TY - JOUR

T1 - Attractor landscapes in Boolean networks with firing memory

T2 - a theoretical study applied to genetic networks

AU - Goles, Eric

AU - Lobos, Fabiola

AU - Ruz, Gonzalo A.

AU - Sené, Sylvain

N1 - Funding Information:
This work has been supported by ECOS-CONICYT C16E01 (EG, FL, GR, SS), FONDECYT 1140090 (EG, FL), Basal Project CMM (GR, EG), FANs program ANR-18-CE40-0002-01 (SS) and PACA Fri Project 2015_01134 (SS).
Publisher Copyright:
© 2020, Springer Nature B.V.

PY - 2020/6/1

Y1 - 2020/6/1

N2 - 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.

AB - 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.

KW - Biological network modeling

KW - Boolean networks

KW - Discrete dynamical systems

UR - http://www.scopus.com/inward/record.url?scp=85084373262&partnerID=8YFLogxK

U2 - 10.1007/s11047-020-09789-0

DO - 10.1007/s11047-020-09789-0

M3 - Article

AN - SCOPUS:85084373262

VL - 19

SP - 295

EP - 319

JO - Natural Computing

JF - Natural Computing

SN - 1567-7818

IS - 2

ER -