Global analytic regularity for structures of co-rank one

We consider real analytic involutive structures V, of co-rank one, defined on a real analytic paracompact orientable manifold M. To each such structure we associate certain connected subsets of M which we call the level sets of V. We prove that analytic regularity propagates along them. With a further assumption on the level sets of V we characterize the global analytic hypoellipticity of a differential operator naturally associated to V. As an application we study a case of tube structures.

Multiple Pathways Analysis of Brain Functional Networks from EEG Signals: An Application to Real Data

In the present study, we propose a theoretical graph procedure to investigate multiple pathways in brain functional networks. By taking into account all the possible paths consisting of h links between the nodes pairs of the network, we measured the global network redundancy R (h) as the number of parallel paths and the global network permeability P (h) as the probability to get connected. We used this procedure to investigate the structural and dynamical changes in the cortical networks estimated from a dataset of high-resolution EEG signals in a group of spinal cord injured (SCI) patients during the attempt of foot movement. In the light of a statistical contrast with a healthy population, the permeability index P (h) of the SCI networks increased significantly (P < 0.01) in the Theta frequency band (3-6 Hz) for distances h ranging from 2 to 4. On the contrary, no significant differences were found between the two populations for the redundancy index R (h) . The most significant changes in the brain functional network of SCI patients occurred mainly in the lower spectral contents. These changes were related to an improved propagation of communication between the closest cortical areas rather than to a different level of redundancy. This evidence strengthens the hypothesis of the need for a higher functional interaction among the closest ROIs as a mechanism to compensate the lack of feedback from the peripheral nerves to the sensomotor areas.

Analytic Methods for the Logic of Proofs

The logic of proofs (lp) was proposed as Gdels missed link between Intuitionistic and S4-proofs, but so far the tableau-based methods proposed for lp have not explored this closeness with S4 and contain rules whose analycity is not immediately evident. We study possible formulations of analytic tableau proof methods for lp that preserve the subformula property. Two sound and complete tableau decision methods of increasing degree of analycity are proposed, KELP and preKELP. The latter is particularly inspired on S4-proofs. The crucial role of proof constants in the structure of lp-proofs methods is analysed. In particular, a method for the abduction of proof constant specifications in strongly analytic preKELP proofs is presented; abduction heuristics and the complexity of the method are discussed.

Hyperfunctions and (analytic) hypoellipticity

In this work we discuss the problem of smooth and analytic regularity for hyperfunction solutions to linear partial differential equations with analytic coefficients. In particular we show that some well known ""sum of squares"" operators, which satisfy Hormander`s condition and consequently are hypoelliptic, admit hyperfunction solutions that are not smooth (in particular they are not distributions).

The Arabidopsis bZIP Gene AtbZIP63 Is a Sensitive Integrator of Transient Abscisic Acid and Glucose Signals

Glucose modulates plant metabolism, growth, and development. In Arabidopsis (Arabidopsis thaliana), Hexokinase1 (HXK1) is a glucose sensor that may trigger abscisic acid (ABA) synthesis and sensitivity to mediate glucose-induced inhibition of seedling development. Here, we show that the intensity of short-term responses to glucose can vary with ABA activity. We report that the transient (2 h/4 h) repression by 2% glucose of AtbZIP63, a gene encoding a basic-leucine zipper (bZIP) transcription factor partially involved in the Snf1-related kinase KIN10-induced responses to energy limitation, is independent of HXK1 and is not mediated by changes in ABA levels. However, high-concentration (6%) glucose-mediated repression appears to be modulated by ABA, since full repression of AtbZIP63 requires a functional ABA biosynthetic pathway. Furthermore, the combination of glucose and ABA was able to trigger a synergistic repression of AtbZIP63 and its homologue AtbZIP3, revealing a shared regulatory feature consisting of the modulation of glucose sensitivity by ABA. The synergistic regulation of AtbZIP63 was not reproduced by an AtbZIP63 promoter-5`-untranslated region:beta-glucuronidase fusion, thus suggesting possible posttranscriptional control. A transcriptional inhibition assay with cordycepin provided further evidence for the regulation of mRNA decay in response to glucose plus ABA. Overall, these results indicate that AtbZIP63 is an important node of the glucose-ABA interaction network. The mechanisms by which AtbZIP63 may participate in the fine-tuning of ABA-mediated abiotic stress responses according to sugar availability (i.e., energy status) are discussed.

