Reduction, Linearization and stability of relative equilibria for mechanical systems on riemannian manifolds

Consider a Riemannian manifold equipped with an infinitesimal isometry. For this setup, a unified treatment is provided, solely in the language of Riemannian geometry, of techniques in reduction, linearization, and stability of relative equilibria. In particular, for mechanical control systems, an explicit characterization is given for the manner in which reduction by an infinitesimal isometry, and linearization along a controlled trajectory "commute." As part of the development, relationships are derived between the Jacobi equation of geodesic variation and concepts from reduction theory, such as the curvature of the mechanical connection and the effective potential. As an application of our techniques, fiber and base stability of relative equilibria are studied. The paper also serves as a tutorial of Riemannian geometric methods applicable in the intersection of mechanics and control theory.

Regulation of Nedd4-2 self-ubiquitination and stability by a PY motif located within its HECT-domain.

Ubiquitin ligases play a pivotal role in substrate recognition and ubiquitin transfer, yet little is known about the regulation of their catalytic activity. Nedd4 (neural-precursor-cell-expressed, developmentally down-regulated 4)-2 is an E3 ubiquitin ligase composed of a C2 domain, four WW domains (protein-protein interaction domains containing two conserved tryptophan residues) that bind PY motifs (L/PPXY) and a ubiquitin ligase HECT (homologous with E6-associated protein C-terminus) domain. In the present paper we show that the WW domains of Nedd4-2 bind (weakly) to a PY motif (LPXY) located within its own HECT domain and inhibit auto-ubiquitination. Pulse-chase experiments demonstrated that mutation of the HECT PY-motif decreases the stability of Nedd4-2, suggesting that it is involved in stabilization of this E3 ligase. Interestingly, the HECT PY-motif mutation does not affect ubiquitination or down-regulation of a known Nedd4-2 substrate, ENaC (epithelial sodium channel). ENaC ubiquitination, in turn, appears to promote Nedd4-2 self-ubiquitination. These results support a model in which the inter- or intra-molecular WW-domain-HECT PY-motif interaction stabilizes Nedd4-2 by preventing self-ubiquitination. Substrate binding disrupts this interaction, allowing self-ubiquitination of Nedd4-2 and subsequent degradation, resulting in down-regulation of Nedd4-2 once it has ubiquitinated its target. These findings also point to a novel mechanism employed by a ubiquitin ligase to regulate itself differentially compared with substrate ubiquitination and stability.

Accurate performance of a rat model of schizophrenia in the water maze depends on visual cue availability and stability: a distortion in cognitive mapping abilities?

Rats were treated postnatally (PND 5-16) with BSO (l-buthionine-(S,R)-sulfoximine) in an animal model of schizophrenia based on transient glutathione deficit. The BSO treated rats were impaired in patrolling a maze or a homing table when adult, yet demonstrated preserved escape learning, place discrimination and reversal in a water maze task [37]. In the present work, BSO rats' performance in the water maze was assessed in conditions controlling for the available visual cues. First, in a completely curtained environment with two salient controlled cues, BSO rats showed little accuracy compared to control rats. Secondly, pre-trained BSO rats were impaired in reaching the familiar spatial position when curtains partially occluded different portions of the room environment in successive sessions. The apparently preserved place learning in a classical water maze task thus appears to require the stability and the richness of visual landmarks from the surrounding environment. In other words, the accuracy of BSO rats in place and reversal learning is impaired in a minimal cue condition or when the visual panorama changes between trials. However, if the panorama remains rich and stable between trials, BSO rats are equally efficient in reaching a familiar position or in learning a new one. This suggests that the BSO accurate performance in the water maze does not satisfy all the criteria for a cognitive map based navigation on the integration of polymodal cues. It supports the general hypothesis of a binding deficit in BSO rats.

Dimensionality of drinking consequences - cross-cultural comparability and stability over time

Despite the long tradition for asking about the negative social and health consequences of alcohol consumption in surveys, little is known about the dimensionality of these consequences. Analysing cross-sectional and longitudinal data from the Nordic Taxation Study collected for Sweden, Finland, and Denmark in two waves in 2003 and 2004 by means of an explorative principal component analysis for categorical data (CATPCA), it is tested whether consequences have a single underlying dimension across cultures. It further tests the reliability, replicability, concurrent and predictive validity of the consequence scales. A one-dimensional solution was commonly preferable. Whereas the two-dimensional solution was unable to distinguish clearly between different concepts of consequences, the one-dimensional solution resulted in interpretable, generally very stable scales within countries across different samples and time.

