Abstract
Mathematical frameworks circumventing the need of mechanistic detail exist to build models of signal transduction networks: graphs, hypergraphs, Boolean Networks, and Petri Nets. Predicting how a signal transduces in a signaling network is essential to understand cellular functions and disease. Different formalisms exist to describe how a signal transduces in a given intracellular signaling network represented in the aforementioned modeling frameworks: elementary signaling modes, T-invariants, extreme pathway analysis, elementary flux modes and simple paths. While these signal transduction formalisms are broadly used in their respective frameworks, few studies have been done emphasizing how these signal transduction methodologies compare or relate to each other. We present an overview of how signal transduction networks have been modelled using graphs, hypergraphs, Boolean Networks, and Petri Nets in the literature. We provide a literary review of the different formalisms for capturing signal transduction in a given model of an intracellular signaling network. We also discuss the existing translations between the different modeling frameworks, and the relationships between their corresponding signal transduction representations that have been described in the literature. Furthermore, as a new formalism of signal transduction, we show how minimal functional routes proposed for signaling networks modeled as Boolean Networks can be captured by computing topological factories, a methodology found in the metabolic networks literature. We further show that in the case of an acyclic B-hypergraph, the definitions are equivalent. In directed graphs, it has been shown that computations of elementary modes via its incidence matrix correspond to computations of simple paths and feedback loops. We show that computing elementary modes based on the incidence matrix of a B-hypergraph fails to capture minimal functional routes.
Footnotes
The article has been rewritten by pushing many of the definitions to the Supplementary information. There is a new example of why simple paths and minimal functional routes are different, and that in general, there is no relationship in the number of simple paths vs minimal functional routes . The main manuscript has been heavily revised and shortened for conciseness. The example of why elementary flux modes and minimal functional routes are different in hypergraphs is now explained more thoroughly
