Non-homogeneous random walks, subdiffusive migration of cells and anomalous chemotaxis

This paper is concerned with a non-homogeneous in space and non-local in time random walk model for anomalous subdiffusive transport of cells. Starting with a Markov model involving a structured probability density function, we derive the non-local in time master equation and fractional equation for the probability of cell position. We show the structural instability of fractional subdiffusive equation with respect to the partial variations of anomalous exponent. We find the criteria under which the anomalous aggregation of cells takes place in the semi-infinite domain.Comment: 18 pages, accepted for publicatio

Preface. Bifurcations and Pattern Formation in Biological Applications

In the preface we present a short overview of articles included in the issue "Bifurcations and pattern formation in biological applications" of the journal Mathematical Modelling of Natural Phenomena

Nuclear Factor of Activated T Cells Balances Angiogenesis Activation and Inhibition

It has been demonstrated that vascular endothelial cell growth factor (VEGF) induction of angiogenesis requires activation of the nuclear factor of activated T cells (NFAT). We show that NFATc2 is also activated by basic fibroblast growth factor and blocked by the inhibitor of angiogenesis pigment epithelial–derived factor (PEDF). This suggests a pivotal role for this transcription factor as a convergence point between stimulatory and inhibitory signals in the regulation of angiogenesis

Selective Inhibition of Vascular Endothelial Growth Factor–Mediated Angiogenesis by Cyclosporin a: Roles of the Nuclear Factor of Activated T Cells and Cyclooxygenase 2

Cyclosporin A (CsA) is an immunosuppressive drug that inhibits the activity of transcription factors of the nuclear factor of activated T cells (NFAT) family, interfering with the induction of cytokines and other inducible genes required for the immune response. Here we show that CsA inhibits migration of primary endothelial cells and angiogenesis induced by vascular endothelial growth factor (VEGF); this effect appears to be mediated through the inhibition of cyclooxygenase (Cox)-2, the transcription of which is activated by VEGF in primary endothelial cells. Consistent with this, we show that the induction of Cox-2 gene expression by VEGF requires NFAT activation. Most important, the CsA-mediated inhibition of angiogenesis both in vitro and in vivo was comparable to the Cox-2 inhibitor NS-398, and reversed by prostaglandin E2. Furthermore, the in vivo corneal angiogenesis induced by VEGF, but not by basic fibroblast growth factor, was selectively inhibited in mice treated with CsA systemically. These findings involve NFAT in the regulation of Cox-2 in endothelial cells, point to a role for this transcription factor in angiogenesis, and may provide a novel mechanism underlying the beneficial effects of CsA in angiogenesis-related diseases such as rheumatoid arthritis and psoriasis

Development of singularities for the compressible Euler equations with external force in several dimensions

We consider solutions to the Euler equations in the whole space from a certain class, which can be characterized, in particular, by finiteness of mass, total energy and momentum. We prove that for a large class of right-hand sides, including the viscous term, such solutions, no matter how smooth initially, develop a singularity within a finite time. We find a sufficient condition for the singularity formation, "the best sufficient condition", in the sense that one can explicitly construct a global in time smooth solution for which this condition is not satisfied "arbitrary little". Also compactly supported perturbation of nontrivial constant state is considered. We generalize the known theorem by Sideris on initial data resulting in singularities. Finally, we investigate the influence of frictional damping and rotation on the singularity formation.Comment: 23 page

Id1 regulates angiogenesis through transcriptional repression of thrombospondin-1

AbstractId proteins are helix-loop-helix transcription factors that regulate tumor angiogenesis. In order to identify downstream effectors of Id1 involved in the regulation of angiogenesis, we performed PCR-select subtractive hybridization on wild-type and Id1 knockout mouse embryo fibroblasts (MEFs). Here we demonstrate that thrombospondin-1 (TSP-1), a potent inhibitor of angiogenesis, is a target of transcriptional repression by Id1. We also show that Id1-null MEFs secrete an inhibitor of endothelial cell migration, which is completely inactivated by depletion of TSP-1. Furthermore, in vivo studies revealed decreased neovascularization in matrigel assays in Id1-null mice compared to their wild-type littermates. This decrease was completely reversed by a TSP-1 neutralizing antibody. We conclude that TSP-1 is a major target for Id1 effects on angiogenesis

Aplicacion del silicato tricalcico como una alternativa biocompatible.

El seleccionar un adecuado material para la obturación apical es un acto fundamental para la resolución de un caso con una lesión periapical persistente; los principales factores que deberá tener este material es su biocompatibilidad y el crear un sellado hermético para evitar filtración; deberá poseer capacidad para inducir osteogénesis y reparación, no desarrollar toxicidad, ser radiopaco y bacteriostático. El Biodentine es un material recientemente introducido al mercado (2011), principalmente compuesto de silicato tricálcico. Es usado para tratamientos de reparación en corona y raíz, reparando perforaciones, resorciones, empleado para apexificaciones y como material de retroobturación; también puede ser utilizado como un sustituto de dentina en caries demasiado extensas.

Dynamical extensions for shell-crossing singularities

We derive global weak solutions of Einstein's equations for spherically symmetric dust-filled space-times which admit shell-crossing singularities. In the marginally bound case, the solutions are weak solutions of a conservation law. In the non-marginally bound case, the equations are solved in a generalized sense involving metric functions of bounded variation. The solutions are not unique to the future of the shell-crossing singularity, which is replaced by a shock wave in the present treatment; the metric is bounded but not continuous.Comment: 14 pages, 1 figur

Global in Time Solutions to Kolmogorov-Feller Pseudodifferential Equations with Small Parameter

The goal in this paper is to demonstrate a new method for constructing global-in-time approximate (asymptotic) solutions of (pseudodifferential) parabolic equations with a small parameter. We show that, in the leading term, such a solution can be constructed by using characteristics, more precisely, by using solutions of the corresponding Hamiltonian system and without using any integral representation. For completeness, we also briefly describe the well-known scheme developed by V.P.Maslov for constructing global-in-time solutions.Comment: 27 page