Random matrix analysis for gene interaction networks in cancer cells

Motivation: The investigation of topological modifications of the gene interaction networks in cancer cells is essential for understanding the desease. We study gene interaction networks in various human cancer cells with the random matrix theory. This study is based on the Cancer Network Galaxy (TCNG) database which is the repository of huge gene interactions inferred by Bayesian network algorithms from 256 microarray experimental data downloaded from NCBI GEO. The original GEO data are provided by the high-throughput microarray expression experiments on various human cancer cells. We apply the random matrix theory to the computationally inferred gene interaction networks in TCNG in order to detect the universality in the topology of the gene interaction networks in cancer cells. Results: We found the universal behavior in almost one half of the 256 gene interaction networks in TCNG. The distribution of nearest neighbor level spacing of the gene interaction matrix becomes the Wigner distribution when the network is large (condensed), and it behaves as Poisson distribution when the network is smaller. We also observe the transition between the Poisson and the Wigner distributions as the threshold of confidence factor of the gene interactions is shifted. We expect that the random matrix theory provides an effective analytical method for investigating the huge interaction networks of the various transcripts in cancer