Ultrasensitivity, as described by Goldbeter and Koshland, has been considered for a long time as a way to realize bistable switches in biological systems. It is not as well recognized that when ultrasensitivity and reinforcing feedback loops are present in a spatially distributed system such as the cell plasmamembrane, they may induce bistability and spatial separation of the system into distinct signaling phases. Here we suggest that bistability of ultrasensitive signaling pathways in a diffusive environment provides a basic mechanism to realize cell membrane polarity. Cell membrane polarization is a fundamental process implicated in several basic biological phenomena, such as differentiation, proliferation, migration and morphogenesis of unicellular and multicellular organisms. We describe a simple, solvable model of cell membrane polarization based on the coupling of membrane diffusion with bistable enzymatic dynamics. The model can reproduce a broad range of symmetry-breaking events, such as those observed in eukaryotic directional sensing, the apico-basal polarization of epithelium cells, the polarization of budding and mating yeast, and the formation of Ras nanoclusters in several cell types.

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Abstract. In this paper we consider the modeling of a selected portion of signal transduction events involved in the angiogenesis process. The detailed model of this process contains a large number of parameters and the data available from wet-lab experiments are not sufficient to obtain reliable estimates for all of them. To overcome this problem, we suggest ways to simplify the detailed representation that result in models with a smaller number of parameters still capturing the overall behaviour of the detailed one.Starting from a detailed stochastic Petri net (SPN) model that accounts for all the reactions of the signal transduction cascade, using structural properties combined with the knowledge of the biological phenomena, we propose a set of model reductions.

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