Testing biological network motif significance with exponential random graph models

Abstract

Analysis of the structure of biological networks often uses statistical tests to establish the over-representation of motifs, which are thought to be important building blocks of such networks, related to their biological functions. However, there is disagreement as to the statistical significance of these motifs, and there are potential problems with standard methods for estimating this significance. Exponential random graph models (ERGMs) are a class of statistical model that can overcome some of the shortcomings of commonly used methods for testing the statistical significance of motifs. ERGMs were first introduced into the bioinformatics literature over ten years ago but have had limited application to biological networks, possibly due to the practical difficulty of estimating model parameters. Advances in estimation algorithms now afford analysis of much larger networks in practical time. We illustrate the application of ERGM to both an undirected protein-protein interaction (PPI) network and directed gene regulatory networks. ERGM models indicate over-representation of triangles in the PPI network, and confirm results from previous research as to over-representation of transitive triangles (feed-forward loop) in an E. coli and a yeast regulatory network. We also confirm, using ERGMs, previous research showing that under-representation of the cyclic triangle (feedback loop) can be explained as a consequence of other topological features.

arXiv commentMajor revision after reviewer comments. Includes supplementary tables and figures

References in corpus (24)

• Power-law distributions in empirical data
• Stochastic blockmodels and community structure in networks
• Biological network comparison using graphlet degree distribution
• A Separable Model for Dynamic Networks
• The Statistical Physics of Real-World Networks
• Modeling social networks from sampled data
• Exponential-Family Random Graph Models for Valued Networks
• Inferring Network Mechanisms: The Drosophila melanogaster Protein Interaction Network
• Quantifying randomness in real networks
• Exponential Random Graph Modeling for Complex Brain Networks
• Statistical Inference for Valued-Edge Networks: Generalized Exponential Random Graph Models
• Systematic Topology Analysis and Generation Using Degree Correlations
• Consistency under sampling of exponential random graph models
• Exponential-Family Models of Random Graphs: Inference in Finite-, Super-, and Infinite Population Scenarios
• Exponential random graph model parameter estimation for very large directed networks
• Thresholding normally distributed data creates complex networks
• Exponential random graph models for networks with community structure
• A statistical model for brain networks inferred from large-scale electrophysiological signals
• Large-scale estimation of random graph models with local dependence
• Consistent structure estimation of exponential-family random graph models with block structure
• Network motifs come in sets: correlations in the randomization process
• Fast Maximum Likelihood estimation via Equilibrium Expectation for Large Network Data
• An efficient counting method for the colored triad census
• A Simple Algorithm for Scalable Monte Carlo Inference