Learning transcriptional regulatory networks from high throughput gene expression data using continuous three-way mutual information

BACKGROUND: Probability based statistical learning methods such as mutual information and Bayesian networks have emerged as a major category of tools for reverse engineering mechanistic relationships from quantitative biological data. In this work we introduce a new statistical learning strategy, MI3 that addresses three common issues in previous methods simultaneously: (1) handling of continuous variables, (2) detection of more complex three-way relationships and (3) better differentiation of causal versus confounding relationships. With these improvements, we provide a more realistic representation of the underlying biological system. RESULTS: We test the MI3 algorithm using both synthetic and experimental data. In the synthetic data experiment, MI3 achieved an absolute sensitivity/precision of 0.77/0.83 and a relative sensitivity/precision both of 0.99. In addition, MI3 significantly outperformed the control methods, including Bayesian networks, classical two-way mutual information and a discrete version of MI3. We then used MI3 and control methods to infer a regulatory network centered at the MYC transcription factor from a published microarray dataset. Models selected by MI3 were numerically and biologically distinct from those selected by control methods. Unlike control methods, MI3 effectively differentiated true causal models from confounding models. MI3 recovered major MYC cofactors, and revealed major mechanisms involved in MYC dependent transcriptional regulation, which are strongly supported by literature. The MI3 network showed that limited sets of regulatory mechanisms are employed repeatedly to control the expression of large number of genes. CONCLUSION: Overall, our work demonstrates that MI3 outperforms the frequently used control methods, and provides a powerful method for inferring mechanistic relationships underlying biological and other complex systems. The MI3 method is implemented in R in the "mi3" package, available under the GNU GPL from and from the R package archive CRAN.