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

The dynamics underlying pseudo-plateau bursting in a pituitary cell model.

This is the final version of the article. Available from BioMed Central via the DOI in this record.Pituitary cells of the anterior pituitary gland secrete hormones in response to patterns of electrical activity. Several types of pituitary cells produce short bursts of electrical activity which are more effective than single spikes in evoking hormone release. These bursts, called pseudo-plateau bursts, are unlike bursts studied mathematically in neurons (plateau bursting) and the standard fast-slow analysis used for plateau bursting is of limited use. Using an alternative fast-slow analysis, with one fast and two slow variables, we show that pseudo-plateau bursting is a canard-induced mixed mode oscillation. Using this technique, it is possible to determine the region of parameter space where bursting occurs as well as salient properties of the burst such as the number of spikes in the burst. The information gained from this one-fast/two-slow decomposition complements the information obtained from a two-fast/one-slow decomposition.This work was supported by NSF grant DMS 0917664 to RB and NIH grant DK 043200 to RB and JT

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

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

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

The Mechanism of Abrupt Transition between Theta and Hyper-Excitable Spiking Activity in Medial Entorhinal Cortex Layer II Stellate Cells

Recent studies have shown that stellate cells (SCs) of the medial entorhinal cortex become hyper-excitable in animal models of temporal lobe epilepsy. These studies have also demonstrated the existence of recurrent connections among SCs, reduced levels of recurrent inhibition in epileptic networks as compared to control ones, and comparable levels of recurrent excitation among SCs in both network types. In this work, we investigate the biophysical and dynamic mechanism of generation of the fast time scale corresponding to hyper-excitable firing and the transition between theta and fast firing frequency activity in SCs. We show that recurrently connected minimal networks of SCs exhibit abrupt, threshold-like transition between theta and hyper-excitable firing frequencies as the result of small changes in the maximal synaptic (AMPAergic) conductance. The threshold required for this transition is modulated by synaptic inhibition. Similar abrupt transition between firing frequency regimes can be observed in single, self-coupled SCs, which represent a network of recurrently coupled neurons synchronized in phase, but not in synaptically isolated SCs as the result of changes in the levels of the tonic drive. Using dynamical systems tools (phase-space analysis), we explain the dynamic mechanism underlying the genesis of the fast time scale and the abrupt transition between firing frequency regimes, their dependence on the intrinsic SC's currents and synaptic excitation. This abrupt transition is mechanistically different from others observed in similar networks with different cell types. Most notably, there is no bistability involved. ‘In vitro’ experiments using single SCs self-coupled with dynamic clamp show the abrupt transition between firing frequency regimes, and demonstrate that our theoretical predictions are not an artifact of the model. In addition, these experiments show that high-frequency firing is burst-like with a duration modulated by an M-current

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

Wound dressings for a proteolytic-rich environment

Wound dressings have experienced continuous and significant changes over the years based on the knowledge of the biochemical events associated with chronic wounds. The development goes from natural materials used to just cover and conceal the wound to interactive materials that can facilitate the healing process, addressing specific issues in non-healing wounds. These new types of dressings often relate with the proteolytic wound environment and the bacteria load to enhance the healing. Recently, the wound dressing research is focusing on the replacement of synthetic polymers by natural protein materials to delivery bioactive agents to the wounds. This article provides an overview on the novel protein-based wound dressings such as silk fibroin keratin and elastin. The improved properties of these dressings, like the release of antibiotics and growth factors, are discussed. The different types of wounds and the effective parameters of healing process will be reviewed