Interior and boundary continuity of the solution of the singular equation (beta(u))t=Lu(beta(u))_ t= Lu

We extendsome results of DiBenedetto and Vespri (Arch. Rational Mech. Anal 132(3) (1995) 247) proving the interior and boundary continuity of bounded solutions of the singular equation

Harnack type estimates and Hölder continuity for non-negative solutions to certain sub-critically singular parabolic partial differential equations

A two-parameter family of Harnack type inequalities for non-negative solutions of a class of singular, quasilinear, homogeneous parabolic equations is established, and it is shown that such estimates imply the Hoelder continuity of solutions. These classes of singular equations include p-Laplacean type equation in the sub-critical range 1<p\le\frac2N/(N+1) and equations of the porous medium type in the sub-critical range 0<m\le(N-2)_+/N

What if? Mouse proteomics after gene inactivation

The complex interactions among proteins and of proteins with small molecular weight protein ligands are overturned every time one of the components of the network is missing. For study purposes, animal models lacking one protein are obtained by experimental manipulation of the genome: in the knocking out approach, a gene is altered through the insertion of an artificial DNA sequence, which halts the transcription-translation sequence of events. In this review we have compiled the research papers that analyze the effects of knocking out individual genes on the proteomes of various tissues/organs throughout the body. We have gathered and organized all the available evidence and then compared the proteomic data in order to stress the context-specificity of the outcome every time two or more organs were investigated in the same KO mice. Finally, in a symmetrical approach to the above, we surveyed whether there is any obvious overlap among the effects of different KO on the same organ, marking affection of general pathways or lacking specificity of the gene targeting. Specific attention was put on the possible involvement of cellular stress markers

SLC6A14, a Pivotal Actor on Cancer Stage: When Function Meets Structure

SLC6A14 (ATB0,+) is a sodium- and chloride-dependent neutral and dibasic amino acid transporter that regulates the distribution of amino acids across cell membranes. The transporter is overexpressed in many human cancers characterized by an increased demand for amino acids; as such, it was recently acknowledged as a novel target for cancer therapy. The knowledge on the molecular mechanism of SLC6A14 transport is still limited, but some elegant studies on related transporters report the involvement of the 12 transmembrane \u3b1-helices in the transport mechanism, and describe structural rearrangements mediated by electrostatic interactions with some pivotal gating residues. In the present work, we constructed a SLC6A14 model in outward-facing conformation via homology modeling and used molecular dynamics simulations to predict amino acid residues critical for substrate recognition and translocation. We docked the proteinogenic amino acids and other known substrates in the SLC6A14 binding site to study both gating regions and the exposed residues involved in transport. Interestingly, some of these residues correspond to those previously identified in other LeuT-fold transporters; however, we could also identify a novel relevant residue with such function. For the first time, by combined approaches of molecular docking and molecular dynamics simulations, we highlight the potential role of these residues in neutral amino acid transport. This novel information unravels new aspects of the human SLC6A14 structure-function relationship and may have important outcomes for cancer treatment through the design of novel inhibitors of SLC6A14-mediated transport

Passing to the Limit in a Wasserstein Gradient Flow: From Diffusion to Reaction

We study a singular-limit problem arising in the modelling of chemical reactions. At finite {\epsilon} > 0, the system is described by a Fokker-Planck convection-diffusion equation with a double-well convection potential. This potential is scaled by 1/{\epsilon}, and in the limit {\epsilon} -> 0, the solution concentrates onto the two wells, resulting into a limiting system that is a pair of ordinary differential equations for the density at the two wells. This convergence has been proved in Peletier, Savar\'e, and Veneroni, SIAM Journal on Mathematical Analysis, 42(4):1805-1825, 2010, using the linear structure of the equation. In this paper we re-prove the result by using solely the Wasserstein gradient-flow structure of the system. In particular we make no use of the linearity, nor of the fact that it is a second-order system. The first key step in this approach is a reformulation of the equation as the minimization of an action functional that captures the property of being a curve of maximal slope in an integrated form. The second important step is a rescaling of space. Using only the Wasserstein gradient-flow structure, we prove that the sequence of rescaled solutions is pre-compact in an appropriate topology. We then prove a Gamma-convergence result for the functional in this topology, and we identify the limiting functional and the differential equation that it represents. A consequence of these results is that solutions of the {\epsilon}-problem converge to a solution of the limiting problem.Comment: Added two sections, corrected minor typos, updated reference

Acute-phase proteins before cerebral ischemia in stroke-prone rats : identification by proteomic

BACKGROUND AND PURPOSE: A high degree of proteinuria has been reported in stroke-prone spontaneously hypertensive rats (SHRSP). We studied the effect of salt loading on the detailed protein pattern of serum and urine in 3 rat strains: Wistar-Kyoto, spontaneously hypertensive rats, and SHRSP, an inbred animal model for a complex form of cerebrovascular disorder resembling the human disease. METHODS: Rats were given a permissive diet and received 1% NaCl in drinking water. The protein pattern in body fluids was assessed over time by 2-dimensional electrophoretic analysis. Brain alterations were monitored by MRI and histology. RESULTS: Several proteins were excreted in urine after weeks of treatment and in advance of stroke: transferrin, hemopexin, albumin, alpha(2)-HS-glycoprotein, kallikrein-binding protein, alpha(1)-antitrypsin, Gc-globulin, and transthyretin. Markers of an inflammatory response, including very high levels of thiostatin, were detected in the serum of SHRSP at least 4 weeks before a stroke occurred. CONCLUSIONS: In SHRSP subjected to salt loading, an atypical inflammatory condition and widespread alterations of vascular permeability developed before the appearance of anomalous features in the brain detected by MRI. Urinary concentrations of each of the excreted serum proteins correlated positively with time before stroke occurred

Pentoxifylline prevents spontaneous brain ischemia in stroke-prone rats

Anti-inflammatory properties of pentoxifylline (PTX) have recently been described. Spontaneously hypertensive stroke-prone rats (SHRSP) constitute an animal model that develops an inflammatory condition that precedes the appearance of brain abnormalities. The aim of the present investigation was to assess: 1) the efficacy of PTX treatment in protecting the neural system in SHRSP, and 2) how its anti-inflammatory properties might be involved in this effect. Male SHRSP fed with a permissive diet received no drug or PTX (100 or 200 mg/kg/day). Brain abnormalities detected by magnetic resonance imaging developed spontaneously in control rats after 42 +/- 3 days, whereas in rats treated with 100 mg/kg/day PTX, abnormalities developed in only 80% of the animals and only after 70 to 80 days. Treatment with a higher dose of PTX (200 mg/kg/day) completely protected the brain from abnormal development. The drug treatment prevented the accumulation of macrophages or CD4+ positive cells, the activation of glia in brain tissues, and the appearance of inflammatory proteins and thiobarbituric acid-reactive substances in body fluids. PTX treatment did induce a greater increase of serum tumor necrosis factor-alpha (TNF-alpha), but not of interleukin (IL)-1beta and IL-6 induced by in vivo administration of lipopolysaccharide (LPS), which suggests a protective role for TNF-alpha. PTX also exerted protective effects when it was administered after the first occurrence of proteinuria (>40 mg/day). These data indicate that PTX treatment dose-dependently prevents the occurrence of spontaneous brain damage by reducing inflammatory events. We also hypothesize that the increase of TNF-alpha by PTX treatment represents a protective mechanism in SHRSP