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The Impact of Self-loops in Random Boolean Network Dynamics: A Simulation Analysis

Part of the Communications in Computer and Information Science book series (CCIS,volume 830)

Abstract

Random Boolean Networks (RBNs) are a popular and successful model of gene regulatory networks, especially for analysing emergent properties of cell dynamics. Since completely random networks are unrealistic, some work has been done to extend the original model with structural and functional properties observed in biological networks. Among recurring motifs identified by experimental studies, auto-regulation seems to play a significant role in gene regulatory networks. In this paper we present a model of auto-regulatory mechanisms by introducing self-loops in RBNs. Experiments are performed to analyse the impact of self-loops in the RBNs asymptotic behaviour. Results show that the number of attractors increases with the amount of self-loops, while their robustness and stability decrease.

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References

  1. Ahnert, S.E., Fink, T.M.A.: Form and function in gene regulatory networks: the structure of network motifs determines fundamental properties of their dynamical state space. J. Roy. Soc. Interface 13(120), 278–289 (2016)

    CrossRef  Google Scholar 

  2. Albert, R.: Scale-free networks in cell biology. J. Cell Sci. 118(Pt 21), 4947–4957 (2005). https://doi.org/10.1242/jcs.02714

    CrossRef  Google Scholar 

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

    MathSciNet  CrossRef  MATH  Google Scholar 

  4. Balleza, E., Alvarez-Buylla, E.R., Chaos, A., Kauffman, S., Shmulevich, I., Aldana, M.: Critical dynamics in genetic regulatory networks: examples from four kingdoms. PLoS One 3(6), e2456 (2008)

    CrossRef  Google Scholar 

  5. Bastolla, U., Parisi, G.: A numerical study of the critical line of Kauffman networks. J. Theor. Biol. 187(1), 117–133 (1997)

    CrossRef  Google Scholar 

  6. Benedettini, S., Roli, A., Serra, R., Villani, M.: Automatic design of boolean networks for modelling cell differentiation. In: Cagnoni, S., Mirolli, M., Villani, M. (eds.) Evolution, Complexity and Artificial Life, pp. 77–89. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-37577-4_5

    CrossRef  Google Scholar 

  7. 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

    CrossRef  Google Scholar 

  8. Chaos, Á., Aldana, M., Espinosa-Soto, C., de León, B.G.P., Arroyo, A.G., Alvarez-Buylla, E.R.: From genes to flower patterns and evolution: dynamic models of gene regulatory networks. J. Plant Growth Regul. 25(4), 278–289 (2006)

    CrossRef  Google Scholar 

  9. Francesca, G., Brambilla, M., Brutschy, A., Trianni, V., Birattari, M.: Automode: a novel approach to the automatic design of control software for robot swarms. Swarm Intell. 8(2), 89–112 (2014)

    CrossRef  Google Scholar 

  10. Harris, S.E., Sawhill, B.K., Wuensche, A., Kauffman, S.: A model of transcriptional regulatory networks based on biases in the observed regulation rules. Complexity 7(4), 23–40 (2002)

    CrossRef  Google Scholar 

  11. Hermsen, R., Ursem, B., ten Wolde, P.R.: Combinatorial gene regulation using auto-regulation. PLoS Comput. Biol. 6(6), 1–13 (2010). https://doi.org/10.1371/journal.pcbi.1000813

    MathSciNet  CrossRef  Google Scholar 

  12. Hoffmann, M., Chang, H.H., Huang, S., Ingber, D.E., Loeffler, M., Galle, J.: Noise-driven stem cell and progenitor population dynamics. PLoS One 3(8), 1–10 (2008). https://doi.org/10.1371/journal.pone.0002922

    Google Scholar 

  13. Kauffman, S.A.: Metabolic stability and epigenesis in randomly constructed genetic nets. J. Theor. Biol. 22(3), 437–467 (1969)

    MathSciNet  CrossRef  Google Scholar 

  14. Kauffman, S.A.: The origins of order. Oxford University Press, Oxford (1993)

    Google Scholar 

  15. Kauffman, S., Peterson, C., Samuelsson, B., Troein, C.: Random boolean network models and the yeast transcriptional network. Proc. Nat. Acad. Sci. 100(25), 14796–14799 (2003)

