The Wnt signaling pathway transducing the stabilization of ?-catenin is essential for metazoan embryo development and is misregulated in many diseases such as cancers. In recent years models have been proposed for the Wnt signaling pathway during the segmentation process in developing embryos. Many of these include negative feedback loops where Axin2 plays a key role. However, Axin2 null mice show no segmentation phenotype. We therefore propose a new model where the negative feedback involves Dkk1 rather than Axin2. We show that this model can exhibit the same type of oscillations as the previous models with Axin2 and as observed in experiments. We show that a spatial Wnt gradient can consistently convert this temporal periodicity into the spatial periodicity of somites, provided the oscillations in new cells arising in the presomitic mesoderm are synchronized with the oscillations of older cells. We further investigate the hypothesis that a change in the Wnt level in the tail bud during the later stages of somitogenesis can lengthen the time period of the oscillations and hence the size and separation of the later somites.
The regulatory system of the transcription factor NF-?B plays a great role in many cell functions, including inflammatory response. Interestingly, the NF-?B system is known to up-regulate production of its own triggering signal-namely, inflammatory cytokines such as TNF, IL-1, and IL-6. In this paper we investigate a previously presented model of the NF-?B, which includes both spatial effects and the positive feedback from cytokines. The model exhibits the properties of an excitable medium and has the ability to propagate waves of high cytokine concentration. These waves represent an optimal way of sending an inflammatory signal through the tissue as they create a chemotactic signal able to recruit neutrophils to the site of infection. The simple model displays three qualitatively different states; low stimuli leads to no or very little response. Intermediate stimuli leads to reoccurring waves of high cytokine concentration. Finally, high stimuli leads to a sustained high cytokine concentration, a scenario which is toxic for the tissue cells and corresponds to chronic inflammation. Due to the few variables of the simple model, we are able to perform a phase-space analysis leading to a detailed understanding of the functional form of the model and its limitations. The spatial effects of the model contribute to the robustness of the cytokine wave formation and propagation.
The 219-residue protein p25? stimulates the fibrillation of ?-synuclein (?SN) in vitro and colocalizes with it in several ?-synucleinopathies. Although p25? does not fibrillate by itself under native conditions in vitro, ?SN-free p25? aggregates have also been observed in vivo in, for example, multiple system atrophy. To investigate which environmental conditions might trigger this aggregation, we investigated the effect of polyanionic biomolecules on p25? aggregation. Heparin, polyglutamate, arachidonic acid micelles, and RNA all induce p25? aggregation. More detailed studies using heparin as template for aggregation reveal that a minimum of 10-14 heparin monosaccharide units per heparin polymer are required. Bona fide fibrils are only formed at intermediate heparin concentrations, possibly because an excess of heparin binding sites blocks the inter-p25? contacts required for amyloid formation. Other polyanions also show an optimum for amyloid formation. Aggregation involves only modest structural changes according to both spectroscopic and proteolytic experiments. The aggregates do not seed aggregation of heparin-free p25?, suggesting that heparin is required in stoichiometric amounts to form organized structures. We are able to reproduce these observations in a model involving two levels of binding of p25? to heparin. We conclude that the modest structural changes that p25? undergoes can promote weak intermolecular contacts and that polyanions such as heparin play a central role in stabilizing these aggregates but in multiple ways, leading to different types of aggregates. This highlights the role of non-protein components in promoting protein aggregation in vivo.
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