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.

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

An interleukin-1 polymorphism additionally intensified by atopy as prognostic factor for aseptic non-mechanical complications in metal knee and hip arthroplasty

Background: In contrast to infection or mechanical issues joint replacement failure following inflammatory adverse reactions is poorly understood. Objective: To assess the association of IL-1β polymorphisms and history of allergy with aseptic non-mechanical complications following arthroplasty. Methods: In 102 patients with aseptic non-mechanically caused symptomatic knee or hip arthroplasty (SA) and 93 patients with asymptomatic arthroplasty (AA) questionnaire-based history, patch test with at least standard series, lymphocyte transformation test (LTT) with nickel, cobalt and chromium and interleukin-1 polymorphism analysis were done. Three polymorphisms of the IL1B gene [IL-1b -3954 (rs1143634), IL-1b -511 (rs16944) and IL-1b -31 (rs1143627)] and one polymorphism of the IL1RN gene [IL1RN intron 2, variable number of tandem repeats, VNTR (rs2234663)] were assessed by PCR and gel electrophoresis. Results: We found no significant difference in smoking history and atopy but 25% versus 10% of self-reported metal allergy in SA versus AA; the patch test (respective, LTT) for metal sensitivity was more often positive in SA patients. The allele 498 bp of the IL1RN polymorphism occurred significantly more often in the SA group (37% versus 11%; p < 0.0001). Upon additional presence of atopy, the difference was even greater (60% vs 10%) (p < 0.000001). There was no association of IL-1 polymorphisms with metal allergy. Conclusion: The IL1RN VNTR allele 498 bp was strongly associated with SA. In patients with a history of atopy, presence of the IL1RN VNTR allele 498 bp led to a four-fold higher SA prevalence compared to patients without this allele

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

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

Challenges Predicting Ligand-Receptor Interactions of Promiscuous Proteins: The Nuclear Receptor PXR

Transcriptional regulation of some genes involved in xenobiotic detoxification and apoptosis is performed via the human pregnane X receptor (PXR) which in turn is activated by structurally diverse agonists including steroid hormones. Activation of PXR has the potential to initiate adverse effects, altering drug pharmacokinetics or perturbing physiological processes. Reliable computational prediction of PXR agonists would be valuable for pharmaceutical and toxicological research. There has been limited success with structure-based modeling approaches to predict human PXR activators. Slightly better success has been achieved with ligand-based modeling methods including quantitative structure-activity relationship (QSAR) analysis, pharmacophore modeling and machine learning. In this study, we present a comprehensive analysis focused on prediction of 115 steroids for ligand binding activity towards human PXR. Six crystal structures were used as templates for docking and ligand-based modeling approaches (two-, three-, four- and five-dimensional analyses). The best success at external prediction was achieved with 5D-QSAR. Bayesian models with FCFP_6 descriptors were validated after leaving a large percentage of the dataset out and using an external test set. Docking of ligands to the PXR structure co-crystallized with hyperforin had the best statistics for this method. Sulfated steroids (which are activators) were consistently predicted as non-activators while, poorly predicted steroids were docked in a reverse mode compared to 5α-androstan-3β-ol. Modeling of human PXR represents a complex challenge by virtue of the large, flexible ligand-binding cavity. This study emphasizes this aspect, illustrating modest success using the largest quantitative data set to date and multiple modeling approaches

Influences of Excluded Volume of Molecules on Signaling Processes on Biomembrane

We investigate the influences of the excluded volume of molecules on biochemical reaction processes on 2-dimensional surfaces using a model of signal transduction processes on biomembranes. We perform simulations of the 2-dimensional cell-based model, which describes the reactions and diffusion of the receptors, signaling proteins, target proteins, and crowders on the cell membrane. The signaling proteins are activated by receptors, and these activated signaling proteins activate target proteins that bind autonomously from the cytoplasm to the membrane, and unbind from the membrane if activated. If the target proteins bind frequently, the volume fraction of molecules on the membrane becomes so large that the excluded volume of the molecules for the reaction and diffusion dynamics cannot be negligible. We find that such excluded volume effects of the molecules induce non-trivial variations of the signal flow, defined as the activation frequency of target proteins, as follows. With an increase in the binding rate of target proteins, the signal flow varies by i) monotonically increasing; ii) increasing then decreasing in a bell-shaped curve; or iii) increasing, decreasing, then increasing in an S-shaped curve. We further demonstrate that the excluded volume of molecules influences the hierarchical molecular distributions throughout the reaction processes. In particular, when the system exhibits a large signal flow, the signaling proteins tend to surround the receptors to form receptor-signaling protein clusters, and the target proteins tend to become distributed around such clusters. To explain these phenomena, we analyze the stochastic model of the local motions of molecules around the receptor.Comment: 31 pages, 10 figure