Influence Networks Compared with Reaction Networks: Semantics, Expressivity and Attractors

Abstract

Biochemical reaction networks are one of the most widely used formalisms in systems biology to describe the molecular mechanisms of high-level cell processes. However, modellers also reason with influence diagrams to represent the positive and negative influences between molecular species and may find an influence network useful in the process of building a reaction network. In this paper, we introduce a formalism of influence networks with forces, and equip it with a hierarchy of Boolean, Petri net, stochastic and differential semantics, similarly to reaction networks with rates. We show that the expressive power of influence networks is the same as that of reaction networks under the differential semantics, but weaker under the discrete semantics. Furthermore, the hierarchy of semantics leads us to consider a (positive) Boolean semantics that cannot test the absence of a species, that we compare with the (negative) Boolean semantics with test for absence of a species in gene regulatory networks à la Thomas. We study the monotonicity properties of the positive semantics and derive from them an algorithm to compute attractors in both the positive and negative Boolean semantics. We illustrate our results on models of the literature about the p53/Mdm2 DNA damage repair system, the circadian clock, and the influence of MAPK signaling on cell-fate decision in urinary bladder cancer.

A single changing hypernetwork to represent (social-)ecological dynamics

“…Conversely, most processes involve many components (variables) simultaneously, such as the communication process requiring the scientist, potentially an organism under examination (the salad), and the audience. This observation remains valid for any subgraph and discipline such as, for example, a physicochemical graph of chemical reactions requiring reactants and catalyzers (Fontana and Buss 1994, Cumming et al 2014, Fages et al 2018. For these reasons, most interactions are called non-dyadic (i.e., not reduced to pairwise interactions), a point that has been made recently for ecological networks too (Werner and Peacor 2003, Golubski et al 2016, Delmas et al 2018.…”

Graphical requirements for multistationarity in reaction networks and their verification in BioModels

“…The signs of the arcs in the reaction-labelled influence multigraph of a reaction system, are given by the sign of ∂v i /∂x j instead of that of ∂f i /∂x j . Even without precise kinetic values, this can be easily computed under the general condition of well-formedness of the reactions [8,10]. This condition is satisfied by the commonly used kinetics such as mass action law, Michaelis-Menten and Hill kinetics, and provides a sanity check for the writing in SBML of ODE models [6].…”

“…For this study, we used our software modelling environment BIOCHAM 4 [9,3] to load all models from the curated branch of BioModels, improve their writing in SBML with well-formed reactions using the algorithm described in [6], compute the conservation laws [28], compute their influence multigraph labelled by the reactions [8,11] and export the labelled multigraph in the Lemon library format 5 . Then we used an implementation in C++ of the algorithm presented in this paper to search for positive circuits with the different refined conditions on the labelled influence multigraph, and evaluate their respective contributions for the analysis of multistationarity in BioModels.…”

On Robustness Computation and Optimization in BIOCHAM-4

“…A BIOCHAM model is composed of a (multi)set of reactions with rate functions, and/or influences with forces, plus possibly events. Such models can be interpreted in a hierarchy of differential, stochastic, Petri net and Boolean semantics [4]. We will focus here on the differential semantics.…”