Geometric Approach to Pontryagin's Maximum Principle

Since the second half of the 20th century, Pontryagin's Maximum Principle has been widely discussed and used as a method to solve optimal control problems in medicine, robotics, finance, engineering, astronomy. Here, we focus on the proof and on the understanding of this Principle, using as much geometric ideas and geometric tools as possible. This approach provides a better and clearer understanding of the Principle and, in particular, of the role of the abnormal extremals. These extremals are interesting because they do not depend on the cost function, but only on the control system. Moreover, they were discarded as solutions until the nineties, when examples of strict abnormal optimal curves were found. In order to give a detailed exposition of the proof, the paper is mostly self\textendash{}contained, which forces us to consider different areas in mathematics such as algebra, analysis, geometry.Comment: Final version. Minors changes have been made. 56 page

Chronic Nicotine Modifies Skeletal Muscle Na,K-ATPase Activity through Its Interaction with the Nicotinic Acetylcholine Receptor and Phospholemman

Our previous finding that the muscle nicotinic acetylcholine receptor (nAChR) and the Na,K-ATPase interact as a regulatory complex to modulate Na,K-ATPase activity suggested that chronic, circulating nicotine may alter this interaction, with long-term changes in the membrane potential. To test this hypothesis, we chronically exposed rats to nicotine delivered orally for 21–31 days. Chronic nicotine produced a steady membrane depolarization of ∼3 mV in the diaphragm muscle, which resulted from a net change in electrogenic transport by the Na,K-ATPase α2 and α1 isoforms. Electrogenic transport by the α2 isoform increased (+1.8 mV) while the activity of the α1 isoform decreased (−4.4 mV). Protein expression of Na,K-ATPase α1 or α2 isoforms and the nAChR did not change; however, the content of α2 subunit in the plasma membrane decreased by 25%, indicating that its stimulated electrogenic transport is due to an increase in specific activity. The physical association between the nAChR, the Na,K-ATPase α1 or α2 subunits, and the regulatory subunit of the Na,K-ATPase, phospholemman (PLM), measured by co-immuno precipitation, was stable and unchanged. Chronic nicotine treatment activated PKCα/β2 and PKCδ and was accompanied by parallel increases in PLM phosphorylation at Ser63 and Ser68. Collectively, these results demonstrate that nicotine at chronic doses, acting through the nAChR-Na,K-ATPase complex, is able to modulate Na,K-ATPase activity in an isoform-specific manner and that the regulatory range includes both stimulation and inhibition of enzyme activity. Cholinergic modulation of Na,K-ATPase activity is achieved, in part, through activation of PKC and phosphorylation of PLM

Gene expression patterns associated with blood-feeding in the malaria mosquito Anopheles gambiae

BACKGROUND: Blood feeding, or hematophagy, is a behavior exhibited by female mosquitoes required both for reproduction and for transmission of pathogens. We determined the expression patterns of 3,068 ESTs, representing ~2,000 unique gene transcripts using cDNA microarrays in adult female Anopheles gambiae at selected times during the first two days following blood ingestion, at 5 and 30 min during a 40 minute blood meal and at 0, 1, 3, 5, 12, 16, 24 and 48 hours after completion of the blood meal and compared their expression to transcript levels in mosquitoes with access only to a sugar solution. RESULTS: In blood-fed mosquitoes, 413 unique transcripts, approximately 25% of the total, were expressed at least two-fold above or below their levels in the sugar-fed mosquitoes, at one or more time points. These differentially expressed gene products were clustered using k-means clustering into Early Genes, Middle Genes, and Late Genes, containing 144, 130, and 139 unique transcripts, respectively. Several genes from each group were analyzed by quantitative real-time PCR in order to validate the microarray results. CONCLUSION: The expression patterns and annotation of the genes in these three groups (Early, Middle, and Late genes) are discussed in the context of female mosquitoes' physiological responses to blood feeding, including blood digestion, peritrophic matrix formation, egg development, and immunity

Ortervirales: A new viral order unifying five families of reverse-transcribing viruses

Reverse-transcribing viruses, which synthesize a copy of genomic DNA from an RNA template, are widespread in animals, plants, algae and fungi (1, 2).

The representation of protein complexes in the Protein Ontology (PRO)

BACKGROUND: Representing species-specific proteins and protein complexes in ontologies that are both human- and machine-readable facilitates the retrieval, analysis, and interpretation of genome-scale data sets. Although existing protin-centric informatics resources provide the biomedical research community with well-curated compendia of protein sequence and structure, these resources lack formal ontological representations of the relationships among the proteins themselves. The Protein Ontology (PRO) Consortium is filling this informatics resource gap by developing ontological representations and relationships among proteins and their variants and modified forms. Because proteins are often functional only as members of stable protein complexes, the PRO Consortium, in collaboration with existing protein and pathway databases, has launched a new initiative to implement logical and consistent representation of protein complexes. DESCRIPTION: We describe here how the PRO Consortium is meeting the challenge of representing species-specific protein complexes, how protein complex representation in PRO supports annotation of protein complexes and comparative biology, and how PRO is being integrated into existing community bioinformatics resources. The PRO resource is accessible at http://pir.georgetown.edu/pro/. CONCLUSION: PRO is a unique database resource for species-specific protein complexes. PRO facilitates robust annotation of variations in composition and function contexts for protein complexes within and between species

