Static analysis of boolean networks based on interaction graphs: A survey

Electronic Notes in Theoretical Computer Science

Volumn 284, Issue , 2012, Pages 93-104

  Paulevé, Loïc ^a   Richard, Adrien ^b  

^a ECOLE CENTRALE DE NANTES   (France)

^b UNIVERSITY OF NICE SOPHIA ANTIPOLIS   (France)

Author keywords

Boolean network; discrete dynamical system; interaction graph; regulatory network

Indexed keywords

BOOLEAN NETWORKS; CLASSICAL APPROACH; COMBINATORIAL EXPLOSION; DISCRETE DYNAMICAL SYSTEMS; DYNAMICAL ANALYSIS; INTERACTION GRAPHS; REGULATORY NETWORK; STATE SPACE;

DYNAMICAL SYSTEMS;

BOOLEAN ALGEBRA;

EID: 84863191619     PISSN: 15710661     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.entcs.2012.05.017     Document Type: Conference Paper

References (50)

1. J. Ahmad, G. Bernot, J.P. Comet, D. Lime, and O. Roux Hybrid modelling and dynamical analysis of gene regulatory networks with delays Complexus 3 2006 231 251
2. J. Aracena Maximum number of fixed points in regulatory boolean networks Bulletin of Mathematical Biology 70 2008 1398 1409
3. J. Aracena, J. Demongeot, and E. Goles Positive and negative circuits in discrete neural networks IEEE Transactions of Neural Networks 15 2004 77 83
4. J. Aracena, E. Goles, A. Moreira, and L. Salinas On the robustness of update schedules in boolean networks Biosystems 97 2009 1 8
5. J.M. Bahi, and C. Michel Convergence of discrete asynchronous iterations International Journal of Computer Mathematics 74 2000 113 125
6. O. Cinquin, and J. Demongeot Positive and negative feedback: strinking a balance between necessary antagonists Journal of Theoretical Biology 216 2002 229 241
7. R. Colón-Reyes, O. Laubenbacher, and B. Pareigis Boolean Monomial Dynamical Systems Annals of Combinatorics 8 2000 425 439
8. H. de Jong Modeling and simulation of genetic regulatory systems: A literature review Journal of Computational Biology 9 2002 67 103
9. D. Endy, and R. Brent Modelling cellular behaviour Nature 409 2001 391 395
10. A.E. German, and W. Just Large attractors in cooperative bi-quadratic Boolean networks. Part I Preprint arXiv:0711.2799 2008
11. L. Glass Combinatorial and topological methods in nonlinear chemical kinetics Journal of Chemical Physics 63 1975 1325 1335
12. L. Glass, and S. Kauffman Logical analysis of continuous, non-linear biochemical control networks Journal of Theoretical Biology 39 1973 103 129
13. E. Goles, and G. Herández Dynamical behaviors of Kauffman networks with and-or gates Journal of Biological Systems 8 2000 151 175
14. E. Goles, and J. Olivos Comportement itératif des fonctions Ãǎ multiseuil Information and Control 45 1980 300 313
15. E. Goles, and L. Salinas Comparison between parallel and serial dynamics of boolean networks Theoretical Computer Science 396 2008 247 253
16. E. Goles, and L. Salinas Sequential operator for filtering cycles in boolean networks Advances in Applied Mathematics 45 2010 346 358
17. J. Gouzé Positive and negative circuits in dynamical systems Journal of Biological Systems 6 1998 11 15
18. W. Just, and A.E. German Large attractors in cooperative bi-quadratic Boolean networks. Part II Preprint arXiv:0801.4546 2008
19. S.A. Kauffman Metabolic stability and epigenesis in randomly connected nets Journal of Theoretical Biology 22 1969 437 467
20. S.A. Kauffman Origins of Order Self-Organization and Selection in Evolution 1993 Oxford University Press
21. A. Naldi, E. Remy, D. Thieffry, and C. Chaouiya A reduction of logical regulatory graphs preserving essential dynamical properties Computational Methods in Systems Biology Lecture Notes in Computer Science vol. 5688 2009 Springer Berlin/Heidelberg 266 280
22. Naldi, A., D. Thieffry and C. Chaouiya, Decision diagrams for the representation and analysis of logical models of genetic networks, in: Proceedings of the 2007 international conference on Computational methods in systems biology, CMSB'07 (2007), pp. 233-247.
23. M. Noual General iteration graphs and boolean automata circuits preprint arXiv:1104.4044 2011
