Harnack's Inequality for Parabolic De Giorgi Classes in Metric Spaces

In this paper we study problems related to parabolic partial differential equations in metric measure spaces equipped with a doubling measure and supporting a Poincare' inequality. We give a definition of parabolic De Giorgi classes and compare this notion with that of parabolic quasiminimizers. The main result, after proving the local boundedness, is a scale and location invariant Harnack inequality for functions belonging to parabolic De Giorgi classes. In particular, the results hold true for parabolic quasiminimizers

G-convergence of elliptic and parabolic operators depending on vector fields

We consider sequences of elliptic and parabolic operators in divergence form and depending on a family of vector fields. We show compactness results with respect to G-convergence, or H-convergence, by means of the compensated compactness theory, in a setting in which the existence of affine functions is not always guaranteed, due to the nature of the family of vector fields

The centrosomal kinase NEK2 is a novel splicing factor kinase involved in cell survival

NEK2 is a serine/threonine kinase that promotes centrosome splitting and ensures correct chromosome segregation during the G2/M phase of the cell cycle, through phosphorylation of specific substrates. Aberrant expression and activity of NEK2 in cancer cells lead to dysregulation of the centrosome cycle and aneuploidy. Thus, a tight regulation of NEK2 function is needed during cell cycle progression. In this study, we found that NEK2 localizes in the nucleus of cancer cells derived from several tissues. In particular, NEK2 co-localizes in splicing speckles with SRSF1 and SRSF2. Moreover, NEK2 interacts with several splicing factors and phosphorylates some of them, including the oncogenic SRSF1 protein. Overexpression of NEK2 induces phosphorylation of endogenous SR proteins and affects the splicing activity of SRSF1 toward reporter minigenes and endogenous targets, independently of SRPK1. Conversely, knockdown of NEK2, like that of SRSF1, induces expression of pro-apoptotic variants from SRSF1-target genes and sensitizes cells to apoptosis. Our results identify NEK2 as a novel splicing factor kinase and suggest that part of its oncogenic activity may be ascribed to its ability to modulate alternative splicing, a key step in gene expression regulation that is frequently altered in cancer cells

Genotoxic stress inhibits ewing sarcoma cell growth by modulating alternative pre-mRNA processing of the RNA helicase DHX9

Alternative splicing plays a key role in the DNA damage response and in cancer. Ewing Sarcomas (ES) are aggressive tumors caused by different chromosomal translocations that yield in-frame fusion proteins driving transformation. RNA profiling reveals genes differentially regulated by UV light irradiation in two ES cell lines exhibiting different sensitivity to genotoxic stress. In particular, irradiation induces a new isoform of the RNA helicase DHX9 in the more sensitive SK-N-MC cells, which is targeted to nonsense-mediated decay (NMD), causing its downregulation. DHX9 protein forms a complex with RNA polymerase II (RNAPII) and EWS-FLI1 to enhance transcription. Silencing of DHX9 in ES cells sensitizes them to UV treatment and impairs recruitment of EWS-FLI1 to target genes, whereas DHX9 overexpression protects ES cells from genotoxic stress. Mechanistically, we found that UV light irradiation leads to enhanced phosphorylation and decreased processivity of RNAPII in SK-N-MC cells, which in turn causes inclusion of DHX9 exon 6A. A similar effect on DHX9 splicing was also elicited by treatment with the chemotherapeutic drug etoposide, indicating a more general mechanism of regulation in response to DNA damage. Our data identify a new NMD-linked splicing event in DHX9 with impact on EWS-FLI1 oncogenic activity and ES cell viability

Periodic Homogenization of strongly nonlinear reaction-diffusion equations with large reaction terms

We study in this paper the periodic homogenization problem related to a strongly nonlinear reaction-diffusion equation. Owing to the large reaction term, the homogenized equation has a rather quite different form which puts together both the reaction and convection effects. We show in a special case that, the homogenized equation is exactly of a convection-diffusion type. The study relies on a suitable version of the well-known two-scale convergence method.Comment: 19 page

