Abstract
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 statesΩ. 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.
Highlights
Gene network is an important tool to study the biological system from the molecular level
Two representative experiments are conducted to verify the efficiency of the obtained results
Since there are no practical data for the state changes of the same type of cells, we can only simulate the transformation process of these cells through Boolean network, and we perform extensive analyses of the data of the state changes of these cells
Summary
Gene network is an important tool to study the biological system from the molecular level. Cheng et al [11] proposed the semi-tensor product (STP) of matrices, which can only represent the logical equation as an algebraic equation, and convert the dynamics of a BCN into a linear discrete-time control system. Based on such reformation, many interesting properties have been obtained for BCN [12,13,14,15,16]. In this study, we proposed an algorithm for inferring the distribution states of the BNs. First, we compute the probability of different BNs’ states and get the value of Ω. The proposed algorithm is highly extensible in various scenarios because of the computational simpleness
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