A Model for the Dynamics of Gene Networks

In this work we propose a model for gene expression based on the theory of random dynamical systems (RDS) and show that it has a "modularity property" in the following sense: given any collection of genes that are linked in a transcriptional network, if each of them is individually described by a certain class of RDS then there is a natural, and essentially unique, prescription for coupling them together, respecting the network topology, in such a way that the collective system formed by all genes is a RDS as well. Moreover, the class of RDS used to describe the individual genes is flexible enough to account for a wide range of stochastic behaviors within the realm of stationary processes.