Random matrix analysis of localization properties of Gene co-expression network

We analyze gene co-expression network under the random matrix theory framework. The nearest neighbor spacing distribution of the adjacency matrix of this network follows Gaussian orthogonal statistics of random matrix theory (RMT). Spectral rigidity test follows random matrix prediction for a certain range, and deviates after wards. Eigenvector analysis of the network using inverse participation ratio (IPR) suggests that the statistics of bulk of the eigenvalues of network is consistent with those of the real symmetric random matrix, whereas few eigenvalues are localized. Based on these IPR calculations, we can divide eigenvalues in three sets; (A) The non-degenerate part that follows RMT. (B) The non-degenerate part, at both ends and at intermediate eigenvalues, which deviate from RMT and expected to contain information about {\it important nodes} in the network. (C) The degenerate part with $zero$ eigenvalue, which fluctuates around RMT predicted value. We identify nodes corresponding to the dominant modes of the corresponding eigenvectors and analyze their structural properties

Network Archaeology: Uncovering Ancient Networks from Present-day Interactions

Often questions arise about old or extinct networks. What proteins interacted in a long-extinct ancestor species of yeast? Who were the central players in the Last.fm social network 3 years ago? Our ability to answer such questions has been limited by the unavailability of past versions of networks. To overcome these limitations, we propose several algorithms for reconstructing a network's history of growth given only the network as it exists today and a generative model by which the network is believed to have evolved. Our likelihood-based method finds a probable previous state of the network by reversing the forward growth model. This approach retains node identities so that the history of individual nodes can be tracked. We apply these algorithms to uncover older, non-extant biological and social networks believed to have grown via several models, including duplication-mutation with complementarity, forest fire, and preferential attachment. Through experiments on both synthetic and real-world data, we find that our algorithms can estimate node arrival times, identify anchor nodes from which new nodes copy links, and can reveal significant features of networks that have long since disappeared.Comment: 16 pages, 10 figure

Bridging topological and functional information in protein interaction networks by short loops profiling

Protein-protein interaction networks (PPINs) have been employed to identify potential novel interconnections between proteins as well as crucial cellular functions. In this study we identify fundamental principles of PPIN topologies by analysing network motifs of short loops, which are small cyclic interactions of between 3 and 6 proteins. We compared 30 PPINs with corresponding randomised null models and examined the occurrence of common biological functions in loops extracted from a cross-validated high-confidence dataset of 622 human protein complexes. We demonstrate that loops are an intrinsic feature of PPINs and that specific cell functions are predominantly performed by loops of different lengths. Topologically, we find that loops are strongly related to the accuracy of PPINs and define a core of interactions with high resilience. The identification of this core and the analysis of loop composition are promising tools to assess PPIN quality and to uncover possible biases from experimental detection methods. More than 96% of loops share at least one biological function, with enrichment of cellular functions related to mRNA metabolic processing and the cell cycle. Our analyses suggest that these motifs can be used in the design of targeted experiments for functional phenotype detection.This research was supported by the Biotechnology and Biological Sciences Research Council (BB/H018409/1 to AP, ACCC and FF, and BB/J016284/1 to NSBT) and by the Leukaemia & Lymphoma Research (to NSBT and FF). SSC is funded by a Leukaemia & Lymphoma Research Gordon Piller PhD Studentship

Influence of homology and node-age on the growth of protein-protein interaction networks

Proteins participating in a protein-protein interaction network can be grouped into homology classes following their common ancestry. Proteins added to the network correspond to genes added to the classes, so that the dynamics of the two objects are intrinsically linked. Here, we first introduce a statistical model describing the joint growth of the network and the partitioning of nodes into classes, which is studied through a combined mean-field and simulation approach. We then employ this unified framework to address the specific issue of the age dependence of protein interactions, through the definition of three different node wiring/divergence schemes. Comparison with empirical data indicates that an age-dependent divergence move is necessary in order to reproduce the basic topological observables together with the age correlation between interacting nodes visible in empirical data. We also discuss the possibility of nontrivial joint partition/topology observables.Comment: 14 pages, 7 figures [accepted for publication in PRE