On the minimization of Dirichlet eigenvalues of the Laplace operator

We study the variational problem \inf \{\lambda_k(\Omega): \Omega\ \textup{open in}\ \R^m,\ |\Omega| < \infty, \ \h(\partial \Omega) \le 1 \}, where $\lambda_k(\Omega)$ is the $k$'th eigenvalue of the Dirichlet Laplacian acting in $L^2(\Omega)$, \h(\partial \Omega) is the $(m-1)$- dimensional Hausdorff measure of the boundary of $\Omega$, and $|\Omega|$ is the Lebesgue measure of $\Omega$. If $m=2$, and $k=2,3, \cdots$, then there exists a convex minimiser $\Omega_{2,k}$. If $m \ge 2$, and if $\Omega_{m,k}$ is a minimiser, then $\Omega_{m,k}^*:= \textup{int}(\overline{\Omega_{m,k}})$ is also a minimiser, and $\R^m\setminus \Omega_{m,k}^*$ is connected. Upper bounds are obtained for the number of components of $\Omega_{m,k}$. It is shown that if $m\ge 3$, and $k\le m+1$ then $\Omega_{m,k}$ has at most $4$ components. Furthermore $\Omega_{m,k}$ is connected in the following cases : (i) $m\ge 2, k=2,$ (ii) $m=3,4,5,$ and $k=3,4,$ (iii) $m=4,5,$ and $k=5,$ (iv) $m=5$ and $k=6$. Finally, upper bounds on the number of components are obtained for minimisers for other constraints such as the Lebesgue measure and the torsional rigidity.Comment: 16 page

Microbiota as a mediator of cancer progression and therapy

Complex and intricate circuitries regulate cellular proliferation, survival, and growth, and alterations of this network through genetic and epigenetic events result in aberrant cellular behaviors, often leading to carcinogenesis. Although specific germline mutations have been recognized as cancer inducers, the vast majority of neoplastic changes in humans occur through environmental exposure, lifestyle, and diet. An emerging concept in cancer biology implicates the microbiota as a powerful environmental factor modulating the carcinogenic process. For example, the intestinal microbiota influences cancer development or therapeutic responses through specific activities (immune responses, metabolites, microbial structures, and toxins). The numerous effects of microbiota on carcinogenesis, ranging from promoting, preventing, or even influencing therapeutic outcomes, highlight the complex relationship between the biota and the host. In this review, we discuss the latest findings on this complex microbial interaction with the host and highlight potential mechanisms by which the microbiota mediates such a wide impact on carcinogenesis

Changes in hemlock looper [Lepidoptera: Geometridae] pupal distribution through a 3-year outbreak cycle

La distribution des chrysalides de l’arpenteuse de la pruche, Lambdina fiscellaria, a été étudiée au cours d’un cycle épidémique d’une durée de trois ans près du Lac Princeton sur l’île d’Anticosti au Québec. Au total, 10 sapins ont été coupés et toutes les chrysalides ont été comptées sur le tronc et les branches (partie non-foliée vs foliée) de la cime inférieure, médiane et supérieure, ainsi que sur le tronc sous la cime. En condition préépidémique, les chrysalides ont principalement été trouvées sur les branches des cimes médianes et supérieures. Durant l’épidémie, la densité des chrysalides n’a pas augmenté dans ces sites de pupaison et les larves se sont surtout transformées en chrysalides sur le tronc, à partir du sol jusque dans la cime médiane, ainsi que sur les branches de la cime inférieure. Peu de chrysalides ont été trouvées sur la partie foliée des branches en période post-épidémique, la plupart étant trouvées sur la partie basale non-foliée qui apparaît comme un endroit préférentiel pour la pupaison de l'arpenteuse de la pruche. De façon à optimiser la détection des augmentations de populations dans les réseaux de surveillance, des pièges à chrysalides devraient être placés à hauteur de poitrine sur le tronc de sapins baumiers.The hemlock looper, Lambdina fiscellaria, pupal distribution was studied through a 3-year outbreak cycle near Lac Princeton on Anticosti Island in Quebec. Over the 3 years, 10 balsam fir trees were cut and all pupae were counted on the stem and branches (non-foliated vs foliated parts) of the lower, middle and upper crowns and on the stem below crown. In pre-outbreak conditions, pupae were mostly found on branches of the middle and upper crowns. During the outbreak, pupal density did not increase on these parts of the trees, since pupae were mostly found on the stem, from the ground to the middle crown, and on branches of the lower crown. Few pupae were found on the foliated portion of branches in post-outbreak conditions but most were found on the basal non-foliated part of branches, which appears to be a preferred location for hemlock looper pupation. In order to optimize detection of population increases in monitoring networks, we suggest using pupal traps at breast height on balsam fir trees

Glafenine-induced intestinal injury in zebrafish is ameliorated by -opioid signaling via enhancement of Atf6-dependent cellular stress responses

