Numerical computation of an Evans function for travelling waves

We demonstrate a geometrically inspired technique for computing Evans functions for the linearised operators about travelling waves. Using the examples of the F-KPP equation and a Keller-Segel model of bacterial chemotaxis, we produce an Evans function which is computable through several orders of magnitude in the spectral parameter and show how such a function can naturally be extended into the continuous spectrum. In both examples, we use this function to numerically verify the absence of eigenvalues in a large region of the right half of the spectral plane. We also include a new proof of spectral stability in the appropriate weighted space of travelling waves of speed $c \geq 2 \sqrt{\delta}$ in the F-KPP equation.Comment: 37 pages, 11 figure

Canards existence in the Hindmarsh-Rose model

In two previous papers we have proposed a new method for proving the existence of "canard solutions" on one hand for three and four-dimensional singularly perturbed systems with only one fast variable and, on the other hand for four-dimensional singularly perturbed systems with two fast variables [J.M. Ginoux and J. Llibre, Qual. Theory Dyn. Syst. 15 (2016) 381-431; J.M. Ginoux and J. Llibre, Qual. Theory Dyn. Syst. 15 (2015) 342010]. The aim of this work is to extend this method which improves the classical ones used till now to the case of three-dimensional singularly perturbed systems with two fast variables. This method enables to state a unique generic condition for the existence of "canard solutions" for such three-dimensional singularly perturbed systems which is based on the stability of folded singularities (pseudo singular points in this case) of the normalized slow dynamics deduced from a well-known property of linear algebra. Applications of this method to a famous neuronal bursting model enables to show the existence of "canard solutions" in the Hindmarsh-Rose model

Canards existence in the Hindmarsh-Rose model

In two previous papers, we have proposed a new method for proving the existence of "canard solutions" on one hand for three- and four-dimensional singularly perturbed systems with only one fast variable and, on the other hand, for four-dimensional singularly perturbed systems with two fast variables; see [4, 5]. The aim of this work is to extend this method, which improves the classical ones used till now to the case of three-dimensional singularly perturbed systems with two fast variables. This method enables to state a unique generic condition for the existence of "canard solutions" for such three-dimensional singularly perturbed systems which is based on the stability of folded singularities (pseudo singular points in this case) of the normalized slow dynamics deduced from a well-known property of linear algebra. Applications of this method to a famous neuronal bursting model enables to show the existence of "canard solutions" in the Hindmarsh-Rose model

Cytotoxic T Lymphocyte Trafficking and Survival in an Augmented Fibrin Matrix Carrier

Cell-based therapies have intriguing potential for the treatment of a variety of neurological disorders. One such example is genetically engineered cytotoxic T lymphocytes (CTLs) that are being investigated in brain tumor clinical trials. The development of methods for CTL delivery is critical to their use in the laboratory and clinical setting. In our study, we determined whether CTLs can migrate through fibrin matrices and if their migration, survival, and function could be modulated by adding chemokines to the matrix. Our results indicated that CTLs can freely migrate through fibrin matrices. As expected, the addition of the monocyte chemotactic protein-1 (MCP-1), also known as chemokine C-C motif ligand 2 (CCL2), to the surrounding media increased egress of the CTLs out of the fibrin clot. Interleukin (IL) -2 and/or IL-15 embedded in the matrix enhanced T cell survival and further promoted T cell migration. The interleukin-13 receptor alpha 2 specific (IL-13R alpha2) T cells that traveled out of the fibrin clot retained the capacity to kill U251 glioma cells. In summary, CTLs can survive and migrate robustly in fibrin matrices. These processes can be influenced by modification of matrix constituents. We conclude that fibrin matrices may be suitable T cell carriers and can be used to facilitate understanding of T cell interaction with the surrounding microenvironment

