Application of Granger causality to gene regulatory network discovery

Granger causality (GC) has been applied to gene regulatory network discovery using DNA microarray time-series data. Since the number of genes is much larger than the data length, a full model cannot be applied in a straightforward manner, hence GC is often applied to genes pairwisely. In this paper, firstly we investigate with synthetic data and point out how spurious causalities (false discoveries) may emerge in pairwise GC detection. In addition, spurious causalities may also arise if the order of the vector autoregressive model is not high enough. Therefore, besides using a suitable model order, we recommend a full model over pairwise GC. This is possible if pairwise GC is first used to identify a network of interactions among only a few genes, and then all these interactions are validated with a full model again. If a full model is not possible, we recommend using model validation techniques to remove spurious discoveries. Secondly, we apply pairwise GC with model validation to a real dataset (HeLa). To estimate the model order, the Akaike information criterion is found to be more suitable than the Bayesian information criterion. Degree distribution and network hubs are obtained and compared with previous publications. The hubs tend to act as sources of interactions rather than receivers of interactions.