Using Temporal Correlation in Factor Analysis for Reconstructing Transcription Factor Activities

Two-level gene regulatory networks consist of the transcription factors (TFs) in the top level and their regulated genes in the second level. The expression profiles of the regulated genes are the observed high-throughput data given by experiments such as microarrays. The activity profiles of the TFs are treated as hidden variables as well as the connectivity matrix that indicates the regulatory relationships of TFs with their regulated genes. Factor analysis (FA) as well as other methods, such as the network component algorithm, has been suggested for reconstructing gene regulatory networks and also for predicting TF activities. They have been applied to E. coli and yeast data with the assumption that these datasets consist of identical and independently distributed samples. Thus, the main drawback of these algorithms is that they ignore any time correlation existing within the TF profiles. In this paper, we extend previously studied FA algorithms to include time correlation within the transcription factors. At the same time, we consider connectivity matrices that are sparse in order to capture the existing sparsity present in gene regulatory networks. The TFs activity profiles obtained by this approach are significantly smoother than profiles from previous FA algorithms. The periodicities in profiles from yeast expression data become prominent in our reconstruction. Moreover, the strength of the correlation between time points is estimated and can be used to assess the suitability of the experimental time interval.