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Natural Computing

Erschienen in:

11.04.2016

Dynamical regimes in non-ergodic random Boolean networks

verfasst von: Marco Villani, Davide Campioli, Chiara Damiani, Andrea Roli, Alessandro Filisetti, Roberto Serra

Erschienen in: Natural Computing | Ausgabe 2/2017

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Abstract

Random boolean networks are a model of genetic regulatory networks that has proven able to describe experimental data in biology. Random boolean networks not only reproduce important phenomena in cell dynamics, but they are also extremely interesting from a theoretical viewpoint, since it is possible to tune their asymptotic behaviour from order to disorder. The usual approach characterizes network families as a whole, either by means of static or dynamic measures. We show here that a more detailed study, based on the properties of system’s attractors, can provide information that makes it possible to predict with higher precision important properties, such as system’s response to gene knock-out. A new set of principled measures is introduced, that explains some puzzling behaviours of these networks. These results are not limited to random Boolean network models, but they are general and hold for any discrete model exhibiting similar dynamical characteristics.

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An attractor basin is the set of states whose evolution lead to the attractor, its size (or dimension) being the cardinality of the set.

We remind that in disordered systems trajectories starting from nearby points typically lead to different attractors.

The estimation is performed on many different initial conditions.

In this case, the averages are around 1, as the ensemble considered is the first historical example of critical systems.

An odd number of nodes avoids the cases with equal quantity of 0s and 1s.

For the reasons discussed above.

See (Serra et al. 2007b) for details on the calculation of these coefficients.

Aldana M (2003) Boolean dynamics of networks with scale-free topology. Phys D 185(1):45–66MathSciNetCrossRefMATH

Aldana M, Coppersmith S, Kadanoff LP (2003) Boolean dynamics with random couplings. In: Kaplan E, Marsden J, Sreenivasan KR (eds) Perspectives and problems in nonlinear science. Springer Applied Mathematical Sciences Series, Berlin, pp 23–90CrossRef

Bagnoli F, Rechtman R, Ruffo S (1992) Damage spreading and lyapunov exponents in cellular automata. Phys Lett A 172(12):34–38CrossRefMATH

Bastolla U, Parisi G (1998a) The modular structure of Kauffman networks. Phys D 115(3–4):219–233CrossRefMATH

Bastolla U, Parisi G (1998b) Relevant elements, magnetization and dynamical properties in Kauffman networks: a numerical study. Phys D 115(3–4):203–218CrossRefMATH

Benedettini S, Villani M, Roli A, Serra R, Manfroni M, Gagliardi A, Pinciroli C, Birattari M (2013) Dynamical regimes and learning properties of evolved boolean networks. Neurocomputing 99:111–123CrossRef

Bornholdt S (2008) Boolean network models of cellular regulation: prospects and limitations. J R Soc Interface 5:S85–S94CrossRef

Campioli D, Villani M, Poli I, Serra R (2011) Dynamical stability in random boolean networks. In: Apolloni B, Bassis S, Esposito A, Morabito FC (eds) Frontiers in Artificial Intelligence and Applications, WIRN, vol 234, 120th edn. IOS Press, Amsterdam

Cheng X, Sun M, Socolar J (2012) Autonomous boolean modelling of developmental gene regulatory networks. J R Soc Interface 10:1–12CrossRef

Damiani C, Serra R, Villani M, Kauffman S, Colacci A (2011) Cell-cell interaction and diversity of emergent behaviours. Syst Biol IET 5(2):137–144CrossRef

Derrida B, Pomeau Y (1986) Random networks of automata: a simple annealed approximation. Europhys Lett 1 1(2):45–49CrossRef

Derrida B, Weisbuch G (1986) Evolution of overlaps between configurations in random boolean networks. J Phys 47:1297–1303CrossRef

Drossel B (2005) Number of attractors in random boolean networks. Phys Rev E 72(1):016110MathSciNetCrossRef

Drossel B (2008) Random boolean networks. In: Schuster HG (ed) Reviews of nonlinear dynamics and complexity, vol 1. Wiley, New York

Fretter C, Szejka A, Drossel B (2009) Perturbation propagation in random and evolved boolean networks. N J Phys 11(0905):0646

Hughes T, Marton M, Jones A, Roberts C, Stoughton R, Armour C, Bennett H, Coffey E, Dai H, He Y, Kidd M, King A, Meyer M, Slade D, Lum P, Stepaniants S, Shoemaker D, Gachotte D, Chakraburtty K, Simon J, Bard M, Friend S (2000) Functional discovery via a compendium of expression profiles. Cell 102(1):109–126CrossRef

Kauffman SA (1969) Metabolic stability and epigenesis in randomly constructed genetic nets. J Theor Biol 22(3):437–467MathSciNetCrossRef

Kauffman SA (1971) Gene regulation networks: a theory of their global structure and behaviour. Top Dev Biol 6:145–182

