Random Matrix Analysis for Gene Interaction Networks in Cancer Cells

Investigations of topological uniqueness of gene interaction networks in cancer cells are essential for understanding the disease. Although cancer is considered to originate from the topological alteration of a huge molecular interaction network in cellular systems, the theoretical study to investigate such complex networks is still insufficient. It is necessary to predict the behavior of a huge complex interaction network from the behavior of a finite size network. Based on the random matrix theory, we study the distribution of the nearest neighbor level spacings P(s) of interaction matrices of gene networks in human cancer cells. The interaction matrices are computed using the Cancer Network Galaxy (TCNG) database which is a repository of gene interactions inferred by a Bayesian network model. 256 NCBI GEO entries regarding gene expressions in human cancer cells have been used for the inference. We observe the Wigner distribution of P(s) when the gene networks are dense networks that have more than ~38,000 edges. In the opposite case, when the networks have smaller numbers of edges, the distribution P(s) becomes the Poisson distribution. We investigate relevance of P(s) both to the sparseness of the networks and to edge frequency factor which is the reliance (likelihood) of the inferred gene interactions.