Theory and Limitations of Genetic Network Inference from Microarray Data

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Abstract
Since the advent of gene expression microarray technology more than 10 years ago, many computational approaches have been developed aimed at using statistical associations between mRNA abundance profiles to predict transcriptional regulatory interactions. The ultimate goal is to develop causal network models describing the transcriptional influences that genes exert on each other (via their protein products), which can be used to predict network disruptions (e.g., mutations) leading to a disease phenotype, as well as the appropriate therapeutic intervention. However, microarray data measure only a small component of the interacting variables in a genetic regulatory network, as cells are known to regulate gene expression via many diverse mechanisms. Although many researchers have acknowledged the questionable interpretation of statistical dependencies between mRNA profiles, very little work has been done on theoretically characterizing the nature of inferred dependencies using models that account for unobserved interacting variables. In this work, we review the theory behind reverse engineering algorithms derived from three separate disciplines-system control theory, graphical models, and information theory-and highlight several mathematical relationships between the various methods. We then apply recent theoretical work on constructing graphical models with latent variables to the context of reverse engineering genetic networks. We demonstrate that even the addition of simple latent variables induces statistical dependencies between non-directly interacting (e.g., co-regulated) genes that cannot be eliminated by conditioning on any observed variables.