Noisy random boolean networks and cell differentiation

Autocatalytic networks are widespread in nature, but theyare difficult to create or to reproduce in laboratory. There are howeverseveral models of coupled reactions which describe a phase transition toan autocatalytic cycle when a certain level of heterogeneity in the compositionof the chemical soup is reached, so it is interesting to understandwhy these phenomena are not easily achieved in the laboratory. For thispurpose we introduce here a model, inspired by a previous one by Kau-man, tailored for the study of such properties. In particular, we take intoaccount the stochastic nature of the dynamics of interacting molecules,in the case of a well stirred tank reactor. We describe the model andwe analyse its behaviour under dierent circumstances. In particular,the onset of an autocatalytic set is studied as the feed is varied, and itsstability is analysed.