Unravelling the Turing bifurcation using spatially varying diffusion coefficients

. The Turing bifurcation is the basic bifurcation generating spatial pattern, and lies at the heart of almost all mathematical models for patterning in biology and chemistry. In this paper the authors determine the structure of this bifurcation for two coupled reaction diffusion equations on a two-dimensional square spatial domain when the diffusion coefficients have a small explicit variation in space across the domain. In the case of homogeneous diffusivities, the Turing bifurcation is highly degenerate. Using a two variable perturbation method, the authors show that the small explicit spatial inhomogeneity splits the bifurcation into two separate primary and two separate secondary bifurcations, with all solution branches distinct. This splitting of the bifurcation is more effective than that given by making the domain slightly rectangular, and shows clearly the structure of the Turing bifurcation and the way in which the! var ious solution branches collapse together as the spatial variation is reduced. The authors determine the stability of the solution branches, which indicates that several new phenomena are introduced by the spatial variation, including stable subcritical striped patterns, and the possibility that stable stripes lose stability supercritically to give stable spotted patterns.. Received: 10 January 1996/Revised version: 3 July 1996     

Diffusion driven instability in an inhomogeneous domain

Diffusion driven instability in reaction-diffusion systems has been proposed as a mechanism for pattern formation in numerous embryological and ecological contexts. However, the possible effects of environmental inhomogeneities has received relatively little attention. We consider a general two species reaction-diffusion model in one space dimension, with one diffusion coefficient a step function of the spatial coordinate. We derive the dispersion relation and the solution of the linearized system. We apply our results to Turing-type models for both embryogenesis and predator-prey interactions. In the former case we derive conditions for pattern to be isolated in one part of the domain, and in the latter we introduce the concept of “environmental instability”. Our results suggest that environmental inhomogeneity could be an important regulator of biological pattern formation.     

Formation of several bacterial c-type cytochromes requires a novel membrane-anchored protein that faces the periplasm

We report here the discovery of a novel bacterial gene (cycH) whose product is involved in the biogenesis of most of the cellular cytochromes c. The cycH gene was detected in the course of characterizing a cytochrome oxidase-deficient Bradyrhizobium japonicum Tn5 mutant (strain CO×3) in which the transposon insertion disrupted cycH. Ali of the c-type cytochromes detectable in aerobically grown B. Japonicum wild-type cells were absent in the C0X3 mutant, with the exception of cytochrome c₁. A secondary phenotypic effect was the spectroscopic absence of the aa₃-type cytochrome c oxidase. The nucleotide sequence of the cloned wild-type cycH gene predicted a membrane-bound 369-amino-acid protein with an M_r of 39727. Results from studies on its membrane topology suggested that approximately 110 N-terminal amino acids are involved in anchoring the protein in the membrane, whereas the remaining two-thirds of the protein are exposed to the periplasm. We postulate that the CycH protein plays an essential role in an as yet unidentified periplasmic step in the biogenesis of holocytochromes c, except that of cytochrome c₁.     

Proton translocation coupled to the oxidation of carbon monoxide to CO2 and H2 in Methanosarcina barkeri

Cell suspensions of acetate-grown Methanosarcina barkeri mediate the conversion of CO and H2O to CO2 and H2. The reaction is coupled with the phosphorylation of ADP. Evidence is presented that CO oxidation by the cells is associated with the transient acidification of the suspension medium. Up to 2 mol vectorial protons were measured/mol CO oxidized when the transmembrane electrical gradient was kept low by the addition of valinomycin (20 nmol/mg protein) and KCl (200 mM) or of KSCN (50 mM). No transient acidification was observed in the presence of the protonophore tetrachlorosalicylanilide which stimulated rather than inhibited CO oxidation. Proton extrusion remained unaltered when the proton-translocating ATPase was specifically inhibited by dicyclohexylcarbodiimide. The latter finding indicates that proton translocation is associated with CO conversion to CO2 and H2 rather than with ATP hydrolysis in the cells. The data substantiate that the coupling of CO oxidation with ADP phosphorylation in M. barkeri occurs via a chemiosmotic mechanism.     