Reverse transcription quantitative real-time polymerase chain reaction reference genes in the spared nerve injury model of neuropathic pain : validation and literature search

La douleur neuropathique est définie comme une douleur causée par une lésion du système nerveux somato-sensoriel. Elle se caractérise par des douleurs exagérées, spontanées, ou déclenchées par des stimuli normalement non douloureux (allodynie) ou douloureux (hyperalgésie). Bien qu'elle concerne 7% de la population, ses mécanismes biologiques ne sont pas encore élucidés. L'étude des variations d'expressions géniques dans les tissus-clés des voies sensorielles (notamment le ganglion spinal et la corne dorsale de la moelle épinière) à différents moments après une lésion nerveuse périphérique permettrait de mettre en évidence de nouvelles cibles thérapeutiques. Elles se détectent de manière sensible par reverse transcription quantitative real-time polymerase chain reaction (RT- qPCR). Pour garantir des résultats fiables, des guidelines ont récemment recommandé la validation des gènes de référence utilisés pour la normalisation des données ("Minimum information for publication of quantitative real-time PCR experiments", Bustin et al 2009). Après recherche dans la littérature des gènes de référence fréquemment utilisés dans notre modèle de douleur neuropathique périphérique SNI (spared nerve injury) et dans le tissu nerveux en général, nous avons établi une liste de potentiels bons candidats: Actin beta (Actb), Glyceraldehyde-3-phosphate dehydrogenase (GAPDH), ribosomal proteins 18S (18S), L13a (RPL13a) et L29 (RPL29), hypoxanthine phosphoribosyltransferase 1 (HPRT1) et hydroxymethyl-bilane synthase (HMBS). Nous avons évalué la stabilité d'expression de ces gènes dans le ganglion spinal et dans la corne dorsale à différents moments après la lésion nerveuse (SNI) en calculant des coefficients de variation et utilisant l'algorithme geNorm qui compare les niveaux d'expression entre les différents candidats et détermine la paire de gènes restante la plus stable. Il a aussi été possible de classer les gènes selon leur stabilité et d'identifier le nombre de gènes nécessaires pour une normalisation la plus précise. Les gènes les plus cités comme référence dans le modèle SNI ont été GAPDH, HMBS, Actb, HPRT1 et 18S. Seuls HPRT1 and 18S ont été précédemment validés dans des arrays de RT-qPCR. Dans notre étude, tous les gènes testés dans le ganglion spinal et dans la corne dorsale satisfont au critère de stabilité exprimé par une M-value inférieure à 1. Par contre avec un coefficient de variation (CV) supérieur à 50% dans le ganglion spinal, 18S ne peut être retenu. La paire de gènes la plus stable dans le ganglion spinal est HPRT1 et Actb et dans la corne dorsale il s'agit de RPL29 et RPL13a. L'utilisation de 2 gènes de référence stables suffit pour une normalisation fiable. Nous avons donc classé et validé Actb, RPL29, RPL13a, HMBS, GAPDH, HPRT1 et 18S comme gènes de référence utilisables dans la corne dorsale pour le modèle SNI chez le rat. Dans le ganglion spinal 18S n'a pas rempli nos critères. Nous avons aussi déterminé que la combinaison de deux gènes de référence stables suffit pour une normalisation précise. Les variations d'expression génique de potentiels gènes d'intérêts dans des conditions expérimentales identiques (SNI, tissu et timepoints post SNI) vont pouvoir se mesurer sur la base d'une normalisation fiable. Non seulement il sera possible d'identifier des régulations potentiellement importantes dans la genèse de la douleur neuropathique mais aussi d'observer les différents phénotypes évoluant au cours du temps après lésion nerveuse.

Improving binding affinity and stability of peptide ligands by substituting glycines with D-amino acids.

Improving the binding affinity and/or stability of peptide ligands often requires testing of large numbers of variants to identify beneficial mutations. Herein we propose a type of mutation that promises a high success rate. In a bicyclic peptide inhibitor of the cancer-related protease urokinase-type plasminogen activator (uPA), we observed a glycine residue that has a positive ϕ dihedral angle when bound to the target. We hypothesized that replacing it with a D-amino acid, which favors positive ϕ angles, could enhance the binding affinity and/or proteolytic resistance. Mutation of this specific glycine to D-serine in the bicyclic peptide indeed improved inhibitory activity (1.75-fold) and stability (fourfold). X-ray-structure analysis of the inhibitors in complex with uPA showed that the peptide backbone conformation was conserved. Analysis of known cyclic peptide ligands showed that glycine is one of the most frequent amino acids, and that glycines with positive ϕ angles are found in many protein-bound peptides. These results suggest that the glycine-to-D-amino acid mutagenesis strategy could be broadly applied.

Validation and clinical use of the CECA, a disease-specific quality of life questionnaire for patients with anogenital Condylomata Acuminata

The aim of this validation study was to assess the measurement properties of the CECA (Spanish acronym for the Specific Questionnaire for Condylomata Acuminata) in patients with anogenital condylomas. A total of 247 patients aged > 18 years completed the questionnaire on 2 occasions as well as the Dermatology Life Quality Index (DLQI). The CECA questionnaire showed good internal consistency (Cronbach's alpha values of 0.86 and 0.91 in the emotional and sexual activity dimensions) and good testretest reliability (intraclass correlation coefficient 0.76 emotional dimension, 0.82 sexual activity dimension). Patients with de novo lesions and those with more extensive lesions and larger number of warts showed poorer health-related quality of life. CECA and DLQI scores correlated moderately. Patients whose lesions cleared at follow-up or with a reduction of >or= 50% showed a better improvement of health-related quality of life. The CECA questionnaire is a valid, reliable and sensitive tool for the assessment of health-related quality of life in patients with anogenital warts.

