Singularity Structure, Symmetries and Integrability of Generalized Fisher Type Nonlinear Diffusion Equation

In this letter, the integrability aspects of a generalized Fisher type equation with modified diffusion in (1+1) and (2+1) dimensions are studied by carrying out a singularity structure and symmetry analysis. It is shown that the Painlev\'e property exists only for a special choice of the parameter ($m=2$). A B\"acklund transformation is shown to give rise to the linearizing transformation to the linear heat equation for this case ($m=2$). A Lie symmetry analysis also picks out the same case ($m=2$) as the only system among this class as having nontrivial infinite dimensional Lie algebra of symmetries and that the similarity variables and similarity reductions lead in a natural way to the linearizing transformation and physically important classes of solutions (including known ones in the literature), thereby giving a group theoretical understanding of the system. For nonintegrable cases in (2+1) dimensions, associated Lie symmetries and similarity reductions are indicated.Comment: 8 page

Control of scroll wave turbulence using resonant perturbations

Turbulence of scroll waves is a sort of spatio-temporal chaos that exists in three-dimensional excitable media. Cardiac tissue and the Belousov-Zhabotinsky reaction are examples of such media. In cardiac tissue, chaotic behaviour is believed to underlie fibrillation which, without intervention, precedes cardiac death. In this study we investigate suppression of the turbulence using stimulation of two different types, "modulation of excitability" and "extra transmembrane current". With cardiac defibrillation in mind, we used a single pulse as well as repetitive extra current with both constant and feedback controlled frequency. We show that turbulence can be terminated using either a resonant modulation of excitability or a resonant extra current. The turbulence is terminated with much higher probability using a resonant frequency perturbation than a non-resonant one. Suppression of the turbulence using a resonant frequency is up to fifty times faster than using a non-resonant frequency, in both the modulation of excitability and the extra current modes. We also demonstrate that resonant perturbation requires strength one order of magnitude lower than that of a single pulse, which is currently used in clinical practice to terminate cardiac fibrillation. Our results provide a robust method of controlling complex chaotic spatio-temporal processes. Resonant drift of spiral waves has been studied extensively in two dimensions, however, these results show for the first time that it also works in three dimensions, despite the complex nature of the scroll wave turbulence.Comment: 13 pages, 12 figures, submitted to Phys Rev E 2008/06/13. Last version: 2008/09/18, after revie

On the Integrability, B\"Acklund Transformation and Symmetry Aspects of a Generalized Fisher Type Nonlinear Reaction-Diffusion Equation

The dynamics of nonlinear reaction-diffusion systems is dominated by the onset of patterns and Fisher equation is considered to be a prototype of such diffusive equations. Here we investigate the integrability properties of a generalized Fisher equation in both (1+1) and (2+1) dimensions. A Painlev\'e singularity structure analysis singles out a special case ($m=2$) as integrable. More interestingly, a B\"acklund transformation is shown to give rise to a linearizing transformation for the integrable case. A Lie symmetry analysis again separates out the same $m=2$ case as the integrable one and hence we report several physically interesting solutions via similarity reductions. Thus we give a group theoretical interpretation for the system under study. Explicit and numerical solutions for specific cases of nonintegrable systems are also given. In particular, the system is found to exhibit different types of travelling wave solutions and patterns, static structures and localized structures. Besides the Lie symmetry analysis, nonclassical and generalized conditional symmetry analysis are also carried out.Comment: 30 pages, 10 figures, to appear in Int. J. Bifur. Chaos (2004

How to infer gene networks from expression profiles

Inferring, or ‘reverse-engineering', gene networks can be defined as the process of identifying gene interactions from experimental data through computational analysis. Gene expression data from microarrays are typically used for this purpose. Here we compared different reverse-engineering algorithms for which ready-to-use software was available and that had been tested on experimental data sets. We show that reverse-engineering algorithms are indeed able to correctly infer regulatory interactions among genes, at least when one performs perturbation experiments complying with the algorithm requirements. These algorithms are superior to classic clustering algorithms for the purpose of finding regulatory interactions among genes, and, although further improvements are needed, have reached a discreet performance for being practically useful

Buckling of scroll waves

A scroll wave in a sufficiently thin layer of an excitable medium with negative filament tension can be stable nevertheless due to filament rigidity. Above a certain critical thickness of the medium, such scroll wave will have a tendency to deform into a buckled, precessing state. Experimentally this will be seen as meandering of the spiral wave on the surface, the amplitude of which grows with the thickness of the layer, until a break-up to scroll wave turbulence happens. We present a simplified theory for this phenomenon and illustrate it with numerical examples.Comment: 4 pages main text + 5 pages appendix, 4+2 figures and a movie, as accepted by Phys Rev Letters 2012/09/2

Effects of essential oils-based supplement and Salmonella infection on gene expression, blood parameters, cecal microbiome and egg production in laying hens

