Attractor landscapes in Boolean networks with firing memory: a theoretical study applied to genetic networks

Eric Goles, Fabiola Lobos, Gonzalo A. Ruz, Sylvain Sené

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

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 λ-phage and that of the genetic control of the floral morphogenesis of the plant Arabidopsis thaliana.

Original languageEnglish
Pages (from-to)295-319
Number of pages25
JournalNatural Computing
Volume19
Issue number2
DOIs
StatePublished - 1 Jun 2020

Keywords

  • Biological network modeling
  • Boolean networks
  • Discrete dynamical systems

Fingerprint

Dive into the research topics of 'Attractor landscapes in Boolean networks with firing memory: a theoretical study applied to genetic networks'. Together they form a unique fingerprint.

Cite this