Mixed mode oscillations in a conceptual climate model

Much work has been done on relaxation oscillations and other simple oscillators in conceptual climate models. However, the oscillatory patterns in climate data are often more complicated than what can be described by such mechanisms. This paper examines complex oscillatory behavior in climate data through the lens of mixed-mode oscillations. As a case study, a conceptual climate model with governing equations for global mean temperature, atmospheric carbon, and oceanic carbon is analyzed. The nondimensionalized model is a fast/slow system with one fast variable (corresponding to ice volume) and two slow variables (corresponding to the two carbon stores). Geometric singular perturbation theory is used to demonstrate the existence of a folded node singularity. A parameter regime is found in which (singular) trajectories that pass through the folded node are returned to the singular funnel in the limiting case where $\epsilon = 0$. In this parameter regime, the model has a stable periodic orbit of type $1^s$ for some $s>0$. To our knowledge, it is the first conceptual climate model demonstrated to have the capability to produce an MMO pattern.Comment: 28 pages, 11 figure

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

Analytic shock-fronted solutions to a reaction-diffusion equation with negative diffusivity

Reaction-diffusion equations (RDEs) model the spatiotemporal evolution of a density field $u(\vec{x},t)$ according to diffusion and net local changes. Usually, the diffusivity is positive for all values of $u$, which causes the density to disperse. However, RDEs with negative diffusivity can model aggregation, which is the preferred behaviour in some circumstances. In this paper, we consider a nonlinear RDE with quadratic diffusivity $D(u) = (u - a)(u - b)$ that is negative for $u\in(a,b)$. We use a non-classical symmetry to construct analytic receding time-dependent, colliding wave, and receding travelling wave solutions. These solutions are initially multi-valued, and we convert them to single-valued solutions by inserting a shock. We examine properties of these analytic solutions including their Stefan-like boundary condition, and perform a phase plane analysis. We also investigate the spectral stability of the $u = 0$ and $u=1$ constant solutions, and prove for certain $a$ and $b$ that receding travelling waves are spectrally stable. Additionally, we introduce an new shock condition where the diffusivity and flux are continuous across the shock. For diffusivity symmetric about the midpoint of its zeros, this condition recovers the well-known equal-area rule, but for non-symmetric diffusivity it results in a different shock position.Comment: 35 pages, 10 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; 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

Substrate specificity of a peptidyl-aminoacyl-l/d-isomerase from frog skin

In the skin of fire-bellied toads (Bombina species), an aminoacyl-l/d-isomerase activity is present which catalyses the post-translational isomerization of the l- to the d-form of the second residue of its substrate peptides. Previously, this new type of enzyme was studied in some detail and genes potentially coding for similar polypeptides were found to exist in several vertebrate species including man. Here, we present our studies to the substrate specificity of this isomerase using fluorescence-labeled variants of the natural substrate bombinin H with different amino acids at positions 1, 2 or 3. Surprisingly, this enzyme has a rather low selectivity for residues at position 2 where the change of chirality at the alpha-carbon takes place. In contrast, a hydrophobic amino acid at position 1 and a small one at position 3 of the substrate are essential. Interestingly, some peptides containing a Phe at position 3 also were substrates. Furthermore, we investigated the role of the amino-terminus for substrate recognition. In view of the rather broad specificity of the frog isomerase, we made a databank search for potential substrates of such an enzyme. Indeed, numerous peptides of amphibia and mammals were found which fulfill the requirements determined in this study. Expression of isomerases with similar characteristics in other species can therefore be expected to catalyze the formation of peptides containing d-amino acids

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

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

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