Loss of Linearity and Symmetrisation in Regulatory Networks

This article aims at giving some new theoretical properties of threshold Boolean automata networks which are good mathematical objects to model biological regulatory networks. The objective is the emphasis of a necessary condition for which these networks, when they are governed by a non-linear evolution law, are sensitive to the influence of boundary conditions. Then, this paper opens an argued discussion about the notion of "symmetrisability'' of regulatory networks which is relevant to understand some specific dynamical behaviours of real biological networks, and shows that this notion allows to explain an important feature of the \emph{Arabidopsis thaliana} floral morphogenesis model.