Subnetwork state functions define dysregulated subnetworks in cancer.

Emerging research demonstrates the potential of protein-protein interaction (PPI) networks in uncovering the mechanistic bases of cancers, through identification of interacting proteins that are coordinately dysregulated in tumorigenic and metastatic samples. When used as features for classification, such coordinately dysregulated subnetworks improve diagnosis and prognosis of cancer considerably over single-gene markers. However, existing methods formulate coordination between multiple genes through additive representation of their expression profiles and utilize fast heuristics to identify dysregulated subnetworks, which may not be well suited to the potentially combinatorial nature of coordinate dysregulation. Here, we propose a combinatorial formulation of coordinate dysregulation and decompose the resulting objective function to cast the problem as one of identifying subnetwork state functions that are indicative of phenotype. Based on this formulation, we show that coordinate dysregulation of larger subnetworks can be bounded using simple statistics on smaller subnetworks. We then use these bounds to devise an efficient algorithm, Crane, that can search the subnetwork space more effectively than existing algorithms. Comprehensive cross-classification experiments show that subnetworks identified by Crane outperform those identified by additive algorithms in predicting metastasis of colorectal cancer (CRC).