Prokineticin 2 Is a Hypothalamic Neuropeptide That Potently Inhibits Food Intake

OBJECTIVE-Prokineticin 2 (PK2) is a hypothalamic neuropeptide expressed in central nervous system areas known to be involved in food intake. We therefore hypothesized that PK2 plays a role in energy homeostasis. RESEARCH DESIGN AND METHODS - We investigated the effect of nutritional status on hypothalamic PK2 expression and effects of PK2 on the regulation of food intake by intracerebro-ventricular (ICV) injection of PK2 and anti-PK2 antibody. Subsequently, we investigated the potential mechanism of action by determining sites of neuronal activation after ICV injection of PK2, the hypothalamic site of action of PK2, and interaction between PK2 and other hypothalamic neuropeptides regulating energy homeostasis. To investigate PK2's potential as a therapeutic target, we investigated the effect of chronic administration in lean and obese mice. RESULTS - Hypothalamic PK2 expression was reduced by fasting. ICV administration of PK2 to rats potently inhibited food intake, whereas anti-PK2 antibody increased food intake, suggesting that PK2 is an anorectic neuropeptide. ICV administration of PK2 increased c-fos expression in proopiomelanocortin neurons of the arcuate nucleus (ARC) of the hypothalamus. In keeping with this, PK2 administration into the ARC reduced food intake and PK2 increased the release of α-melanocyte-stimulating hormone (α-MSH) from ex vivo hypothalamic explants. In addition, ICV coadministration of the α-MSH antagonist agouti-related peptide blocked the anorexigenic effects of PK2. Chronic peripheral administration of PK2 reduced food and body weight in lean and obese mice. CONCLUSIONS - This is the first report showing that PK2 has a role in appetite regulation and its anorectic effect is mediated partly via the melanocortin system. © 2010 by the American Diabetes Association

CD36 Participates in PrP106–126-Induced Activation of Microglia

Microglial activation is a characteristic feature of the pathogenesis of prion diseases. The molecular mechanisms that underlie prion-induced microglial activation are not very well understood. In the present study, we investigated the role of the class B scavenger receptor CD36 in microglial activation induced by neurotoxic prion protein (PrP) fragment 106–126 (PrP106–126). We first examined the time course of CD36 mRNA expression upon exposure to PrP106–126 in BV2 microglia. We then analyzed different parameters of microglial activation in PrP106–126-treated cells in the presence or not of anti-CD36 monoclonal antibody (mAb). The cells were first incubated for 1 h with CD36 monoclonal antibody to block the CD36 receptor, and were then treated with neurotoxic prion peptides PrP106–126. The results showed that PrP106–126 treatment led to a rapid yet transitory increase in the mRNA expression of CD36, upregulated mRNA and protein levels of proinflammatory cytokines (IL-1β, IL-6 and TNF-α), increased iNOS expression and nitric oxide (NO) production, stimulated the activation of NF-κB and caspase-1, and elevated Fyn activity. The blockade of CD36 had no effect on PrP106–126-stimulated NF-κB activation and TNF-α protein release, abrogated the PrP106–126-induced iNOS stimulation, downregulated IL-1β and IL-6 expression at both mRNA and protein levels as well as TNF-α mRNA expression, decreased NO production and Fyn phosphorylation, reduced caspase-1 cleavage induced by moderate PrP106–126 –treatment, but had no effect on caspase-1 activation after treatment with a high concentration of PrP106–126. Together, these results suggest that CD36 is involved in PrP106–126-induced microglial activation and that the participation of CD36 in the interaction between PrP106–126 and microglia may be mediated by Src tyrosine kinases. Our findings provide new insights into the mechanisms underlying the activation of microglia by neurotoxic prion peptides and open perspectives for new therapeutic strategies for prion diseases by modulation of CD36 signaling

Epithelial-Mesenchymal Transition in Cancer: Parallels Between Normal Development and Tumor Progression

From the earliest stages of embryonic development, cells of epithelial and mesenchymal origin contribute to the structure and function of developing organs. However, these phenotypes are not always permanent, and instead, under the appropriate conditions, epithelial and mesenchymal cells convert between these two phenotypes. These processes, termed Epithelial-Mesenchymal Transition (EMT), or the reverse Mesenchymal-Epithelial Transition (MET), are required for complex body patterning and morphogenesis. In addition, epithelial plasticity and the acquisition of invasive properties without the full commitment to a mesenchymal phenotype are critical in development, particularly during branching morphogenesis in the mammary gland. Recent work in cancer has identified an analogous plasticity of cellular phenotypes whereby epithelial cancer cells acquire mesenchymal features that permit escape from the primary tumor. Because local invasion is thought to be a necessary first step in metastatic dissemination, EMT and epithelial plasticity are hypothesized to contribute to tumor progression. Similarities between developmental and oncogenic EMT have led to the identification of common contributing pathways, suggesting that the reactivation of developmental pathways in breast and other cancers contributes to tumor progression. For example, developmental EMT regulators including Snail/Slug, Twist, Six1, and Cripto, along with developmental signaling pathways including TGF-β and Wnt/β-catenin, are misexpressed in breast cancer and correlate with poor clinical outcomes. This review focuses on the parallels between epithelial plasticity/EMT in the mammary gland and other organs during development, and on a selection of developmental EMT regulators that are misexpressed specifically during breast cancer