24. L. Paulevé, M. Magnin, and O. Roux Abstract Interpretation of Dynamics of Biological Regulatory Networks Proceedings of The First International Workshop on Static Analysis and Systems Biology Electronic Notes in Theoretical Computer Science 272 2011 43 56
25. Paulevé, L., M. Magnin and O. Roux, Static Analysis by Abstract Interpretation of Biological Regulatory Networks Dynamics, Research Report hal-00574353, IRCCyN (2011). URL http://hal.archives-ouvertes.fr/hal-00574353.
26. L. Paulevé, and A. Richard Topological Fixed Points in Boolean Networks Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 348 2010 825 828
27. E. Plathe, T. Mestl, and S. Omholt Feedback loops, stability and multistationarity in dynamical systems Journal of Biological Systems 3 1995 569 577
28. É. Remy, P. Ruet, and D. Thieffry Graphic requirements for multistability and attractive cycles in a boolean dynamical framework Advances in Applied Mathematics 41 2008 335 350
29. A. Richard An extension of a combinatorial fixed point theorem of shih and dong Advances in Applied Mathematics 41 2008 620 627
30. A. Richard Positive circuits and maximal number of fixed points in discrete dynamical systems Discrete Applied Mathematics 157 2009 3281 3288
31. A. Richard Negative circuits and sustained oscillations in asynchronous automata networks Advances in Applied Mathematics 44 2010 378 392
32. A. Richard Local negative circuits and fixed points in non-expansive boolean networks Discrete Applied Mathematics 159 2011 1085 1093
33. A. Richard, and J.-P. Comet Necessary conditions for multistationarity in discrete dynamical systems Discrete Applied Mathematics 155 2007 2403 2413
34. F. Robert Iterations sur des ensembles finis et automates cellulaires contractants Linear Algebra and its Applications 29 1980 393 412
35. F. Robert Discrete iterations: a metric study Computational Mathematics vol. 6 1986 Springer
36. F. Robert Les systèmes dynamiques discrets Mathématiques et Applications vol. 19 1995 Springer
37. M.-H. Shih, and J.-L. Dong A combinatorial analogue of the jacobian problem in automata networks Advances in Applied Mathematics 34 2005 30 46
38. M.-H. Shih, and J.-L. Ho Solution of the Boolean Markus-Yamabe problem Advances in Applied Mathematics 22 1999 60 102
39. H. Siebert, and A. Bockmayr Incorporating time delays into the logical analysis of gene regulatory networks C. Priami, Computational Methods in Systems Biology Lecture Notes in Computer Science vol. 4210 2006 Springer Berlin/Heidelberg 169 183
40. E. Snoussi Qualitative dynamics of a piecewise-linear differential equations: a discrete mapping approach Dynamics and stability of Systems 4 1989 189 207
41. E. Snoussi Necessary conditions for multistationarity and stable periodicity Journal of Biological Systems 6 1998 3 9
42. E. Snoussi, and R. Thomas Logical identification of all steady states: the concept of feedback loop caracteristic states Bull. Math. Biol. 55 1993 973 991
43. C. Soulé Graphical requirements for multistationarity ComPlexUs 1 2003 123 133
44. C. Soulé Mathematical approaches to differentiation and gene regulation C. R. Paris Biologies 329 2006 13 20
45. M. Tchente Cycles generated by sequential iterations Discrete Applied Mathematics 20 1988 165 172
46. R. Thomas Boolean formalization of genetic control circuits Journal of Theoretical Biology 42 1973 563 585
47. R. Thomas On the relation between the logical structure of systems and their ability to generate multiple steady states or sustained oscillations Springer Series in Synergies vol. 9 1980 180 193
48. R. Thomas, and R. d'Ari Biological Feedback 1990 CRC Press
49. R. Thomas, and M. Kaufman Multistationarity, the basis of cell differentiation and memory. ii. logical analysis of regulatory networks in terms of feedback circuits Chaos: An Interdisciplinary Journal of Nonlinear Science 11 2001 180 195
50. Twardziok, S., H. Siebert and A. Heyl, Stochasticity in reactions: a probabilistic boolean modeling approach, in: CMSB, 2010, pp. 76-85.