Analysis of the gene expression profile of mouse male meiotic germ cells

Wide genome analysis of difference in gene expression between spermatogonial populations from 7-day-old mice and pachytene spermatocytes from 18-day-old mice was performed using Affymetrix gene chips representing approximately 12,500 mouse known genes or EST sequences, spanning approximately 1/3rd of the mouse genome. To delineate differences in the profile of gene expression between mitotic and meiotic stages of male germ cell differentiation, expressed genes were grouped in functional clusters. The analysis confirmed the previously described pre-meiotic or meiotic expression for several genes, in particular for those involved in the regulation of the mitotic and meiotic cell cycle, and for those whose transcripts are accumulated during the meiotic stages to be translated later in post-meiotic stages. Differential expression of several additional genes was discovered. In few cases (pro-apoptotic factors Bak, Bad and Bax), data were in conflict with the previously published stage-dependent expression of genes already known to be expressed in male germ cells. Northern blot analysis of selected genes confirmed the results obtained with the microarray chips. Six of these were novel genes specifically expressed in pachytene spermatocytes: a chromatin remodeling factor (chrac1/YCL1), a homeobox gene (hmx1), a novel G-coupled receptor for an unknown ligand (Gpr19), a glycoprotein of the intestinal epithelium (mucin 3), a novel RAS activator (Ranbp9), and the A630056B21Rik gene (predicted to encode a novel zinc finger protein). These studies will help to delineate the global patterns of gene expression characterizing male germ cell differentiation for a better understanding of regulation of spermatogenesis in mammals

Nucleic Acids Res

NEK2 is a serine/threonine kinase that promotes centrosome splitting and ensures correct chromosome segregation during the G2/M phase of the cell cycle, through phosphorylation of specific substrates. Aberrant expression and activity of NEK2 in cancer cells lead to dysregulation of the centrosome cycle and aneuploidy. Thus, a tight regulation of NEK2 function is needed during cell cycle progression. In this study, we found that NEK2 localizes in the nucleus of cancer cells derived from several tissues. In particular, NEK2 co-localizes in splicing speckles with SRSF1 and SRSF2. Moreover, NEK2 interacts with several splicing factors and phosphorylates some of them, including the oncogenic SRSF1 protein. Overexpression of NEK2 induces phosphorylation of endogenous SR proteins and affects the splicing activity of SRSF1 toward reporter minigenes and endogenous targets, independently of SRPK1. Conversely, knockdown of NEK2, like that of SRSF1, induces expression of pro-apoptotic variants from SRSF1-target genes and sensitizes cells to apoptosis. Our results identify NEK2 as a novel splicing factor kinase and suggest that part of its oncogenic activity may be ascribed to its ability to modulate alternative splicing, a key step in gene expression regulation that is frequently altered in cancer cells

Abstract kinetic equations with positive collision operators

We consider "forward-backward" parabolic equations in the abstract form $Jd \psi / d x + L \psi = 0$, $0< x < \tau \leq \infty$, where $J$ and $L$ are operators in a Hilbert space $H$ such that $J=J^*=J^{-1}$, $L=L^* \geq 0$, and $\ker L = 0$. The following theorem is proved: if the operator $B=JL$ is similar to a self-adjoint operator, then associated half-range boundary problems have unique solutions. We apply this theorem to corresponding nonhomogeneous equations, to the time-independent Fokker-Plank equation $\mu \frac {\partial \psi}{\partial x} (x,\mu) = b(\mu) \frac {\partial^2 \psi}{\partial \mu^2} (x, \mu)$, $0<x<\tau$, $\mu \in \R$, as well as to other parabolic equations of the "forward-backward" type. The abstract kinetic equation $T d \psi/dx = - A \psi (x) + f(x)$, where $T=T^*$ is injective and $A$ satisfies a certain positivity assumption, is considered also.Comment: 20 pages, LaTeX2e, version 2, references have been added, changes in the introductio