Reference material for radionuclides in sediment IAEA-384 (Fangataufa Lagoon sediment)

Author Posting. © Springer, 2007. This is the author's version of the work. It is posted here by permission of Springer for personal use, not for redistribution. The definitive version was published in Journal of Radioanalytical and Nuclear Chemistry 273 (2007): 383-393, doi:10.1007/s10967-007-6898-4.A reference material designed for the determination of anthropogenic and natural radionuclides in sediment, IAEA-384 (Fangataufa Lagoon sediment), is described and the results of certification are presented. The material has been certified for 8 radionuclides (40K, 60Co, 155Eu, 230Th, 238U, 238Pu, 239+240Pu and 241Am). Information values are given for 12 radionuclides (90Sr, 137Cs, 210Pb (210Po), 226Ra, 228Ra, 232Th, 234U, 235U, 239Pu, 240Pu and 241Pu). Less reported radionuclides include 228Th, 236U, 239Np and 242Pu. The reference material may be used for quality management of radioanalytical laboratories engaged in the analysis of radionuclides in the environment, as well as for the development and validation of analytical methods and for training purposes. The material is available from IAEA in 100 g units

Decreased Neutrophil Apoptosis in Quiescent ANCA-Associated Systemic Vasculitis

Background: ANCA-Associated Systemic Vasculitis (AASV) is characterized by leukocytoclasis, accumulation of unscavenged apoptotic and necrotic neutrophils in perivascular tissues. Dysregulation of neutrophil cell death may contribute directly to the pathogenesis of AASV. less thanbrgreater than less thanbrgreater thanMethods: Neutrophils from Healthy Blood Donors (HBD), patients with AASV most in complete remission, Polycythemia Vera (PV), Systemic Lupus Erythematosus (SLE), Rheumatoid Arthritis (RA) and renal transplant recipients (TP) were incubated in vitro, and the rate of spontaneous apoptosis was measured by FACS. Plasma levels of cytokines and sFAS were measured with cytometric bead array and ELISA. Expression of pro/anti-apoptotic factors, transcription factors C/EBP-alpha, C/EBP-beta and PU.1 and inhibitors of survival/JAK2-pathway were measured by real-time-PCR. less thanbrgreater than less thanbrgreater thanResults: AASV, PV and RA neutrophils had a significantly lower rate of apoptosis compared to HBD neutrophils (AASV 50 +/- 14% vs. HBD 64 +/- 11%, p andlt; 0.0001). In RA but not in AASV and PV, low apoptosis rate correlated with increased plasma levels of GM-CSF and high mRNA levels of anti-apoptotic factors Bcl-2A1 and Mcl-1. AASV patients had normal levels of G-CSF, GM-CSF and IL-3. Both C/EBP-alpha, C/EBP-beta were significantly higher in neutrophils from AASV patients than HBD. Levels of sFAS were significantly higher in AASV compared to HBD. less thanbrgreater than less thanbrgreater thanConclusion: Neutrophil apoptosis rates in vitro are decreased in AASV, RA and PV but mechanisms seem to differ. Increased mRNA levels of granulopoiesis-associated transcription factors and increased levels of sFAS in plasma were observed in AASV. Additional studies are required to define the mechanisms behind the decreased apoptosis rates, and possible connections with accumulation of dying neutrophils in regions of vascular lesions in AASV patients.Funding Agencies|Swedish Research Council|71X-15152|Crafoord Foundation||</p

Protein Phosphatase 2A Interacts with the Na+,K+-ATPase and Modulates Its Trafficking by Inhibition of Its Association with Arrestin

Background: The P-type ATPase family constitutes a collection of ion pumps that form phosphorylated intermediates during ion transport. One of the best known members of this family is the Na +,K +-ATPase. The catalytic subunit of the Na +,K +-ATPase includes several functional domains that determine its enzymatic and trafficking properties. Methodology/Principal Findings: Using the yeast two-hybrid system we found that protein phosphatase 2A (PP2A) catalytic C-subunit is a specific Na +,K +-ATPase interacting protein. PP-2A C-subunit interacted with the Na +,K +-ATPase, but not with the homologous sequences of the H +,K +-ATPase. We confirmed that the Na +,K +-ATPase interacts with a complex of A- and C-subunits in native rat kidney. Arrestins and G-protein coupled receptor kinases (GRKs) are important regulators of G-protein coupled receptor (GPCR) signaling, and they also regulate Na +,K +-ATPase trafficking through direct association. PP2A inhibits association between the Na +,K +-ATPase and arrestin, and diminishes the effect of arrestin on Na +,K +-ATPase trafficking. GRK phosphorylates the Na +,K +-ATPase and PP2A can at least partially reverse this phosphorylation. Conclusions/Significance: Taken together, these data demonstrate that the sodium pump belongs to a growing list of io

Resolution of inflammation: a new therapeutic frontier

Dysregulated inflammation is a central pathological process in diverse disease states. Traditionally, therapeutic approaches have sought to modulate the pro- or anti-inflammatory limbs of inflammation, with mixed success. However, insight into the pathways by which inflammation is resolved has highlighted novel opportunities to pharmacologically manipulate these processes — a strategy that might represent a complementary (and perhaps even superior) therapeutic approach. This Review discusses the state of the art in the biology of resolution of inflammation, highlighting the opportunities and challenges for translational research in this field