Simple Summary Salmonellosis is one of the most severe zoonotic diseases transmitted to humans through animal products (especially poultry meat and eggs). Essential oils (EOs)-based feed additives in poultry nutrition are a possible alternative replacement of antimicrobials to fight this infection. In the present study on laying hens, we tested a phytobiotic, Intebio®, and elucidated formation of immune response and changes in cecal microbiocenosis and biochemical/immunological variables in blood caused by Salmonella. Changes in differential gene expression were observed at both one and seven days post-inoculation in the hens’ intestines, revealing similarities with known mammalian/human tissue-specific expression. The results of this study suggest that the challenge of birds with Salmonella had a negative effect, while phytobiotic intake had a positive effect on the status of their gastrointestinal microbiome, their level of metabolism, and their performance. Abstract One of the main roles in poultry resistance to infections caused by Salmonella is attributed to host immunity and intestinal microbiota. We conducted an experiment that involved challenging Lohmann White laying hens with Salmonella Enteritidis (SE), feeding them a diet supplemented with an EOs-based phytobiotic Intebio®. At 1 and 7 days post-inoculation, the expression profiles of eight genes related to immunity, transport of nutrients in the intestine, and metabolism were examined. Cecal microbiome composition and blood biochemical/immunological indices were also explored and egg production traits recorded. As a result, the SE challenge of laying hens and Intebio® administration had either a suppressive or activating effect on the expression level of the studied genes (e.g., IL6 and BPIFB3), the latter echoing mammalian/human tissue-specific expression. There were also effects of the pathogen challenge and phytobiotic intake on the cecal microbiome profiles and blood biochemical/immunological parameters, including those reflecting the activity of the birds’ immune systems (e.g., serum bactericidal activity, β-lysine content, and immunoglobulin levels). Significant differences between control and experimental subgroups in egg performance traits (i.e., egg weight/number/mass) were also found. The phytobiotic administration suggested a positive effect on the welfare and productivity of poultry

Investigating adverse effects of chronic dietary exposure to herbicide glyphosate on zootechnical characteristics and clinical, biochemical and immunological blood parameters in broiler chickens

Although the herbicide glyphosate is widely used globally and considered safe, more evidence of its adverse effects on animals and humans is accumulating. The present investigation was aimed at evaluating the impact of different glyphosate concentrations on zootechnical characteristics and clinical, biochemical and immunological blood parameters in Ross 308 broiler chickens. Four groups were employed, including untreated control and three experimental groups fed diets enriched with glyphosate at doses of 10, 20 and 100 ppm that conformed to 0.5, 1 and 5 maximum residue limits, respectively. The results showed that glyphosate is a stress factor triggering a multifaceted effect on important blood parameters (e.g., white blood cell and phagocytic counts), which was shown for the first time in the experiments involving productive meat-type poultry. It was first revealed that glyphosate-induced changes in blood parameters may be related to a negative impact on the zootechnical characteristics including the digestive tract organ development and body weight gain. The study findings suggested that exposure to glyphosate in the feedstuffs can adversely affect the physiological condition and productivity of broilers

Model-Based Deconvolution of Cell Cycle Time-Series Data Reveals Gene Expression Details at High Resolution

In both prokaryotic and eukaryotic cells, gene expression is regulated across the cell cycle to ensure “just-in-time” assembly of select cellular structures and molecular machines. However, present in all time-series gene expression measurements is variability that arises from both systematic error in the cell synchrony process and variance in the timing of cell division at the level of the single cell. Thus, gene or protein expression data collected from a population of synchronized cells is an inaccurate measure of what occurs in the average single-cell across a cell cycle. Here, we present a general computational method to extract “single-cell”-like information from population-level time-series expression data. This method removes the effects of 1) variance in growth rate and 2) variance in the physiological and developmental state of the cell. Moreover, this method represents an advance in the deconvolution of molecular expression data in its flexibility, minimal assumptions, and the use of a cross-validation analysis to determine the appropriate level of regularization. Applying our deconvolution algorithm to cell cycle gene expression data from the dimorphic bacterium Caulobacter crescentus, we recovered critical features of cell cycle regulation in essential genes, including ctrA and ftsZ, that were obscured in population-based measurements. In doing so, we highlight the problem with using population data alone to decipher cellular regulatory mechanisms and demonstrate how our deconvolution algorithm can be applied to produce a more realistic picture of temporal regulation in a cell

The Carbon Assimilation Network in Escherichia coli Is Densely Connected and Largely Sign-Determined by Directions of Metabolic Fluxes

Gene regulatory networks consist of direct interactions but also include indirect interactions mediated by metabolites and signaling molecules. We describe how these indirect interactions can be derived from a model of the underlying biochemical reaction network, using weak time-scale assumptions in combination with sensitivity criteria from metabolic control analysis. We apply this approach to a model of the carbon assimilation network in Escherichia coli. Our results show that the derived gene regulatory network is densely connected, contrary to what is usually assumed. Moreover, the network is largely sign-determined, meaning that the signs of the indirect interactions are fixed by the flux directions of biochemical reactions, independently of specific parameter values and rate laws. An inversion of the fluxes following a change in growth conditions may affect the signs of the indirect interactions though. This leads to a feedback structure that is at the same time robust to changes in the kinetic properties of enzymes and that has the flexibility to accommodate radical changes in the environment