The Gracilis Myocutaneous Free Flap: A Quantitative Analysis of the Fasciocutaneous Blood Supply and Implications for Autologous Breast Reconstruction

BACKGROUND: Mastectomies are one of the most common surgical procedures in women of the developed world. The gracilis myocutaneous flap is favoured by many reconstructive surgeons due to the donor site profile and speed of dissection. The distal component of the longitudinal skin paddle of the gracilis myocutaneous flap is unreliable. This study quantifies the fasciocutaneous vascular territories of the gracilis flap and offers the potential to reconstruct breasts of all sizes. METHODS: Twenty-seven human cadaver dissections were performed and injected using lead oxide into the gracilis vascular pedicles, followed by radiographic studies to identify the muscular and fasciocutaneous perforator patterns. The vascular territories and choke zones were characterized quantitatively using the 'Lymphatic Vessel Analysis Protocol' (LVAP) plug-in for Image J® software. RESULTS: We found a step-wise decrease in the average vessel density from the upper to middle and lower thirds of both the gracilis muscle and the overlying skin paddle with a significantly higher average vessel density in the skin compared to the muscle. The average vessel width was greater in the muscle. Distal to the main pedicle, there were either one (7/27 cases), two (14/27 cases) or three (6/27 cases) minor pedicles. The gracilis angiosome was T-shaped and the maximum cutaneous vascular territory for the main and first minor pedicle was 35 × 19 cm and 34 × 10 cm, respectively. CONCLUSION: Our findings support the concept that small volume breast reconstructions can be performed on suitable patients, based on septocutaneous perforators from the minor pedicle without the need to harvest any muscle, further reducing donor site morbidity. For large reconstructions, if a 'T' or tri-lobed flap with an extended vertical component is needed, it is important to establish if three territories are present. Flap reliability and size may be optimized following computed tomographic angiography and surgical delay

Tension, Free Space, and Cell Damage in a Microfluidic Wound Healing Assay

We use a novel, microfluidics-based technique to deconstruct the classical wound healing scratch assay, decoupling the contribution of free space and cell damage on the migratory dynamics of an epithelial sheet. This method utilizes multiple laminar flows to selectively cleave cells enzymatically, and allows us to present a 'damage free' denudation. We therefore isolate the influence of free space on the onset of sheet migration. First, we observe denudation directly to measure the retraction in the cell sheet that occurs after cell-cell contact is broken, providing direct and quantitative evidence of strong tension within the sheet. We further probe the mechanical integrity of the sheet without denudation, instead using laminar flows to selectively inactivate actomyosin contractility. In both cases, retraction is observed over many cell diameters. We then extend this method and complement the enzymatic denudation with analogies to wounding, including gradients in signals associated with cell damage, such as reactive oxygen species, suspected to play a role in the induction of movement after wounding. These chemical factors are evaluated in combination with the enzymatic cleavage of cells, and are assessed for their influence on the collective migration of a non-abrasively denuded epithelial sheet. We conclude that free space alone is sufficient to induce movement, but this movement is predominantly limited to the leading edge, leaving cells further from the edge less able to move towards the wound. Surprisingly, when coupled with a gradient in ROS to simulate the chemical effects of abrasion however, motility was not restored, but further inhibited.Massachusetts Institute of Technology. Presidential FellowshipNational Institutes of Health (U.S.). Biotechnology Training FellowshipSingapore-MIT Alliance for Research and TechnologyMassachusetts Institute of Biotechnology Training GrantMassachusetts Institute of Technology (Open-source Funding