Long time behavior of the Caginalp system with singular potentials and dynamic boundary conditions

This paper is devoted to the study of the well-posedness and the long time behavior of the Caginalpphase-field model with singular potentials and dynamic boundary conditions.Thanks to a suitable definition of solutions, coinciding with the strong ones underproper assumptions on the bulk and surfacepotentials, we are able to get dissipative estimates, leading tothe existence of the global attractor with finite fractal dimension,as well as of an exponential attractor

Ras superfamily GEFs and GAPs: validated and tractable targets for cancer therapy?

There is now considerable and increasing evidence for a causal role of aberrant activity of the Ras superfamily of small GTPases in human cancers. These GTPases act as GDP-GTP-regulated binary switches that control many fundamental cellular processes. A common mechanism of GTPase deregulation in cancer is the deregulated expression and/or activity of their regulatory proteins, guanine nucleotide exchange factors (GEFs) that promote formation of the active GTP-bound state and GTPase activating proteins (GAPs) that return the GTPase to its GDP-bound inactive state. We assess the association of GEFs and GAPs with cancer and their druggability for cancer therapeutics

Global existence for a nonstandard viscous Cahn--Hilliard system with dynamic boundary condition

In this paper, we study a model for phase segregation taking place in a spatial domain that was introduced by Podio-Guidugli in Ric. Mat. 55 (2006), pp. 105-118. The model consists of a strongly coupled system of nonlinear parabolic differential equations, in which products between the unknown functions and their time derivatives occur that are difficult to handle analytically. In contrast to the existing literature about this PDE system, we consider here a dynamic boundary condition involving the Laplace-Beltrami operator for the order parameter. This boundary condition models an additional nonconserving phase transition occurring on the surface of the domain. Different well-posedness results are shown, depending on the smoothness properties of the involved bulk and surface free energies

Longtime behavior of nonlocal Cahn-Hilliard equations

Here we consider the nonlocal Cahn-Hilliard equation with constant mobility in a bounded domain. We prove that the associated dynamical system has an exponential attractor, provided that the potential is regular. In order to do that a crucial step is showing the eventual boundedness of the order parameter uniformly with respect to the initial datum. This is obtained through an Alikakos-Moser type argument. We establish a similar result for the viscous nonlocal Cahn-Hilliard equation with singular (e.g., logarithmic) potential. In this case the validity of the so-called separation property is crucial. We also discuss the convergence of a solution to a single stationary state. The separation property in the nonviscous case is known to hold when the mobility degenerates at the pure phases in a proper way and the potential is of logarithmic type. Thus, the existence of an exponential attractor can be proven in this case as well

On a diffuse interface model for tumour growth with non-local interactions and degenerate mobilities

We study a non-local variant of a diffuse interface model proposed by Hawkins--Darrud et al. (2012) for tumour growth in the presence of a chemical species acting as nutrient. The system consists of a Cahn--Hilliard equation coupled to a reaction-diffusion equation. For non-degenerate mobilities and smooth potentials, we derive well-posedness results, which are the non-local analogue of those obtained in Frigeri et al. (European J. Appl. Math. 2015). Furthermore, we establish existence of weak solutions for the case of degenerate mobilities and singular potentials, which serves to confine the order parameter to its physically relevant interval. Due to the non-local nature of the equations, under additional assumptions continuous dependence on initial data can also be shown.Comment: 28 page

Global compactness for a class of quasi-linear elliptic problems

We prove a global compactness result for Palais-Smale sequences associated with a class of quasi-linear elliptic equations on exterior domains.Comment: 19 page

Fam65b is a new transcriptional target of FOXO1 that regulates RhoA signaling for T lymphocyte migration

