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

Classification and stability of simple homoclinic cycles in R^5

The paper presents a complete study of simple homoclinic cycles in R^5. We find all symmetry groups Gamma such that a Gamma-equivariant dynamical system in R^5 can possess a simple homoclinic cycle. We introduce a classification of simple homoclinic cycles in R^n based on the action of the system symmetry group. For systems in R^5, we list all classes of simple homoclinic cycles. For each class, we derive necessary and sufficient conditions for asymptotic stability and fragmentary asymptotic stability in terms of eigenvalues of linearisation near the steady state involved in the cycle. For any action of the groups Gamma which can give rise to a simple homoclinic cycle, we list classes to which the respective homoclinic cycles belong, thus determining conditions for asymptotic stability of these cycles.Comment: 34 pp., 4 tables, 30 references. Submitted to Nonlinearit

Interactions of local climatic, biotic and hydrogeochemical processes facilitate phosphorus dynamics along an Everglades forest-marsh gradient

Ecosystem nutrient cycling is often complex because nutrient dynamics within and between systems are mediated by the interaction of biological and geochemical conditions operating at different temporal and spatial scales. Vegetated patches in semiarid and wetland landscapes have been shown to exemplify some of these patterns and processes. We investigated biological and geochemical factors suggested to contribute to phosphorus (P) movement and availability along a forest-marsh gradient in an Everglades tree island. Our study illustrated processes that are consistent with the chemohydrodynamic nutrient (CHNT) hypothesis and the trigger-transfer, pulse-reserve (TTPR) model developed for semiarid systems. Comparison with the TTPR model was constructive as it elaborated several significant patterns and processes of the tree island ecosystem including: (1) concentration of the limiting resource (P) in the source patch (High Head which constitutes the reserve) compared with the resource-poor landscape, (2) soil zone calcite precipitation requiring strong seasonality for evapotranspiration to promote conditions for secondary soil development and calcium phosphate reprecipitation, (3) rewetting of previously dry soils by early wet season precipitation events, and (4) antecedent conditions of the source patch, including landscape position that modulated the effect of the precipitation trigger. Thus, our study showed how water availability drives soil water P dynamics and, potentially, stability of mineral soil P in this tree island ecosystem. In landscapes with extensive water management, these processes can be asynchronous with the seasonality of hydrologic dynamics, tipping the balance between a sink and source of a limiting nutrient

Bifurcations of periodic orbits with spatio-temporal symmetries

Motivated by recent analytical and numerical work on two- and three-dimensional convection with imposed spatial periodicity, we analyse three examples of bifurcations from a continuous group orbit of spatio-temporally symmetric periodic solutions of partial differential equations. Our approach is based on centre manifold reduction for maps, and is in the spirit of earlier work by Iooss (1986) on bifurcations of group orbits of spatially symmetric equilibria. Two examples, two-dimensional pulsating waves (PW) and three-dimensional alternating pulsating waves (APW), have discrete spatio-temporal symmetries characterized by the cyclic groups Z_n, n=2 (PW) and n=4 (APW). These symmetries force the Poincare' return map M to be the nth iterate of a map G: M=G^n. The group orbits of PW and APW are generated by translations in the horizontal directions and correspond to a circle and a two-torus, respectively. An instability of pulsating waves can lead to solutions that drift along the group orbit, while bifurcations with Floquet multiplier +1 of alternating pulsating waves do not lead to drifting solutions. The third example we consider, alternating rolls, has the spatio-temporal symmetry of alternating pulsating waves as well as being invariant under reflections in two vertical planes. This leads to the possibility of a doubling of the marginal Floquet multiplier and of bifurcation to two distinct types of drifting solutions. We conclude by proposing a systematic way of analysing steady-state bifurcations of periodic orbits with discrete spatio-temporal symmetries, based on applying the equivariant branching lemma to the irreducible representations of the spatio-temporal symmetry group of the periodic orbit, and on the normal form results of Lamb (1996). This general approach is relevant to other pattern formation problems, and contributes to our understanding of the transition from ordered to disordered behaviour in pattern-forming systems

Classification of Protein Kinases on the Basis of Both Kinase and Non-Kinase Regions

BACKGROUND: Protein phosphorylation is a generic way to regulate signal transduction pathways in all kingdoms of life. In many organisms, it is achieved by the large family of Ser/Thr/Tyr protein kinases which are traditionally classified into groups and subfamilies on the basis of the amino acid sequence of their catalytic domains. Many protein kinases are multi-domain in nature but the diversity of the accessory domains and their organization are usually not taken into account while classifying kinases into groups or subfamilies. METHODOLOGY: Here, we present an approach which considers amino acid sequences of complete gene products, in order to suggest refinements in sets of pre-classified sequences. The strategy is based on alignment-free similarity scores and iterative Area Under the Curve (AUC) computation. Similarity scores are computed by detecting common patterns between two sequences and scoring them using a substitution matrix, with a consistent normalization scheme. This allows us to handle full-length sequences, and implicitly takes into account domain diversity and domain shuffling. We quantitatively validate our approach on a subset of 212 human protein kinases. We then employ it on the complete repertoire of human protein kinases and suggest few qualitative refinements in the subfamily assignment stored in the KinG database, which is based on catalytic domains only. Based on our new measure, we delineate 37 cases of potential hybrid kinases: sequences for which classical classification based entirely on catalytic domains is inconsistent with the full-length similarity scores computed here, which implicitly consider multi-domain nature and regions outside the catalytic kinase domain. We also provide some examples of hybrid kinases of the protozoan parasite Entamoeba histolytica. CONCLUSIONS: The implicit consideration of multi-domain architectures is a valuable inclusion to complement other classification schemes. The proposed algorithm may also be employed to classify other families of enzymes with multi-domain architecture