GeneCount: genome-wide calculation of absolute tumor DNA copy numbers from array comparative genomic hybridization data

Absolute tumor DNA copy numbers can currently be achieved only on a single gene basis by using fluorescence in situ hybridization (FISH). We present GeneCount, a method for genome-wide calculation of absolute copy numbers from clinical array comparative genomic hybridization data. The tumor cell fraction is reliably estimated in the model. Data consistent with FISH results are achieved. We demonstrate significant improvements over existing methods for exploring gene dosages and intratumor copy number heterogeneity in cancers.     

A complete classification of epistatic two-locus models

Background

The study of epistasis is of great importance in statistical genetics in fields such as linkage and association analysis and QTL mapping. In an effort to classify the types of epistasis in the case of two biallelic loci Li and Reich listed and described all models in the simplest case of 0/1 penetrance values. However, they left open the problem of finding a classification of two-locus models with continuous penetrance values.

Results

We provide a complete classification of biallelic two-locus models. In addition to solving the classification problem for dichotomous trait disease models, our results apply to any instance where real numbers are assigned to genotypes, and provide a complete framework for studying epistasis in QTL data. Our approach is geometric and we show that there are 387 distinct types of two-locus models, which can be reduced to 69 when symmetry between loci and alleles is accounted for. The model types are defined by 86 circuits, which are linear combinations of genotype values, each of which measures a fundamental unit of interaction.

Conclusion

The circuits provide information on epistasis beyond that contained in the additive × additive, additive × dominance, and dominance × dominance interaction terms. We discuss the connection between our classification and standard epistatic models and demonstrate its utility by analyzing a previously published dataset.     

Prolonged, granulocyte-macrophage colony-stimulating factor-dependent, neutrophil survival following rheumatoid synovial fibroblast activation by IL-17 and TNFalpha

Introduction

A surprising feature of the inflammatory infiltrate in rheumatoid arthritis is the accumulation of neutrophils within synovial fluid and at the pannus cartilage boundary. Recent findings suggest that a distinct subset of IL-17-secreting T-helper cells (T_H17 cells) plays a key role in connecting the adaptive and innate arms of the immune response and in regulating neutrophil homeostasis. We therefore tested the hypothesis that synovial fibroblasts bridge the biological responses that connect T_H17 cells to neutrophils by producing neutrophil survival factors following their activation with IL-17.

Methods

IL-17-expressing cells in the rheumatoid synovium, and IL-17-expressing cells in the peripheral blood, and synovial fluid were examined by confocal microscopy and flow cytometry, respectively. Peripheral blood neutrophils were cocultured either with rheumatoid arthritis synovial fibroblasts (RASF) or with conditioned medium from RASF that had been pre-exposed to recombinant human IL-17, TNFα or a combination of the two cytokines. Neutrophils were harvested and stained with the vital mitochondrial dye 3,3''-dihexyloxacarbocyanine iodide before being enumerated by flow cytometry.

Results

T_H17-expressing CD4⁺ cells were found to accumulate within rheumatoid synovial tissue and in rheumatoid arthritis synovial fluid. RASF treated with IL-17 and TNFα (RASF_IL-17/TNF) effectively doubled the functional lifespan of neutrophils in coculture. This was entirely due to soluble factors secreted from the fibroblasts. Specific depletion of granulocyte–macrophage colony-stimulating factor from RASF_IL-17/TNF-conditioned medium demonstrated that this cytokine accounted for approximately one-half of the neutrophil survival activity. Inhibition of phosphatidylinositol-3-kinase and NF-κB pathways showed a requirement for both signalling pathways in RASF_IL-17/TNF-mediated neutrophil rescue.

Conclusion

The increased number of neutrophils with an extended lifespan found in the rheumatoid synovial microenvironment is partly accounted for by IL-17 and TNFα activation of synovial fibroblasts. T_H17-expressing T cells within the rheumatoid synovium are likely to contribute significantly to this effect.