An Information Theoretic Approach to Constructing Robust Boolean Gene Regulatory Networks

We introduce a class of finite systems models of gene regulatory networks exhibiting behavior of the cell cycle. The model is an extension of a Boolean network model. The system spontaneously cycles through a finite set of internal states, tracking the increase of an external factor such as cell mass, and also exhibits checkpoints in which errors in gene expression levels due to cellular noise are automatically corrected. We present a 7-gene network based on Projective Geometry codes, which can correct, at every given time, one gene expression error. The topology of a network is highly symmetric and requires using only simple Boolean functions that can be synthesized using genes of various organisms. The attractor structure of the Boolean network contains a single cycle attractor. It is the smallest nontrivial network with such high robustness. The methodology allows construction of artificial cell cycle gene regulatory networks with the number of phases larger than in natural cell cycle.