A SAT-based algorithm for finding attractors in synchronous boolean networks

IEEE/ACM Transactions on Computational Biology and Bioinformatics

Volumn 8, Issue 5, 2011, Pages 1393-1399

  Dubrova, Elena ^a   Teslenko, Maxim ^a  

^a ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

attractor; Boolean network; Bounded model checking; gene regulatory network; SAT

Indexed keywords

ATTRACTOR; BOOLEAN NETWORKS; BOUNDED MODEL CHECKING; GENE REGULATORY NETWORK; SAT;

ALGORITHMS; BOOLEAN ALGEBRA; DECISION THEORY; DYNAMICAL SYSTEMS; GENES; MODEL CHECKING;

COMPUTER SIMULATION;

ALGORITHM; ANIMAL; ARABIDOPSIS; ARTICLE; BIOLOGICAL MODEL; BIOLOGY; COMPUTER SIMULATION; GENE REGULATORY NETWORK; GENETIC DATABASE; MAMMAL; METHODOLOGY; SIGNAL TRANSDUCTION; STATISTICAL MODEL; YEAST;

ALGORITHMS; ANIMALS; ARABIDOPSIS; COMPUTATIONAL BIOLOGY; COMPUTER SIMULATION; DATABASES, GENETIC; GENE REGULATORY NETWORKS; MAMMALS; MODELS, GENETIC; MODELS, STATISTICAL; SIGNAL TRANSDUCTION; YEASTS;

EID: 79960906495     PISSN: 15455963     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCBB.2010.20     Document Type: Article

References (46)

