Spectral analysis of Gene co-expression network of Zebrafish

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, 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. Introduction. – Gene expression information captured in microarrays data for a variety of environmental and genetic perturbations promises to yield unprecedented insights into the organization and functioning of biological systems [1–4]. The challenge no longer lies in obtaining gene expression profile, but rather in interpreting the results to gain insight into biological mechanisms. It has been increasingly realized that dissecting the genetic and chemical circuitry prevents us from further understanding the biological processes as a whole. In order to understand the complexities involved, all reactions and processes should be analyzed together. To this end, network theory has been getting fast recognition to study systems which could be defined in terms of units and interactions among them [5–7]. In this view one approach is to study the co-expression of genes, and to build up gene-sets working together. A gene co-expression network is defined by a set of nodes corresponding to genes, and a list of edges corresponding to co-expression. Using gene co-expression to recover co-regulated genetic modules is a standard approach adapted in system biology [9]. We utilize gene expression data from Zebrafish exposed to various toxicants as study model [8]. The Zebrafish is an increasingly popular model not only for vertebrate development [10] but also for understanding human diseases [11] and toxicology [12]. We analyze the gene co-expression network constructed from Zebrafish data under the random matrix theory (RMT) framework. RMT was initially proposed to explain the statistical properties of nuclear spectra [13]. Later this theory was successfully applied in the study of the spectra of different complex systems such as disordered systems, quantum chaotic systems, and large complex atoms [14]. Further studies illustrate the usefulness of RMT in understanding the statistical properties of the empirical cross-correlation matrices appearing in the study of multivariate time series