Pathway analysis with signaling hypergraphs

Abstract

Signaling pathways play an important role in the cell's response to its environment. Signaling pathways are often represented as directed graphs, which are not adequate for modeling reactions such as complex assembly and dissociation, combinatorial regulation, and protein activation/inactivation. More accurate representations such as directed hypergraphs remain underutilized. In this paper, we present an extension of a directed hypergraph that we call a signaling hypergraph. We formulate a problem that asks what proteins and interactions must be involved in order to stimulate a specific response downstream of a signaling pathway. We relate this problem to computing the shortest acyclic B-hyperpath in a signaling hypergraph -an NP-hard problem -and present a mixed integer linear program to solve it. We demonstrate that the shortest hyperpaths computed in signaling hypergraphs are far more informative than shortest paths found in corresponding graph representations. Our results illustrate the potential of signaling hypergraphs as an improved representation of signaling pathways and motivate the development of novel hypergraph algorithms.

Pathway Analysis with Signaling Hypergraphs

“…We first present the algorithm for computing shortest acyclic B -hyperpaths from previous work [5] and then prove the algorithm’s correctness using the lemmas in Section 3.4. We describe our approach to computing minimum s - t B -hyperpaths in two parts.…”

“…In previous work, we formally defined the signaling hypergraph as a powerful representation of signaling pathway structure. We used signaling hypergraphs to address two general classes of questions that may be posed on pathways [5]: Is there a set of reactions that begins at protein A and terminate at protein B ?If we are given a set of reactions annotated to a specific pathway P and a comprehensive signaling network $\mathrm{scriptH}$, can we identify un-annotated reactions in $\mathrm{scriptH}$ that are likely to be in P ?…”

“…First, we describe signaling hypergraphs [5] and B -hyperpaths and provide examples of these concepts. Second, we prove that computing the acyclic B -hyperpath with the smallest number of hyperedges is NP-complete, even in a restricted setting where hypergraphs have a bounded number of possible reactants and products involved in each reaction.…”

“…Second, we prove that computing the acyclic B -hyperpath with the smallest number of hyperedges is NP-complete, even in a restricted setting where hypergraphs have a bounded number of possible reactants and products involved in each reaction. Third, we prove that the mixed integer linear program (MILP) [5] returns the shortest acyclic B -hyperpath in a signaling hypergraph. Finally, we find shortest B -hyperpaths in signaling hypergraphs constructed from a signaling pathway database (summarized below).…”

Connectivity Measures for Signaling Pathway Topologies

“…Factor graphs [26] have been used to infer pathway activity from heterogeneous data types. Hypergraphs [27,28] are generalizations of directed graphs that allow multiple inputs and outputs, and their realization as a model for signaling pathways is emerging [9,11,29]. Other models such as Petri nets [30] and logic networks [31,32] move away from structural network analysis and towards discrete dynamic modeling.…”