A Study of 3-gene Regulation Networks Using NK-Boolean Network Model and Fuzzy Logic Networking

Boolean network theory, proposed by Stuart A. Kauffman about 3 decades ago, is more general than the cellular automata theory of von Neumann. This theory has many potential applications, and one especially significant application is in the modeling of genetic networking behavior. In order to understand the genomic regulations of a living cell, one must investigate the chaotic phenomena of some simple Boolean networks. We studied a very basic and simple 3-genes regulation network. Different combinations of the three basic logic elements: AND, OR and COMPLEMENT resulted in different logic functions. We studied the influence of these logic functions on steady state behavior of the attractors and limit cycles patterns of cells. In evaluating the degrees of gene expression using Boolean network theory, it is necessary to quantize the expression levels to “1” and “0”. “1” indicates that the gene is expressed and a protein is formed; “0” indicates that the gene is not expressed at all. However, gene expression occurs in many stages, and it is not uncommon for the expression of a gene to cease in one of the intermediate steps. Thus, there is a need for the development of a model to represent the varying degrees of gene expression. We used Fuzzy Logic Networking to circumvent the information loss associated with quantization. Hopefully, a complete dictionary of the classification or taxonomy, of all possible chaotic patterns can be established, as it is useful in the sense that more complex chaotic behavior resulted from gene regulation can be derived from the basic patterns in it. It is highly possible that the “reverse engineering” problem can be completely solved theoretically for the 3-gene networks.