Mitochondrial ATP-sensitive K(+) channels as redox signals to liver mitochondria in response to hypertriglyceridemia

We have recently demonstrated that hypertriglyceridemic (HTG) mice present both elevated body metabolic rates and mild mitochondrial uncoupling in the liver owing to stimulated activity of the ATP-sensitive potassium channel (mitoK(ATP)). Because lipid excess normally leads to cell redox imbalance, we examined the hepatic oxidative status in this model. Cell redox imbalance was evidenced by increased total levels of carbonylated proteins, malondialdehydes, and GSSG/GSH ratios in HTG livers compared to wild type. In addition, the activities of the extramitochondrial enzymes NADPH oxidase and xanthine oxidase were elevated in HTG livers. In contrast, Mn-superoxide dismutase activity and content, a mitochondrial matrix marker, were significantly decreased in HTG livers. isolated HTG liver mitochondria presented lower rates of H(2)O(2) production, which were reversed by mitoK(ATP) antagonists. In vivo antioxidant treatment with N-acetylcysteine decreased both mitoKATP activity and metabolic rates in HTG mice. These data indicate that high levels of triglycerides increase reactive oxygen generation by extramitochondrial enzymes that promote MitoK(ATP) activation. The mild uncoupling mediated by mitoK(ATP) increases metabolic rates and protects mitochondria against oxidative damage. Therefore, a biological role for mitoK(ATP) is a redox sensor is shown here for the first time in an in vivo model of systemic and cellular lipid excess, (C) 2009 Elsevier Inc. All rights reserved.

Metabotropic glutamate receptors transduce signals for neurite outgrowth after binding of the prion protein to laminin gamma 1 chain

The prion protein (PrP(C)) is highly expressed in the nervous system, and its abnormal conformer is associated with prion diseases. PrP(C) is anchored to cell membranes by glycosylphosphatidylinositol, and transmembrane proteins are likely required for PrP(C)-mediated intracellular signaling. Binding of laminin (Ln) to PrP(C) modulates neuronal plasticity and memory. We addressed signaling pathways triggered by PrP(C)-Ln interaction in order to identify transmembrane proteins involved in the transduction of PrP(C)-Ln signals. The Ln gamma 1-chain peptide, which contains the Ln binding site for PrP(C), induced neuritogenesis through activation of phospholipase C (PLC), Ca(2+) mobilization from intracellular stores, and protein kinase C and extracellular signal-regulated kinase (ERK1/2) activation in primary cultures of neurons from wild-type, but not PrP(C)-null mice. Phage display, coimmunoprecipitation, and colocalization experiments showed that group I metabotropic glutamate receptors (mGluR1/5) associate with PrP(C). Expression of either mGluR1 or mGluR5 in HEK293 cells reconstituted the signaling pathways mediated by PrP(C)-Ln gamma 1 peptide interaction. Specific inhibitors of these receptors impaired PrP(C)-Ln gamma 1 peptide-induced signaling and neuritogenesis. These data show that group I mGluRs are involved in the transduction of cellular signals triggered by PrP(C)-Ln, and they support the notion that PrP(C) participates in the assembly of multiprotein complexes with physiological functions on neurons.-Beraldo, F. H., Arantes, C. P., Santos, T. G., Machado, C. F., Roffe, M., Hajj, G. N., Lee, K. S., Magalhaes, A. C., Caetano, F. A., Mancini, G. L., Lopes, M. H., Americo, T. A., Magdesian, M. H., Ferguson, S. S. G., Linden, R., Prado, M. A. M., Martins, V. R. Metabotropic glutamate receptors trans-duce signals for neurite outgrowth after binding of the prion protein to laminin gamma 1 chain. FASEB J. 25, 265-279 (2011). www.fasebj.org