Assessing co-regulation of directly linked genes in biological networks using microarray time series analysis

Differential expression of genes detected with the analysis of high throughput genomic experiments is a commonly used intermediate step for the identification of signaling pathways involved in the response to different biological conditions. The impact analysis was the first approach for the analysis of signaling pathways involved in a certain biological process that was able to take into account not only the magnitude of the expression change of the genes but also the topology of signaling pathways including the type of each interactions between the genes. In the impact analysis, signaling pathways are represented as weighted directed graphs with genes as nodes and the interactions between genes as edges. Edges weights are represented by a β factor, the regulatory efficiency, which is assumed to be equal to 1 in inductive interactions between genes and equal to -1 in repressive interactions. This study presents a similarity analysis between gene expression time series aimed to find correspondences with the regulatory efficiency, i.e. the β factor as found in a widely used pathway database. Here, we focused on correlations among genes directly connected in signaling pathways, assuming that the expression variations of upstream genes impact immediately downstream genes in a short time interval and without significant influences by the interactions with other genes. Time series were processed using three different similarity metrics. The first metric is based on the bit string matching; the second one is a specific application of the Dynamic Time Warping to detect similarities even in presence of stretching and delays; the third one is a quantitative comparative analysis resulting by an evaluation of frequency domain representation of time series: the similarity metric is the correlation between dominant spectral components. These three approaches are tested on real data and pathways, and a comparison is performed using Information Retrieval benchmark tools, indicating the frequency approach as the best similarity metric among the three, for its ability to detect the correlation based on the correspondence of the most significant frequency components.