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In this paper we present a complete classification of the isolated central configurations of the five-body problem with equal masses. This is accomplished by using the polyhedral homotopy method to approximate all the isolated solutions of the Albouy-Chenciner equations. The existence of exact solutions, in a neighborhood of the approximated ones, is then verified using the Krawczyk method. Although the Albouy-Chenciner equations for the five-body problem are huge, it is possible to solve them in a reasonable amount of time.

The fabrication of crystalline COF materials with predictable structures and desirable features is one of the crystal engineering strategic goals. Many synthetic factors play an invisible role in the crystallization...

We report herein the synthesis of two carbazole-thiophene-based conjugated microporous polymers (Cz-3Th and Cz-4Th CMPs) with various degrees of planarity for photocatalytic hydrogen evolution from water. Interestingly, depending upon the...

The specialized cholesterol/sphingolipid-rich membrane domains termed lipid rafts are highly dynamic in the cancer cells, which rapidly assemble effector molecules to form a sorting platform essential for oncogenic signaling transduction in response to extra- or intracellular stimuli. Density-based membrane flotation, subcellular fractionation, cell surface biotinylation, and co-immunoprecipitation analyses of bichalcone analog ((E)-1-(4-Hydroxy-3-((4-(4-((E)-3-(pyridin-3-yl)acryloyl)phenyl)piperazin-1-yl)methyl)phenyl)-3-(pyridin-3-yl)prop-2-en-1-one (TSWU-BR4)-treated cancer cells showed dissociation between GRP78 and p85α conferring the recruitment of PTEN to lipid raft membranes associated with p85α. Ectopic expression of GRP78 could overcome induction of lipid raft membrane-associated p85α–unphosphorylated PTEN complex formation and suppression of GRP78−PI3K−Akt−GTP-Rac1-mediated and GRP78-regulated PERK−Nrf2 antioxidant pathway and cancer cell invasion by TSWU-BR4. Using specific inducer, inhibitor, or short hairpin RNA for ASM demonstrated that induction of the lipid raft membrane localization and activation of ASM by TSWU-BR4 is responsible for perturbing homeostasis of cholesterol and ceramide levels in the lipid raft and ER membranes, leading to alteration of GRP78 membrane trafficking and subsequently inducing p85α–unphosphorylated PTEN complex formation, causing disruption of GRP78−PI3K−Akt−GTP-Rac1-mediated signal and ER membrane-associated GRP78-regulated oxidative stress balance, thus inhibiting cancer cell invasion. The involvement of the enrichment of ceramide to lipid raft membranes in inhibition of NF-κB-mediated MMP-2 expression was confirmed through attenuation of NF-κB activation using C2-ceramide, NF-κB specific inhibitors, ectopic expression of NF-κB p65, MMP-2 promoter-driven luciferase, and NF-κB-dependent reporter genes. In conclusion, localization of ASM in the lipid raft membranes by TSWU-BR4 is a key event for initiating formation of ceramide-enriched lipid raft membrane platforms, which causes delocalization of GRP78 from the lipid raft and ER membranes to the cytosol and formation of p85α–unphosphorylated PTEN complexes to attenuate the GRP78-regulated oxidative stress balance and GRP78−p85α−Akt−GTP-Rac1−NF-κB−MMP-2-mediated cancer cell invasion.