Characterization of the Darboux point for particular classes of problems

A minimal sufficient condition for global optimality involving the Darboux point, analogous to the minimal sufficient condition of local optimality involving the conjugate point, is presented. The Darboux point is then characterized for optimal control problems with linear dynamics, cost functionals with a general terminal state term and an integrand quadratic in the state and control, and general terminal conditions. The Darboux point is shown to be the supremum of a sequence of conjugate points. If the terminal state term is quadratic, along with a scalar quadratic boundary condition, then the Darboux point is also the time at which the Riccati matrix becomes unbounded, giving a characterization of the unboundedness of the Riccati matrix at points which are not in general conjugate points.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45212/1/10957_2004_Article_BF01268173.pd

The Darboux point

A theory of global optimality based upon the Darboux-point concept is developed. A definition is proposed for the Darboux point, and the Darboux point is shown to exist on nonglobally optimal trajectories under relatively general conditions. A mutually exclusive classification of Darboux points is noted, and several properties are proved for one of these classes (the Type-1 Darboux point). Numerous examples are included to illustrate the Darboux-point definition and properties.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45205/1/10957_2004_Article_BF00932789.pd

NP-hardness of Deciding Convexity of Quartic Polynomials and Related Problems

We show that unless P=NP, there exists no polynomial time (or even pseudo-polynomial time) algorithm that can decide whether a multivariate polynomial of degree four (or higher even degree) is globally convex. This solves a problem that has been open since 1992 when N. Z. Shor asked for the complexity of deciding convexity for quartic polynomials. We also prove that deciding strict convexity, strong convexity, quasiconvexity, and pseudoconvexity of polynomials of even degree four or higher is strongly NP-hard. By contrast, we show that quasiconvexity and pseudoconvexity of odd degree polynomials can be decided in polynomial time.Comment: 20 page

Polarized secretion of Leukemia Inhibitory Factor

<p>Abstract</p> <p>Background</p> <p>The direction of cytokine secretion from polarized cells determines the cytokine's cellular targets. Leukemia inhibitory factor (LIF) belongs to the interleukin-6 (IL-6) family of cytokines and signals through LIFR/gp130. Three factors which may regulate the direction of LIF secretion were studied: the site of stimulation, signal peptides, and expression levels. Stimulation with IL-1β is known to promote IL-6 secretion from the stimulated membrane (apical or basolateral) in the human intestinal epithelial cell line Caco-2. Since LIF is related to IL-6, LIF secretion was also tested in Caco-2 following IL-1β stimulation. Signal peptides may influence the trafficking of LIF. Two isoforms of murine LIF, LIF-M and LIF-D, encode different signal peptides which have been associated with different locations of the mature protein in fibroblasts. To determine the effect of the signal peptides on LIF secretion, secretion levels were compared in Madin-Darby canine kidney (MDCK) clones which expressed murine LIF-M or LIF-D or human LIF under the control of an inducible promoter. Low and high levels of LIF expression were also compared since saturation of the apical or basolateral route would reveal specific transporters for LIF.</p> <p>Results</p> <p>When Caco-2 was grown on permeable supports, LIF was secreted constitutively with around 40% secreted into the apical chamber. Stimulation with IL-1β increased LIF production. After treating the apical surface with IL-1β, the percentage secreted apically remained similar to the untreated, whereas, when the cells were stimulated at the basolateral surface only 20% was secreted apically. In MDCK cells, an endogenous LIF-like protein was detected entirely in the apical compartment. The two mLIF isoforms showed no difference in their secretion patterns in MDCK. Interestingly, about 70% of murine and human LIF was secreted apically from MDCK over a 400-fold range of expression levels within clones and a 200,000-fold range across clones.</p> <p>Conclusion</p> <p>The site of stimulation affected the polarity of LIF secretion, while, signal peptides and expression levels did not. Exogenous LIF is transported in MDCK without readily saturated steps.</p

