Attractor landscapes in Boolean networks with firing memory: a theoretical study applied to genetic networks
Goles
E
author
Lobos
F
author
Ruz
G
A
author
Sene
S
author
2020
English
In this paper we study the dynamical behavior of Boolean networks with firing memory, namely Boolean networks whose vertices are updated synchronously depending on their proper Boolean local transition functions so that each vertex remains at its firing state a finite number of steps. We prove in particular that these networks have the same computational power than the classical ones, i.e. any Boolean network with firing memory composed of m vertices can be simulated by a Boolean network by adding vertices. We also prove general results on specific classes of networks. For instance, we show that the existence of at least one delay greater than 1 in disjunctive networks makes such networks have only fixed points as attractors. Moreover, for arbitrary networks composed of two vertices, we characterize the delay phase space, i.e. the delay values such that networks admits limit cycles or fixed points. Finally, we analyze two classical biological models by introducing delays: the model of the immune control of the lambda\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda $$\end{document}-phage and that of the genetic control of the floral morphogenesis of the plant Arabidopsis thaliana.
Discrete dynamical systems
Boolean networks
Biological network modeling
WOS:000531210800001
exported from refbase (show.php?record=1139), last updated on Mon, 11 Jan 2021 16:07:19 -0300
text
10.1007/s11047-020-09789-0
Goles_etal2020
Natural Computing
Nat. Comput.
2020
Springer
continuing
periodical
academic journal
19
2
295
319
1567-7818