Top

Natural Computing

Published in:

25-10-2018

Boolean dynamics revisited through feedback interconnections

Authors: Madalena Chaves, Daniel Figueiredo, Manuel A. Martins

Published in: Natural Computing | Issue 1/2020

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

Boolean models of physical or biological systems describe the global dynamics of the system and their attractors typically represent asymptotic behaviors. In the case of large networks composed of several modules, it may be difficult to identify all the attractors. To explore Boolean dynamics from a novel viewpoint, we will analyse the dynamics emerging from the composition of two known Boolean modules. The state transition graphs and attractors for each of the modules can be combined to construct a new asymptotic graph which will (1) provide a reliable method for attractor computation with partial information; (2) illustrate the differences in dynamical behavior induced by the updating strategy (asynchronous, synchronous, or mixed); and (3) show the inherited organization/structure of the original network’s state transition graph.

previous article On the influence of the interaction graph on a finite dynamical system

next article Maximum sensitivity to update schedules of elementary cellular automata over periodic configurations

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Abou-Jaoudé W, Traynard P, Monteiro P, Saez-Rodriguez J, Helikar T, Thieffry D, Chaouiya C (2016) Logical modeling and dynamical analysis of cellular networks. Front Genet 7:94

Akutsu T, Melkman A, Tamura T, Yamamoto M (2011) Determining a singleton attractor of a boolean network with nested canalyzing functions. J Comput Biol 18(10):1275–1290MathSciNet

Baccala R, Kono D, Theofilopoulos A (2005) Interferons as pathogenic effectors in autoimmunity. Immunol Rev 204:9–26

Baldazzi V, Ropers D, Markowicz Y, Kahn D, Geiselmann J, de Jong H (2010) The carbon assimilation network in Escherichia coli is densely connected and largely sign-determined by directions of metabolic fluxes. PLoS Comput Biol 6(6):e1000812MathSciNet

Chaves M, Albert R, Sontag E (2005) Robustness and fragility of boolean models for genetic regulatory networks. J Theor Biol 235(3):431–449MathSciNet

Chaves M, Carta A (2015) Attractor computation using interconnected boolean networks: testing growth rate models in E. coli. Theor Comput Sci 599:47–63MathSciNetMATH

Chaves M, Preto M (2013) Hierarchy of models: from qualitative to quantitative analysis of circadian rhythms in cyanobacteria. Chaos 23(2):025113MathSciNetMATH

Chaves M, Tournier L (2011) Predicting the asymptotic dynamics of large biological networks by interconnections of Boolean modules. In: Proceedings of 50th conference decision and control and European control conference, Orlando, Florida, USA

Chaves M, Tournier L (2018) Analysis tools for interconnected boolean networks with biological applications. Front Physiol 9:586

Comet JP, Bernot G, Das A, Diener F, Massot C, Cessieux A (2012) Simplified models for the mammalian circadian clock. Procedia Comput Sci 11:127–138

Crama Y, Hammer P (2011) Boolean functions: theory, algorithms, and applications. Cambridge University Press, New YorkMATH

Demongeot J, Elena A, Sené S (2008) Robustness in regulatory networks: a multi-disciplinary approach. Acta Biotheor 56(1):27–49

Demongeot J, Goles E, Morvan M, Noual M, Sené S (2010) Attraction basins as gauges of robustness against boundary conditions in biological complex systems. PLOS One 5(8):1–18

Devloo V, Hansen P, Labbé M (2003) Identification of all steady states in large networks by logical analysis. Bull Math Biol 65:1025–1051MATH

Diestel R (2005) Graph theory, 3rd edn. Springer, HeidelbergMATH

Dong G, Yang Q, Wang Q, Kim YI, Wood T, Osteryoung K, van Oudenaarden A, Golden S (2010) Elevated atpase activity of kaic applies a circadian checkpoint on cell division in synechococcus elongatus. Cell 140:529–539

Fauré A, Naldi A, Chaouiya C, Thieffry D (2006) Dynamical analysis of a generic boolean model for the control of the mammalian cell cycle. Bioinformatics 22(14):124–131

Feillet C, Krusche P, Tamanini F, Janssens R, Downey M, Martin P, Teboul M, Saito S, Lévi F, Bretschneider T, van der Horst G, Delaunay F, Rand D (2014) Phase locking and multiple oscillating attractors for the coupled mammalian clock and cell cycle. PNAS 111(27):9828–9833

Feillet C, van der Horst G, Lévi F, Rand D, Delaunay F (2015) Coupling between the circadian clock and cell cycle oscillators: implication for healthy cells and malignant growth. Front Neurol 6:96

García-Gomez M, Azpeitia E, Alvarez-Buylla E (2017) A dynamic genetic-hormonal regulatory network model explains multiple cellular behaviors of the root apical meristem of Arabidopsis thaliana. PLoS Comput Biol 13(4):e1005488

Garg A, Di Cara A, Xenarios I, Mendoza L, De Micheli G (2008) Synchronous versus asynchronous modeling of gene regulatory networks. Bioinformatics 24(17):1917–1925

Gerard C, Goldbeter A (2009) Temporal self-organization of the cyclin/Cdk network driving the mammalian cell cycle. PNAS 106(51):21643–21648

