Aberrant behaviours of reaction diffusion self-organisation models on growing domains in the presence of gene expression time delays

Turing’s pattern formation mechanism exhibits sensitivity to the details of the initial conditions suggesting that, in isolation, it cannot robustly generate pattern within noisy biological environments. Nonetheless, secondary aspects of developmental self-organisation, such as a growing domain, have been shown to ameliorate this aberrant model behaviour. Furthermore, while in-situ hybridisation reveals the presence of gene expression in developmental processes, the influence of such dynamics on Turing’s model has received limited attention. Here, we novelly focus on the Gierer–Meinhardt reaction diffusion system considering delays due the time taken for gene expression, while incorporating a number of different domain growth profiles to further explore the influence and interplay of domain growth and gene expression on Turing’s mechanism. We find extensive pathological model behaviour, exhibiting one or more of the following: temporal oscillations with no spatial structure, a failure of the Turing instability and an extreme sensitivity to the initial conditions, the growth profile and the duration of gene expression. This deviant behaviour is even more severe than observed in previous studies of Schnakenberg kinetics on exponentially growing domains in the presence of gene expression (Gaffney and Monk in Bull. Math. Biol. 68:99–130, 2006). Our results emphasise that gene expression dynamics induce unrealistic behaviour in Turing’s model for multiple choices of kinetics and thus such aberrant modelling predictions are likely to be generic. They also highlight that domain growth can no longer ameliorate the excessive sensitivity of Turing’s mechanism in the presence of gene expression time delays. The above, extensive, pathologies suggest that, in the presence of gene expression, Turing’s mechanism would generally require a novel and extensive secondary mechanism to control reaction diffusion patterning

Mitochondrial Oxidative Stress Alters a Pathway in Caenorhabditis elegans Strongly Resembling That of Bile Acid Biosynthesis and Secretion in Vertebrates

Mammalian bile acids (BAs) are oxidized metabolites of cholesterol whose amphiphilic properties serve in lipid and cholesterol uptake. BAs also act as hormone-like substances that regulate metabolism. The Caenorhabditis elegans clk-1 mutants sustain elevated mitochondrial oxidative stress and display a slow defecation phenotype that is sensitive to the level of dietary cholesterol. We found that: 1) The defecation phenotype of clk-1 mutants is suppressed by mutations in tat-2 identified in a previous unbiased screen for suppressors of clk-1. TAT-2 is homologous to ATP8B1, a flippase required for normal BA secretion in mammals. 2) The phenotype is suppressed by cholestyramine, a resin that binds BAs. 3) The phenotype is suppressed by the knock-down of C. elegans homologues of BA–biosynthetic enzymes. 4) The phenotype is enhanced by treatment with BAs. 5) Lipid extracts from C. elegans contain an activity that mimics the effect of BAs on clk-1, and the activity is more abundant in clk-1 extracts. 6) clk-1 and clk-1;tat-2 double mutants show altered cholesterol content. 7) The clk-1 phenotype is enhanced by high dietary cholesterol and this requires TAT-2. 8) Suppression of clk-1 by tat-2 is rescued by BAs, and this requires dietary cholesterol. 9) The clk-1 phenotype, including the level of activity in lipid extracts, is suppressed by antioxidants and enhanced by depletion of mitochondrial superoxide dismutases. These observations suggest that C. elegans synthesizes and secretes molecules with properties and functions resembling those of BAs. These molecules act in cholesterol uptake, and their level of synthesis is up-regulated by mitochondrial oxidative stress. Future investigations should reveal whether these molecules are in fact BAs, which would suggest the unexplored possibility that the elevated oxidative stress that characterizes the metabolic syndrome might participate in disease processes by affecting the regulation of metabolism by BAs

Uptake of the Necrotic Serpin in Drosophila melanogaster via the Lipophorin Receptor-1

The humoral response to fungal and Gram-positive infections is regulated by the serpin-family inhibitor, Necrotic. Following immune-challenge, a proteolytic cascade is activated which signals through the Toll receptor. Toll activation results in a range of antibiotic peptides being synthesised in the fat-body and exported to the haemolymph. As with mammalian serpins, Necrotic turnover in Drosophila is rapid. This serpin is synthesised in the fat-body, but its site of degradation has been unclear. By “freezing” endocytosis with a temperature sensitive Dynamin mutation, we demonstrate that Necrotic is removed from the haemolymph in two groups of giant cells: the garland and pericardial athrocytes. Necrotic uptake responds rapidly to infection, being visibly increased after 30 mins and peaking at 6–8 hours. Co-localisation of anti-Nec with anti-AP50, Rab5, and Rab7 antibodies establishes that the serpin is processed through multi-vesicular bodies and delivered to the lysosome, where it co-localises with the ubiquitin-binding protein, HRS. Nec does not co-localise with Rab11, indicating that the serpin is not re-exported from athrocytes. Instead, mutations which block late endosome/lysosome fusion (dor, hk, and car) cause accumulation of Necrotic-positive endosomes, even in the absence of infection. Knockdown of the 6 Drosophila orthologues of the mammalian LDL receptor family with dsRNA identifies LpR1 as an enhancer of the immune response. Uptake of Necrotic from the haemolymph is blocked by a chromosomal deletion of LpR1. In conclusion, we identify the cells and the receptor molecule responsible for the uptake and degradation of the Necrotic serpin in Drosophila melanogaster. The scavenging of serpin/proteinase complexes may be a critical step in the regulation of proteolytic cascades

Reggie-1/flotillin-2 promotes secretion of the long-range signalling forms of Wingless and Hedgehog in Drosophila

The lipid-modified morphogens Wnt and Hedgehog diffuse poorly in isolation yet can spread over long distances in vivo, predicting existence of two distinct forms of these mophogens. The first is poorly mobile and activates short-range target genes. The second is specifically packed for efficient spreading to induce long-range targets. Subcellular mechanisms involved in the discriminative secretion of these two forms remain elusive. Wnt and Hedgehog can associate with membrane microdomains, but the function of this association was unknown. Here we show that a major protein component of membrane microdomains, reggie-1/flotillin-2, plays important roles in secretion and spreading of Wnt and Hedgehog in Drosophila. Reggie-1 loss-of-function results in reduced spreading of the morphogens, while its overexpression stimulates secretion of Wnt and Hedgehog and expands their diffusion. The resulting changes in the morphogen gradients differently affect the short- and long-range targets. In its action reggie-1 appears specific for Wnt and Hedgehog. These data suggest that reggie-1 is an important component of the Wnt and Hedgehog secretion pathway dedicated to formation of the mobile pool of these morphogens

Numerical Investigation of Solid-Solid Phase Change Problem

[Entchev P. B.; Енчев П. Б.