On logical bifurcation diagrams

JOURNAL OF THEORETICAL BIOLOGY

卷:466

Article

Abou-Jaoude, Wassim¹  Monteiro, Pedro T.² 

[1] PSL Res Univ, INSERM, CNRS, Dept Biol,Ecole Normale Super,IBENS, F-75005 Paris, France

[2] Univ Lisbon, Inst Super Tecn, INESC ID, Lisbon, Portugal

关键词: Logical modeling;    Piecewise-linear differential equations;    Logical parameters;    Bifurcation diagrams;    Hasse diagrams;    p53-Mdm2 network;   

DOI  :  10.1016/j.jtbi.2019.01.008

来源: Elsevier

【 摘 要 】

Bifurcation theory provides a powerful framework to analyze the dynamics of differential systems as a function of specific parameters. Abou-Jaoucle et al. (2009) introduced the concept of logical bifurcation diagrams, an analog of bifurcation diagrams for the logical modeling framework. In this work, we propose a formal definition of this concept. Since logical models are inherently discrete, we use the piecewise differential (PWLD) framework to introduce the underlying bifurcation parameters. Given a regulatory graph, a set of PWLD models is mapped to a set of logical models consistent with this graph, thereby linking continuous changes of bifurcation parameters to sequences of valuations of logical parameters. A logical bifurcation diagram corresponds then to a sequence of valuations of the logical parameters (with their associated set of attractors) consistent with at least one bifurcation diagram of the set of PWLD models. Necessary conditions on logical bifurcation diagrams in the general case, as well as a characterization of these diagrams in the Boolean case, exploiting a partial order between the logical parameters, are provided. We also propose a procedure to determine a logical bifurcation diagram of maximum length, starting from an initial valuation of the logical parameters, in the Boolean case. Finally, we apply our methodology to the analysis of a biological model of the p53-Mdm2 network. (C) 2019 The Authors. Published by Elsevier Ltd.

【 授权许可】

Free