A mathematical framework for critical transitions: normal forms, variance and applications

Critical transitions occur in a wide variety of applications including mathematical biology, climate change, human physiology and economics. Therefore it is highly desirable to find early-warning signs. We show that it is possible to classify critical transitions by using bifurcation theory and normal forms in the singular limit. Based on this elementary classification, we analyze stochastic fluctuations and calculate scaling laws of the variance of stochastic sample paths near critical transitions for fast subsystem bifurcations up to codimension two. The theory is applied to several models: the Stommel-Cessi box model for the thermohaline circulation from geoscience, an epidemic-spreading model on an adaptive network, an activator-inhibitor switch from systems biology, a predator-prey system from ecology and to the Euler buckling problem from classical mechanics. For the Stommel-Cessi model we compare different detrending techniques to calculate early-warning signs. In the epidemics model we show that link densities could be better variables for prediction than population densities. The activator-inhibitor switch demonstrates effects in three time-scale systems and points out that excitable cells and molecular units have information for subthreshold prediction. In the predator-prey model explosive population growth near a codimension two bifurcation is investigated and we show that early-warnings from normal forms can be misleading in this context. In the biomechanical model we demonstrate that early-warning signs for buckling depend crucially on the control strategy near the instability which illustrates the effect of multiplicative noise.Comment: minor corrections to previous versio

Destabilization of the thermohaline circulation by transient perturbations to the hydrological cycle

We reconsider the problem of the stability of the thermohaline circulation as described by a two-dimensional Boussinesq model with mixed boundary conditions. We determine how the stability properties of the system depend on the intensity of the hydrological cycle. We define a two-dimensional parameters' space descriptive of the hydrology of the system and determine, by considering suitable quasi-static perturbations, a bounded region where multiple equilibria of the system are realized. We then focus on how the response of the system to finite-amplitude surface freshwater forcings depends on their rate of increase. We show that it is possible to define a robust separation between slow and fast regimes of forcing. Such separation is obtained by singling out an estimate of the critical growth rate for the anomalous forcing, which can be related to the characteristic advective time scale of the system.Comment: 37 pages, 8 figures, submitted to Clim. Dy

Isolation of a Glucosamine Binding Leguminous Lectin with Mitogenic Activity towards Splenocytes and Anti-Proliferative Activity towards Tumor Cells

A dimeric 64-kDa glucosamine-specific lectin was purified from seeds of Phaseolus vulgaris cv. “brown kidney bean.” The simple 2-step purification protocol involved affinity chromatography on Affi-gel blue gel and gel filtration by FPLC on Superdex 75. The lectin was absorbed on Affi-gel blue gel and desorbed using 1M NaCl in the starting buffer. Gel filtration on Superdex 75 yielded a major absorbance peak that gave a single 32-kDa band in SDS-PAGE. Hemagglutinating activity was completely preserved when the ambient temperature was in the range of 20°C–60°C. However, drastic reduction of the activity occurred at temperatures above 65°C. Full hemagglutinating activity of the lectin was observed at an ambient pH of 3 to 12. About 50% activity remained at pH 0–2, and only residual activity was observed at pH 13–14. Hemagglutinating activity of the lectin was inhibited by glucosamine. The brown kidney bean lectin elicited maximum mitogenic activity toward murine splenocytes at 2.5 µM. The mitogenic activity was nearly completely eliminated in the presence of 250 mM glucosamine. The lectin also increased mRNA expression of the cytokines IL-2, TNF-α and IFN-γ. The lectin exhibited antiproliferative activity toward human breast cancer (MCF7) cells, hepatoma (HepG2) cells and nasopharyngeal carcinoma (CNE1 and CNE2) cells with IC50 of 5.12 µM, 32.85 µM, 3.12 µM and 40.12 µM respectively after treatment for 24 hours. Flow cytometry with Annexin V and propidum iodide staining indicated apoptosis of MCF7 cells. Hoechst 33342 staining also indicated formation of apoptotic bodies in MCF7 cells after exposure to brown kidney bean lectin. Western blotting revealed that the lectin-induced apoptosis involved ER stress and unfolded protein response

Intervening with Urinary Tract Infections Using Anti-Adhesives Based on the Crystal Structure of the FimH–Oligomannose-3 Complex

