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Using answer set programming to deal with boolean networks and attractor computation: application to gene regulatory networks of cells

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Abstract

Deciphering gene regulatory networks’ functioning is an essential step for better understanding of life, as these networks play a fundamental role in the control of cellular processes. Boolean networks have been widely used to represent gene regulatory networks. They allow to describe the dynamics of complex gene regulatory networks straightforwardly and efficiently. The attractors are essential in the analysis of the dynamics of a Boolean network. They explain that a particular cell can acquire specific phenotypes that may be transmitted over several generations. In this work, we consider a new representation of Boolean networks’ dynamics based on a new semantics used in Answer Set Programming (ASP). We use logic programs and ASP to express and deal with gene regulatory networks seen as Boolean networks, and develop a method to detect all the attractors of such networks. We first show how to represent and deal with general Boolean networks for the synchronous and asynchronous updates modes, where the computation of attractors requires a simulation of these networks’ dynamics. Then, we propose an approach for the particular case of circular networks where no simulation is needed. This last specific case plays an essential role in biological systems. We show several theoretical properties; in particular, simple attractors of the gene networks are represented by the stable models of the corresponding logic programs and cyclic attractors by its extra-stable models. These extra-stable models correspond to the extra-extensions of the new semantics that are not captured by the semantics of stable models. We then evaluate the proposed approach for general Boolean networks on real biological networks and the one dedicated to the case of circular networks on Boolean networks generated randomly. The obtained results for both approaches are encouraging.

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Data Availability

The benchmarks are available with the identifier https://zenodo.org/record/8103494

References

  1. De Jong, H.: Modeling and simulation of genetic regulatory systems: a literature review. J. Comput. Biol. 9(1), 67–103 (2002)

    Article  MathSciNet  Google Scholar 

  2. Tran, N., Baral, C.: Hypothesizing about signaling networks. J. Appl. Log. 7, 253–274 (2009)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  4. Kauffman, S.A., et al.: The origins of order: Self-organization and selection in evolution. Oxford University Press, (1993)

  5. Shmulevich, I., Dougherty, E.R., Zhang, W.: From boolean to probabilistic Boolean networks as models of genetic regulatory networks. Proc. IEEE 90(11), 1778–1792 (2002)

    Article  Google Scholar 

  6. Garg, A., Xenarios, I., Mendoza, L., DeMicheli, G: An efficient method for dynamic analysis of gene regulatory networks and in silico gene perturbation experiments, pp. 62–76 (2007). Springer

  7. De Jong, H., Page, M.: Search for steady states of piecewise-linear differential equation models of genetic regulatory networks. IEEE/ACM Trans. Comput. Biol. Bioinforma. 5(2), 208–222 (2008)

    Article  Google Scholar 

  8. Mendoza, L.: A network model for the control of the differentiation process in Th cells. BioSyst. 84(2), 101–114 (2006)

    Article  Google Scholar 

  9. Espinosa-Soto, C., Padilla-Longoria, P., Alvarez-Buylla, E.R.: A gene regulatory network model for cell-fate determination during Arabidopsis thaliana flower development that is robust and recovers experimental gene expression profiles. Plant Cell 16(11), 2923–2939 (2004)

    Article  Google Scholar 

  10. Marek, V.W., Truszczynski, M.L.: Stable models and an alternative logic programming paradigm. Logic Programming Paradigm, pp. 375–398 (1999)

  11. Lin, F., Zhao, Y.: Assat: Computing answer sets of a logic program by SAT solvers. Artificial Intelligence, pp. 115–137 (2004)

  12. Gebser, M., Kaufmann, B., Neumann, A., Schaub, T.: Conflict-driven answer set solving. In: Veloso, M.M. (ed.) IJCAI 2007, Proceedings of the 20th International joint conference on artificial intelligence, Hyderabad, India, January 6-12, 2007, p. 386 (2007)

  13. Simons, P., Nimelä, I., Soininen, T.: Extending and implementing the stable model semantic. Artif. Intell. 138, 181–234 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  14. Alviano, M., Dodaro, C., Faber, W, Leone, N., Ricca, F.: Wasp: A native ASP solver based on constraint learning. In: International conference on logic programming and nonmonotonic reasoning, pp. 54–66 (2013). Springer