Validation and reproducibility of a semi-quantitative Food Frequency Questionnaire for use in elderly Swiss women.

OBJECTIVE: The principal aim of this study was to develop a Swiss Food Frequency Questionnaire (FFQ) for the elderly population for use in a study to investigate the influence of nutritional factors on bone health. The secondary aim was to assess its validity and both short-term and long-term reproducibility. DESIGN: A 4-day weighed record (4 d WR) was applied to 51 randomly selected women of a mean age of 80.3 years. Subsequently, a detailed FFQ was developed, cross-validated against a further 44 4-d WR, and the short- (1 month, n = 15) and long-term (12 months, n = 14) reproducibility examined. SETTING: French speaking part of Switzerland. SUBJECTS: The subjects were randomly selected women recruited from the Swiss Evaluation of the Methods of Measurement of Osteoporotic Fracture cohort study. RESULTS: Mean energy intakes by 4-d WR and FFQ showed no significant difference [1564.9 kcal (SD 351.1); 1641.3 kcal (SD 523.2) respectively]. Mean crude nutrient intakes were also similar (with nonsignifcant P-values examining the differences in intake) and ranged from 0.13 (potassium) to 0.48 (magnesium). Similar results were found in the reproducibility studies. CONCLUSION: These findings provide evidence that this FFQ adequately estimates nutrient intakes and can be used to rank individuals within distributions of intake in specific populations.

Validation and performance comparison of two carbon isotope ratio methods to control the misuse of androgens in humans.

Carbon isotope ratio of androgens in urine specimens is routinely determined to exclude an abuse of testosterone or testosterone prohormones by athletes. Increasing application of gas chromatography/combustion/isotope ratio mass spectrometry (GC/C/IRMS) in the last years for target and systematic investigations on samples has resulted in the demand for rapid sample throughput as well as high selectivity in the extraction process particularly in the case of conspicuous samples. For that purpose, we present herein the complimentary use of an SPE-based assay and an HPLC fractionation method as a two-stage strategy for the isolation of testosterone metabolites and endogenous reference compounds prior to GC/C/IRMS analyses. Assays validation demonstrated acceptable performance in terms of intermediate precision (range: 0.1-0.4 per thousand) and Bland-Altman analyses revealed no significant bias (0.2 per thousand). For further validation of this two-stage analyses strategy, all the specimens (n=124) collected during a major sport event were processed.

A repeated GGA motif is critical for the activity and stability of the riboregulator RsmY of Pseudomonas fluorescens.

The riboregulator RsmY of Pseudomonas fluorescens strain CHA0 is an example of small regulatory RNAs belonging to the global Rsm/Csr regulatory systems controlling diverse cellular processes such as glycogen accumulation, motility, or formation of extracellular products in various bacteria. By binding multiple molecules of the small regulatory protein RsmA, RsmY relieves the negative effect of RsmA on the translation of several target genes involved in the biocontrol properties of strain CHA0. RsmY and functionally related riboregulators have repeated GGA motifs predicted to be exposed in single-stranded regions, notably in the loops of hairpins. The secondary structure of RsmY was corroborated by in vivo cleavage with lead acetate. RsmY mutants lacking three or five (out of six) of the GGA motifs showed reduced ability to derepress the expression of target genes in vivo and failed to bind the RsmA protein efficiently in vitro. The absence of GGA motifs in RsmY mutants resulted in reduced abundance of these transcripts and in a shorter half-life (< or = 6 min as compared with 27 min for wild type RsmY). These results suggest that both the interaction of RsmY with RsmA and the stability of RsmY strongly depend on the GGA repeats and that the ability of RsmY to interact with small regulatory proteins such as RsmA may protect this RNA from degradation.

Non-Quasi-Competitiveness and Stability in Cournot's Model

This paper retakes previous work of the authors, about the relationship between non-quasi-competitiveness (the increase in price caused by an increase in the number of oligopolists) and stability of the equilibrium in the classical Cournot oligopoly model. Though it has been widely accepted in the literature that the loss of quasi-competitiveness is linked, in the long run as new firms entered the market, to instability of the model, the authors in their previous work put forward a model in which a situation of monopoly changed to duopoly losing quasi-competitiveness but maintaining the stability of the equilibrium. That model could not, at the time, be extended to any number of oligopolists. The present paper exhibits such an extension. An oligopoly model is shown in which the loss of quasi-competitiveness resists the presence in the market of as many firms as one wishes and where the successive Cournot's equilibrium points are unique and asymptotically stable. In this way, for the first time, the conjecture that non-quasi- competitiveness and instability were equivalent in the long run, is proved false.