Existence results of positive solutions for Kirchhoff type equations via bifurcation methods

In this paper we address the following Kirchhoff type problem \begin{equation*} \left\{ \begin{array}{ll} -\Delta(g(|\nabla u|_2^2) u + u^r) = a u + b u^p& \mbox{in}~\Omega, u>0& \mbox{in}~\Omega, u= 0& \mbox{on}~\partial\Omega, \end{array} \right. \end{equation*} in a bounded and smooth domain $\Omega$ in ${\rm I}\hskip -0.85mm{\rm R}$. By using change of variables and bifurcation methods, we show, under suitable conditions on the parameters $a,b,p,r$ and the nonlinearity $g$, the existence of positive solutions.Comment: 18 pages, 1 figur

Using association rules mining to explore pattern of Chinese medicinal formulae (prescription) in treating and preventing breast cancer recurrence and metastasis.

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Overall scheme of the regulatory network involved in the inhibitory effect of ISL on breast cancer neoangiogenesis.

<p>Overall scheme of the regulatory network involved in the inhibitory effect of ISL on breast cancer neoangiogenesis.</p

ISL suppressed VEGFR-2 kinase activity and its downstream signaling.

<p>(A) HUVECs were treated with various concentrations of ISL for 12 h under the stimulation of VEGF (20 ng/ml). Western blotting results showed that the p-VEGFR-2 expression was gradually down-regulated with the increasing dose of ISL; (B) ISL inhibited VEGFR-2 kinase activity. VEGFR-2 and various concentrations of ISL were incubated in kinase reaction buffer in 96-well plates coated with a poly-Glu-Tyr substrate. Phosphorylation of the substrate was monitored with a purified phosphotyrosine specific monocolonal antibody conjugated to horseradish peroxidase followed by chromogenic reaction with horseradish peroxidase substrate. The inhibition IC 50 of ISL on VEGFR-2 activation was determined about 100 nM; (C) Whole-cell extracts were collected and analyzed by Co-IP assay and Western blotting using antibodies against VEGF, VEGFR-2 and P^Tyr1175-VEGFR-2. The results showed that ISL did not interfere with VEGF binding to VEGFR-2; (D) The VEGFR-2 downstream signalings including p-ERK/ERK, p-JNK/JNK, p-AKT/AKT and eNOS were also inhibited after ISL administration demonstrated by Western blotting. Meanwhile, the MMPs activities in the supernatants of HUVECs treated with ISL were also analyzed by gelatin zymography. The results indicated that the MMP-2 activity was also down-regulated by ISL. (All values represented as mean ± SD, n = 3, *<i>P</i><0.05, ** <i>P</i><0.01 <i>versus</i> untreated control).</p

ISL interacted with the ATP-binding site of VEGFR-2 kinase domain.

<p>The CDOCKER module in Discovery studio (DS) 2.1 was applied to predict the binding mode of ISL with the ATP-binding domain of VEGFR-2. The results revealed that ISL could stably bind to the ATP-binding pocket near the hinge region. Detailed interaction mode were displayed in the upper panel, where ISL could form 2–3 potential hydrogen bonds with the residues Glu885 and Asp1046. A <b>π-π</b> stacking interaction with Lys868 is also occurred. The other benzene ring of ISL could form potential hydrogen bonds with Cys919, which benefits the balance of ISL in VEGFR-2 binding.</p

ISL suppressed sprout formation on the chick aortic ring.

<p>The chick aortic ring was embedded in Matrigel and fed with M199 serum free medium containing various concentrations of ISL in the presence of VEGF. (A) ISL exhibited dose-dependently inhibition effects (a: 0; b: 5 µM, c: 10 µM; d: 20 µM) on the sprout formation after 3 days; (B) ISL at 20 µM significantly inhibited sprout formation in a time-dependent manner from 24 h to 72 h; (C) Sprout inhibition effects of ISL was reversed after ISL removed from the culture system. Aortic rings were firstly incubated with ISL (20 uM ) for 48 h. The culture medium was then replaced with fresh medium without ISL and further incubation with VEGF stimulation for 72 h, the sprout was re-organized and growing, indicating ISL brought little toxicity effects on the normal tissues. (All values represented as means ± SD, n = 3, * <i>P</i><0.05 <i>versus</i> untreated control).</p

ISL inhibited tumor growth and angiogenesis on MDA-MB-231 breast cancer xenografts.

