Transition Dependency: A Gene-Gene Interaction Measure for Times Series Microarray Data

Biological processes in the cell such as biochemical interactions and regulatory activities involve complicated dependency relationships among genes. It is one of the most fundamental aims in biology to build up appropriate models for inferring such dependency relationships. Time series microarray data consist of trajectories of gene expression profiles at multiple time points, which provide an innovative platform for biologists to investigate the dynamic nature of gene dependencies. Such gene-gene dependencies are attributed to some physical interactions among encoded proteins or between an encoded protein and genes, or through coregulation of some common transcription factors. Although from the microarray data, we cannot directly learn about how these physical interactions work, we can still make inference whether or not there is a dependency relationship between two genes' transcriptional changes via some mathematical models. The notion of gene-gene interaction in this article refers to such dependency relationship in the expression levels.Many methods have been proposed to detect gene-gene interactions using microarray data [1–3]. A traditional approach is to cluster genes using pairwise Pearson or Spearman correlations as a distance measure [4–6]. Pearson correlation captures linear dependencies and depends on normality assumption. Spearman correlation measures the concordance in the ranks of data and is invariant to any monotonic transformations on the data. As it does not rely on any normality or linearity assumptions, it is often used as a robust statistic to identify the coexpression patterns in genes. When applied on a pair of time series data, calculating both Pearson and Spearman correlations implicitly assumes that all the paired measurements across different time points are independent replications. This calculation is too simplistic to adequately describe the complex relationship between two time series, in which the dependency may be beyond a linear