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Evolving Critical Boolean Networks

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Artificial Life and Evolutionary Computation (WIVACE 2018)

Abstract

Random Boolean networks are a widely acknowledged model for cell dynamics. Previous studies have shown the possibility of achieving Boolean networks with given characteristics by means of evolutionary techniques. In this work we make a further step towards more biologically plausible models by aiming at evolving networks with a given fraction of active nodes along the attractors, while constraining the evolutionary process to move across critical networks. Results show that this path along criticality does not impede to climb the mount of improbable, yet biologically realistic requirements.

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Notes

  1. 1.

    In other words, we aim to obtain a divergence between the grey level and the Boolean functions’ bias, being not interested in reaching a particular final grey level

  2. 2.

    The position of these mutations within the string coding the individuals is randomly chosen, whereas their direction (0 → 1 or 1 → 0) is predisposed to reach the desired bias.

References

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

    Article  MathSciNet  Google Scholar 

  • Aldana, M., Coppersmith, S., Kadanoff, L.P.: Boolean dynamics with random couplings. In: Kaplan, E., Marsden, J., Sreenivasan, K.R. (eds.) Perspectives and Problems in Nonlinear Science, pp. 23–89. Springer, New York (2003). https://doi.org/10.1007/978-0-387-21789-5_2

    Chapter  Google Scholar 

  • Aldana, M., Balleza, E., Kauffman, S.A., Resendiz, O.: Robustness and evolvability in genetic regulatory networks. J. Theor. Biol. 245, 433–448 (2007)

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Bornholdt, S.: Boolean network models of cellular regulation: prospects and limitations. J. R. Soc. Interface 5, S85–S94 (2008)

    Article  Google Scholar 

  • Braccini, M., Roli, A., Villani, M., Serra, R.: Automatic design of Boolean networks for cell differentiation. In: Rossi, F., Piotto, S., Concilio, S. (eds.) WIVACE 2016. CCIS, vol. 708, pp. 91–102. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-57711-1_8

    Chapter  Google Scholar 

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

    Article  Google Scholar 

  • Daniels, B.C., et al.: Criticality distinguishes the ensemble of biological regulatory networks. Phys. Rev. Lett. 121, 138102 (2018)

    Article  Google Scholar 

  • Damiani, C., Kauffman, Stuart A., Serra, R., Villani, M., Colacci, A.: Information transfer among coupled random Boolean networks. In: Bandini, S., Manzoni, S., Umeo, H., Vizzari, G. (eds.) ACRI 2010. LNCS, vol. 6350, pp. 1–11. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15979-4_1

    Chapter  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Di Stefano, M.L., Villani, M., La Rocca, L., Kauffman, S.A., Serra, R.: Dynamically critical systems and power-law distributions: avalanches revisited. In: Rossi, F., Mavelli, F., Stano, P., Caivano, D. (eds.) WIVACE 2015. CCIS, vol. 587, pp. 29–39. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-32695-5_3

    Chapter  Google Scholar 

  • Drossel, B.: Random boolean networks. In: Schuster, H.G. (ed.) Reviews of Nonlinear Dynamics and Complexity, vol. 1. Wiley, New York (2008)

    Google Scholar 

  • Gershenson, C.: Classification of random Boolean networks. In: Standish, R.K., Bedau, M.A., Abbass, H.A. (eds.) Artificial Life VIII: Proceedings of the Eight International Conference on Artificial Life, Sydney, Australia, pp. 1–8. MIT Press (2002)

    Google Scholar 

  • Gershenson, C.: Guiding the self-organization of random Boolean networks. Theory Biosci. 131, 181–191 (2012)

    Article  Google Scholar 

  • Graudenzi, A., Serra, R., Villani, M., Damiani, C., Colacci, A., Kauffman, S.A.: Dynamical properties of a Boolean model of gene regulatory network with memory. J. Comput. Biol. 18, 1291–1305 (2011a)

    Article  MathSciNet  Google Scholar 

  • Graudenzi, A., Serra, R., Villani, M., Colacci, A., Kauffman, S.A.: Robustness analysis of a Boolean model of gene regulatory network with memory. J. Comput. Biol. 18(4), 559–577 (2011b)

    Article  MathSciNet  Google Scholar 

  • Harris, S.E., Sawhill, B.K., Wuensche, A., Kauffman, S.A.: A model of transcriptional regulatory networks based on biases in the observed regulation rules. Complexity 7, 23–40 (2002)

