

For a given timelike displacement vector the covariant Hamiltonian quasi-local energy expression requires a proper choice of reference spacetime. We propose a program for determining the reference by embedding a neighborhood of the two-sphere boundary in the dynamic spacetime into a Minkowski reference, so that the two sphere is embedded isometrically, and then extremizing the energy to determine the embedding variables. Applying this idea to Schwarzschild spacetime, we found that for each given future timelike displacement vector our program gives a unique energy value. The static observer measures the maximal energy. Applied to the Friedmann-Lemaitre-Robertson-Walker spacetime, we find that the maximum energy value is nonnegative; the associated displacement vector is the unit dual mean curvature vector, and the expansion of the two-sphere boundary matches that of its reference image. For these spherically symmetric cases the reference determined by our program is equivalent to isometrically matching the geometry at the two-sphere boundary and taking the displacement vector to be orthogonal to the spacelike constant coordinate time hypersurface, like the timelike Killing vector of the Minkowski reference.Comment: 12 page

Charged particles in external fields as physical examples of quasi-exactly solvable models: a unified treatment

We present a unified treatment of three cases of quasi-exactly solvable problems, namely, charged particle moving in Coulomb and magnetic fields, for both the Schr\"odinger and the Klein-Gordon case, and the relative motion of two charged particles in an external oscillator potential. We show that all these cases are reducible to the same basic equation, which is quasi-exactly solvable owing to the existence of a hidden $sl_2$ algebraic structure. A systematic and unified algebraic solution to the basic equation using the method of factorization is given. Analytic expressions of the energies and the allowed frequencies for the three cases are given in terms of the roots of one and the same set of Bethe ansatz equations.Comment: RevTex, 15 pages, no figure

Hyperbolic Space Cosmologies

We present a systematic study of accelerating cosmologies obtained from M/string theory compactifications of hyperbolic spaces with time-varying volume. A set of vacuum solutions where the internal space is a product of hyperbolic manifolds is found to give qualitatively the same accelerating four-dimensional FLRW universe behavior as a single hyperbolic space. We also examine the possibility that our universe is a hyperbolic space and provide exact Milne type solutions, as well as intersecting S-brane solutions. When both the usual 4D spacetime and the m-dimensional internal space are hyperbolic, we find eternally accelerating cosmologies for $m\geq 7$, with and without form field backgrounds. In particular, the effective potential for a magnetic field background in the large 3 dimensions is positive definite with a local minimum and thus enhances the eternally accelerating expansion.Comment: 33 pages, 2 figures; v2 refs added; v3 minor change in text, JHEP versio

Damping in 2D and 3D dilute Bose gases

Damping in 2D and 3D dilute gases is investigated using both the hydrodynamical approach and the Hartree-Fock-Bogoliubov (HFB) approximation . We found that the both methods are good for the Beliaev damping at zero temperature and Landau damping at very low temperature, however, at high temperature, the hydrodynamical approach overestimates the Landau damping and the HFB gives a better approximation. This result shows that the comparison of the theoretical calculation using the hydrodynamical approach and the experimental data for high temperature done by Vincent Liu (PRL {\bf21} 4056 (1997)) is not proper. For two-dimensional systems, we show that the Beliaev damping rate is proportional to $k^3$ and the Landau damping rate is proportional to $T^2$ for low temperature and to $T$ for high temperature. We also show that in two dimensions the hydrodynamical approach gives the same result for zero temperature and for low temperature as HFB, but overestimates the Landau damping for high temperature.Comment: 11 pages, 4 figure

Density-Matrix Spectra of Solvable Fermionic Systems

We consider non-interacting fermions on a lattice and give a general result for the reduced density matrices corresponding to parts of the system. This allows to calculate their spectra, which are essential in the DMRG method, by diagonalizing small matrices. We discuss these spectra and their typical features for various fermionic quantum chains and for the two-dimensional tight-binding model.Comment: 12 pages and 9 figure

Quasi-local Energy for Spherically Symmetric Spacetimes

We present two complementary approaches for determining the reference for the covariant Hamiltonian boundary term quasi-local energy and test them on spherically symmetric spacetimes. On the one hand, we isometrically match the 2-surface and extremize the energy. This can be done in two ways, which we call programs I (without constraint) and II (with additional constraints). On the other hand, we match the orthonormal 4-frames of the dynamic and the reference spacetimes. Then, if we further specify the observer by requiring the reference displacement to be the timelike Killing vector of the reference, the result is the same as program I, and the energy can be positive, zero, or even negative. If, instead, we require that the Lie derivatives of the two-area along the displacement vector in both the dynamic and reference spacetimes to be the same, the result is the same as program II, and it satisfies the usual criteria: the energies are non-negative and vanish only for Minkowski (or anti-de Sitter) spacetime.Comment: 16 pages, no figure

Hamilton-Jacobi Tunneling Method for Dynamical Horizons in Different Coordinate Gauges

Previous work on dynamical black hole instability is further elucidated within the Hamilton-Jacobi method for horizon tunneling and the reconstruction of the classical action by means of the null-expansion method. Everything is based on two natural requirements, namely that the tunneling rate is an observable and therefore it must be based on invariantly defined quantities, and that coordinate systems which do not cover the horizon should not be admitted. These simple observations can help to clarify some ambiguities, like the doubling of the temperature occurring in the static case when using singular coordinates, and the role, if any, of the temporal contribution of the action to the emission rate. The formalism is also applied to FRW cosmological models, where it is observed that it predicts the positivity of the temperature naturally, without further assumptions on the sign of the energy.Comment: Standard Latex document, typos corrected, refined discussion of tunneling picture, subsection 5.1 remove