    CrossRef  Google Scholar 

  16. Kauffman, S.A.: Homeostasis and differentiation in random genetic control networks. Nature 224(5215), 177–178 (1969). http://www.nature.com/doifinder/10.1038/224177a0

    CrossRef  Google Scholar 

  17. McAdams, H., Arkin, A.: Stochastic mechanisms in gene expression. Proc. Nat. Acad. Sci. 94(3), 814–819 (1997). http://www.pnas.org/content/94/3/814.abstract

    CrossRef  Google Scholar 

  18. Montagna, S., Viroli, M., Roli, A.: A framework supporting multi-compartment stochastic simulation and parameter optimisation for investigating biological system development. Simul. Trans. Soc. Model. Simul. Int. 91, 666–685 (2015)

    Google Scholar 

  19. Paroni, A., Graudenzi, A., Caravagna, G., Damiani, C., Mauri, G., Antoniotti, M.: CABeRNET: a cytoscape app for augmented boolean models of gene regulatory networks. BMC Bioinf. 17, 64–75 (2016)

    CrossRef  Google Scholar 

  20. Pinho, R., Garcia, V., Irimia, M., Feldman, M.W.: Stability depends on positive autoregulation in boolean gene regulatory networks. PLoS Comput. Biol. 10(11), 1–14 (2014). https://doi.org/10.1371/journal.pcbi.1003916

    CrossRef  Google Scholar 

  21. 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)

    MathSciNet  CrossRef  MATH  Google Scholar 

  22. 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 (2004)

    MathSciNet  CrossRef  Google Scholar 

  23. Serra, R., Villani, M., Agostini, L.: On the dynamics of random boolean networks with scale-free outgoing connections. Phys. A: Stat. Mech. Appl. 339(3–4), 665–673 (2004). http://www.sciencedirect.com/science/article/B6TVG-4C477JP-1/2/f6e8e45217874ad364008f770689a964

    MathSciNet  CrossRef  Google Scholar 

  24. Shen-Orr, S.S., Milo, R., Mangan, S., Alon, U.: Network motifs in the transcriptional regulation network of Escherichia coli. Nat. Genet. 31(1), 64–68 (2002)

    CrossRef  Google Scholar 

  25. Shetty, R.P., Endy, D., Knight, T.F.: Engineering biobrick vectors from biobrick parts. J. Biol. Eng. 2(1), 5 (2008). https://doi.org/10.1186/1754-1611-2-5

    CrossRef  Google Scholar 

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

    CrossRef  Google Scholar 

  27. Shmulevich, I., Kauffman, S.A., Aldana, M.: Eukaryotic cells are dynamically ordered or critical but not chaotic. Proc. Nat. Acad. Sci. U.S.A. 102(38), 13439–13444 (2005). http://www.ncbi.nlm.nih.gov/pubmed/16155121%5Cnwww.pubmedcentral.nih.gov/articlerender.fcgi?artid=PMC1224670

    CrossRef  Google Scholar 

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

    CrossRef  Google Scholar 

  29. Yeger-Lotem, E., Sattath, S., Kashtan, N., Itzkovitz, S., Milo, R., Pinter, R.Y., Alon, U., Margalit, H.: Network motifs in integrated cellular networks of transcription protein interaction. Proc. Nat. Acad. Sci. U.S.A. 101(16), 5934–5939 (2004). http://www.pnas.org/content/101/16/5934.abstract

    CrossRef  Google Scholar 

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Montagna, S., Braccini, M., Roli, A. (2018). The Impact of Self-loops in Random Boolean Network Dynamics: A Simulation Analysis. In: Pelillo, M., Poli, I., Roli, A., Serra, R., Slanzi, D., Villani, M. (eds) Artificial Life and Evolutionary Computation. WIVACE 2017. Communications in Computer and Information Science, vol 830. Springer, Cham. https://doi.org/10.1007/978-3-319-78658-2_8

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  • DOI: https://doi.org/10.1007/978-3-319-78658-2_8

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