Efficient Generation of Germ Line Transmitting Chimeras from C57BL/6N ES Cells by Aggregation with Outbred Host Embryos

Genetically modified mouse strains derived from embryonic stem (ES) cells have become essential tools for functional genomics and biomedical research. Large scale mutagenesis projects are producing libraries of mutant C57BL/6 (B6) ES cells to enable the functional annotation of every gene of the mouse genome. To realize the utility of these resources, efficient and accessible methods of generating mutant mice from these ES cells are necessary. Here, we describe a combination of ICR morula aggregation and a chemically-defined culture medium with widely available and accessible components for the high efficiency generation of germline transmitting chimeras from C57BL/6N ES cells. Together these methods will ease the access of the broader biomedical research community to the publicly available B6 ES cell resources

Histone H1 Depletion Impairs Embryonic Stem Cell Differentiation

Pluripotent embryonic stem cells (ESCs) are known to possess a relatively open chromatin structure; yet, despite efforts to characterize the chromatin signatures of ESCs, the role of chromatin compaction in stem cell fate and function remains elusive. Linker histone H1 is important for higher-order chromatin folding and is essential for mammalian embryogenesis. To investigate the role of H1 and chromatin compaction in stem cell pluripotency and differentiation, we examine the differentiation of embryonic stem cells that are depleted of multiple H1 subtypes. H1c/H1d/H1e triple null ESCs are more resistant to spontaneous differentiation in adherent monolayer culture upon removal of leukemia inhibitory factor. Similarly, the majority of the triple-H1 null embryoid bodies (EBs) lack morphological structures representing the three germ layers and retain gene expression signatures characteristic of undifferentiated ESCs. Furthermore, upon neural differentiation of EBs, triple-H1 null cell cultures are deficient in neurite outgrowth and lack efficient activation of neural markers. Finally, we discover that triple-H1 null embryos and EBs fail to fully repress the expression of the pluripotency genes in comparison with wild-type controls and that H1 depletion impairs DNA methylation and changes of histone marks at promoter regions necessary for efficiently silencing pluripotency gene Oct4 during stem cell differentiation and embryogenesis. In summary, we demonstrate that H1 plays a critical role in pluripotent stem cell differentiation, and our results suggest that H1 and chromatin compaction may mediate pluripotent stem cell differentiation through epigenetic repression of the pluripotency genes

Are LIF and Related Cytokines Functionally Equivalent?

International audienceLeukemia inhibitory factor (LIF) is structurally related to interleukin-6 (IL-6), oncostatin M (OSM), and ciliary neurotrophic factor (CNTF). Since LIF-deficient mice do not exhibit overt phenotypic effects in cell types known to be targets for LIF action in vitro, we examined the ability of IL-6, OSM, and CNTF to reproduce the effects of LIF in five different bioassays. OSM, CNTF, and LIF are able to promote embryonic stem cell growth and to maintain them in an undifferentiated state as marked by a high alkaline phosphatase activity (ED50 are, respectively, 0.5, 3 and 1 ng/ml). Whereas LIF and OSM maintain close to 100% of ES cells in an undifferentiated state, CNTF, at optimal concentrations, prevents differentiation of only 60% of the ES population. Murine 7TD1 hybridoma cell growth is induced only in the presence of IL-6 (ED50 = 0.1 ng/ml). Both LIF and OSM stimulate DA1a cell proliferation (ED50 are, respectively, 1 and 12 ng/ml). OSM appears, therefore, to act as a weak agonist of LIF-dependent processes on murine cells, however, with a 10-fold lower specific activity than that of LIF, which is in agreement with human OSM cross-reacting with the murine LIF-R. Though IL-6, LIF, and OSM all stimulate haptoglobin and fibrinogen production by human HepG2 hepatoma cells, the dose-response curves of these three factors exhibit very different characteristics. CNTF stimulates acute-phase protein production by HepG2 cells only at high concentrations (greater than 1 microgram/ml). A549 epithelial cells are subjected to growth inhibition only in the presence of OSM (ED50 = 6 ng/ml), even though they expressed LIF-R and gp130 transcripts. These data suggest that OSM and LIF act on human cells through different receptors. Altogether, these results indicate that none of the factors examined in this study are precisely interchangeable in terms of their biological actions

