Construction of synergy networks from gene expression data related to disease

• A new and credible information theoretic definition of synergy is proposed.
• A computationally efficient method for computing conditional entropy is proposed and justified.
• A synergy network is constructed from identified synergistic genes.
• The interaction of PTGDS and XBP1 is found to be most significant in prostate cancer.
• Synergistic gene pairs are found to play important role in cancer biology.

A few methods have been developed to determine whether genes collaborate with each other in relation to a particular disease using an information theoretic measure of synergy. Here, we propose an alternative definition of synergy and justify that our definition improves upon the existing measures of synergy in the context of gene interactions. We use this definition on a prostate cancer data set consisting of gene expression levels in both cancerous and non-cancerous samples and identify pairs of genes which are unable to discriminate between cancerous and non-cancerous samples individually but can do so jointly when we take their synergistic property into account. We also propose a very simple yet effective technique for computation of conditional entropy at a very low cost. The worst case complexity of our method is O(n) while the best case complexity of a state-of-the-art method is O(n2). Furthermore, our method can also be extended to find synergistic relation among triplets or even among a larger number of genes. Finally, we validate our results by demonstrating that these findings cannot be due to pure chance and provide the relevance of the synergistic pairs in cancer biology.

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