Minimum-time control of boolean networks

SIAM Journal on Control and Optimization

Volumn 51, Issue 4, 2013, Pages 2869-2892

  Laschov, Dmitriy ^a   Margaliot, Michael ^a  

^a TEL AVIV UNIVERSITY   (Israel)

Author keywords

Gene regulation networks; Lambda switch; Logical systems; Necessary condition for optimality; Positive linear switched systems; Systems biology; Timeoptimal control; Variational analysis

Indexed keywords

CONDITION FOR OPTIMALITY; GENE REGULATION NETWORK; LOGICAL SYSTEM; POSITIVE LINEAR SWITCHED SYSTEMS; SYSTEMS BIOLOGY; TIME OPTIMAL CONTROL; VARIATIONAL ANALYSIS;

CONSTRAINT THEORY; GENES; SWITCHING CIRCUITS;

FEEDBACK;

EID: 84882455003     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/110844660     Document Type: Article

References (80)

1. G. K. Ackers, A. D. Johnson, and M. A. Shea, Quantitative model for gene regulation by λ repressor, Proc. Natl. Acad. Sci. USA, 79 (1982), pp. 1129-1133. (Pubitemid 12114078)
2. A. A. Agrachev and Y. L. Sachkov, Control Theory from the Geometric Viewpoint, Encyclopedia Math. Sci. 87, Springer-Verlag, Berlin, 2004.
3. T. Akutsu, M. Hayashida, W.-K. Ching, and M. K. Ng, Control of Boolean networks: Hardness results and algorithms for tree structured networks, J. Theoret. Biol., 244 (2007), pp. 670-679. (Pubitemid 46148979)
4. R. Albert and A.-L. Barabasi, Dynamics of complex systems: Scaling laws or the period of Boolean networks, Phys. Rev. Lett., 84 (2000), pp. 5660-5663.
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. Theoret. Biol., 223 (2003), pp. 1-18. (Pubitemid 36627542)
6. M. Aldana, Boolean dynamics of networks with scale-free topology, Phys. D, 185 (2003), pp. 45-66.
7. U. Alon, An Introduction to Systems Biology: Design Principles of Biological Circuits, Chapman & Hall/CRC, Boca Raton, FL, 2006.
8. A. Arkin, J. Ross, and H. H. McAdams, Stochastic kinetic analysis of developmental pathway bifurcation in phage lambda-infected Escherichia coli cells, Genetics, 149 (1998), pp. 1633-1648. (Pubitemid 28375939)
9. N. E. Barabanov, Lyapunov exponent and joint spectral radius: Some known and new results, in Proceedings of the 44th IEEE Conference on Decision and Control, Seville, Spain, 2005, pp. 2332-2337.
10. H. Bolouri, Computational Modelling of Gene Regulatory Networks - A Primer, Imperial College Press, London, 2008.
11. B. Bonnard and M. Chyba, Singular Trajectories and Their Role in Control Theory, Springer- Verlag, Berlin, 2003.
12. S. Bornholdt, Boolean network models of cellular regulation: Prospects and limitations, J. R. Soc. Interface, 5 (2008), pp. S85-S94. (Pubitemid 351915287)
13. A. Chaos, M. Aldana, C. Espinosa-Soto, B. G. P. de Leon, A. G. Arroyo, and E. R. Alvarez-Buylla, From genes to flower patterns and evolution: Dynamic models of gene regulatory networks, J. Plant Growth Regul., 25 (2006), pp. 278-289. (Pubitemid 44967973)
14. M. Chaves, R. Albert, and E. D. Sontag, Robustness and fragility of Boolean models for genetic regulatory networks, J. Theoret. Biol., 235 (2005), pp. 431-449. (Pubitemid 40693191)
15. D. Cheng, Input-state approach to Boolean networks, IEEE Trans. Neural Networks, 20 (2009), pp. 512-521.
16. D. Cheng, Disturbance decoupling of Boolean control networks, IEEE Trans. Automat. Control, 56 (2011), pp. 2-10.
17. D. Cheng and Y. Dong, Semi-tensor product of matrices and its some applications to physics, Methods Appl. Anal., 10 (2003), pp. 565-588. (Pubitemid 40083673)