Characterization of a binding protein for leukemia inhibitory factor localized in extracellular matrix

International audienceLeukemia Inhibitory Factor (LIF) interacts with two classes of high affinity binding sites on rat UMR cells cultured in monolayer. One class of binding sites was found to be localized in the extracellular matrix (ECM) after removal of cells from the culture dish. The interaction of LIF with ECM-localized binding sites is not dependent upon either glycosylation of LIF or the presence of extracellular glycosyaminoglycans. Chemical cross-linking studies demonstrate that LIF interacts with a 200-kD cell-associated protein and a 140-kD ECM-localized protein. A 140-kD protein could also be specifically precipitated from solubilised metabolically radiolabeled UMR ECM by antibodies directed against LIF by virtue of its ability to form a stable complex with unlabeled LIF. In addition, soluble LIF associated with this ECM-localized protein is biologically active in terms of inhibition of ES cell differentiation. The properties of ECM-localized 140-kD species are very similar to those of the secreted form of the LIF receptor suggesting that the ECM localization of LIF and LIF signal transduction may be closely coupled

Presence of basic fibroblast growth factor receptors in bovine brain membranes.

International audienceWe described a protocol for purification of bovine brain membranes suitable to study the binding of iodinated basic fibroblast growth factor (FGF) to bovine brain membrane preparation. The binding of 125I basic FGF to brain membranes reached equilibrium within 30 min at 20 degrees C, was reversible, and displaced by an excess of unlabeled basic FGF. Scatchard analysis of the data revealed that two classes of binding sites could be detected with an apparent Kd of 30 pM and a capacity of 0.24 pmol/mg of membrane proteins for the high affinity binding site and Kd of 3 nM with a capacity of 51 pmol/mg of membrane proteins for the low affinity binding site. Cross-linking experiments of labeled basic FGF to brain membrane receptor yield the formation of a single major complex with an apparent molecular mass of 170 kDa which is similar to the value obtained for the high affinity binding site for basic FGF on target cells in tissue culture. Hence these data present the first biochemical evidence suggesting that membrane purified from bovine brain contain two classes of specific binding sites for basic FGF and confirm results described with cells grown in vitro

Purification of a heparin binding FGF receptor (HB-FGFR) from adult bovine brain membranes.

International audienceA new form of high affinity fibroblast growth factor receptor has been purified from adult bovine brain membranes. Purification was performed by chromatography on DEAE-Trisacryl and wheat germ agglutinin-agarose followed by FGF-2 affinity chromatography. Affinity labeling of purified fractions with 125I-FGF-2 showed after cross-linking a 170-kDa complex, suggesting the existence of a 150-kDa FGF receptor. No cross-reactivity with anti-FGF receptor 1 (FGFR-1 or flg) or with anti-receptor 2 (FGFR-2 or bek) antibodies could be detected with this partially purified receptor. Heparitinase treatment of the partially purified FGF receptor abolished the formation of the ligand receptor complex. The complex was restored in the presence of heparin in a dose dependent fashion, supporting the idea that heparin-like molecules are needed for proper binding. Further purification of the receptor was achieved by heparin-Sepharose affinity chromatography and yielded a purification of over 320,000-fold. The purified receptor fraction was radiolabeled and loaded on RPLC C4 column. Eluted fractions were analysed by SDS-PAGE. A major 150-kDa band was detected. These data show for the first time a new form of FGF receptor isolated from bovine brain membranes. This purified receptor displays affinity for heparin and was therefore named heparin binding FGF receptor (HB-FGFR). It remains unclear whether the receptor is a proteo-heparin sulfate or whether heparans are strongly associated and therefore are copurified. Large scale preparations are in progress for core protein structure studies