Using a State-Space Model and Location Analysis to Infer Time-Delayed Regulatory Networks

Microarray technology allows researchers to study expression profiles of thousands of genes simultaneously. One of the ultimate goals for measuring expression data is to reverse engineer the internal structure and function of a transcriptional regulation network that governs, for example, the development of an organism, or the response of the organism to the changes in the external environment. Some of these investigations also entail measurement of gene expression over a time course after perturbing the organism. This is usually achieved by measuring changes in gene expression levels over time in response to an initial stimulation such as environmental pressure or drug addition. The data collected from time-course experiments are subjected to cluster analysis to identify patterns of expression triggered by the perturbation [12]. A fundamental assumption is that genes sharing similar expression patterns are commonly regulated, and that the genes are involved in related biological functions. Biologists refer to this as "guilt by association." Some frequently used clustering methods for finding coregulated genes are hierarchical clustering, trajectory clustering, -means clustering, principal component analysis (PCA), and self-organizing maps (SOMs). A general review of these clustering techniques is presented by Belacel et al. [3].A gene network derived by the above clustering methods is often represented as a wiring diagram. Cluster analysis groups genes with similar time-based expression patterns (i.e., trajectories) and infers shared regulatory control of the genes. The clustering result allows one to find the part-to-part correspondences between genes. The extents of gene-gene interactions are captured by heuristic distances generated by the analysis. The network diagram produced provides insights into the underlying molecular interaction network structure.Two major limitations of conventional clustering methods are that they cannot capture the effects of regulato