Comparison of statistical methods for finding network motifs

There has been much recent interest in systems biology for investigating the structure of gene regulatory systems. Such networks are often formed of specific patterns, or network motifs, that are interesting from a biological point of view. Our aim in the present paper is to compare statistical methods specifically with regard to the question of how well they can detect such motifs. One popular approach is by network analysis with Gaussian graphical models (GGMs), which are statistical models associated with undirected graphs, where vertices of the graph represent genes and edges indicate regulatory interactions. Gene expression microarray data allow us to observe the amount of mRNA simultaneously for a large number of genes p under different experimental conditions n, where p is usually much larger than n prohibiting the use of standard methods. We therefore compare the performance of a number of procedures that have been specifically designed to address this large p-small n issue: G-Lasso estimation, Neighbourhood selection, Shrinkage estimation using empirical Bayes for model selection, and PC-algorithm. We found that all approaches performed poorly on the benchmark E. coli network. Hence we systematically studied their ability to detect specific network motifs, pairs, hubs and cascades, in extensive simulations. We conclude that all methods have difficulty detecting hubs, but the PC-algorithm is most promising.