Annotation Enrichment Analysis: An Alternative Method for Evaluating the Functional Properties of Gene Sets

Gene annotation databases (compendiums maintained by the scientific community that describe the biological functions performed by individual genes) are commonly used to evaluate the functional properties of experimentally derived gene sets. Overlap statistics, such as Fisher's Exact Test (FET), are often employed to assess these associations, but don't account for non-uniformity in the number of genes annotated to individual functions or the number of functions associated with individual genes. We find FET is strongly biased toward over-estimating overlap significance if a gene set has an unusually high number of annotations. To correct for these biases, we develop Annotation Enrichment Analysis (AEA), which properly accounts for the non-uniformity of annotations. We show that AEA is able to identify biologically meaningful functional enrichments that are obscured by numerous false-positive enrichment scores in FET, and we therefore suggest it be used to more accurately assess the biological properties of gene sets

Mixing patterns and community structure in networks

Common experience suggests that many networks might possess community structure - division of vertices into groups, with a higher density of edges within groups than between them. Here we describe a new computer algorithm that detects structure of this kind. We apply the algorithm to a number of real-world networks and show that they do indeed possess non-trivial community structure. We suggest a possible explanation for this structure in the mechanism of assortative mixing, which is the preferential association of network vertices with others that are like them in some way. We show by simulation that this mechanism can indeed account for community structure. We also look in detail at one particular example of assortative mixing, namely mixing by vertex degree, in which vertices with similar degree prefer to be connected to one another. We propose a measure for mixing of this type which we apply to a variety of networks, and also discuss the implications for network structure and the formation of a giant component in assortatively mixed networks.Comment: 21 pages, 9 postscript figures, 2 table

Robustness of Network Measures to Link Errors

In various applications involving complex networks, network measures are employed to assess the relative importance of network nodes. However, the robustness of such measures in the presence of link inaccuracies has not been well characterized. Here we present two simple stochastic models of false and missing links and study the effect of link errors on three commonly used node centrality measures: degree centrality, betweenness centrality, and dynamical importance. We perform numerical simulations to assess robustness of these three centrality measures. We also develop an analytical theory, which we compare with our simulations, obtaining very good agreement.Comment: 9 pages, 9 figure

Dynamical Instability in Boolean Networks as a Percolation Problem

Boolean networks, widely used to model gene regulation, exhibit a phase transition between regimes in which small perturbations either die out or grow exponentially. We show and numerically verify that this phase transition in the dynamics can be mapped onto a static percolation problem which predicts the long-time average Hamming distance between perturbed and unperturbed orbits