An Information Theoretic Approach to Constructing Robust Boolean Gene Regulatory Networks

Abstract

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.

Two Discrete Stochastic Cellular Automata Models of Cancer Stem Cell Proliferation

“…Genes may be turned into boolean structures which would then be applied as a rule for each individual cell [11], [12]. This should create more individualized cell models and be directly applicable in clinical situations by creating individualized tumor models.…”

Quasi-cyclic codes exhibiting the gene regulatory network of the cell cycle

“…If the cell mass increases, the state of the network = 111001 moves from C m to C m+1 or C m to C m+1 for non-zero values of m. If the cell mass does not increase, the state of the network will remain unchanged. Otherwise, the cell cycle process will be blocked by moving to the zero codeword (dead state [6]). Cycling through codewords is shown in Fig.…”

“…Recently, there has been a surge in interest in relations between the cell cycle network topology and its robustness [1]- [5]. This problem has been approached from a variety of different angles and using numerous analytical methods, including Boolean network (BN) models (for more details, see [6] and references therein). In this context the fundamental theoretical problem is to find the simplest network topology that results in dynamics similar to that of the cell cycle.…”

“…Such networks exhibit two genotypes similar to two "cell types", with the same number of expressed genes. The gene interactions are motivated by our recent work [6] in which we described a 7-gene BN based on a different type of code. The network proposed in this paper has only three phases and a smaller number of genes.…”

Inference of gene regulatory networks by integrating gene expressions and genetic perturbations

“…In order to identify regulatory interactions among genes, quite a number of network inference methods have been developed by using gene expression data such as gene microarray. Those methods can be generally classified into different theoretical categories: Boolean networks [2], Mutual Information [3], Bayesian networks (BN) [4], and Regression [5]. As each method has its own advantages and limitations under different assumptions and network model such as acyclic or cyclic network and directed or undirected network, there should be trade-offs in inferences given a different target network structure and applications [6].…”