Hong C, Hwang J, Cho KH, Shin I (2015) An efficient steady-state analysis method for large boolean networks with high maximum node connectivity. PLoS ONE 10(12):e0145734

Irons D (2006) Improving the efficiency of attractor cycle identification in Boolean networks. Phys D 217:7–21MathSciNetMATH

Jarrah A, Raposa B, Laubenbacher R (2007) Nested canalyzing, unate cascade, and polynomial functions. Phys D 233(2):167–174MathSciNetMATH

Kauffman S, Peterson C, Samuelsson B, Troein C (2004) Genetic networks with canalyzing boolean rules are always stable. PNAS 101(49):17102–17107

Klamt S, Saez-Rodriguez J, Lindquist J, Simeoni L, Gilles E (2006) A methodology for the structural and functional analysis of signaling and regulatory networks. BMC Bioinform 7(1):56

Klarner H, Bockmayr A, Siebert H (2014) Computing symbolic steady states of boolean networks. In: Was J, Sirakoulis G, Bandini S (eds) Cellular automata, LNCS, vol 8751. Springer, Heidelberg, pp 561–570

Klarner H, Siebert H (2015) Approximating attractors of boolean networks by iterative CTL model checking. Front Bioeng Biotechnol 3:130

Mendoza L, Xenarios I (2006) A method for the generation of standardized qualitative dynamical systems of regulatory networks. Theor Biol Med Model 3(1):13

Mori T, Flöttmann M, Krantz M, Akutsu T, Klipp E (2015) Stochastic simulation of boolean rxncon models: towards quantitative analysis of large signaling networks. BMC Syst Biol 9(45):1–9

Ortiz-Gutiérrez E, García-Cruz K, Azpeitia E, Castillo A, Sánchez M, Alvarez-Buylla E (2015) A dynamic gene regulatory network model that recovers the cyclic behavior of Arabidopsis thaliana cell cycle. PLoS Comput Biol 11(9):e1004486

Plikus MV, Vollmers C, de la Cruz D, Chaix A, Ramos R, Panda S, Chuong CM (2013) Local circadian clock gates cell cycle progression of transient amplifying cells during regenerative hair cycling. PNAS 110(23):E2106–E2115

Purnick P, Weiss R (2009) The second wave of synthetic biology: from modules to systems. Nat Rev Mol Cell Biol 10(6):410

Rust M, Markson J, Lane W, Fisher D, O’Shea E (2007) Ordered phosphorylation governs oscillation of a three-protein circadian clock. Science 318:809

Saez-Rodriguez J, Simeoni L, Lindquist JA, Hemenway R, Bommhardt U, Arndt B, Haus UU, Weismantel R, Gilles ED, Klamt S, Schraven B (2007) A logical model provides insights into T cell receptor signaling. PLoS Comput Biol 3(8):e163MathSciNet

Shmulevich I, Dougherty E, Kim S, Zhang W (2002) Probabilistic boolean networks: a rule-based uncertainty model for gene regulatory networks. Bioinformatics 18(2):261–274

Sontag E (1998) Mathematical control theory, 2nd edn. Springer, New YorkMATH

Stoll G, Caron B, Viara E, Dugourd A, Zinovyev A, Naldi A, Kroemer G, Barillot E, Calzone L (2017) Maboss 2.0: an environment for stochastic boolean modeling. Bioinformatics 33(4):2226–2228

Tournier L, Chaves M (2013) Interconnection of asynchronous Boolean networks, asymptotic and transient dynamics. Automatica 49(4):884–893MathSciNetMATH

Vecchio DD, Ninfa A, Sontag E (2008) Modular cell biology: retroactivity and insulation. Mol Syst Biol 4:161

Veliz-Cuba A, Aguilar B, Hinkelmann F, Laubenbacher R (2014) Steady state analysis of boolean molecular network models via model reduction and computational algebra. BMC Bioinform 15:221

Wang RS, Saadatpour A, Albert R (2012) Boolean modeling in systems biology: an overview of methodology and applications. Phys Biol 9:055001

Zañudo J, Albert R (2013) An effective network reduction approach to find the dynamical repertoire of discrete dynamic networks. Chaos 23(2):025111MathSciNetMATH

Zhang R, Shah M, Yang J, Nyland S, Liu X, Yun J, Albert R, Loughran TP Jr (2008) Network model of survival signaling in large granular lymphocyte leukemia. PNAS 105(42):16308–16313

Title: Boolean dynamics revisited through feedback interconnections
Authors: Madalena Chaves
Daniel Figueiredo
Manuel A. Martins
Publication date: 25-10-2018
Publisher: Springer Netherlands
Published in: Natural Computing / Issue 1/2020
Print ISSN: 1567-7818
Electronic ISSN: 1572-9796
DOI: https://doi.org/10.1007/s11047-018-9716-8

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Other articles of this Issue 1/2020

Maximum sensitivity to update schedules of elementary cellular automata over periodic configurations

Tribute to Prof. Jacques Demongeot: conversations at the National Bar

Generation and robustness of Boolean networks to model Clostridium difficile infection

A tutorial on elementary cellular automata with fully asynchronous updating

Concurrency in Boolean networks

Preface

Premium Partner