Nonlinear diffusion equations with degenerate fast-decay mobility by coordinate transformation

We prove an existence and uniqueness result for solutions to nonlinear diffusion equations with degenerate mobility posed on a bounded interval for a certain density $u$. In case of \emph{fast-decay} mobilities, namely mobilities functions under a Osgood integrability condition, a suitable coordinate transformation is introduced and a new nonlinear diffusion equation with linear mobility is obtained. We observe that the coordinate transformation induces a mass-preserving scaling on the density and the nonlinearity, described by the original nonlinear mobility, is included in the diffusive process. We show that the rescaled density $\rho$ is the unique weak solution to the nonlinear diffusion equation with linear mobility. Moreover, the results obtained for the density $\rho$ allow us to motivate the aforementioned change of variable and to state the results in terms of the original density $u$ without prescribing any boundary conditions

On a chemotaxis-hapotaxis model with nonlinear diffusion modelling multiple sclerosis

We investigated existence of global weak solutions for a system of chemotaxis-hapotaxis type with nonlinear degenerate diffusion, arising in modelling Multiple Sclerosis disease. The model consists of three equations describing the evolution of macrophages ($m$), cytokine ($c$) and apoptotic oligodendrocytes ($d$). The main novelty in our work is the presence of a nonlinear diffusivity $D(m)$, which results to be more appropriate from the modelling point of view. Under suitable assumptions and for sufficiently regular initial data, adapting the strategy in [30,44], we show the existence of global bounded solutions for the model analysed

Histochemical detection of the lectin-binding carbohydrates in the zona pellucida during oocyte growth in the wild boar (Sus scrofa scrofa)

The changes that occur in the carbohydrate composition of zona pellucida glycoproteins during oocyte maturation in the wild-boar were studied using periodic-acid Schiff (PAS), High Iron Diamine (HID) and Low Iron Diamine (LID). Lectin staining was performed with a panel of 11 HRP-lectin conjugates combined with neuraminidase digestion and chemical treatments. There were few internal glucidic residues, such as N-acetylglucosamine, in the wild boar zona pellucida but there were many subterminal beta-N-acetylgalactosamine, alpha- and beta-galactose determinants masked by sialic acid. In addition, beta-N-acetylgalactosamine, beta-galactose-(1-3)-N-acetylgalactosamine and beta-galactose-(1-4)-N-acetylglucosamine were detected in the sulphated form in the terminal and/or subterminal position. Some differences in the lectin reactive sites occurred in the zona pellucida, depending on the stage of oocyte maturatio

Variations in the lectin-binding on the zona pellucida during oocyte growth in some wild ungulates

The aim of the present study was to examine the glycoconjugate modifications occurring in the zona pellucida during oocyte growth in fallow, red and roe deer using a battery of lectins combined with sialidase digestion and chemical treatments. This histochemical approach allowed us to sequence the oligosaccharidic side chains of the zona pellucida glycoproteins in these wild ungulates. The most effective lectins in the zona pellucida of these species were SBA, PNA, RCA-I GSA-IB4, and WGA, indicating the presence of beta-D-N-Acetylgalactosamine, beta-D-Galactose, alpha-D-Galactose and N-Acetylglucosamine residues. Additionally, sialic acid moieties were demonstrated. We also observed differences in the glycosidic residue content and in their spatial distribution, depending on the species and stage of follicle development

Adenovirus type 5 E4 Orf3 protein targets promyelocytic leukaemia (PML) protein nuclear domains for disruption via a sequence in PML isoform II that is predicted as a protein interaction site by bioinformatic analysis

Human adenovirus type 5 infection causes the disruption of structures in the cell nucleus termed promyelocytic leukaemia (PML) protein nuclear domains or ND10, which contain the PML protein as a critical component. This disruption is achieved through the action of the viral E4 Orf3 protein, which forms track-like nuclear structures that associate with the PML protein. This association is mediated by a direct interaction of Orf3 with a specific PML isoform, PMLII. We show here that the Orf3 interaction properties of PMLII are conferred by a 40 aa residue segment of the unique C-terminal domain of the protein. This segment was sufficient to confer interaction on a heterologous protein. The analysis was informed by prior application of a bioinformatic tool for the prediction of potential protein interaction sites within unstructured protein sequences (predictors of naturally disordered region analysis; PONDR). This tool predicted three potential molecular recognition elements (MoRE) within the C-terminal domain of PMLII, one of which was found to form the core of the Orf3 interaction site, thus demonstrating the utility of this approach. The sequence of the mapped Orf3-binding site on PML protein was found to be relatively poorly conserved across other species; however, the overall organization of MoREs within unstructured sequence was retained, suggesting the potential for conservation of functional interactions