Emergent Properties of Gene Regulatory Networks: Models and Data

  • Roberto Serra
  • Marco Villani


We emphasize here the importance of generic models of biological systems that aim at describing the features that are common to a wide class of systems, instead of studying in detail a specific subsystem in a specific cell type or organism. Among generic models of gene regulatory networks, Random Boolean networks (RBNs) are reviewed in depth, and it is shown that they can accurately describe some important experimental data, in particular the statistical properties of the perturbations of gene expression levels induced by the knock-out of a single gene. It is also shown that this kind of study may shed light on a candidate general dynamical property of biological systems. Several biologically plausible modifications of the original model are reviewed and discussed, and it is also show how RBNs can be applied to describe cell differentiation.


Dynamical systems Emergent properties Generic properties Gene regulatory networks Random boolean networks Modeling Gene knock-outs Cell differentiation 



Random Boolean Network


Deoxyribonucleic acid


Ribonucleic acid


micro RNA (short RNA molecule)


messenger RNA


complementary DNA


Scale-free Random Boolean Network


Threshold Ergodic Sets



We have developed our understanding of genetic network dynamics interacting with several scientists and collaborators. In particular, we are grateful to Stuart Kauffman who shared with us much of his insight, and of his evolving vision. Among several students and collaborators let us mention in particular Chiara Damiani, Alessandro Filisetti, Alex Graudenzi (the complete list would be too long). We also had the privilege of discussing our ideas with some biologists, in particular with Annamaria Colacci. On a more general ground, our understanding of the role of modeling such complex systems has been shaped in several fruitful discussions and joint works with David Lane and Gianni Zanarini, although of course we take full responsibility of the positions taken in this chapter. The present work has been partly supported by the Miur Project MITICA (FISR nr. 2982/Ric) and by the EU-FET projects MD (ref. 284625) and INSITE (ref. 271574) under the 7th Framework Programme.


