Attractors Perturbations in Biological Modelling: Avalanches and Cellular Differentiation

We describe here and discuss in detail the model of random Boolean networks (RBNs). Although these models have been widely studied, they still present some unexpected mathematical features, and we discuss in particular their stability properties, introducing and commenting a new measure (attractor sensitivity) that seems particularly relevant for their application to the dynamics of gene regulatory networks. We also review some results that show that RBNs can properly account for data on perturbations induced by gene knock-out in real organisms. Moreover, we show that this comparison between model and data also sheds light on the important hypothesis that living beings tend to live in, or close to, critical states. Last but not least, we show that adding noise to RBNs can lead to a nice model of cell differentiation