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PLOS ONE  2013 

Majority Rules with Random Tie-Breaking in Boolean Gene Regulatory Networks

DOI: 10.1371/journal.pone.0069626

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Abstract:

We consider threshold Boolean gene regulatory networks, where the update function of each gene is described as a majority rule evaluated among the regulators of that gene: it is turned ON when the sum of its regulator contributions is positive (activators contribute positively whereas repressors contribute negatively) and turned OFF when this sum is negative. In case of a tie (when contributions cancel each other out), it is often assumed that the gene keeps it current state. This framework has been successfully used to model cell cycle control in yeast. Moreover, several studies consider stochastic extensions to assess the robustness of such a model. Here, we introduce a novel, natural stochastic extension of the majority rule. It consists in randomly choosing the next value of a gene only in case of a tie. Hence, the resulting model includes deterministic and probabilistic updates. We present variants of the majority rule, including alternate treatments of the tie situation. Impact of these variants on the corresponding dynamical behaviours is discussed. After a thorough study of a class of two-node networks, we illustrate the interest of our stochastic extension using a published cell cycle model. In particular, we demonstrate that steady state analysis can be rigorously performed and can lead to effective predictions; these relate for example to the identification of interactions whose addition would ensure that a specific state is absorbing.

References

[1]  de Jong H (2002) Modeling and simulation of genetic regulatory systems: a literature review. J Comput Biol 1: 67–103.
[2]  Fisher J, Henzinger T (2007) Executable cell biology. Nat Biotechnol 25: 1239–1249.
[3]  Kauffman SA (1969) Metabolic stability and epigenesis in randomly constructed genetic nets. J Theor Biol 22: 437–67.
[4]  Thomas R (1973) Boolean formalization of genetic control circuits. J Theor Biol 42: 563–85.
[5]  Bornholdt S (2008) Boolean network models of cellular regulation: prospects and limitations. J R Soc Interface 5 Suppl 1: S85–94.
[6]  Glass L, Siegelmann HT (2010) Logical and symbolic analysis of robust biological dynamics. Curr Opin Genet Dev 20: 644–9.
[7]  Thomas R, D'Ari R (1990) Biological feedback. Boca Raton: CRC Press.
[8]  Li F, Long T, Lu Y, Ouyang Q, Tang C (2004) The yeast cell-cycle network is robustly designed. Proc Natl Acad Sci U S A 101: 4781–6.
[9]  Fauré A, Naldi A, Chaouiya C, Thieffry D (2006) Dynamical analysis of a generic boolean model for the control of the mammalian cell cycle. Bioinformatics 22: 124–131.
[10]  Davidich MI, Bornholdt S (2008) Boolean network model predicts cell cycle sequence of fission yeast. PLoS One 3: e1672.
[11]  Fauré A, Thieffry D (2009) Logical modelling of cell cycle control in eukaryotes: a comparative study. Mol Biosyst 5: 1569–81.
[12]  Fauré A, Naldi A, Lopez F, Chaouiya C, Ciliberto A, et al. (2009) Modular logical modelling of the budding yeast cell cycle. Mol Biosyst 5: 1787–96.
[13]  Irons DJ (2009) Logical analysis of the budding yeast cell cycle. J Theor Biol 257: 543–559.
[14]  Mendoza L, Xenarios I (2006) A method for the generation of standardized qualitative dynamical systems of regulatory networks. Theor Biol Med Model 3: 13.
[15]  Za?udo J, Aldana M, Martínez-Mekler G (2011) Boolean threshold networks: Virtues and limitations for biological modeling. In: Niiranen S, Ribeiro A, editors, Information Processing and Biological Systems, Springer Berlin Heidelberg, volume 11 of Intelligent Systems Reference Library. pp. 113–151.
[16]  McCulloch WS, Pitts W (1943) A logical calculus of the ideas immanent in nervous activity. Bulletin of Mathematical Biophysics 5: 115–133.
[17]  Shmulevich I, Dougherty ER, Kim S, Zhang W (2002) Probabilistic boolean networks: a rule-based uncertainty model for gene regulatory networks. Bioinformatics 18: 261–74.
[18]  Zhang Y, Qian M, Ouyang Q, Deng M, Li F, et al. (2006) Stochastic model of yeast cell-cycle network. Physica D: Nonlinear Phenomena 219: 35–39.
[19]  Lee WB, Huang JY (2009) Robustness and topology of the yeast cell cycle boolean network. FEBS Lett 583: 927–32.
[20]  Alvarez-Buylla ER, Chaos A, Aldana M, Benítez M, Cortes-Poza Y, et al. (2008) Floral morphogenesis: stochastic explorations of a gene network epigenetic landscape. PLoS One 3: e3626.
[21]  Murrugarra D, Veliz-Cuba A, Aguilar B, Arat S, Laubenbacher R (2012) Modeling stochasticity and variability in gene regulatory networks. EURASIP J Bioinform Syst Biol 2012: 5.
[22]  Garg A, Mohanram K, Di Cara A, De Micheli G, Xenarios I (2009) Modeling stochasticity and robustness in gene regulatory networks. Bioinformatics 25: i101–9.
[23]  Hopfield JJ (1982) Neural networks and physical systems with emergent collective computational abilities. Proc Natl Acad Sci U S A 79: 2554–8.
[24]  Braunewell S, Bornholdt S (2007) Superstability of the yeast cell-cycle dynamics: ensuring causality in the presence of biochemical stochasticity. J Theor Biol 245: 638–43.
[25]  Stoll G, Rougemont J, Naef F (2007) Representing perturbed dynamics in biological network models. Phys Rev E 76: 011917.
[26]  Remy E, Ruet P (2008) From minimal signed circuits to the dynamics of boolean regulatory networks. Bioinformatics 24: i220–6.
[27]  Kemeny JG, Snell JL (1976) Finite Markov chains. New York: Springer-Verlag.
[28]  Levin DA, Peres Y, Wilmer EL (2009) Markov chains and mixing times. Providence, R.I.: American Mathematical Society.
[29]  Coutinho R, Fernandez B, Lima R, Meyroneinc A (2006) Discrete time piecewise affine models of genetic regulatory networks. J Math Biol 52: 524–70.
[30]  Robert F (1995) Les systèmes dynamiques discrets, volume 19. Berlin: Springer.

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