1. B. Alberts, D. Bray, J. Lewis, M. Ra, K. Roberts, and J.D. Watson, Molecular Biology of the Cell. Garland Publishing, 1994.
2. T. Schlitt and A. Brazma, "Current Approaches to Gene Regulatory Network Modelling," BMC Bioinformatics, vol. 8, Suppl 6: S9, 2007.
3. S.A. Kauffman, "Metabolic Stability and Epigenesis in Randomly Constructed Nets," J. Theoretical Biology, vol. 22, pp. 437-467, 1969.
4. S. Huang and D.E. Ingber, "Shape-Dependent Control of Cell Growth, Differentiation, and Apoptosis: Switching between Attractors in Cell Regulatory Networks," Experimental Cell Research, vol. 26, no. 1, pp. 91-103, 2000.
5. R. Albert and H.G. Othmer, "The Topology of the Regulatory Interactions Predicts the Expression Pattern of the Segment Polarity Genes in Drosophila Melanogaster," J. Theoretical Biology, vol. 223, no. 1, pp. 1-18, 2003. (Pubitemid 36627542)
6. M.I. Davidich and S. Bornholdt, "Boolean Network Model Predicts Cell Cycle Sequence of Fission Yeast," PLoS ONE, vol. 3, no. 2, p. e1672, 2008.
7. S.A. Kauffman and E.D. Weinberger, "The NK Model of Rugged Fitness Landscapes and Its Application to Maturation of the Immune Response," J. Theoretical Biology, vol. 141, pp. 211-245, 1989. (Pubitemid 20036173)
8. S. Bornholdt and T. Rohlf, "Topological Evolution of Dynamical Networks: Global Criticality from Local Dynamics," Physical Rev. Letters, vol. 84, pp. 6114-6117, 2000.
9. A. Chaos, M. Aldana, C. Espinosa-Soto, B. Leon, A. Arroyo, and E. Alvarez-Buylla, "From Genes to Flower Patterns and Evolution: Dynamic Models of Gene Regulatory Networks," Plant Growth Regulation, vol. 25, no. 4, pp. 278-289, 2006. (Pubitemid 44967973)
10. H. de Jong and M. Page, "Search for Steady States of Piecewise-Linear Differential Equation Models of Genetic Regulatory Networks," IEEE/ACM Trans. Computational Biology and Bioinformatics, vol. 5, no. 2, pp. 208-222, Apr.-June 2008. (Pubitemid 351695261)
11. A. Biere, A. Cimatti, E. Clarke, M. Fujita, and Y. Zhu, "Symbolic Model Checking Using SAT Procedures Instead of BDDs," Proc. Design Automation Conf. (DAC '99), pp. 317-320, June 1999.
12. G. Batt, D. Ropers, H. de Jong, J. Geiselmann, R. Mateescu, M. Page, and D. Schneider, "Validation of Qualitative Models of Genetic Regulatory Networks by Model Checking: Analysis of the Nutritional Stress Response in Escherichia Coli," Bioinformatics, vol. 21, no. 1, pp. 19-28, 2005.
13. V. Mysore and B. Mishra, "Algorithmic Algebraic Model Checking IV: Characterization of Metabolic Networks," Proc. Int'l Conf. Algebraic Biology (AB '07), pp. 170-184, July 2007.
14. M. Calder, V. Vyshemirsky, D. Gilbert, and R. Orton, "Analysis of Signalling Pathways Using the PRISM Model Checker," Proc. Int'l Conf. Computational Methods in Systems Biology (CMSB '05), pp. 179-190, Apr. 2005.
15. D. Gilbert, M. Heiner, and S. Lehrack, "A Unifying Framework for Modelling and Analysing Biochemical Pathways Using Petri Nets," Proc. Int'l Conf. Computational Methods in Systems Biology (CMSB '07), pp. 200-216, Sept. 2007.
16. P. Ballarini, R. Mardare, and I. Mura, "Analysing Biochemical Oscillation through Probabilistic Model Checking," Electronic Notes Theoretical Computer Science, vol. 229, no. 1, pp. 3-19, 2009.
17. C.J. Langmead and S.K. Jha, "Symbolic Approaches for Finding Control Strategies in Boolean Networks," Bioinformatics and Computational Biology, vol. 2, no. 7, pp. 323-338, 2009.
18. R. Thomas and R. D'Ari, Biological Feedback. CRC Press, 1990.
19. E. Dubrova, "Random Multiple-Valued Networks: Theory and Applications," Proc. Int'l Symp. Multiple-Valued Logic (ISMVL '06), pp. 27-33, May 2006.
20. A. Garg, L. Mendoza, I. Xenarios, and G. DeMicheli, "Modeling of Multiple Valued Gene Regulatory Networks," Proc. 29th IEEE Int'l Conf. Eng. In Medicine and Biology Soc. (EMBC '07), pp. 1398-1404, Aug. 2007.
21. E.M. Clarke, D. Kroening, J. Ouaknine, and O. Strichman, "Completeness and Complexity of Bounded Model Checking," Proc. Fifth Int'l Conf. Verification, Model Checking, and Abstract Interpretation (VMCAI '04), pp. 85-96, Jan. 2004.
22. J. Burch et al., "Symbolic Model Checking: 1020 States and Beyond," Proc. Fifth Ann. IEEE Symp. Logic in Computer Science, pp. 1-33, 1990.
23. D. Kroening and O. Strichman, "Efficient Computation of Recurrence Diameters," Proc. Fourth Int'l Conf. Verification, Model Checking, and Abstract Interpretation (VMCAI '03), pp. 298-309, Jan. 2003.
