Determining the Maximum States of the Ensemble Distribution of Boolean Networks

Abstract

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Inference of the gene regulation mechanism from gene expression patterns has become increasingly popular, in recent years, with the advent of microarray technology. Obtaining the states of genes and their regulatory relationships would greatly enable the scientists to investigate and understand the mechanisms of the diseases. However, it is still a big challenge to determine relationships from several thousands of genes. Here, we simplify the above complex gene state determination problem as an inference of the distribution of the ensemble Boolean networks (BNs). In order to investigate and calculate the distribution of the BNs’ states, we first compute the probabilities of the different BNs’ states and obtain the number of states Ω. Then, we find the maximum possible distribution of the number of the BNs’ states and calculate the fluctuation of the distribution. Finally, two representative experiments are conducted, and the efficiency of the obtained results is verified. The proposed algorithm is conceptually concise and easily applicable to many other realistic models; furthermore, it is highly extensible for various situations.

Keywords

• network
• Gaussian distribution
• state pattern
• gene expression
• Boolean