Abstract
The process of cell differentiation manifests properties such as non-uniform robustness and asymmetric transitions among cell types. In this paper we adopt Boolean networks to model cellular differentiation, where attractors (or set of attractors) in the network landscape epitomise cell types. Since changes in network topology and functions strongly impact attractor landscape characteristics, in this paper we study how self-loops influence diversified robustness and asymmetry of transitions. The purpose of this study is to identify the best configuration for a network owning these properties. Our results show that a moderate amount of self-loops make random Boolean networks more suitable to reproduce differentiation phenomena. This is a further evidence that self-loops play an important role in genetic regulatory networks.
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- 1.
As done in [11].
References
Ahnert, S., Fink, T.: Form and function in gene regulatory networks: the structure of network motifs determines fundamental properties of their dynamical state space. J. R. Soc. Interface 13(120), 278–289 (2016)
Braccini, M., Roli, A., Villani, M., Serra, R.: A comparison between threshold ergodic sets and stochastic simulation of boolean networks for modelling cell differentiation. In: Pelillo, M., Poli, I., Roli, A., Serra, R., Slanzi, D., Villani, M. (eds.) WIVACE 2017. CCIS, vol. 830, pp. 116–128. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78658-2_9
Furusawa, C., Kaneko, K.: A dynamical-systems view of stem cell biology. Science 338, 215–217 (2012)
Huang, S.: The molecular and mathematical basis of Waddington’s epigenetic landscape: a framework for post-Darwinian biology? Bioessays 34(2), 149–157 (2012)
Huang, S., Eichler, G., Bar-Yam, Y., Ingber, D.: Cell fates as high-dimensional attractor states of a complex gene regulatory network. Phys. Rev. Lett. 94, 128701:1–128701:4 (2005)
Huang, S., Ernberg, I., Kauffman, S.: Cancer attractors: a systems view of tumors from a gene network dynamics and developmental perspective. In: Seminars in Cell & Developmental Biology, vol. 20, no. 7, pp. 869–876 (2009). Structure and Function of the Golgi Apparatus and Systems Approaches to Cell and Developmental Biology
Joo, J.I., Zhou, J.X., Huang, S., Cho, K.H.: Determining relative dynamic stability of cell states using boolean network model. Sci. Rep. 8(1), 12077 (2018)
Kauffman, S.: The Origins of Order: Self-Organization and Selection in Evolution. Oxford University Press, Oxford (1993)
Kauffman, S.: A proposal for using the ensemble approach to understand genetic regulatory networks. J. Theor. Biol. 230, 581–590 (2004)
Mojtahedi, M., et al.: Cell fate decision as high-dimensional critical state transition. PLOS Biol. 14(12), e2000640:1–e2000640:28 (2016)
Montagna, S., Braccini, M., Roli, A.: 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.) WIVACE 2017. CCIS, vol. 830, pp. 104–115. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78658-2_8
Nykter, M., et al.: Gene expression dynamics in the macrophage exhibit criticality. Proc. Nat. Acad. Sci. 105(6), 1897–1900 (2008)
Raj, A., Rifkin, S., Andersen, E., Van Oudenaarden, A.: Variability in gene expression underlies incomplete penetrance. Nature 463(7283), 913–918 (2010)
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)
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)
Villani, M., Barbieri, A., Serra, R.: A dynamical model of genetic networks for cell differentiation. PloS One 6(3), e17703 (2011)
Zhou, J., Samal, A., Fouquier d’Hérouël, A., Price, N., Huang, S.: Relative stability of network states in boolean network models of gene regulation in development. Biosystems 142–143, 15–24 (2016)
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We thank the anonymous referees for useful comments and suggestions. Andrea Roli is a member of the INdAM Research group GNCS.
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Braccini, M., Montagna, S., Roli, A. (2019). Self-loops Favour Diversification and Asymmetric Transitions Between Attractors in Boolean Network Models. 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_3
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