  1. 1.
    Kleiber M (1932) Body size and metabolism. Hilgardia 6:315–351Google Scholar
  2. 2.
    West GB, Brown JH (2005) The origin of allometric scaling laws in biology from genome to ecosystems. J Exp Biol 208:1575–1592PubMedCrossRefGoogle Scholar
  3. 3.
    West GB, Brown JH, Enquist BJ (1999) The fourth dimension of life: fractal geometry and allometric scaling of organisms. Science 284:1677–1679PubMedCrossRefGoogle Scholar
  4. 4.
    Kauffman SA (1993) The origins of order. Oxford University Press, New YorkGoogle Scholar
  5. 5.
    Langton CG (1992) Life at the edge of chaos. In: Langton CG, Taylor C, Farmer JD, Rasmussen S (eds) Artificial life II. Addison-Wesley, Reading, pp 41–91Google Scholar
  6. 6.
    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 293–301Google Scholar
  7. 7.
    Kauffman SA (1995) At home in the universe. Oxford University Press, New YorkGoogle Scholar
  8. 8.
    Longo G, Bailly F (2008) Extended critical situations: the physical singularity of life phenomena. J Biol Syst 16(2):309–336CrossRefGoogle Scholar
  9. 9.
    Schmulevich A, Kauffman SA, Aldana M (2005) Eukaryotic cells are dynamically ordered or critical but not chaotic. PNAS 102:13439–13444CrossRefGoogle Scholar
  10. 10.
    Benedettini S, Villani M, Roli A, Serra R, Manfroni M, Gagliardi A, Pinciroli C, Birattari M (2012) Dynamical regimes and learning properties of evolved Boolean networks. Neurocomputing ElsevierGoogle Scholar
  11. 11.
    Alberts B, Johnson A, Lewis J, Raff M, Roberts K, Walter P (2007) Molecular biology of the cell. ISBN: 9780815341055Google Scholar
  12. 12.
    Frisch U, d’Humieres D, Hasslacher B, Lallemand P, Pomeau Y, Rivet JP (1987) Lattice gas hydrodynamics in two and three dimensions. Complex Syst 1:649707Google Scholar
  13. 13.
    Frisch U, Hasslacher B, Pomeau Y (1986) Lattice-gas automata for the Navier-Stokes equation. Phys Rev Lett 56(14):1505–1508PubMedCrossRefGoogle Scholar
  14. 14.
    Aldana M, Coppersmith S, Kadanoff LP (2003) Boolean dynamics with random couplings. In: Kaplan E, Marsden JE, Sreenivasan KR (eds) Perspectives and problems in nonlinear science. Springer, New York, pp 23–89CrossRefGoogle Scholar
  15. 15.
    Derrida B, Pomeau Y (1986) Random networks of automata: a simple annealed approximation. Europhys Lett 1:45–49CrossRefGoogle Scholar
  16. 16.
    Langton CG (1990) Computation at the edge of chaos. Physica D 42Google Scholar
  17. 17.
    Bastolla U, Parisi G (1998) The modular structure of Kauffman networks. Physica D 115:219–233CrossRefGoogle Scholar
  18. 18.
    Bastolla U, Parisi G (1998) Relevant elements, magnetization and dynamical properties in Kauffman networks: a numerical study. Physica D 115:203–218CrossRefGoogle Scholar
  19. 19.
    Socolar JES, Kauffman SA (2003) Scaling in ordered and critical random Boolean networks. Phys Rev Lett 90Google Scholar
  20. 20.
    Aldana M, Balleza E, Kauffman SA, Resendiz O (2007) Robustness and evolvability in genetic regulatory networks. J Theor Biol 245:433–448PubMedCrossRefGoogle Scholar
  21. 21.
    Balleza E, Alvarez-Buylla E, Chaos A, Kauffman SA, Shmulevich I, Aldana M (2008) Critical dynamics in genetic regulatory networks: examples from four kingdoms. PLoS ONE 3:e2456PubMedCentralPubMedCrossRefGoogle Scholar
  22. 22.
    Villani M, Serra R, Graudenzi A, Kauffman SA (2007) Why a simple model of genetic regulatory networks describes the distribution of avalanches in gene expression data. J Theor Biol 249:449–460Google Scholar
  23. 23.
    Shmulevich I, Kauffman SA (2004) Activities and sensitivities in Boolean network models. Phys Rev Lett 93Google Scholar
  24. 24.
    Szejka A, Mihaljev T, Drossel B (2008) The phase diagram of random threshold networks. New J Phys 10:063009CrossRefGoogle Scholar
  25. 25.
    Villani M, Serra R (in press) Attractors perturbations in biological modeling: avalanches and cellular differentiation In: Cagnoni S, Mirolli M, Villani M (eds) Evolution, complexity and artificial life. SpringerGoogle Scholar
  26. 26.
    Harris SE, Sawhill BK, Wuensche A, Kauffman SA (2001) A model of transcriptional regulatory networks based on biases in the observed regulation rules. Complexity 7(4):23–40CrossRefGoogle Scholar
  27. 27.
    Raeymaekers L (2002) Dynamics of Boolean networks controlled by biologically meaningful functions. J Theor Biol 218:331–341PubMedCrossRefGoogle Scholar
  28. 28.
    Serra R, Graudenzi A, Villani M (2009) Genetic regulatory networks and neural networks. In: Apolloni B, Bassis S, Marinaro M (eds) New directions in neural networks. IOS Press, Amsterdam, pp 109–117Google Scholar
  29. 29.
    Kauffman SA (1969) Metabolic stability and epigenesis in randomly constructed nets. J Theor Biol 22:437–467PubMedCrossRefGoogle Scholar