<p>(A) Nude mice bearing breast cancer were treated with the vehicle or ISL (25 and 50 mg/kg/d). The results showed that ISL significantly attenuated breast cancer growth in a dose-dependent manner; (B) The tumor weights in ISL- treated group were significantly decreased in comparison with the vehicle control; (C) The body weights between control and ISL-treated group had little differences, indicating ISL might have little toxicity effects on mice; (D) The tumor tissues removed from mice were processed for immunohistochemistry detected with antibodies for CD31, VEGF, p-VEGFR-2 and MMP-2. The results showed that the tumor MVD was significantly inhibited by ISL. Meanwhile, ISL significantly suppressed the expression of VEGF, p-VEGFR-2 and MMP-2 <i>in vivo</i>; (E) HE analysis demonstrated that ISL had little influences on the micro-morphology of normal tissues including heart, liver, spleen, lung and kidney (All values represented as means ± SD, n = 6, * <i>P</i><0.05, <i>versus</i> control).</p

ISL inhibited VEGF-induced tube formation, invasion and migration.

<p>(A) HUVECs were seeded at a density of 1×10⁴ cells/well per 24-well plate. Plates were previously coated with Matrigel and stimulated with VEGF (20 ng/ml) in the presence or absence of ISL (a: 0; b: 5 µM, c: 10 µM; d: 20 µM) for 12 h. The results showed that ISL significantly abrogated the formation of capillary network; (B) HUVECs at a density of 5×10⁵ cells/ml were plated onto the upper membrane of 6-well transwell coated with Matrigel. After 24 h, cells that invasive to the opposite side of the membrane were counted (a: 0; b: 5 µM, c: 10 µM; d: 20 µM). The results revealed that ISL decreased invasive ability of HUVECs in a dose-dependent manner; (C) HUVECs at a density of 5×10⁵ cells/ml were seeded in a 6-well plate for wound healing assay. The results showed that ISL (20 µM) significantly inhibited endothelial cells migration under the stimulation of VEGF (All values represented as mean ± SD, n = 3, *<i>P</i><0.05 <i>versus</i> untreated control).</p

ISL inhibited endothelial cells proliferation.

<p>(A) After incubation with various concentrations of ISL for 48 h with and without VEGF stimulation, the number of endothelial cells were counted. The results showed that the HUVEC proliferation was inhibited by ISL in a dose-dependent manner; (B) Breast cancer cells MDA-MB-231, MCF-7 and endothelial cells were treated with various concentrations of ISL and cells were counted after 48 h. ISL exhibited a specific proliferation inhibition effect on endothelial cells in comparison with that of breast cancer cells. Data are represented as a percentage of the vehicle-treated control; (C) Endothelial cells were treated with various concentrations of ISL plus with VEGF stimulation for 48 h and labeling with BrdU. DNA synthesis was measured by enzyme-linked immunosorbent assay. ISL significantly suppressed DNA synthesis of endothelial cells in a dose-dependent manner; (D) Cell cycle analysis revealed that after ISL (20 µM) treatment for 48 h, the cell cycle of HUVECs was significantly arrested at G2/M checkpoint; (E) Endothelial cells culture supernatants after ISL treatment were collected and analyzed for LDH activity assay. The results showed that ISL administration did not lead to LDH release from cells, indicating that ISL has little cytotoxicty effect on endothelial cells; (F) After ISL (20 µM) administration for 48 h, there has little morphological changes of endothelial cells, further implying that ISL brought limited toxicity effects on HUVECs at low doses. (All values represented as mean ± SD, n = 6, *<i>P</i><0.05, ** <i>P</i><0.01 <i>versus</i> untreated control).</p

MOESM4 of Relationship between Chinese medicine dietary patterns and the incidence of breast cancer in Chinese women in Hong Kong: a retrospective cross-sectional survey

Additional file 4. Questionnaire-N-dietary