18. D. Cheng, Z. Li, and H. Qi, Realization of Boolean control networks, Automatica, 46 (2010), pp. 62-69.
19. D. Cheng and H. Qi, Controllability and observability of Boolean control networks, Automatica, 45 (2009), pp. 1659-1667.
20. D. Cheng and H. Qi, A linear representation of dynamics of Boolean networks, IEEE Trans. Automat. Control, 55 (2010), pp. 2251-2258.
21. D. Cheng and H. Qi, State-space analysis of Boolean networks, IEEE Trans. Neural Networks, 21 (2010), pp. 584-594.
22. D. Cheng, H. Qi, and Z. Li, Analysis and Control of Boolean Networks, Springer-Verlag, London, 2011.
23. P. Cull, Linear analysis of switching nets, Biological Cybernetics, 8 (1971), pp. 31-39.
24. P. Cull, Control of switching nets, Biological Cybernetics, 19 (1975), pp. 137-145.
25. A. Datta, A. Choudhary, M. L. Bittner, and E. R. Dougherty, External control in Markovian genetic regulatory networks, Machine Learning, 52 (2003), pp. 169-191.
26. A. Datta, R. Pal, A. Choudhary, and E. R. Dougherty, Control approaches for probabilistic gene regulatory networks, IEEE Signal Process. Mag., 24 (2010), pp. 54-63.
27. B. Derrida and Y. Pomeau, Random networks of automata: A simple annealed approximation, Europhys. Lett., 1 (1986), pp. 45-49.
28. B. Drossel, T. Mihaljev, and F. Greil, Number and length of attractors in a critical Kauffman model with connectivity one, Phys. Rev. Lett., 94 (2005), 088701.
29. C. Espinosa-Soto, P. Padilla-Longoria, and E. R. Alvarez-Buylla, 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 (2004), pp. 2923-2939. (Pubitemid 41075743)
30. L. Fainshil and M. Margaliot, A maximum principle for the stability analysis of positive bilinear control systems with applications to positive linear switched systems, SIAM J. Control Optim., 50 (2012), pp. 2193-2215.
31. L. Fainshil, M. Margaliot, and P. Chigansky, On the stability of positive linear switched systems under arbitrary switching laws, IEEE Trans. Automat. Control, 54 (2009), pp. 897-899.
32. E. Fornasini and M. E. Valcher, Reachability of a class of discrete-time positive switched systems, SIAM J. Control Optim., 49 (2011), pp. 162-184.
33. D. G. Green, T. G. Leishman, and S. Sadedin, The emergence of social consensus in Boolean networks, in Proceedings of the IEEE Symposium on Artificial Life (ALIFE'07), Honolulu, HI, 2007, pp. 402-408. (Pubitemid 47431267)
34. S. Gupta, S. S. Bisht, R. Kukreti, S. Jain, and S. K. Brahmachari, Boolean network analysis of a neurotransmitter signaling pathway, J. Theoret. Biol., 244 (2007), pp. 463-469. (Pubitemid 46027147)
35. L. Gurvits, R. Shorten, and O. Mason, On the stability of switched positive linear systems, IEEE Trans. Automat. Control, 52 (2007), pp. 1099-1103. (Pubitemid 47034040)
36. M. H. Hassoun, Fundamentals of Artificial Neural Networks, MIT Press, Cambridge, MA, 1995.
37. T. Helikar, N. Kochi, J. Konvalina, and J. Rogers, Boolean modeling of biochemical networks, Open Bioinformatics J., 5 (2011), pp. 16-25.
38. F. Hinkelmann and R. Laubenbacher, Boolean models of bistable biological systems, Discrete Contin. Dyn. Syst. Ser. S, 4 (2011), pp. 1443-1456.
39. S. Huang, Regulation of cellular states in mammalian cells from a genomewide view, in Gene Regulation and Metabolism, J. Collado-Vides and R. Hofestadt, eds., MIT Press, Cambridge, MA, 2002, pp. 181-220.