    Article  Google Scholar 

  • Holland, J.H.: Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence. U Michigan Press, Oxford (1975)

    MATH  Google Scholar 

  • Kauffman, S.A.: The Origins of Order. Oxford University Press, Oxford (1993)

    Google Scholar 

  • Kauffman, S.A.: At Home in the Universe. Oxford University Press, Oxford (1995)

    Google Scholar 

  • Kauffman, S.A., Peterson, C., Samuelsson, B., Troein, C.: Random Boolean networks models and the yeast transcriptional networks. PNAS 100, 14796–14799 (2003)

    Article  Google Scholar 

  • Mihaljev, T., Drossel, B.: Evolution of a population of random Boolean networks. Eur. Phys. J. B 67, 259 (2009)

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Raeymaekers, L.: Dynamics of Boolean networks controlled by biologically meaningful functions. J. Theor. Biol. 218(3), 331–341 (2002)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  • Roli, A., Benedettini, S., Birattari, M., et al.: Robustness, evolvability and complexity in Boolean network robots. In: Proceedings of ECCS 2011—European Conference on Complex Systems (2011a)

    Google Scholar 

  • Roli, A., Benedettini, S., Serra, R., Villani, M.: Analysis of attractor distances in random Boolean networks. In: Apolloni, B., Bassis, S., Esposito, A., Morabito, C. (eds.) Proceedings of WIRN2010, the 20th Italian Workshop on Neural Nets IOS Press, Amsterdam (2011b)

    Google Scholar 

  • Roli, A., Villani, M., Serra, R., Benedettini, S., Pinciroli, C., Birattari, M.: Dynamical properties of artificially evolved Boolean network robots. In: Gavanelli, M., Lamma, E., Riguzzi, F. (eds.) AI*IA 2015. LNCS (LNAI), vol. 9336, pp. 45–57. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-24309-2_4

    Chapter  Google Scholar 

  • Roli, A., Villani, M., Filisetti, A., Serra, R.: Dynamical criticality: overview and open questions. J. Syst. Sci. Complex 31, 647–663 (2018)

    Article  Google Scholar 

  • Sapienza, D., Villani, M., Serra, R.: Dynamical properties of a gene-protein model. In: Pelillo, M., Poli, I., Roli, A., Serra, R., Slanzi, D., Villani, M. (eds.) WIVACE 2017. CCIS, vol. 830, pp. 142–152. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78658-2_11

    Chapter  Google Scholar 

  • Serra, R., Villani, M., Salvemini, A.: Continuous genetic networks. Parallel Comput. 27, 663–683 (2001)

    Article  MathSciNet  Google Scholar 

  • Serra, R., Villani, M.: Perturbing the regular topology of cellular automata: implications for the dynamics. In: Bandini, S., Chopard, B., Tomassini, M. (eds.) ACRI 2002. LNCS, vol. 2493, pp. 168–177. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-45830-1_16

    Chapter  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  • Serra, R., Villani, M., Agostini, L.: On the dynamics of Boolean networks with scale-free outgoing connections. Phys. A 339, 665–673 (2004b)

    Article  MathSciNet  Google Scholar 

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

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Szejka, A., Drossel, B.: Evolution of canalizing Boolean networks Eur. Phys. J. B 56, 373–380 (2007)

    Google Scholar 

  • Villani, M., Barbieri, A., Serra, R.: A dynamical model of genetic networks for cell differentiation. PLoS ONE 6(3), e17703 (2011)

    Article  Google Scholar 

  • Villani, M., Campioli, D., Damiani, C., Roli, A., Filisetti, A., Serra, R.: Dynamical regimes in non-ergodic random Boolean networks. Nat. Comput. 16(2), 353–363 (2017)

    Article  MathSciNet  Google Scholar 

  • Villani, M., La Rocca, L., Kauffman, S.A., Serra, R.: Dynamical criticality in gene regulatory networks. Complexity, 2018, 5980636 (2018)

    Google Scholar 

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Correspondence to Salvatore Magrì or Marco Villani .

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Magrì, S., Villani, M., Roli, A., Serra, R. (2019). Evolving Critical Boolean Networks. In: Cagnoni, S., Mordonini, M., Pecori, R., Roli, A., Villani, M. (eds) Artificial Life and Evolutionary Computation. WIVACE 2018. Communications in Computer and Information Science, vol 900. Springer, Cham. https://doi.org/10.1007/978-3-030-21733-4_2

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  • DOI: https://doi.org/10.1007/978-3-030-21733-4_2

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