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 network 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 gene regulatory networks with the number of phases larger than in natural cell cycle.

1 Introduction

Biochemical origins and pathways involved in many cell processes are subject of extensive research and many of them are well understood. Also well known are the structure, function, and modes of interaction of their corresponding enzymes. However, the understanding of the joint response of these components is still in its infancy. Thousands of proteins are active in a cell, and their activity regulates other proteins, whether they act alone or as parts of multiprotein complexes. Proteins affecting the activity, or expression level, of some genes are themselves transcribed by other genes. Thus, each gene is regulated by a number of genes in a constellation known as a gene regulatory network (GRN).