Boundary Conditions on Internal Three-Body Wave Functions

For a three-body system, a quantum wave function $\Psi^\ell_m$ with definite $\ell$ and $m$ quantum numbers may be expressed in terms of an internal wave function $\chi^\ell_k$ which is a function of three internal coordinates. This article provides necessary and sufficient constraints on $\chi^\ell_k$ to ensure that the external wave function $\Psi^\ell_m$ is analytic. These constraints effectively amount to boundary conditions on $\chi^\ell_k$ and its derivatives at the boundary of the internal space. Such conditions find similarities in the (planar) two-body problem where the wave function (to lowest order) has the form $r^{|m|}$ at the origin. We expect the boundary conditions to prove useful for constructing singularity free three-body basis sets for the case of nonvanishing angular momentum.Comment: 41 pages, submitted to Phys. Rev.

Negative Feedback Regulation of the Yeast Cth1 and Cth2 mRNA Binding Proteins Is Required for Adaptation to Iron Deficiency and Iron Supplementation

Iron (Fe) is an essential element for all eukaryotic organisms because it functions as a cofactor in a wide range of biochemical processes. Cells have developed sophisticated mechanisms to tightly control Fe utilization in response to alterations in cellular demands and bioavailability. In response to Fe deficiency, the yeast Saccharomyces cerevisiae activates transcription of the CTH1 and CTH2 genes, which encode proteins that bind to AU-rich elements (AREs) within the 3′ untranslated regions (3′UTRs) of many mRNAs, leading to metabolic reprogramming of Fe-dependent pathways and decreased Fe storage. The precise mechanisms underlying Cth1 and Cth2 function and regulation are incompletely understood. We report here that the Cth1 and Cth2 proteins specifically bind in vivo to AREs located at the 3′UTRs of their own transcripts in an auto- and cross-regulated mechanism that limits their expression. By mutagenesis of the AREs within the CTH2 transcript, we demonstrate that a Cth2 negative-feedback loop is required for the efficient decline in Cth2 protein levels observed upon a rapid rise in Fe availability. Importantly, Cth2 autoregulation is critical for the appropriate recovery of Fe-dependent processes and resumption of growth in response to a change from Fe deficiency to Fe supplementation

Metric tensor as the dynamical variable for variable cell-shape molecular dynamics

We propose a new variable cell-shape molecular dynamics algorithm where the dynamical variables associated with the cell are the six independent dot products between the vectors defining the cell instead of the nine cartesian components of those vectors. Our choice of the metric tensor as the dynamical variable automatically eliminates the cell orientation from the dynamics. Furthermore, choosing for the cell kinetic energy a simple scalar that is quadratic in the time derivatives of the metric tensor, makes the dynamics invariant with respect to the choice of the simulation cell edges. Choosing the densitary character of that scalar allows us to have a dynamics that obeys the virial theorem. We derive the equations of motion for the two conditions of constant external pressure and constant thermodynamic tension. We also show that using the metric as variable is convenient for structural optimization under those two conditions. We use simulations for Ar with Lennard-Jones parameters and for Si with forces and stresses calculated from first-principles of density functional theory to illustrate the applications of the method.Comment: 10 pages + 6 figures, Latex, to be published in Physical Review

Scarring Effects on Tunneling in Chaotic Double-Well Potentials

The connection between scarring and tunneling in chaotic double-well potentials is studied in detail through the distribution of level splittings. The mean level splitting is found to have oscillations as a function of energy, as expected if scarring plays a role in determining the size of the splittings, and the spacing between peaks is observed to be periodic of period {$2\pi\hbar$} in action. Moreover, the size of the oscillations is directly correlated with the strength of scarring. These results are interpreted within the theoretical framework of Creagh and Whelan. The semiclassical limit and finite-{$\hbar$} effects are discussed, and connections are made with reaction rates and resonance widths in metastable wells.Comment: 22 pages, including 11 figure

Mechanically Induced Amorphization of Diaqua-bis(Omeprazolate)-Magnesium Dihydrate

The influence of milling diaqua-bis(omeprazolate)-magnesium dihydrate (DABOMD), an active pharmaceutical ingredient (API), was investigated. DABOMD was processed in a planetary ball mill at different milling times, from 1 to 300 min. The milling process resulted in a prominent comminution (size reduction) and amorphization of the API. DABOMD amorphization was identified with various characterization techniques including thermogravimetric analysis, differential scanning calorimetry, powder X-ray diffraction, and attenuated total reflection-Fourier transform infrared spectroscopy. The solid–solid crystalline to amorphous phase transformation is driven by compression, shear stresses, and heat generated in the planetary ball mill. This leads to distortion and breakage of hydrogen bonds, release of water molecules from the crystalline lattice of DABOMD and the accumulation of defects, and eventually a collapse of the crystalline order. Model fitting of the kinetics of comminution and the amorphization of DABOMD revealed a series of events: a rapid comminution at the start of milling driven by crystal cleavage of DABOMD, followed by partial amorphization, which is driven by rapid water diffusion, and subsequently, a slow steady comminution and amorphization

Novel multiple sclerosis susceptibility loci implicated in epigenetic regulation

We conducted a genome-wide association study (GWAS) on multiple sclerosis (MS) susceptibility in German cohorts with 4888 cases and 10,395 controls. In addition to associations within the major histocompatibility complex (MHC) region, 15 non-MHC loci reached genome-wide significance. Four of these loci are novel MS susceptibility loci. They map to the genes L3MBTL3, MAZ, ERG, and SHMT1. The lead variant at SHMT1 was replicated in an independent Sardinian cohort. Products of the genes L3MBTL3, MAZ, and ERG play important roles in immune cell regulation. SHMT1 encodes a serine hydroxymethyltransferase catalyzing the transfer of a carbon unit to the folate cycle. This reaction is required for regulation of methylation homeostasis, which is important for establishment and maintenance of epigenetic signatures. Our GWAS approach in a defined population with limited genetic substructure detected associations not found in larger, more heterogeneous cohorts, thus providing new clues regarding MS pathogenesis

Lipopolysaccharide-binding protein and future Parkinson's disease risk: a European prospective cohort

INTRODUCTION: Lipopolysaccharide (LPS) is the outer membrane component of Gram-negative bacteria. LPS-binding protein (LBP) is an acute-phase reactant that mediates immune responses triggered by LPS and has been used as a blood marker for LPS. LBP has recently been indicated to be associated with Parkinson's disease (PD) in small-scale retrospective case-control studies. We aimed to investigate the association between LBP blood levels with PD risk in a nested case-control study within a large European prospective cohort. METHODS: A total of 352 incident PD cases (55% males) were identified and one control per case was selected, matched by age at recruitment, sex and study center. LBP levels in plasma collected at recruitment, which was on average 7.8 years before diagnosis of the cases, were analyzed by enzyme linked immunosorbent assay. Odds ratios (ORs) were estimated for one unit increase of the natural log of LBP levels and PD incidence by conditional logistic regression. RESULTS: Plasma LBP levels were higher in prospective PD cases compared to controls (median (interquartile range) 26.9 (18.1-41.0) vs. 24.7 (16.6-38.4) µg/ml). The OR for PD incidence per one unit increase of log LBP was elevated (1.46, 95% CI 0.98-2.19). This association was more pronounced among women (OR 2.68, 95% CI 1.40-5.13) and overweight/obese subjects (OR 1.54, 95% CI 1.09-2.18). CONCLUSION: The findings suggest that higher plasma LBP levels may be associated with an increased risk of PD and may thus pinpoint to a potential role of endotoxemia in the pathogenesis of PD, particularly in women and overweight/obese individuals