  15. Erdem, E., Gelfond, M., Leone, N.: Applications of answer set programming. AI Mag. 37, 53–68 (2016)

    Google Scholar 

  16. Khaled, T., Benhamou, B., Siegel, P.: A new method for computing stable models in logic programming. Tools with Artificial Intelligence (ICTAI), pp. 800–807 (2018)

  17. Khaled, T., Benhamou, B.: Symmetry breaking in a new stable model search method. 22nd International Conference on Logic for Programming Artificial Intelligence and Reasoning (LPAR-22), Kalpa Publications in Computing 9, 58–74 (2018)

  18. Benhamou, B., Siegel, P.: A new semantics for logic programs capturing and extending the stable model semantics. Tools with Artificial Intelligence (ICTAI), pp. 25–32 (2012)

  19. Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. ICLP/SLP 50, 1070–1080 (1988)

    Google Scholar 

  20. Khaled, T., Benhamou, B.: An ASP-based approach for attractor enumeration in synchronous and asynchronous Boolean networks. Proceedings 35th International Conference on Logic Programming, ICLP 2019, Las Cruces, NM, USA, 295–301 (2019)

  21. Khaled, T., Benhamou, B.: An ASP-based approach for boolean networks representation and attractor detection. In: LPAR, pp. 317–333 (2020)

  22. Trinh, V.-G., Hiraishi, K., Benhamou, B.: Computing attractors of large-scale asynchronous Boolean networks using minimal trap spaces. In: Proceedings of the 13th ACM International conference on bioinformatics, computational biology and health informatics, pp. 1–10 (2022)

  23. Jacob, F., Monod, J.: Genetic regulatory mechanisms in the synthesis of proteins. J. Mol. Biol. 3(3), 318–356 (1961)

    Article  Google Scholar 

  24. Zheng, D., Yang, G., Li, X., Wang, Z., Liu, F., He, L.: An efficient algorithm for computing attractors of synchronous and asynchronous Boolean networks. PloS One 8(4), 60593 (2013)

    Article  Google Scholar 

  25. Thomas, R.: On the relation between the logical structure of systems and their ability to generate multiple steady states or sustained oscillations. In: Numerical methods in the study of critical phenomena, pp. 180–193 (1981)

  26. Remy, E.., Mossé, B.., Chaouiya, C.., Thieffry, D..: A description of dynamical graphs associated to elementary regulatory circuits. Bioinforma. 19(suppl–2), 172–178 (2003)

    Article  MATH  Google Scholar 

  27. Gelfond, M., Lifschitz, V.: Classical negation in logic programs and disjunctive databases. New Gener. Comput. 9, 365–385 (1991)

    Article  MATH  Google Scholar 

  28. Williams, R., Gomes, C.P., Selman, B.: Backdoors to typical case complexity. Int. Jt. Conf. Artif. Intell. 18, 1173–1178 (2003)

    Google Scholar 

  29. Davis, M., Logemann, G., Loveland, D.: A machine program for theorem proving. Commun. ACM 5, 394–397 (1962)

    Article  MathSciNet  MATH  Google Scholar 

  30. Gebser, M., Kaminski, R., Kaufmann, B., Schaub, T.: Multi-shot ASP solving with clingo. Theory Pract. Log. Program. 19(1), 27–82 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  31. Dubrova, E., Teslenko, M.: A SAT-based algorithm for finding attractors in synchronous Boolean networks. IEEE/ACM Trans. Comput. Biol. Bioinforma. 8(5), 1393–1399 (2011)

    Article  Google Scholar 

  32. Garg, A., Xenarios, I., Mendoza, L., DeMicheli, G.: An efficient method for dynamic analysis of gene regulatory networks and in silico gene perturbation experiments. In: Annual international conference on research in computational molecular biology, pp. 62–76 (2007). Springer

  33. Ay, F., Xu, F., Kahveci, T.: Scalable steady state analysis of Boolean biological regulatory networks. PloS One 4(12), 7992 (2009)

    Article  Google Scholar 

  34. Davidich, M.I., Bornholdt, S.: Boolean network model predicts cell cycle sequence of fission yeast. PloS One 3(2), 1672 (2008)

    Article  MATH  Google Scholar 

  35. Klarner, H., Streck, A., Siebert, H.: PyBoolNet: a python package for the generation, analysis and visualization of Boolean networks. Bioinform. 33(5), 770–772 (2017). https://doi.org/10.1093/bioinformatics/btw682

