 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 on the statistical significance of these motifs and the methods used to determine it. Exponential random graph models (ERGMs) are a class of statistical model that overcome many 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  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 these methods to both an undirected protein-protein interaction (PPI) network and directed regulatory and neural networks. We confirm some , but not all, prior results as to motif significance in these data sets. Code and datasets are freely available at URL
Background: 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 on the statistical significance of these motifs and the methods used to determine it. 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 , possibly due to the practical difficulty of estimating model parameters. Advances in estimation algorithms now afford analysis of much larger networks in practical time. Results: We illustrate the application of these methods to both an undirected protein-protein interaction (PPI) network and directed gene regulatory networks. We confirm the over-representation of triangles in the PPI network and transitive triangles (feed-forward loop) in an E. coli regulatory network , but not in a yeast regulatory network. We also confirm using this method previous research showing that under-representation of the cyclic triangle (feedback loop) can be explained as a consequence of other topological features. Conclusion: ERGMs allow the over- or under-representation of multiple non-independent structural configurations to be tested simultaneously in a single model. This can overcome some of the problems recently identified in mainstream methods for motif identification, specifically assumptions of normally distributed motif frequencies and independence of motifs.
A
Background:
R
overcome many
can overcome some
A
, possibly
A
Results:
R
regulatory and neural
gene regulatory
R
some
the over-representation of triangles in the PPI network and transitive triangles (feed-forward loop) in an E. coli regulatory network
R
all, prior results as to motif significance in these data sets. Code and datasets are freely available at URL
in a yeast regulatory network. We also confirm using this method previous research showing that under-representation of the cyclic triangle (feedback loop) can be explained as a consequence of other topological features. Conclusion: ERGMs allow the over- or under-representation of multiple non-independent structural configurations to be tested simultaneously in a single model. This can overcome some of the problems recently identified in mainstream methods for motif identification, specifically assumptions of normally distributed motif frequencies and independence of motifs.