Sharp Nash inequalities on manifolds with boundary in the presence of symmetries

In this paper we establish the best constant $\widetilde A_{opt}(\bar{M})$ for the Trace Nash inequality on a $n-$dimensional compact Riemannian manifold in the presence of symmetries, which is an improvement over the classical case due to the symmetries which arise and reflect the geometry of manifold. This is particularly true when the data of the problem is invariant under the action of an arbitrary compact subgroup $G$ of the isometry group $Is(M,g)$, where all the orbits have infinite cardinal

Intermediate filament–membrane attachments function synergistically with actin-dependent contacts to regulate intercellular adhesive strength

By tethering intermediate filaments (IFs) to sites of intercellular adhesion, desmosomes facilitate formation of a supercellular scaffold that imparts mechanical strength to a tissue. However, the role IF–membrane attachments play in strengthening adhesion has not been directly examined. To address this question, we generated Tet-On A431 cells inducibly expressing a desmoplakin (DP) mutant lacking the rod and IF-binding domains (DPNTP). DPNTP localized to the plasma membrane and led to dissociation of IFs from the junctional plaque, without altering total or cell surface distribution of adherens junction or desmosomal proteins. However, a specific decrease in the detergent-insoluble pool of desmoglein suggested a reduced association with the IF cytoskeleton. DPNTP-expressing cell aggregates in suspension or substrate-released cell sheets readily dissociated when subjected to mechanical stress whereas controls remained largely intact. Dissociation occurred without lactate dehydrogenase release, suggesting that loss of tissue integrity was due to reduced adhesion rather than increased cytolysis. JD-1 cells from a patient with a DP COOH-terminal truncation were also more weakly adherent compared with normal keratinocytes. When used in combination with DPNTP, latrunculin A, which disassembles actin filaments and disrupts adherens junctions, led to dissociation up to an order of magnitude greater than either treatment alone. These data provide direct in vitro evidence that IF–membrane attachments regulate adhesive strength and suggest furthermore that actin- and IF-based junctions act synergistically to strengthen adhesion

Sharp constants in weighted trace inequalities on Riemannian manifolds

We establish some sharp weighted trace inequalities W^{1,2}(\rho^{1-2\sigma}, M)\hookrightarrow L^{\frac{2n}{n-2\sigma}}(\pa M) on $n+1$ dimensional compact smooth manifolds with smooth boundaries, where $\rho$ is a defining function of $M$ and $\sigma\in (0,1)$. This is stimulated by some recent work on fractional (conformal) Laplacians and related problems in conformal geometry, and also motivated by a conjecture of Aubin.Comment: 34 page

A note on Kuttler-Sigillito's inequalities

We provide several inequalities between eigenvalues of some classical eigenvalue problems on domains with $C^2$ boundary in complete Riemannian manifolds. A key tool in the proof is the generalized Rellich identity on a Riemannian manifold. Our results in particular extend some inequalities due to Kutller and Sigillito from subsets of $\mathbb{R}^2$ to the manifold setting

Deposition of microparticles by neutrophils onto inflamed epithelium: a new mechanism to disrupt epithelial intercellular adhesions and promote transepithelial migration

Neutrophil [polymorphonuclear leukocyte (PMN)] transepithelial migration (TEM) is a hallmark of inflammatory mucosal disorders. PMN TEM is associated with epithelial injury; however, mechanisms involved in this process are not well defined. The current work describes a new mechanism whereby deposition of PMN membranederived microparticles (PMNâ MPs) onto intestinal epithelial cells (IECs) during TEM leads to loss of epithelial cadherins, thus promoting epithelial injury and increased PMN recruitment. PMNâ MPs secreted by activated PMNs during TEM displayed a high level of enzymatically activematrixmetalloproteinase 9 (MMPâ 9), and were capable of mediating potent effects on IEC integrity. Isolated PMNâ MPs efficiently bound to IEC monolayers and induced cleavage of desmogleinâ 2 (DSGâ 2) but not Eâ cadherin, leading to disruption of IEC intercellular adhesions. Furthermore, PMNâ MP binding to intestinal epithelium in vitro in transwell assays and in vivo in ligated intestinal loop preparations facilitated increases in PMN TEM. These effects were MMPâ 9 dependent and were reversed in the presence of specific pharmacological inhibitors. Finally, we demonstrated that IEC Dsgâ 2 serves as a barrier for migrating PMNs, and its removal by PMNâ MPâ associated MMPâ 9 facilitates PMNtrafficking across epithelial layers. Our findings thus implicate PMNâ MPs in PMNâ mediated inflammation and epithelial damage, as observed in inflammatory disorders ofmucosal surfaces.â Butinâ Israeli, V., Houser, M.C., Feng, M., Thorp, E. B., Nusrat, A., Parkos, C. A, Sumagin, R. Deposition of microparticles by neutrophils onto inflamed epithelium: anewmechanism to disrupt epithelial intercellular adhesions and promote transepithelialmigration. FASEB J. 30, 4007â 4020 (2016). www.fasebj.orgPeer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/154234/1/fsb2fasebj30120734r.pd