Ayumi Kikkawa | Searcharxiv

arXiv2019

Spectral analysis for gene communities in cancer cells

We investigate gene interaction networks in various cancer cells by spectral analysis of the adjacency matrices. We observe localization of the networks on hub genes which have extraordinarily many links. The eigenvector centralities take finite values only on special nodes when the hub degree exceeds a critical value $d_c \simeq 40$. The degree correlation function shows the disassortative behavior in the large degrees, and the nodes whose degrees $d \gtrsim 40$ have tendencies to link to small degree nodes. The communities of the gene networks centered at the hub genes are extracted by the amount of node degree discrepancies between linked nodes. We verify the Wigner-Dyson distribution of the nearest neighbor eigenvalues spacing distribution $P(s)$ in the small degree discrepancy communities, and the Poisson $P(s)$ in the communities of large degree discrepancies including the hubs.

q-bio.MN↗

arXiv2018

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 this disease. Based on the random matrix theory, we study the distribution of the nearest neighbor level spacings $P(s)$ of interaction matrices for 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 selected for the Bayesian network calculations in TCNG. We observe the Wigner distribution of $P(s)$ when the gene networks are dense networks that have more than $\sim 38,000$ 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 size of the networks and to edge frequencies that manifest reliance of the inferred gene interactions.

q-bio.MN↗