40. S. Kauffman, Differentiation of malignant to benign cells, J. Theoret. Biol., 31 (1971), pp. 429-451.
41. S. Kauffman, C. Peterson, B. Samuelsson, and C. Troein, Random Boolean network models and the yeast transcriptional network, Proc. Natl. Acad. Sci. USA, 100 (2003), pp. 14796-14799. (Pubitemid 37517970)
42. S. A. Kauffman, Metabolic stability and epigenesis in randomly constructed genetic nets, J. Theoret. Biol., 22 (1969), pp. 437-467.
43. S. A. Kauffman, Origins of Order: Self-Organization and Selection in Evolution, Oxford University Press, New York, 1993.
44. S. Keerthi and E. Gilbert, Computation of minimum-time feedback control laws for discretetime systems with state-control constraints, IEEE Trans. Automat. Control, 32 (1987), pp. 432-435. (Pubitemid 17582709)
45. G. Langholz, J. L. Mott, and A. Kandel, Foundations of Digital Logic Design, World Scientific, Singapore, 1998.
46. D. Laschov and M. Margaliot, Mathematical modeling of the λ switch: A fuzzy logic approach, J. Theoret. Biol., 260 (2009), pp. 475-489.
47. D. Laschov and M. Margaliot, A maximum principle for single-input Boolean control networks, IEEE Trans. Automat. Control, 56 (2011), pp. 913-917.
48. D. Laschov and M. Margaliot, Controllability of Boolean control networks via the Perron- Frobenius theory, Automatica, 48 (2012), pp. 1218-1223.
49. D. Laschov and M. Margaliot, A Pontryagin maximum principle for multiinput Boolean control networks, in Recent Advances in Dynamics and Control of Neural Networks, E. Kaslik and S. Sivasundaram, eds., Cambridge Scientific Publishers, to appear.
50. D. Laschov, M. Margaliot, and G. Even, Observability of Boolean networks: A graphtheoretic approach, Automatica, to appear (2013).
51. F. Li, T. Long, Y. Lu, Q. Ouyang, and C. Tang, The yeast cell-cycle network is robustly designed, Proc. Natl. Acad. Sci. USA, 101 (2004), pp. 4781-4786. (Pubitemid 38469154)
52. S. Li, S. M. Assmann, and R. Albert, Predicting essential components of signal transduction networks: A dynamic model of guard cell abscisic acid signaling, PLoS Biol., 4 (2006), pp. 1732-1748. (Pubitemid 44610093)
53. D. Liberzon, Calculus of Variations and Optimal Control Theory, Princeton University Press, Princeton, NJ, 2011.
54. Q. Liu, X. Guo, and T. Zhou, Optimal control for probabilistic Boolean networks, IETSystems Biol., 4 (2010), pp. 99-107.
55. J. X. Luo and M. S. Turner, Functionality and metagraph disintegration in Boolean networks, J. Theoret. Biol., 282 (2011), pp. 65-70.
56. B. Luque and R. V. Sole, Lyapunov exponents in random Boolean networks, Phys. A, 284 (2000), pp. 33-45.
57. M. Margaliot, Stability analysis of switched systems using variational principles: An introduction, Automatica, 42 (2006), pp. 2059-2077. (Pubitemid 44647189)
58. M. Margaliot and M. S. Branicky, Nice reachability for planar bilinear control systems with applications to planar linear switched systems, IEEE Trans. Automat. Control, 54 (2009), pp. 1430-1435.
59. M. Margaliot and D. Liberzon, Lie-algebraic stability conditions for nonlinear switched systems and differential inclusions, Systems Control Lett., 55 (2006), pp. 8-16. (Pubitemid 41737276)
60. O. C. Martin and A. Wagner, Multifunctionality and robustness trade-offs in model genetic circuits, Biophys. J., 94 (2008), pp. 2927-2937.
61. O. Mason and R. Shorten, Some results on the stability of positive switched linear systems, in Proceedings of the 43rd IEEE Conference on Decision and Control, 2004, pp. 4601-4606. (Pubitemid 40307750)
