Spectral analysis of gene co-expression network of Zebrafish

¹ School of Science, Indian Institute of Technology Indore - IET-DAVV Campus Khandwa Road, Indore 452017, India
² Department of Biological Sciences, National University of Singapore - 117546, Republic of Singapore
³ School of Life Sciences/Comp Sciences DAVV - Indore 452017, India
⁴ NUS Graduate School for Integrative Sciences and Engineering - 117456, Republic of Singapore
⁵ Department of Physics and Centre for Computational Science and Engineering, National University of Singapore 117546, Republic of Singapore
⁶ Department of Mathematics, National University of Singapore - 117456, Republic of Singapore

^(a) sarika@iiti.ac.in

Received: 29 May 2012
Accepted: 19 July 2012

Abstract

We analyze the gene expression data of Zebrafish under the combined framework of complex networks and random matrix theory. The nearest-neighbor spacing distribution of the corresponding matrix spectra follows random matrix predictions of Gaussian orthogonal statistics. Based on the eigenvector analysis we can divide the spectra into two parts, the first part for which the eigenvector localization properties match with the random matrix theory predictions, and the second part for which they show deviation from the theory and hence are useful to understand the system-dependent properties. Spectra with the localized eigenvectors can be characterized into three groups based on the eigenvalues. We explore the position of localized nodes from these different categories. Using an overlap measure, we find that the top contributing nodes in the different groups carry distinguished structural features. Furthermore, the top contributing nodes of the different localized eigenvectors corresponding to the lower eigenvalue regime form different densely connected structure well separated from each other. Preliminary biological interpretation of the genes, associated with the top contributing nodes in the localized eigenvectors, suggests that the genes corresponding to same vector share common features.