    Article  Google Scholar 

  36. Gebser, M., Kaufmann, B., Kaminski, R., Ostrowski, M., Schaub, T., Schneider, M.: Potassco: The Potsdam answer set solving collection. AI Commun. 24(2), 107–124 (2011). https://doi.org/10.3233/AIC-2011-0491

    Article  MathSciNet  MATH  Google Scholar 

  37. Sanchez-Corrales, Y.-E., Alvarez-Buylla, E.R., Mendoza, L.: The Arabidopsis thaliana flower organ specification gene regulatory network determines a robust differentiation process. J. Theor. Biol. 264(3), 971–983 (2010)

    Article  MATH  Google Scholar 

  38. Li, F., Long, T., Lu, Y., Ouyang, Q., Tang, C.: The yeast cell-cycle network is robustly designed. Proc. Natl. Acad. Sci. 101(14), 4781–4786 (2004)

    Article  Google Scholar 

  39. Kaufman, M., Urbain, J., Thomas, R.: Towards a logical analysis of the immune response. J. Theor. Biol. 114(4), 527–561 (1985)

    Article  MathSciNet  Google Scholar 

  40. Sánchez, L., Thieffry, D.: A logical analysis of the Drosophila gap-gene system. J. Theor. Biol. 211(2), 115–141 (2001)

    Article  Google Scholar 

  41. Albert, R., Othmer, H.G.: The topology of the regulatory interactions predicts the expression pattern of the segment polarity genes in Drosophila melanogaster. J. Theor. Biol. 223(1), 1–18 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  42. González, A., Chaouiya, C., Thieffry, D.: Logical modelling of the role of the Hh pathway in the patterning of the Drosophila wing disc. Bioinforma. 24(16), 234–240 (2008)

    Article  Google Scholar 

  43. Berntenis, N., Ebeling, M.: Detection of attractors of large Boolean networks via exhaustive enumeration of appropriate subspaces of the state space. BMC Bioinforma. 14(1), 1–10 (2013)

    Article  Google Scholar 

  44. He, Q., Xia, Z., Lin, B.: An efficient approach of attractor calculation for large-scale Boolean gene regulatory networks. J. Theor. Biol. 408, 137–144 (2016). https://doi.org/10.1016/j.jtbi.2016.08.006

    Article  MathSciNet  MATH  Google Scholar 

  45. He, Q., Xia, Z., Lin, B.: P_UNSAT approach of attractor calculation for Boolean gene regulatory networks. J. Theor. Biol. 447, 171–177 (2018). https://doi.org/10.1016/j.jtbi.2018.03.037

    Article  MATH  Google Scholar 

  46. Gebser, M., Schaub, T., Thiele, S., Veber, P.: Detecting inconsistencies in large biological networks with answer set programming. Theor. Prac. Log. Program. 11(2–3), 323–360 (2011). https://doi.org/10.1017/s1471068410000554

    Article  MathSciNet  MATH  Google Scholar 

  47. Inoue, K.: Logic programming for Boolean networks. In: 22nd International joint conference on artificial intelligence (2011)

  48. Mushthofa, M., Torres, G., Van de Peer, Y., Marchal, K., De Cock, M.: Asp-g: an ASP-based method for finding attractors in genetic regulatory networks. Bioinforma. 30(21), 3086–3092 (2014)

    Article  Google Scholar 

  49. Fayruzov, T., De Cock, M., Cornelis, C, Vermeir, D.: Modeling protein interaction networks with answer set programming. In: 2009 IEEE International conference on bioinformatics and biomedicine, pp. 99–104 (2009). IEEE

  50. Apt, K.R., Blair, H.A., Walker, A.: Towards a theory of declarative knowledge. In: Foundations of deductive databases and logic programming, pp. 89–148 (1988)

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Authors and Affiliations

  1. Aix-Marseille University, University of Toulon, CNRS, LIS, Marseille, France

    Tarek Khaled, Belaid Benhamou & Van-Giang Trinh

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  1. Tarek Khaled
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  2. Belaid Benhamou
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  3. Van-Giang Trinh
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Tarek Khaled and Belaid Benhamou are contributed equally to this work.

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Khaled, T., Benhamou, B. & Trinh, VG. Using answer set programming to deal with boolean networks and attractor computation: application to gene regulatory networks of cells. Ann Math Artif Intell 91, 713–750 (2023). https://doi.org/10.1007/s10472-023-09886-7

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