Inference of gene pathways using mixture Bayesian networks

Inference of gene networks typically relies on measurements across a wide range of conditions or treatments. Although one network structure is predicted, the relationship between genes could vary across conditions. A comprehensive approach to infer general and condition-dependent gene networks was evaluated. This approach integrated Bayesian network and Gaussian mixture models to describe continuous microarray gene expression measurements, and three gene networks were predicted.

The first reconstructions of a circadian rhythm pathway in honey bees and an adherens junction pathway in mouse embryos were obtained. In addition, general and condition-specific gene relationships, some unexpected, were detected in these two pathways and in a yeast cell-cycle pathway. The mixture Bayesian network approach identified all (honey bee circadian rhythm and mouse adherens junction pathways) or the vast majority (yeast cell-cycle pathway) of the gene relationships reported in empirical studies. Findings across the three pathways and data sets indicate that the mixture Bayesian network approach is well-suited to infer gene pathways based on microarray data. Furthermore, the interpretation of model estimates provided a broader understanding of the relationships between genes. The mixture models offered a comprehensive description of the relationships among genes in complex biological processes or across a wide range of conditions. The mixture parameter estimates and corresponding odds that the gene network inferred for a sample pertained to each mixture component allowed the uncovering of both general and condition-dependent gene relationships and patterns of expression.

This study demonstrated the two main benefits of learning gene pathways using mixture Bayesian networks. First, the identification of the optimal number of mixture components supported by the data offered a robust approach to infer gene relationships and estimate gene expression profiles. Second, the classification of conditions and observations into groups that support particular mixture components helped to uncover both gene relationships that are unique or common across conditions. Results from the application of mixture Bayesian networks substantially augmented the understanding of gene networks and demonstrated the added-value of this methodology to infer gene networks.