Abstract
Regulatory interaction networks are often studied on their dynamical side (existence of attractors, study of their stability). We focus here also on their robustness, that is their ability to offer the same spatiotemporal patterns and to resist to external perturbations such as losses of nodes or edges in the networks interactions architecture, changes in their environmental boundary conditions as well as changes in the update schedule (or updating mode) of the states of their elements (e.g., if these elements are genes, their synchronous coexpression mode versus their sequential expression). We define the generic notions of boundary, core, and critical vertex or edge of the underlying interaction graph of the regulatory network, whose disappearance causes dramatic changes in the number and nature of attractors (e.g., passage from a bistable behaviour to a unique periodic regime) or in the range of their basins of stability. The dynamic transition of states will be presented in the framework of threshold Boolean automata rules. A panorama of applications at different levels will be given: brain and plant morphogenesis, bulbar cardio-respiratory regulation, glycolytic/oxidative metabolic coupling, and eventually cell cycle and feather morphogenesis genetic control.
Highlights
The cell metabolism is regulated by interaction networks [1,2] bringing together elementary macromolecules like genes and their expression products, proteins, in a complex organization made of numerous weak interactions.The aim of this paper is to show how mathematical networks theories like graphs and dynamical systems theories are necessary to give a mechanistic description of how a cell, a tissue or an organ work from the emergent properties of their constitutive interacting metabolisms
The flowering regulatory network of Arabidopsis thaliana is sensitive to the change of updating mode, because it loses all the seven limit cycles observed in the parallel mode when we let it evolve with the sequential mode
We have studied in this paper the robustness of regulatory interaction networks, especially the influence of boundaries in threshold Boolean automata networks
Summary
The cell metabolism is regulated by interaction networks [1,2] bringing together elementary macromolecules like genes and their expression products, proteins, in a complex organization made of numerous weak interactions (due to physicochemical forces like electrostatic or van der Waals forces). We notice that “network motifs” are crucial to the complexity paradigm They are common patterns of interconnections between elements as well as super-structures, modeled by deterministic kinetic non-linear rules coming from the classical enzymology and from the genetic networks theory [3,4,5,6,7,8,9,10,11], e.g., from Henri-Michaelis-Menten, Hill, Monod-Wyman-Changeux and Thomas equations (Figure 2). Probabilistic versions of these rules exist accounting for the variability of the systems trajectories around their average behaviour [12,13]. Network, coherent feed-forward double path (3), triple negative and quintuple positive circuits (4), 3-switch (5), negative (6) and positive regulons (7)
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