Beside their analgesic properties, opiates exert beneficial effects on the intestinal wound healing response. In this study, we investigated the role of μ-opioid receptor (MOR) signaling on the unfolded protein response (UPR) using a novel zebrafish model of NSAID-induced intestinal injury. The NSAID glafenine was administered to zebrafish larvae at 5 days post-fertilization (dpf) for up to 24 hours in the presence or absence of the MOR-specific agonist DALDA. By analysis with histology, transmission electron microscopy and vital dye staining, glafenine-treated zebrafish showed evidence of endoplasmic reticulum and mitochondrial stress, with disrupted intestinal architecture and halted cell stress responses, alongside accumulation of apoptotic intestinal epithelial cells in the lumen. Although the early UPR marker BiP was induced with glafenine-induced injury, downstream atf6 and s-xbp1 expression were paradoxically not increased, explaining the halted cell stress responses. The μ-opioid agonist DALDA protected against glafenine-induced injury through induction of atf6-dependent UPR. Our findings show that DALDA prevents glafenine-induced epithelial damage through induction of effective UPR

Tumor Necrosis Factor (TNF) α Increases Collagen Accumulation and Proliferation in Intestinal Myofibroblasts via TNF Receptor 2

Intestinal fibrosis is an incurable complication of Crohn's disease involving increased numbers of collagen-producing myofibroblasts. Tumor necrosis factor (TNF) alpha has defined proinflammatory roles in Crohn's disease but its role in fibrosis is unclear. We tested the hypothesis that TNFalpha increases collagen accumulation and proliferation in intestinal myofibroblasts and has additive effects in combination with insulin-like growth factor (IGF) I. The mechanisms, TNF receptor isoform, and downstream signaling pathways were examined. Intestinal myofibroblasts from wild-type (WT) mice or mice homozygous for disruption of genes encoding TNFR1 (TNFR1-/-), TNFR2 (TNFR2-/-), or both (TNFR1/2-/-), were treated with TNFalpha, IGF-I, or both. In WT cells, TNFalpha and IGF-I stimulated type I collagen accumulation and DNA synthesis in an additive manner. IGF-I, but not TNFalpha, stimulated type I collagen gene activation. TNFalpha, but not IGF-I, induced tissue inhibitor of metalloproteinase-1 (TIMP-1) expression and reduced matrix metalloproteinases-2 activity and collagen degradation. TNFalpha also activated ERK1/2. These responses to TNFalpha were absent in TNFR2-/- and TNFR1/2-/- myofibroblasts, whereas TNFR1-/- cells showed similar responses to WT. Inhibition of ERK1/2 diminished TNFalpha induced DNA synthesis in WT and TNFR1-/- cells. Differences in TNFalpha-induced STAT3/DNA binding activity and not NFkappaB and AP-1 transcriptional activation correlated with impaired collagen accumulation/TIMP-1 induction in TNFR2(-/-) cells. Constitutively active STAT3 rescued TIMP-1 expression in TNFR2-/- cells. We conclude that TNFalpha and IGF-I may additively contribute to fibrosis during intestinal inflammation. TNFR2 is a primary mediator of fibrogenic actions of TNFalpha acting through ERK1/2 to stimulate proliferation and through STAT3 to stimulate TIMP-1 and inhibit collagen degradation

Solid state image sensor research, phase 2

Solid state image sensor arra

GSK3β inhibition blocks melanoma cell/host interactions by downregulating N-cadherin expression and decreasing FAK phosphorylation.

This study addresses the role of glycogen synthase kinase (GSK)-3β signaling in the tumorigenic behavior of melanoma. Immunohistochemical staining revealed GSK3β to be focally expressed in the invasive portions of 12 and 33% of primary and metastatic melanomas, respectively. GSK3 inhibitors and small interfering RNA (siRNA) knockdown of GSK3β were found to inhibit the motile behavior of melanoma cells in scratch wound, three-dimensional collagen-implanted spheroid, and modified Boyden chamber assays. Functionally, inhibition of GSK3β signaling was found to suppress N-cadherin expression at the messenger RNA and protein levels, and was associated with decreased expression of the transcription factor Slug. Pharmacological and genetic ablation of GSK3β signaling inhibited the adhesion of melanoma cells to both endothelial cells and fibroblasts and prevented transendothelial migration, an effect rescued by the forced overexpression of N-cadherin. A further role for GSK3β signaling in invasion was suggested by the ability of GSK3β inhibitors and siRNA knockdown to block phosphorylation of focal adhesion kinase (FAK) and increase the size of focal adhesions. In summary, we have, to our knowledge, demonstrated a previously unreported role for GSK3β in modulating the motile and invasive behavior of melanoma cells through N-cadherin and FAK. These studies suggest the potential therapeutic utility of inhibiting GSK3β in defined subsets of melanoma

Gut microbial diversity is reduced by the probiotic VSL#3 and correlates with decreased TNBS-induced colitis:

Compositional changes within the normal intestinal microbiota have been associated with the development of various intestinal inflammatory disorders such as pouchitis and inflammatory bowel diseases (IBD). Therefore, it has been speculated that manipulation of a dysbiotic intestinal microbiota has the potential to restore microbial homeostasis and attenuate inflammation