Abstract
Boolean networks are an important formalism for modelling biological systems and have attracted much attention in recent years. An important challenge in Boolean networks is to exhaustively find attractors, which represent steady states of a biological network. In this paper, we propose a new approach to improve the efficiency of BDD-based attractor detection. Our approach includes a monolithic algorithm for small networks, an enumerative strategy to deal with large networks, a method to accelerate attractor detection based on an analysis of the network structure, and two heuristics on ordering BDD variables. We demonstrate the performance of our approach on a number of examples and on a realistic model of apoptosis in hepatocytes. We compare it with one existing technique in the literature.
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References
Kauffman S. Homeostasis and differentiation in random genetic control networks. Nature, 1969, 224: 177–178
Huang S. Genomics, complexity and drug discovery: insights from Boolean network models of cellular regulation. Pharmacogenomics, 2001, 2: 203–222
Needham C J, Manfield I W, Bulpitt A J, et al. From gene expression to gene regulatory networks in Arabidopsis thaliana. BMC Syst Biol, 2009, 3: 85
Garg A, Xenarios L, Mendoza L, et al. An efficient method for dynamic analysis of gene regulatory networks and in silico gene perturbation experiments. In: Proceedings of 11th Annual Conference on Research in Computational Molecular Biology. Berlin: Springer, 2007. 62–76
Somogyi R, Greller L D. The dynamics of molecular networks: applications to therapeutic discovery. Drug Discov Today, 2001, 6: 1267–1277
Raeymaekers L. Dynamics of Boolean networks controlled by biologically meaningful functions. J Theor Biol, 2002, 218: 331–341
Irons D J. Improving the efficiency of attractor cycle identification in Boolean networks. Phys D, 2006, 217: 7–21
Dubrova E, Teslenko M, Martinelli A. Kauffman networks: analysis and applications. In: Proceedings of 2005 IEEE/ACM International Conference on Computer-Aided Design. Washington DC: IEEE, 2005. 479–484
Garg A, Di Cara A, Xenarios L, et al. Synchronous versus asynchronous modeling of gene regulatory networks. Bioinformatics, 2008, 24: 1917–1925
Zheng D S, Yang G W, Li X Y, et al. An efficient algorithm for computing attractors of synchronous and asynchronous Boolean networks. PLoS ONE, 2013, 8: e60593
Dubrova E, Teslenko M. A SAT-based algorithm for finding attractors in synchronous Boolean networks. IEEE/ACM Trans Comput Biol Bioinf, 2011, 8: 1393–1399
Zhao Y, Kim J, Filippone M. Aggregation algorithm towards large-scale Boolean network analysis. IEEE Trans Automat Contr, 2013, 58: 1976–1985
Guo W S, Yang G W, Wu W, et al. A parallel attractor finding algorithm based on Boolean satisfiability for genetic regulatory networks. PLoS ONE, 2014, 9: e94258
Kauffman S. Metabolic stability and epigenesis in randomly constructed genetic nets. J Theor Biol, 1969, 22: 437–467
Mushthofa M, Torres G, Van de Peer Y, et al. ASP-G: an ASP-based method for finding attractors in genetic regulatory networks. Bioinformatics, 2014, 30: 3086–3092
Shmulevich I, Edward R D. Probabilistic Boolean Networks: the Modeling and Control of Gene Regulatory Networks. Philadelphia: SIAM Press, 2010
Lee C. Representation of switching circuits by binary-decision programs. Bell Syst Tech J, 1959, 38: 985–999
Akers S B. Binary decision diagrams. IEEE Trans Comput, 1978, 100: 509–516
Bollig B, Wegener L. Improving the variable ordering of OBDDs is NP-complete. IEEE Trans Comput, 1996, 45: 993–1002
Bryant R E. Symbolic Boolean manipulation with ordered binary-decision diagrams. ACM Comput Surv, 1992, 24: 293–318
Drechsler R. Verification of multi-valued logic networks. In: Proceedings of 26th Symposium on Multiple-Valued Logic. Washington DC: IEEE, 1996. 10–15
Malik S, Wang A R, Brayton R K, et al. Logic verification using binary decision diagrams in a logic synthesis environment. In: Proceedings of IEEE International Conference on Computer-Aided Design. Washington DC: IEEE, 1988. 6–9
Lomuscio A, Qu H Y, Raimondi F. MCMAS: an open-source model checker for the verification of multi-agent systems. Int J Softw Tools Technol Transf, 2015, doi: 10.1007/s10009-015-0378-x
Mizera A, Pang J, Yuan Q X. ASSA-PBN: an approximate steady-state analyser of probabilistic Boolean networks. In: Proceedings of 13th International Symposium on Automated Technology for Verification and Analysis. Berlin: Springer, 2015. 214–220. Software available at http://satoss.uni.lu/software/ASSA-PBN/
Schlatter R, Schmich K, Vizcarra I A, et al. ON/OFF and beyond—a Boolean model of apoptosis. PLoS Comput Biol, 2009, 5: e1000595
Trairatphisan P, Mizera A, Pang J, et al. optPBN: an optimisation toolbox for probabilistic Boolean networks. PLoS ONE, 2014, 9: e98001
Mizera A, Pang J, Yuan Q X. Reviving the two-state Markov chain approach. Technical Report. 2015. Available online at http://arxiv.org/abs/1501.01779
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Yuan, Q., Qu, H., Pang, J. et al. Improving BDD-based attractor detection for synchronous Boolean networks. Sci. China Inf. Sci. 59, 080101 (2016). https://doi.org/10.1007/s11432-016-5594-9
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DOI: https://doi.org/10.1007/s11432-016-5594-9