Graphical requirements for multistationarity in reaction networks and their verification in BioModels. (14th December 2018)

• Record Type: Journal Article
• Authors: Baudier, Adrien; Fages, François; Soliman, Sylvain
• Is Part Of: Journal of theoretical biology. Volume 459(2018)
• Page Start: 79
• Page End: 89
• Publication Date: 2018-12-14
• Subjects: Multistability -- Reaction networks -- Influence networks -- Positive circuits -- Systems biology; Biology -- Periodicals; Biological Science Disciplines -- Periodicals; Biology -- Periodicals; Biologie -- Périodiques; Theoretische biologie; Biology; Periodicals; 571.05
• DOI: 10.1016/j.jtbi.2018.09.024
• Languages: English
• ISSNs: 0022-5193

Abstract

Highlights: Graphical requirements for multistationarity in biochemical reaction networks. Efficient graph rewriting algorithm for checking those conditions. Faster than symbolic computation methods by several orders of magnitude. Applied to the model repository BioModels. Graphical abstract: Abstract: Thomas' necessary conditions for the existence of multiple steady states in gene networks have been proved by Soulé with high generality for dynamical systems defined by differential equations. When applied to (protein) reaction networks however, those conditions do not provide information since they are trivially satisfied as soon as there is a bimolecular or a reversible reaction. Refined graphical requirements have been proposed to deal with such cases. In this paper, we present for the first time a graph rewriting algorithm for checking the refined conditions given by Soliman, and evaluate its practical performance by applying it systematically to the curated branch of the BioModels repository. This algorithm analyzes all reaction networks (of size up to 430 species) in less than 0.05 second per network, and permits to conclude to the absence of multistationarity in 160 networks over 506. The short computation times obtained in this graphical approach are in sharp contrast to the Jacobian-based symbolic computation approach. We also discuss the case of one extra graphical condition by arc rewiring that allows us to conclude on 20 more networks of this benchmark but with a high computational cost. Finally, we study with some details the case of phosphorylation cycles and MAPK signalling models which show the importance of modelling the intermediate complexations with the enzymes in order to correctly analyze the multistationarity capabilities of such biochemical reaction networks.