62. T. Monovich and M. Margaliot, Analysis of discrete-time linear switched systems: A variational approach, SIAM J. Control Optim., 49 (2011), pp. 808-829.
63. T. Monovich and M. Margaliot, A second-order maximum principle for discrete-time bilinear control systems with applications to discrete-time linear switched systems, Automatica, 47 (2011), pp. 1489-1495.
64. A. B. Oppenheim, O. Kobiler, J. Stavans, D. L. Court, and S. Adhya, Switches in bacteriophage lambda development, Ann. Rev. Genetics, 39 (2005), pp. 409-429. (Pubitemid 43011121)
65. R. Pal, A. Datta, and E. R. Dougherty, Optimal infinite horizon control for probabilistic Boolean networks, IEEE Trans. Signal Process., 54 (2006), pp. 2375-2387. (Pubitemid 43805580)
66. M. Ptashne, A Genetic Switch, 3rd ed., Cold Spring Harbor Laboratory Press, Cold Spring Harbor, NY, 2004.
67. X. Qian and E. R. Dougherty, Effect of function perturbation on the steady-state distribution of genetic regulatory networks: Optimal structural intervention, IEEE Trans. Signal Process., 56 (2008), pp. 4966-4976.
68. B. Samuelsson and C. Troein, Superpolynomial growth in the number of attractors in Kauffman networks, Phys. Rev. Lett., 90 (2003), 098701.
69. H. Schattler, Time optimal feedback control for nonlinear systems: A geometric approach, in Geometry of Feedback and Optimal Control, B. Jakubczyk and W. Respondek, eds., Marcel Dekker, New York, 1998, pp. 383-421.
70. J. L. Schiff, Cellular Automata: A Discrete View of the World, Wiley-Interscience, Hoboken, NJ, 2008.
71. Y. Sharon and M. Margaliot, Third-order nilpotency, finite switchings and asymptotic stability, J. Differential Equations, 233 (2007), pp. 136-150. (Pubitemid 44824770)
72. I. Shmulevich, E. R. Dougherty, S. Kim, and W. Zhang, Probabilistic Boolean networks: A rule-based uncertainty model for gene regulatory networks, Bioinformatics, 18 (2002), pp. 261-274. (Pubitemid 34183104)
73. I. Shmulevich, E. R. Dougherty, and W. Zhang, From Boolean to probabilistic Boolean networks as models of genetic regulatory networks, Proc. IEEE, 90 (2002), pp. 1778-1792.
74. I. Shmulevich, E. R. Dougherty, and W. Zhang, Gene perturbation and intervention in probabilistic Boolean networks, Bioinformatics, 18 (2002), pp. 1319-1331. (Pubitemid 35244189)
75. Z. Szallasi and S. Liang, Modeling the normal and neoplastic cell cycle with "realistic Boolean genetic networks": Their application for understanding carcinogenesis and assessing therapeutic strategies, Pac. Symp. Biocomput., 3 (1998), pp. 66-76.
76. D. Thieffry and R. Thomas, Dynamical behaviour of biological regulatory networks II: Immunity control in bacteriophage lambda, Bull. Math. Biol., 57 (1995), pp. 277-297.
77. J. Vohradsky, Neural model of the genetic network, J. Biol. Chem., 276 (2001), pp. 36168-36173.
78. G. Wegrzyn and A. Wegrzyn, Genetic switches during bacteriophage lambda development, Progress in Nucleic Acid Research and Molecular Biology, 79 (2005), pp. 1-48. (Pubitemid 43591148)
79. Y. Zhao, A Floyd-like algorithm for optimization of mix-valued logical control networks, in Proceedings of the 30th Chinese Control Conference (CCC2011), 2011, pp. 1972-1977.
80. Y. Zhao, H. Qi, and D. Cheng, Input-state incidence matrix of Boolean control networks and its applications, Systems Control Lett., 59 (2010), pp. 767-774.