An integer linear programming approach for finding deregulated subgraphs in regulatory networks

Abstract

Deregulation of cell signaling pathways plays a crucial role in the development of tumors. The identification of such pathways requires effective analysis tools that facilitate the interpretation of expression differences. Here, we present a novel and highly efficient method for identifying deregulated subnetworks in a regulatory network. Given a score for each node that measures the degree of deregulation of the corresponding gene or protein, the algorithm computes the heaviest connected subnetwork of a specified size reachable from a designated root node. This root node can be interpreted as a molecular key player responsible for the observed deregulation. To demonstrate the potential of our approach, we analyzed three gene expression data sets. In one scenario, we compared expression profiles of non-malignant primary mammary epithelial cells derived from BRCA1 mutation carriers and of epithelial cells without BRCA1 mutation. Our results suggest that oxidative stress plays an important role in epithelial cells of BRCA1 mutation carriers and that the activation of stress proteins may result in avoidance of apoptosis leading to an increased overall survival of cells with genetic alterations. In summary, our approach opens new avenues for the elucidation of pathogenic mechanisms and for the detection of molecular key players.

Networks, uncertainty, applications and a crusade for optimality

“…The (CYCLE ) model of [Backes et al, 2011] has been developed for directed graphs (regulatory networks) with K-cardinality constraints, i.e., any feasible solution has to be comprised by exactly K nodes (for a given K > 1). Executables of this implementation are available online [see GeneTrail].…”

“…In the next section we will discuss several models that enable elimination of arc variables in the MIP models. [Backes et al, 2011] Recently, in [Backes et al, 2011] a new MIP model for the MWCS is introduced which avoids the explicit use of arc variables. Let C denote the family of all directed cycles in G. The new model, that we will denote by (CYCLE ), reads as follows:…”

“…Another application arises in the area of system biology [see Dittrich et al, 2008, Yamamoto et al, 2009, Backes et al, 2011. In [Yamamoto et al, 2009], the authors suggest the cardinality-constrained MWCS in order to detect core source components in gene networks, which seem to be responsible for the difference between normal cells and mutant cells.…”

“…Maximum weight connected subgraphs are considered to be good candidates for these core source components. A directed version of the MWCS has been considered in [Backes et al, 2011], where the most deregulated connected subnetwork in regulatory pathways with the highest sum of node scores (arising from expression data) is searched. In their model, they call a subgraph connected if all the nodes are reachable from one node, also called the root in the subgraph.…”

“…However, in their recent work, [Backes et al, 2011] attack the MWCS directly, which has the advantage to avoid variables for the arcs. The authors suggest a new integer linear programming formulation which is based on node variables only.…”