  30. 30.
    Hughes TR, Marton MJ, Jones AR, Roberts CJ, Stoughton R, Armour CD, Bennett HA, Coffey E, Dai H, He YD, Kidd MJ, King AM, Meyer MR, Slade D, Lum PY, Stepaniants SB, Shoemaker DD, Gachotte D, Chakraburtty K, Simon J, Bard M, Friend SH (2000) Functional discovery via a compendium of expression profiles. Cell 102:109–126PubMedCrossRefGoogle Scholar
  31. 31.
    Serra R, Villani M, Semeria A (2003) Robustness to damage of biological and synthetic networks. In: Banzhaf W, Christaller T, Dittrich P, Kim JT, Ziegler J (eds) Advances in artificial life. Lecture notes in artificial intelligence, 2801. Springer, Heidelberg, pp 706–715Google Scholar
  32. 32.
    Serra R, Villani M, Semeria A (2004) Genetic network models and statistical properties of gene expression data in knock-out experiments. J Theor Biol 227:149–157PubMedCrossRefGoogle Scholar
  33. 33.
    Lee TI, Rinaldi NJ, Robert F, Odom DT et al (2002) Transcriptional regulatory networks in Saccharomyces Cerevisiae. Science 25 298(5594):799–804Google Scholar
  34. 34.
    Ramo P, Kesseli J, Yli-Harja O (2006) Perturbation avalanches and criticality in gene regulatory networks. J Theor Biol 242:164–170PubMedCrossRefGoogle Scholar
  35. 35.
    Serra R, Villani M, Salvemini A (2001) Continuous genetic networks. Parallel Comput 27:663–683CrossRefGoogle Scholar
  36. 36.
    Solè RV, Luque B, Kauffman SA (2011) Phase transition in random networks with multiple states working papers of Santa Fe Institute,
  37. 37.
    Kappler K, Edwards R, Glass L (2003) Dynamics in high dimensional model gene networks. Signal Process 83:789–798CrossRefGoogle Scholar
  38. 38.
    de Jong H (2002) Modeling and simulation of genetic regulatory systems: a literature review. J Comput Biol 9(1): 67–103 (Mary Ann Liebert, Inc.)Google Scholar
  39. 39.
    Ironi L, Panzeri L, Plahte E, Simoncini V (2011) Dynamics of actively regulated gene networks. Physica D 240:779–794. doi: 10.1016/j.physd.2010.12.010 CrossRefGoogle Scholar
  40. 40.
    Roli A, Vernocchi F, Serra R (2008) Continuous network models of gene expression in knock-out experiments: a preliminary study. In: Serra R, Villani M, Poli I (eds) Artificial life and evolutionary computation—Proceedings of WIVACE 2008. World Scientific PublishingGoogle Scholar
  41. 41.
    Klemm K, Bornholdt S (2005) Stable and unstable attractors in Boolean networks. Phys Rev E 72:055101–055104CrossRefGoogle Scholar
  42. 42.
    Darabos C, Giacobini M, Tomassini M (2009) Generalized Boolean networks: how spatial and temporal choices influence their dynamics computational methodologies. In: Das S, Caragea D, Hsu WH, Welch SM (eds) Gene regulatory networks. Medical Information Science Reference; 1 edn. USA. ISBN: 1605666858Google Scholar
  43. 43.
    Gershenson C (2002) Classification of random Boolean networks. In: Standish RK, Abbass HA, Bedau MA (eds) Artificial life VIII. MIT Press, Cambridge, pp 1–8Google Scholar
  44. 44.
    Gershenson C (2004) Updating schemes in random Boolean networks: Do they really matter? In: Pollack J, Bedau M, Husbands P, Ikegami T, Watson RA (eds) Artificial life IX, Proceedings of the 9th international conference on the simulation and synthesis of living systems. MIT Press, pp 238–243Google Scholar
  45. 45.
    Serra R, Villani M, Agostini L (2004) On the dynamics of Boolean networks with scale-free outgoing connections. Physica A 339:665–673CrossRefGoogle Scholar
  46. 46.
    Graudenzi A, Serra R, Villani M, Colacci A, Kauffman SA (2011) Robustness analysis of a Boolean model of gene regulatory network with memory. J Comput Biol 18(4) (Mary Ann Liebert, Inc., publishers, NY)Google Scholar
  47. 47.
    Graudenzi A, Serra R, Villani M, Damiani C, Colacci A, Kauffman SA (2011a) Dynamical properties of a Boolean model of gene regulatory network with memory. J Comput Biol 18 (Mary Ann Liebert, Inc., publishers, NY)Google Scholar
  48. 48.
    Watts DJ, Strogatz SH (1998) Collective dynamics of small world networks. Nature 393:440PubMedCrossRefGoogle Scholar
  49. 49.
    Barabasi AL, Albert R (1999) Emergence of scaling in random networks. Science 286:509–512PubMedCrossRefGoogle Scholar
  50. 50.
    Kitsak M, Riccaboni M, Havlin S, Pammolli F, Stanley HE (2010) Scale-free models for the structure of business firm networks. Phys Rev E 81:036117CrossRefGoogle Scholar
  51. 51.
    Aldana M (2003) Boolean dynamics of networks with scale-free topology. Physica D 185:45–66CrossRefGoogle Scholar
  52. 52.
    Serra R, Villani M, Graudenzi A, Colacci A, Kauffman SA (2008) The simulation of gene knock-out in scale-free random Boolean models of genetic networks. Netw Heterogen Media 3(2):333–343CrossRefGoogle Scholar
  53. 53.