Kauffman SA (1993) The origins of order. Oxford University Press, Oxford

Kauffman SA (1995) At home in the universe. Oxford University Press, Oxford

Luque B, Solé RV (2000) Lyapunov exponents in random boolean networks. Phys A 284:33–45CrossRef

Mesot B, Teuscher C (2005) Deducing local rules for solving global tasks with random boolean networks. Phys D 211(12):88–106MathSciNetCrossRefMATH

Moreira A, Amaral L (2005) Canalizing Kauffman networks: nonergodicity and its effect on their critical behavior. Phys Rev Lett 94(21):218702CrossRef

Packard NH (1988) Adaptation toward the edge of chaos. In: Kelso JAS, Mandell AJ, Shlesinger MF (eds) Dynamic patterns in complex systems. World Scientific, Singapore, pp 293–301

Ramo P, Kesseli J, Yli-Harja O (2006) Perturbation avalanches and criticality in gene regulatory networks. J Theor Biol 242(1):164–170MathSciNetCrossRefMATH

Serra R, Villani M (2002) Perturbing the regular topology of cellular automata: Implications for the dynamics. In: Proceedings of the 5th international conference on cellular automata for research and industry, Springer, London, ACRI’01, pp 168–177

Serra R, Villani M, Semeria A (2004) Genetic network models and statistical properties of gene expression data in knock-out experiments. J Theor Biol 227:149–157MathSciNetCrossRef

Serra R, Villani M, Ingrami P, SAK, (2006) Coupled random boolean network forming an artificial tissue. In: LNCS 4173, pp 548–556

Serra R, Villani M, Damiani C, Graudenzi A, Colacci A, Kauffman SA (2007a) Interacting random boolean networks. In: Jost J, Helbing D (eds) Proceedings of ECCS07: European Conference on Complex Systems

Serra R, Villani M, Graudenzi A, Kauffman SA (2007b) Why a simple model of genetic regulatory networks describes the distribution of avalanches in gene expression data. J Theor Biol 246(3):449–460MathSciNetCrossRef

Serra R, Villani M, Damiani C, Graudenzi A, Colacci A (2008a) The diffusion of perturbations in a model of coupled random boolean networks. In: Umeo H, Morishiga S, Nishinari K, Komatsuzaki T, Banidini S (eds) Cellular Automata (proceedings of 8th International Conference on Cellular Auotomata ACRI 2008, Yokohama, September 2008). Springer Lecture Notes in Computer Science, Berlin, vol 5191, pp 315– 322. ISBN: 0302-9743

Serra R, Villani M, Graudenzi A, Colacci A, Kauffman SA (2008b) The simulation of gene knock-out in scale-free random boolean models of genetic networks. Netw Heterog Media 2(3):333–343MathSciNetCrossRefMATH

Serra R, Graudenzi A, Villani M (2009) Genetic regulatory networks and neural networks. In: New Directions in Neural Networks—18th Italian Workshop on Neural Networks: WIRN, pp 109–117

Serra R, Villani M, Barbieri A, Kauffman S, Colacci A (2010) On the dynamics of random Boolean networks subject to noise: attractors, ergodic sets and cell types. J Theor Biol 265(2):185–193. doi:10.1016/j.jtbi.2010.04.012 MathSciNetCrossRef

Shmulevich I, Kauffman S (2004) Activities and sensitivities in boolean network models. Phys Rev Lett 93(048701):1–4

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

Shmulevich I, Kauffman SA, Aldana M (2005) Eukaryotic cells are dynamically ordered or critical but not chaotic. PNAS 102(38):13439–13444CrossRef

Socolar JES, Kauffman SA (2003) Scaling in ordered and critical random boolean networks. Phys Rev Lett 90(6):068702CrossRef

Szejka A, Mihaljev T, Drossel B (2008) The phase diagram of random threshold networks. New J Phys 10(6):063009CrossRef

Villani M, Serra R (2014) Attractors perturbations in biological modelling: avalanches and cellular differentiation. In: Cagnoni S, Mirolli M, Villani M (eds) Evolution, complexity and artificial life. Springer, Berlin, pp 59–76CrossRef

Villani M, Barbieri A, Serra R (2011) A dynamical model of genetic networks for cell differentiation. PloS one 6(3):e17703CrossRef

Villani M, Serra R, Barbieri A, Roli A, Kauffman S, Colacci A (2013) The influence of the introduction of a semi-permeable membrane in a stochastic model of catalytic reaction networks. In: ECCS 2013, European Conference on Complex Systems (poster presentation)

Titel: Dynamical regimes in non-ergodic random Boolean networks
verfasst von: Marco Villani
Davide Campioli
Chiara Damiani
Andrea Roli
Alessandro Filisetti
Roberto Serra
Publikationsdatum: 11.04.2016
Verlag: Springer Netherlands
Erschienen in: Natural Computing / Ausgabe 2/2017
Print ISSN: 1567-7818
Elektronische ISSN: 1572-9796
DOI: https://doi.org/10.1007/s11047-016-9552-7

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