Electroproduction, photoproduction, and inverse electroproduction of pions in the first resonance region

Methods are set forth for determining the hadron electromagnetic structure in the sub-$N\bar{N}$-threshold timelike region of the virtual-photon ``mass'' and for investigating the nucleon weak structure in the spacelike region from experimental data on the process $\pi N\to e^+e^- N$ at low energies. These methods are formulated using the unified description of photoproduction, electroproduction, and inverse electroproduction of pions in the first resonance region in the framework of the dispersion-relation model and on the basis of the model-independent properties of inverse electroproduction. Applications of these methods are also shown.Comment: The revised published version; Revtex4, 18 pages, 6 figure

Importance of bile composition for diagnosis of biliary obstructions

Determination of the cause of a biliary obstruction is often inconclusive from serum analysis alone without further clinical tests. To this end, serum markers as well as the composition of bile of 74 patients with biliary obstructions were determined to improve the diagnoses. The samples were collected from the patients during an endoscopic retrograde cholangiopancreatography (ERCP). The concentration of eight bile salts, specifically sodium cholate, sodium glycocholate, sodium taurocholate, sodium glycodeoxycholate, sodium chenodeoxycholate, sodium glycochenodeoxycholate, sodium taurodeoxycholate, and sodium taurochenodeoxycholate as well as bile cholesterol were determined by HPLC-MS. Serum alanine aminotransferase (ALT), aspartate transaminase (AST), and bilirubin were measured before the ERCP. The aim was to determine a diagnostic factor and gain insights into the influence of serum bilirubin as well as bile salts on diseases. Ratios of conjugated/unconjugated, primary/secondary, and taurine/glycine conjugated bile salts were determined to facilitate the comparison to literature data. Receiver operating characteristic (ROC) curves were determined, and the cut-off values were calculated by determining the point closest to (0,1). It was found that serum bilirubin was a good indicator of the type of biliary obstruction; it was able to differentiate between benign obstructions such as choledocholithiasis (at the concentration of >11 µmol/L) and malignant changes such as pancreatic neoplasms or cholangiocarcinoma (at the concentration of >59 µmol/L). In addition, it was shown that conjugated/unconjugated bile salts confirm the presence of an obstruction. With lower levels of conjugated/unconjugated bile salts the possibility for inflammation and, thus, neoplasms increase

The regularized visible fold revisited

The planar visible fold is a simple singularity in piecewise smooth systems. In this paper, we consider singularly perturbed systems that limit to this piecewise smooth bifurcation as the singular perturbation parameter $\epsilon\rightarrow 0$. Alternatively, these singularly perturbed systems can be thought of as regularizations of their piecewise counterparts. The main contribution of the paper is to demonstrate the use of consecutive blowup transformations in this setting, allowing us to obtain detailed information about a transition map near the fold under very general assumptions. We apply this information to prove, for the first time, the existence of a locally unique saddle-node bifurcation in the case where a limit cycle, in the singular limit $\epsilon\rightarrow 0$, grazes the discontinuity set. We apply this result to a mass-spring system on a moving belt described by a Stribeck-type friction law

Ribosomal protein S6 mRNA is a biomarker upregulated in multiple sclerosis, downregulated by interferon treatment, and affected by season

Background

Protective essential oil attenuates influenza virus infection: An in vitro study in MDCK cells

<p>Abstract</p> <p>Background</p> <p>Influenza is a significant cause of morbidity and mortality. The recent pandemic of a novel H1N1 influenza virus has stressed the importance of the search for effective treatments for this disease. Essential oils from aromatic plants have been used for a wide variety of applications, such as personal hygiene, therapeutic massage and even medical practice. In this paper, we investigate the potential role of an essential oil in antiviral activity.</p> <p>Methods</p> <p>We studied a commercial essential oil blend, On Guard™, and evaluated its ability in modulating influenza virus, A/PR8/34 (PR8), infection in Madin-Darby canine kidney (MDCK) cells. Influenza virus was first incubated with the essential oil and infectivity in MDCK cells was quantified by fluorescent focus assay (FFA). In order to determine the mechanism of effects of essential oil in viral infection inhibition, we measured hemagglutination (HA) activity, binding and internalization of untreated and oil-treated virus in MDCK cells by flow cytometry and immunofluorescence microscopy. In addition, the effect of oil treatment on viral transcription and translation were assayed by relative end-point RT-PCR and western blot analysis.</p> <p>Results</p> <p>Influenza virus infectivity was suppressed by essential oil treatment in a dose-dependent manner; the number of nascent viral particles released from MDCK cells was reduced by 90% and by 40% when virus was treated with 1:4,000 and 1:6,000 dilutions of the oil, respectively. Oil treatment of the virus also decreased direct infection of the cells as the number of infected MDCK cells decreased by 90% and 45% when virus was treated with 1:2,000 and 1:3,000 dilutions of the oil, respectively. This was not due to a decrease in HA activity, as HA was preserved despite oil treatment. In addition, oil treatment did not affect virus binding or internalization in MDCK cells. These effects did not appear to be due to cytotoxicity of the oil as MDCK cell viability was only seen with concentrations of oil that were 2 to 6 times greater than the doses that inhibited viral infectivity. RT-PCR and western blotting demonstrated that oil treatment of the virus inhibited viral NP and NS1 protein, but not mRNA expression.</p> <p>Conclusions</p> <p>An essential oil blend significantly attenuates influenza virus PR8 infectivity <it>in vitro </it>without affecting viral binding or cellular internalization in MDCK cells. Oil treated virus continued to express viral mRNAs but had minimal expression of viral proteins, suggesting that the antiviral effect may be due to inhibition of viral protein translation.</p