Automatic Design of Boolean Networks for Modelling Cell Differentiation

  • Stefano BenedettiniEmail author
  • Andrea Roli
  • Roberto Serra
  • Marco Villani


A mathematical model based on Random Boolean Networks (RBNs) has been recently proposed to describe the main features of cell differentiation. The model captures in a unique framework all the main phenomena involved in cell differentiation and can be subject to experimental testing. A prominent role in the model is played by cellular noise, which somehow controls the cell ontogenetic process from the stem, totipotent state to the mature, completely differentiated one. Noise is high in stem cells and decreases while the cell undergoes the differentiation process. A limitation of the current mathematical model is that RBNs, as an ensemble, are not endowed with the property of showing a smooth relation between noise level and the differentiation stages of cells. In this work, we show that it is possible to generate an ensemble of Boolean networks (BNs) that can satisfy such a requirement, while keeping the other main relevant statistical features of classical RBNs. This ensemble is designed by means of an optimisation process, in which a stochastic local search (SLS) optimises an objective function which accounts for the requirements the network ensemble has to fulfil.


Local Search Boolean Function Truth Table Boolean Network Transition Graph 
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  1. 1.
    Serra, R., Villani, M., Barbieri, A., Kauffman, S.A., 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)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Villani, M., Barbieri, A., Serra, R.: A dynamical model of genetic networks for cell differentiation. PLoS One 6(3), e17703, 1–9 (2011)Google Scholar
  3. 3.
    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)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Aldana, M., Balleza, E., Kauffman, S.A., Resendiz, O.: Robustness and evolvability in genetic regulatory networks. J. Theor. Biol. 245, 433–448 (2007)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Balleza, E., Alvarez-Buylla, E.R., Chaos, A., Kauffman, S.A., Shmulevich, I., Aldana, M.: Critical dynamics in genetic regulatory networks: Examples from four kingdoms. PLoS One 3(6), e2456 (2008)CrossRefGoogle Scholar
  6. 6.
    Ribeiro, A.S., Kauffman, S.A.: Noisy attractors and ergodic sets in models of gene regulatory networks. J. Theor. Biol. 247(4), 743–755 (2007)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Kauffman, S.A.: A proposal for using the ensemble approach to understand genetic regulatory networks. J. Theor. Biol. 230, 581–590 (2004)CrossRefMathSciNetGoogle Scholar
  8. 8.
    Hoos, H.H., Stützle, T.: Stochastic Local Search: Foundations and Applications. Morgan Kaufmann, San Francisco (2005)Google Scholar
  9. 9.
    Roli, A., Arcaroli, C., Lazzarini, M., Benedettini, S.: Boolean networks design by genetic algorithms. In: Villani, M., Cagnoni, S. (eds.) Proceedings of CEEI 2009 - Workshop on Complexity, Evolution and Emergent Intelligence, Reggio Emilia, Italy, 2009Google Scholar
  10. 10.
    Benedettini, S., Roli, A., Serra, R., Villani, M.: Stochastic local search to automatically design Boolean networks with maximally distant attractors. In: Di Chio, C., Cagnoni, S., Cotta, C., Ebner, M., Ekárt, A., Esparcia-Alcázar, A., Merelo, J., Neri, F., Preuss, M., Richter, H., Togelius, J., Yannakakis, G. (eds.) Applications of Evolutionary Computation. Lecture Notes in Computer Science, vol. 6624, pp. 22–31. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  11. 11.
    Roli, A., Manfroni, M., Pinciroli, C., Birattari, M.: On the design of Boolean network robots. In: Di Chio, C., Cagnoni, S., Cotta, C., Ebner, M., Ekárt, A., Esparcia-Alcázar, A., Merelo, J., Neri, F., Preuss, M., Richter, H., Togelius, J., Yannakakis, G. (eds.) Applications of Evolutionary Computation. Lecture Notes in Computer Science, vol. 6624, pp. 43–52. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  12. 12.
    Kauffman, S.A.: The Origins of Order: Self-Organization and Selection in Evolution. Oxford University Press, Oxford (1993)Google Scholar
  13. 13.
    Lourenço, H., Martin, O., Stützle, T.: Iterated local search. In: Glover, F., Kochenberger, G. (eds.) Handbook of Metaheuristics. International Series in Operations Research & Management Science, vol. 57, pp. 320–353. Springer, New York (2003)CrossRefGoogle Scholar
  14. 14.
    Li, F., Long, T., Lu, Y., Ouyang, Q., Tang, C.: The yeast cell-cycle network is robustly designed. Natl. Acad. Sci. 101(14), 4781–4786 (2004)CrossRefGoogle Scholar
  15. 15.
    Wikipedia: Strongly connected component — Wikipedia, The Free Encyclopedia, 2011. [Online; accessed November 18, 2013]Google Scholar
  16. 16.
    Derrida, B., Pomeau, Y.: Random networks of automata: A simple annealed approximation. Europhys. Lett. 1(2), 45–49 (1986)CrossRefGoogle Scholar
  17. 17.
    Bastolla, U., Parisi, G.: Closing probabilities in the Kauffman model: An annealed computation. Phys. D. 98, 1–25 (1996)CrossRefzbMATHGoogle Scholar
  18. 18.
    Shmulevich, I., Kauffman, S.A., Aldana, M.: Eukaryotic cells are dynamically ordered or critical but not chaotic. Proc. Natl. Aca. Sci. USA 102(38), 13439–13444 (2005)CrossRefGoogle Scholar
  19. 19.
    Frigge, M., Hoaglin, D.C., Iglewicz, B.: Some implementations of the boxplot. Am. Stat. 43(1), 50–54 (1989)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Stefano Benedettini
    • 1
    Email author
  • Andrea Roli
    • 1
  • Roberto Serra
    • 2
  • Marco Villani
    • 2
  1. 1.DEIS-Cesena Alma Mater StudiorumUniversità di BolognaBolognaItaly
  2. 2.Faculty of MathematicalPhysical and Natural Sciences Università di Modena e Reggio Emilia & European Centre for Living TechnologyVeniceItaly

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