On a classical renorming construction of V. Klee

We further develop a classical geometric construction of V. Klee and show, typically, that if X is a nonreflexive Banach space with separable dual, then X admits an equivalent norm vertical bar . vertical bar which is Frechet differentiable, locally uniformly rotund, its dual norm vertical bar . vertical bar* is uniformly Gateaux differentiable, the weak* and the norm topologies coincide on the sphere of (X*, vertical bar . vertical bar*) and, yet, vertical bar . vertical bar* is not rotund. This proves (a stronger form of) a conjecture of V. Klee. (C) 2011 Elsevier Inc.Supported in part by a grant AVOZ 101 905 03 and IAA 100190901 (Czech Republic).Guirao Sánchez, AJ.; Montesinos Santalucia, V.; Zizler, V. (2012). On a classical renorming construction of V. Klee. Journal of Mathematical Analysis and Applications. 385(1):458-465. https://doi.org/10.1016/j.jmaa.2011.06.059S458465385

Reduced firing rates of pyramidal cells in the frontal cortex of APP/PS1 can be restored by acute treatment with levetiracetam

Contains fulltext : 229488.pdf (publisher's version ) (Closed access) Contains fulltext : 229488pre.pdf (Author’s version preprint ) (Open Access)In recent years, aberrant neural oscillations in various cortical areas have emerged as a common physiological hallmark across mouse models of amyloid pathology and patients with Alzheimer's disease. However, much less is known about the underlying effect of amyloid pathology on single cell activity. Here, we used high-density silicon probe recordings from frontal cortex area of 9-month-old APP/PS1 mice to show that local field potential power in the theta and beta band is increased in transgenic animals, whereas single-cell firing rates, specifically of putative pyramidal cells, are significantly reduced. At the same time, these sparsely firing pyramidal cells phase-lock their spiking activity more strongly to the ongoing theta and beta rhythms. Furthermore, we demonstrated that the antiepileptic drug, levetiracetam, counteracts these effects by increasing pyramidal cell firing rates in APP/PS1 mice and uncoupling pyramidal cells and interneurons. Overall, our results highlight reduced firing rates of cortical pyramidal cells as a pathophysiological phenotype in APP/PS1 mice and indicate a potentially beneficial effect of acute levetiracetam treatment

SlCCD7 controls strigolactone biosynthesis, shoot branching and mycorrhiza-induced apocarotenoid formation in tomato.

The regulation of shoot branching is an essential determinant of plant architecture, integrating multiple external and internal signals. One of the signaling pathways regulating branching involves the MAX (more axillary branches) genes. Two of the genes within this pathway, MAX3/CCD7 and MAX4/CCD8, encode carotenoid cleavage enzymes involved in generating a branch-inhibiting hormone, recently identified as strigolactone. Here, we report the cloning of SlCCD7 from tomato. As in other species, SlCCD7 encodes an enzyme capable of cleaving cyclic and acyclic carotenoids. However, the SlCCD7 protein has 30 additional amino acids of unknown function at its C terminus. Tomato plants expressing a SlCCD7 antisense construct display greatly increased branching. To reveal the underlying changes of this strong physiological phenotype, a metabolomic screen was conducted. With the exception of a reduction of stem amino acid content in the transgenic lines, no major changes were observed. In contrast, targeted analysis of the same plants revealed significantly decreased levels of strigolactone. There were no significant changes in root carotenoids, indicating that relatively little substrate is required to produce the bioactive strigolactones. The germination rate of Orobanche ramosa seeds was reduced by up to 90% on application of extract from the SlCCD7 antisense lines, compared with the wild type. Additionally, upon mycorrhizal colonization, C13 cyclohexenone and C14 mycorradicin apocarotenoid levels were greatly reduced in the roots of the antisense lines, implicating SlCCD7 in their biosynthesis. This work demonstrates the diverse roles of MAX3/CCD7 in strigolactone production, shoot branching, source–sink interactions and production of arbuscular mycorrhiza-induced apocarotenoids