Attraction Basins as Gauges of Robustness against Boundary Conditions in Biological Complex Systems

One fundamental concept in the context of biological systems on which researches have flourished in the past decade is that of the apparent robustness of these systems, i.e., their ability to resist to perturbations or constraints induced by external or boundary elements such as electromagnetic fields acting on neural networks, micro-RNAs acting on genetic networks and even hormone flows acting both on neural and genetic networks. Recent studies have shown the importance of addressing the question of the environmental robustness of biological networks such as neural and genetic networks. In some cases, external regulatory elements can be given a relevant formal representation by assimilating them to or modeling them by boundary conditions. This article presents a generic mathematical approach to understand the influence of boundary elements on the dynamics of regulation networks, considering their attraction basins as gauges of their robustness. The application of this method on a real genetic regulation network will point out a mathematical explanation of a biological phenomenon which has only been observed experimentally until now, namely the necessity of the presence of gibberellin for the flower of the plant Arabidopsis thaliana to develop normally

Production of an extracellular milk-clotting activity during development in Myxococcus xanthus.

We describe here an extracellular proteolytic activity secreted during both growth and submerged development by Myxococcus xanthus DK1622. This activity yields the clotting of kappa-casein at pH 6 and is inhibited by specific inhibitors of aspartic proteases. Secretion of this milk-clotting proteolytic activity (of Mcp) is time regulated during the developmental cycle, with a large increase near 9 h poststarvation, but its production does not require cell-cell contact. The lack of secretion of this activity by several developmental mutants in submerged development conditions shows that Mcp production is developmentally regulated