Escherichia coli strains adhere to the normally sterile human uroepithelium using type 1 pili, that are long, hairy surface organelles exposing a mannose-binding FimH adhesin at the tip. A small percentage of adhered bacteria can successfully invade bladder cells, presumably via pathways mediated by the high-mannosylated uroplakin-Ia and alpha3beta1 integrins found throughout the uroepithelium. Invaded bacteria replicate and mature into dense, biofilm-like inclusions in preparation of fluxing and of infection of neighbouring cells, being the major cause of the troublesome recurrent urinary tract infections.We demonstrate that alpha-D-mannose based inhibitors of FimH not only block bacterial adhesion on uroepithelial cells but also antagonize invasion and biofilm formation. Heptyl alpha-D-mannose prevents binding of type 1-piliated E. coli to the human bladder cell line 5637 and reduces both adhesion and invasion of the UTI89 cystitis isolate instilled in mouse bladder via catheterization. Heptyl alpha-D-mannose also specifically inhibited biofilm formation at micromolar concentrations. The structural basis of the great inhibitory potential of alkyl and aryl alpha-D-mannosides was elucidated in the crystal structure of the FimH receptor-binding domain in complex with oligomannose-3. FimH interacts with Man alpha1,3Man beta1,4GlcNAc beta1,4GlcNAc in an extended binding site. The interactions along the alpha1,3 glycosidic bond and the first beta1,4 linkage to the chitobiose unit are conserved with those of FimH with butyl alpha-D-mannose. The strong stacking of the central mannose with the aromatic ring of Tyr48 is congruent with the high affinity found for synthetic inhibitors in which this mannose is substituted for by an aromatic group.The potential of ligand-based design of antagonists of urinary tract infections is ruled by the structural mimicry of natural epitopes and extends into blocking of bacterial invasion, intracellular growth and capacity to fluxing and of recurrence of the infection

Introduction to the special issue on the statistical mechanics of climate

We introduce the special issue on the Statistical Mechanics of Climate by presenting an informal discussion of some theoretical aspects of climate dynamics that make it a topic of great interest for mathematicians and theoretical physicists. In particular, we briefly discuss its nonequilibrium and multiscale properties, the relationship between natural climate variability and climate change, the different regimes of climate response to perturbations, and critical transitions

Grand Challenges for Biological and Environmental Research: A Long-Term Vision

The interactions and feedbacks among plants, animals, microbes, humans, and the environment ultimately form the world in which we live. This world is now facing challenges from a growing and increasingly affluent human population whose numbers and lifestyles are driving ever greater energy demand and impacting climate. These and other contributing factors will make energy and climate sustainability extremely difficult to achieve over the 20-year time horizon that is the focus of this report. Despite these severe challenges, there is optimism that deeper understanding of our environment will enable us to mitigate detrimental effects, while also harnessing biological and climate systems to ensure a sustainable energy future. This effort is advanced by scientific inquiries in the fields of atmospheric chemistry and physics, biology, ecology, and subsurface science - all made possible by computing. The Office of Biological and Environmental Research (BER) within the Department of Energy's (DOE) Office of Science has a long history of bringing together researchers from different disciplines to address critical national needs in determining the biological and environmental impacts of energy production and use, characterizing the interplay of climate and energy, and collaborating with other agencies and DOE programs to improve the world's most powerful climate models. BER science focuses on three distinct areas: (1) What are the roles of Earth system components (atmosphere, land, oceans, sea ice, and the biosphere) in determining climate? (2) How is the information stored in a genome translated into microbial, plant, and ecosystem processes that influence biofuel production, climate feedbacks, and the natural cycling of carbon? (3) What are the biological, geochemical, and physical forces that govern the behavior of Earth's subsurface environment? Ultimately, the goal of BER science is to support experimentation and modeling that can reliably predict the outcomes and behaviors of complex biological and environmental systems, leading to robust solutions for DOE missions and strategic goals. In March 2010, the Biological and Environmental Research Advisory Committee held the Grand Challenges for Biological and Environmental Research: A Long-Term Vision workshop to identify scientific opportunities and grand challenges for BER science in the coming decades and to develop an overall strategy for drafting a long-term vision for BER. Key workshop goals included: (1) Identifying the greatest scientific challenges in biology, climate, and the environment that DOE will face over a 20-year time horizon. (2) Describing how BER should be positioned to address those challenges. (3) Determining the new and innovative tools needed to advance BER science. (4) Suggesting how the workforce of the future should be trained in integrative system science. This report lays out grand research challenges for BER - in biological systems, climate, energy sustainability, computing, and education and workforce training - that can put society on a path to achieve the scientific evidence and predictive understanding needed to inform decision making and planning to address future energy needs, climate change, water availability, and land use

Copernicus Marine Service ocean state report, issue 4

This is the final version. Available from Taylor & Francis via the DOI in this record. FCT/MCTE