    Bornholdt S (2001) Modeling genetic networks and their evolution: a complex dynamical systems perspective. Biol Chem 382:1289–1299PubMedCrossRefGoogle Scholar
  54. 54.
    Bhan A, Galas DJ, Dewey TG (2002) A duplication growth model of gene expression networks. Bioinformatics 18(11):1486–1493PubMedCrossRefGoogle Scholar
  55. 55.
    Enemark J, Sneppen K (2007) Analyzing a stochastic model for evolving regulatory networks by unbiased gene duplication. JSTAT 0:P11007Google Scholar
  56. 56.
    Aldana M, Cluzel P (2003) A natural class of robust networks. PNAS 100(15):8710–8714PubMedCentralPubMedCrossRefGoogle Scholar
  57. 57.
    Fretter C, Drossel B (2008) Response of Boolean networks to perturbations. Eur Phys J B 62:365–371CrossRefGoogle Scholar
  58. 58.
    Gershenson C, Kauffman SA, Shmulevich I (2006) The role of redundancy in the robustness of random Boolean networks. In: Rocha LM, Yaeger LS, Bedau MA, Floreano D, Goldstone RL, Vespignani A (eds) Artificial life X, Proceedings of the 10th international conference on the simulation and synthesis of living systems. MIT Press, pp 35–42Google Scholar
  59. 59.
    van Oss C, Panfilov AV, Hogeweg P, Siegert F, Weijer CJ (1996) Spatial pattern formation during aggregation of the slime mould Dictyostelium discoideum. J Theor Biol 181:203–213PubMedCrossRefGoogle Scholar
  60. 60.
    Damiani C, Kauffman SA, Serra R, Villani M, Colacci A (2010) Information transfer among coupled random Boolean networks. In: Bandini S et al (eds) ACRI 2010 LNCS 6350. Springer, Berlin, pp 1–11Google Scholar
  61. 61.
    Damiani C, Serra R, Villani M, Kauffman SA, Colacci A (2011) Cell-cell interaction and diversity of emergent behaviours. IET Syst Biol 5(2):137–144. doi: 10.1049/iet-syb.2010.0039 PubMedCrossRefGoogle Scholar
  62. 62.
    Ribeiro AS, Kauffman SA (2007) Noisy attractors and ergodic sets in models of gene regulatory networks. J Theor Biol 247(4):743–755PubMedCrossRefGoogle Scholar
  63. 63.
    Blake WJ, KLrn M, Cantor CR, Collins JJ (2003) Noise in eukaryotic gene expression. Nature 422:633–637PubMedCrossRefGoogle Scholar
  64. 64.
    Eldar A, Elowitz MB (2010) Functional roles for noise in genetic circuits. Nature 467:167–173PubMedCentralPubMedCrossRefGoogle Scholar
  65. 65.
    Lestas I, Paulsson J, Ross NE, Vinnicombe G (2008) Noise in gene regulatory net-works. IEEE Trans Automat Contr 53:189–200CrossRefGoogle Scholar
  66. 66.
    McAdams HH, Arkin A (1997) Stochastic mechanisms in gene expression. PNAS 94:814–819PubMedCentralPubMedCrossRefGoogle Scholar
  67. 67.
    Raj A, van Oudenaarden A (2008) Nature, nurture, or chance: stochastic gene expression and its consequences. Cell 135(2):216–226PubMedCentralPubMedCrossRefGoogle Scholar
  68. 68.
    Swain PS, Elowitz MB, Siggia ED (2002) Intrinsic and extrinsic contributions to stochasticity in gene expression. PNAS 99:12795–12800PubMedCentralPubMedCrossRefGoogle Scholar
  69. 69.
    Serra R, Villani M, Barbieri A, Kauffman SA, Colacci A (2010) On the dynamics of random Boolean networks subject to noise: attractors, ergodic sets and cell types. J Theor Biol 265:185–193PubMedCrossRefGoogle Scholar
  70. 70.
    Villani M, Barbieri A, Serra R (2011) A dynamical model of genetic networks for cell differentiation. PLoS ONE 6(3):e17703PubMedCentralPubMedCrossRefGoogle Scholar
  71. 71.
    Villani M, Serra R, Barbieri A, Roli A, Kauffman SA, Colacci A (2010) Noisy random Boolean networks and cell differentiation. In: Proceedings of ECCS2010—European conference on complex systemsGoogle Scholar
  72. 72.
    Baron MH (1993) Reversibility of the differentiated state in somatic cells. Curr Opin Cell Biol 5(6):1050–1056PubMedCrossRefGoogle Scholar
  73. 73.
    Johnson NC, Dillard ME, Baluk P, McDonald DM, Harvey NL et al (2008) Lymphatic endothelial cell identity is reversible and its maintenance requires Prox1 activity. Genes Dev 22:3282–3291PubMedCentralPubMedCrossRefGoogle Scholar
  74. 74.
    Takahashi K, Yamanaka S (2006) Induction of pluripotent stem cells from mouse embryonic and adult fibroblasts cultures by defined factors. Cell 126(4):663–676PubMedCrossRefGoogle Scholar
  75. 75.
    Takahashi K, Tanabe K, Ohnuki M, Narita M, Ichisaka T et al (2007) Induction of pluripotent stem cells from adult human fibroblasts by defined factors. Cell 131(5):861–872PubMedCrossRefGoogle Scholar
  76. 76.
    Vierbuchen T, Ostermeier A, Pang ZP, Kokubu Y, Sudhof TC et al (2010) Direct con-version of fibroblasts to functional neurons by defined factors. Nature 463:1035–1041PubMedCentralPubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of Physics, Computer Science and MathematicsModena and Reggio Emilia UniversityModenaItaly
  2. 2.European Centre for Living Technology, Ca’MinichVeneziaItaly

Personalised recommendations