De novo identification of maximally deregulated subnetworks based on multi-omics data with DeRegNet

Abstract

Abstract With a growing amount of (multi-)omics data being available, the extraction of knowledge from these datasets is still a difficult problem. Classical enrichment-style analyses require predefined pathways or gene sets that are tested for significant deregulation to assess whether the pathway is functionally involved in the biological process under study. De novo identification of these pathways can reduce the bias inherent in predefined pathways or gene sets. At the same time, the definition and efficient identification of these pathways de novo from large biological networks is a challenging problem. We present a novel algorithm, DeRegNet, for the identification of maximally deregulated subnetworks on directed graphs based on deregulation scores derived from (multi-)omics data. DeRegNet can be interpreted as maximum likelihood estimation given a certain probabilistic model for de-novo subgraph identification. We use fractional integer programming to solve the resulting combinatorial optimization problem. We can show that the approach outperforms related algorithms on simulated data with known ground truths. On a publicly available liver cancer dataset we can show that DeRegNet can identify biologically meaningful subgraphs suitable for patient stratification. DeRegNet is freely available as open-source software. This document contains additional figures supporting the main paper de novo identification of maximally deregulated subnetworks based on multi-omics data with DeRegNet. This document contains details concerning the Material and Methods outlined in the main paper de novo identification of maximally deregulated subnetworks based on multi-omics data with DeRegNet. It provides details about the following topics: Directions on how to run the DeRegNet software Definition and derivation of the probabilistic model underlying DeRegNet, as well as the proof that DeRegNet corresponds to maximum likelihood estimation under outlined model DeRegNet in the context of the general optimization problem referred to as the Maximum Average Weight Connected Subgraph Problem and its relatives Proofs of certain structural properties of DeRegNet solutions Different application modes of the DeRegNet algorithms Fractional mixed-integer programming as it relates to the solution of DeRegNet instances Lazy constraints in branch-and-cut MILP solvers as it relates to DeRegNet Further solution technology employed for solving DeRegNet instances DeRegNet benchmark simulations Use of DeRegNet subgraphs as a basis for feature engineering for survival prediction on the TCGA-LIHC dataset