Connectivity Measures for Signaling Pathway Topologies

Abstract

Characterizing cellular responses to different extrinsic signals is an active area of research, and curated pathway databases describe these complex signaling reactions. Here, we revisit a fundamental question in signaling pathway analysis: are two molecules "connected" in a network? This question is the first step towards understanding the potential influence of molecules in a pathway, and the answer depends on the choice of modeling framework. We examined the connectivity of Reactome signaling pathways using four different pathway representations. We find that Reactome is very well connected as a graph, moderately well connected as a compound graph or bipartite graph, and poorly connected as a hypergraph (which captures many-to-many relationships in reaction networks). We present a novel relaxation of hypergraph connectivity that iteratively increases connectivity from a node while preserving the hypergraph topology. This measure, B-relaxation distance, provides a parameterized transition between hypergraph connectivity and graph connectivity. B-relaxation distance is sensitive to the presence of small molecules that participate in many functionally unrelated reactions in the network. We also define a score that quantifies one pathway's downstream influence on another, which can be calculated as B-relaxation distance gradually relaxes the connectivity constraint in hypergraphs. Computing this score across all pairs of 34 Reactome pathways reveals two case studies of pathway influence, and we describe the specific reactions that contribute to the large influence score. Our method lays the groundwork for other generalizations of graph-theoretic concepts to hypergraphs in order to facilitate signaling pathway analysis.

Capturing complex interactions in disease ecology with simplicial sets

“…For the former, hyperedge. Franzese et al (2019) developed B-relaxation distance as a measure of connectivity within a directed hypergraph of signalling pathways. Finally, a measure of hypergraph similarity has been developed to facilitate comparisons between higher-order structures (Surana et al, 2021).…”

Computing Signal Transduction in Signaling Networks modeled as Boolean Networks, Petri Nets, and Hypergraphs

“…The definition of B-connection is a recursive one: given s ∈ V , we say u is B-connected to s ∈ G if either s = u or there exists a hyperedge e i ∈ BS(u) such that for each w ∈ T (e i ), w is B-connected to s. The concept of B-connection is supposed to capture that all reactants must be present in order for a signal to be transduced [72]. The concept of B-relaxation distance has been recently introduced to provide a parametrization between hypergraph B-connectivity and graph connectivity [26]. Let B G (s) be the set of hypernodes that are B-connected to s ∈ G .…”