Forkhead box Os (FOXOs) transcription factors favor both T cell quiescence and trafficking through their control of the expression of genes involved in cell cycle progression, adhesion and homing. Here, we report that the product of the fam65b gene is a new transcriptional target of FOXO1 that regulates RhoA activity. We show that Fam65b binds the small GTPase RhoA via a non canonical domain and represses its activity by decreasing its GTP loading. As a consequence, Fam65b negatively regulates chemokine-induced responses such as adhesion, morphological polarisation and migration. Therefore, these results show the existence of a new functional link between FOXO1 and RhoA pathways, through which the FOXO1 target Fam65b tonically dampens chemokine-induced migration by repressing RhoA activity

Existence of continuous eigenvalues for a class of parametric problems involving the (p,2)-laplacian operator

We discuss a parametric eigenvalue problem, where the differential operator is of (p,2)-Laplacian type. We show that, when p≠2, the spectrum of the operator is a half line, with the end point formulated in terms of the parameter and the principal eigenvalue of the Laplacian with zero Dirichlet boundary conditions. Two cases are considered corresponding to p>2 and p2, and to infinity in the case of p<2

The Toll-Like Receptor Gene Family Is Integrated into Human DNA Damage and p53 Networks

In recent years the functions that the p53 tumor suppressor plays in human biology have been greatly extended beyond “guardian of the genome.” Our studies of promoter response element sequences targeted by the p53 master regulatory transcription factor suggest a general role for this DNA damage and stress-responsive regulator in the control of human Toll-like receptor (TLR) gene expression. The TLR gene family mediates innate immunity to a wide variety of pathogenic threats through recognition of conserved pathogen-associated molecular motifs. Using primary human immune cells, we have examined expression of the entire TLR gene family following exposure to anti-cancer agents that induce the p53 network. Expression of all TLR genes, TLR1 to TLR10, in blood lymphocytes and alveolar macrophages from healthy volunteers can be induced by DNA metabolic stressors. However, there is considerable inter-individual variability. Most of the TLR genes respond to p53 via canonical as well as noncanonical promoter binding sites. Importantly, the integration of the TLR gene family into the p53 network is unique to primates, a recurrent theme raised for other gene families in our previous studies. Furthermore, a polymorphism in a TLR8 response element provides the first human example of a p53 target sequence specifically responsible for endogenous gene induction. These findings—demonstrating that the human innate immune system, including downstream induction of cytokines, can be modulated by DNA metabolic stress—have many implications for health and disease, as well as for understanding the evolution of damage and p53 responsive networks

The domain architecture of large guanine nucleotide exchange factors for the small GTP-binding protein Arf

BACKGROUND: Small G proteins, which are essential regulators of multiple cellular functions, are activated by guanine nucleotide exchange factors (GEFs) that stimulate the exchange of the tightly bound GDP nucleotide by GTP. The catalytic domain responsible for nucleotide exchange is in general associated with non-catalytic domains that define the spatio-temporal conditions of activation. In the case of small G proteins of the Arf subfamily, which are major regulators of membrane trafficking, GEFs form a heterogeneous family whose only common characteristic is the well-characterized Sec7 catalytic domain. In contrast, the function of non-catalytic domains and how they regulate/cooperate with the catalytic domain is essentially unknown. RESULTS: Based on Sec7-containing sequences from fully-annotated eukaryotic genomes, including our annotation of these sequences from Paramecium, we have investigated the domain architecture of large ArfGEFs of the BIG and GBF subfamilies, which are involved in Golgi traffic. Multiple sequence alignments combined with the analysis of predicted secondary structures, non-structured regions and splicing patterns, identifies five novel non-catalytic structural domains which are common to both subfamilies, revealing that they share a conserved modular organization. We also report a novel ArfGEF subfamily with a domain organization so far unique to alveolates, which we name TBS (TBC-Sec7). CONCLUSION: Our analysis unifies the BIG and GBF subfamilies into a higher order subfamily, which, together with their being the only subfamilies common to all eukaryotes, suggests that they descend from a common ancestor from which species-specific ArfGEFs have subsequently evolved. Our identification of a conserved modular architecture provides a background for future functional investigation of non-catalytic domains