24. E. Dubrova, M. Teslenko, and A. Martinelli, "Kauffman Networks: Analysis and Applications," Proc. IEEE/ACM Int'l Conf. Computer-Aided Design, pp. 479-484, Nov. 2005.
25. S. Bilke and F. Sjunnesson, "Stability of the Kauffman Model," Physical Rev. E, vol. 65, p. 016129, 2001.
26. J.E.S. Socolar and S.A. Kauffman, "Scaling in Ordered and Critical Random Boolean Networks," Physical Rev. Letters, vol. 90, no. 6, p. 068702, 2003.
27. C. Oosawa, "Effects of Alternative Connectivity on Behavior of Randomly Constructed Boolean Networks," Physica D: Nonlinear Phenomena, vol. 170, no. 2, pp. 143-161, 2002. (Pubitemid 34813926)
28. L. Raeymaekers, "Dynamics of Boolean Networks Controlled by Biologically Meaningful Functions," J. Theoretical Biology, vol. 218, no. 3, pp. 331-341, 2002. (Pubitemid 35191833)
29. T. Akutsu, S. Kuhara, O. Maruyama, and S. Miyano, "A System for Identifying Genetic Networks from Gene Expression Patterns Produced by Gene Disruptions and Overexpressions," Genome Informatics, vol. 9, pp. 151-160, 1998.
30. T. Tamura and T. Akutsu, "An Improved Algorithm for Detecting a Singleton Attractor in a Boolean Network Consisting of AND/OR Nodes," Proc. Third Int'l Conf. Algebraic Biology (AB '08), pp. 216-229, July/Aug. 2008.
31. T. Akutsu and T. Tamura, "On Finding a Fixed Point in a Boolean Network with Maximum Indegree 2," IEICE Trans. Fundamentals of Electronics, Comm. and Computer Sciences, vol. E92.A, no. 8, pp. 1771-1778, 2009.
32. A. Naldi, D. Thieffry, and C. Chaouiya, "Decision Diagrams for the Representation and Analysis of Logical Models of Genetic Networks," Proc. Int'l Conf. Computational Methods in Systems Biology (CMSB '07), pp. 233-247, Sept. 2007.
33. R. Thomas, "Regulatory Networks Seen as Asynchronous Automata: A Logical Description," J. Theoretical Biology, vol. 153, pp. 1-23, 1991.
34. D.J. Irons, "Improving the Efficiency of Attractor Cycle Identification in Boolean Networks," Physica D: Nonlinear Phenomena, vol. 217, pp. 7-21, 2006. (Pubitemid 44287871)
35. E. Dubrova and M. Teslenko, "Kauffman Networks: From Nature to Electronics," Proc. Notes of IEEE Int'l Workshop Logic Synthesis, pp. 56-60, June 2005.
36. A. Garg, I. Xenarios, L. Mendoza, and G. De Micheli, "An Efficient Method for Dynamic Analysis of Gene Regulatory Networks and in Silico Gene Perturbation Experiments," Proc. 11th Ann. Int'l Conf. Research in Computational Molecular Biology (RECOMB '07), pp. 62-76, Apr. 2007. (Pubitemid 47164532)
37. G. Hasteer, A. Mathur, and P. Banerjee, "An Implicit Algorithm for Finding Steady States and Its Application to FSM Verification," Proc. Design Automation Conf. (DAC '98), pp. 611-614, June 1998.
38. A. Xie and P.A. Beerel, "Implicit Enumeration of Strongly Connected Components," Proc. Int'l Conf. Computer-Aided Design (ICCAD '99), pp. 37-40, Nov. 1999. (Pubitemid 30560582)
39. V. Devloo, P. Hansen, and M. Labb, "Identification of All Steady States in Large Biological Systems by Logical Analysis," Bull. of Math. Biology, vol. 65, no. 6, pp. 1025-1051, 2003. (Pubitemid 37446843)
40. L. Bordeaux, Y. Hamadi, and L. Zhang, "Propositional Satisfiability and Constraint Programming: A Comparative Survey," ACM Computing Surveys, vol. 38, no. 4, p. 12, 2006.
41. N. Een and N. Sorensson, "MiniSat-A SAT Solver with Conflict-Clause Minimization," Proc. Int'l Conf. Theory and Applications of Satisfiability Testing (SAT '05), June 2005.
42. F. Li, T. Long, Y. Lu, Q. Ouyang, and C. Tang, "The Yeast Cell-Cycle Network is Robustly Designed," Proc. Nat'l Academy of Sciences USA, vol. 101, no. 14, pp. 4781-4786, 2004. (Pubitemid 38469154)
43. A. Faure, A. Naldi, C. Chaouiya, and D. Thieffry, "Dynamical Analysis of a Generic Boolean Model for the Control of the Mammalian Cell Cycle," Bioinformatics, vol. 22, pp. e124-e131(1), 2006. (Pubitemid 44288280)
44. S. Klamt, J. Saez-Rodriguez, J.A. Lindquist, L. Simeoni, and E.D. Gilles, "A Methodology for the Structural and Functional Analysis of Signaling and Regulatory Networks," BMC Bioinformatics, vol. 7, article no. 56, 2006.
45. L. Mendoza and I. Xenarios, "A Method for the Generation of Standardized Qualitative Dynamical Systems of Regulatory Networks," Theoretical Biology and Medical Modelling, vol. 3, no. 1, pp. 13-31, 2006.
46. A. Garg, A. Di Cara, I. Xenarios, L. Mendoza, and G. De Micheli, "Synchronous Versus Asynchronous Modeling of Gene Regulatory Networks," Bioinformatics, vol. 24, no. 17, pp. 1917-1925, 2008.