Context-sensitive probabilistic boolean networks: Steady-state properties, reduction, and steady-state approximation

IEEE Transactions on Signal Processing

Volumn 58, Issue 2, 2010, Pages 879-890

  Pal, Ranadip ^a  

^a Department of Electrical and Computer Engineering   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATE METHODS; APPROXIMATION METHODS; CONTEXT-SENSITIVE; CONTROL POLICY; EFFECT SYSTEM; GENETIC REGULATORY NETWORKS; INTERVENTION METHODS; OPTIMAL CONTROL STRATEGY; PROBABILISTIC BOOLEAN NETWORKS; REDUCTION TECHNIQUES; SIZE-REDUCTION; STEADY STATE PROBABILITIES; STEADY-STATE BEHAVIORS;

APPROXIMATION THEORY; COMPUTATIONAL COMPLEXITY; GENETIC ENGINEERING;

PROBABILITY DISTRIBUTIONS;

EID: 74949119596     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2009.2030832     Document Type: Article

References (42)

1. H. De Jong, "Modeling and simulation of genetic regulatory systems: A literature review," J. Comput. Biol., vol.9, pp. 67-103, 2001.
2. I. Shmulevich and E. R. Dougherty, Genomic Signal Processing. Princeton, NJ: Princeton Univ. Press, 2007.
3. J. M. Bower and H. Bolouri, Computational Modeling of Genetic and Biochemical Networks, 1st ed. Boston, MA: MIT Press, 2001.
4. R. Sharan and T. Ideker, "Modeling cellular machinery through biological network comparison," Nat. Biotechnol., vol.24, pp. 427-433, 2006.
5. E. D. Conrad and J. J. Tyson, "Modeling molecular interaction networks with nonlinear ordinary differential equations," in System Modeling in Cell Biology From Concepts to Nuts and Bolts. Cambridge, MA: MIT Press, 2006, pp. 97-123.
6. D. S. Douglas and S. Jones, Differential Equations and Mathematical Biology, 1st ed. Boca Raton, FL: Chapman & Hall/CRC, 2003.
7. L. Qian, H. Wang, and E. Dougherty, "Inference of noisy nonlinear differential equation models for gene regulatory networks using genetic programming and Kalman filtering," IEEE Trans. Signal Process., vol.56, no.7, pp. 3327-3339, 2008.
8. M. de Hoon, S. Imoto, and S. Miyano, Inferring Gene Regulatory Networks From Time-Ordered Gene Expression Data Using Differential Equations. Berlin, Germany: Springer, 2002.
9. J. Goutsias and S. Kim, "Stochastic transcriptional regulatory systems with time delays: A mean-field approximation," J. Comput. Biol., vol.13, pp. 1049-1076, 2006.
10. J. Goutsias and S. Kim, "A nonlinear discrete dynamical model for transcriptional regulation: Construction and properties," Biophys. J., vol.86, pp. 1922-1945, 2004.
11. A. Margolin, I. Nemenman, K. Basso, U. Klein, C. Wiggins, G. Stolovitzky, R. D. Favera, and A. Califano, "Aracne: An algorithm for reconstruction of genetic networks in a mammalian cellular context," BMC Bioinf., vol.7, 2006.
12. L. Glass and S. A. Kauffman, "The logical analysis of continuous, nonlinear biochemical control networks," J. Theor. Biol., vol.39, pp. 103-129, 1973.
13. S. A. Kauffman, "Metabolic stability and epigenesis in randomly constructed genetic nets," Theor. Biol., vol.22, pp. 437-467, 1969.
14. S. A. Kauffman, The Origins of Order: Self-Organization and Selection in Evolution. New York: Oxford Univ. Press, 1993.
15. R. Somogyi and C. Sniegoski, "Modeling the complexity of gene networks: Understanding multigenic and pleiotropic regulation," Complexity, vol.1, pp. 45-63, 1996.
16. 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," Proc. Pac. Symp. Biocomput., vol.3, pp. 66-76, 1998.
17. R. Thomas, D. Thieffry, and M. Kaufman, "Dynamical behavior of genetic regulatory networks i. biological role of feedback loops and practical use of the concept of the loop-characteristic state," Bull. Math. Biol., vol.57, pp. 247-276, 1995.
18. A. Wuensche, "Genomic regulation modeled as a network with basins of attraction," Proc. Pac. Symp. Biocomput., vol.3, pp. 89-102, 1998.
19. S. Huang, "Gene expression profiling, genetic networks, and cellular states: An integrating concept for tumorigenesis and drug discovery," Molec. Med., vol.77, pp. 469-480, 1999.
20. A. Faure, A. Naldi, C. Chaouiya, and D. Theiffry, "Dynamical analysis of a generic boolean model for the control of the mammalian cell cycle," Bioinformatics, vol.22, pp. 124-131, 2006.
21. J. C. Sible and J. J. Tyson, "Mathematical modeling as a tool for investigating cell cycle control networks," Methods, vol.41, pp. 238-247, 2007.
22. J. J. Tyson, A. Csikasz-Nagy, and B. Novak, "The dynamics of cell cycle regulation," Bioessays, vol.24, pp. 1095-1109, 2002.
23. I. Shmulevich, E. R. Dougherty, S. Kim, and W. Zhang, "Probabilistic boolean networks: A rule-based uncertainty model for gene regulatory networks," Bioinformatics, vol.18, pp. 261-274, 2002.
24. I. Shmulevich, E. R. Dougherty, and W. Zhang, "From boolean to probabilistic boolean networks as models of genetic regulatory networks," Proc. IEEE, vol.90, pp. 1778-1792, 2002.
25. M. Brun, E. R. Dougherty, and I. Shmulevich, "Steady-state probabilities for attractors in probabilistic Boolean networks," Signal Process., vol.85, pp. 1993-2013, 2005.
26. R. Pal, A. Datta, M. L. Bittner, and E. R. Dougherty, "Intervention in context-sensitive probabilistic boolean networks," Bioinformatics, vol.21, pp. 1211-1218, 2005.
27. B. Faryabi, G. Vahedi, J.-F. Chamberland, A. Datta, and E. R. Dougherty, "Intervention in context-sensitive probabilistic boolean networks revisited," EURASIP J. Bioinf. Syst. Biol., vol.2009, p. ID360864, 2009.
28. R. Pal, A. Datta, and E. R. Dougherty, "Robust intervention in probabilistic Boolean networks," IEEE Trans. Signal Process., vol.56, no.3, pp. 1280-1294, Mar. 2008.
29. I. Ivanov and E. R. Dougherty, "Reduction mappings between probabilistic boolean networks," EURASIP J. Appl. Signal Process., vol.4, pp. 125-131, 2004.
30. I. Ivanov, R. Pal, and E. R. Dougherty, "Dynamics-preserving sizereduction mappings for probabilistic Boolean networks," IEEE Trans. Signal Process., vol.55, no.5, pp. 2310-2322, May 2007.
31. E. R. Dougherty and I. Shmulevich, "Mappings between probabilistic boolean networks," Signal Process., vol.83, pp. 799-809, 2003.
32. W. K. Ching, S. Zhang, M. K. Ng, and T. Akutsu, "An approximation method for solving the steady-state probability distribution of probabilistic boolean networks," Bioinformatics, vol.23, pp. 1511-1518, 2007.
33. R. Layek, A. Datta, R. Pal, and E. R. Dougherty, "Adaptive intervention in probabilistic boolean networks," in Proc. Amer. Contr. Conf., accepted for publication.
34. A. Datta, A. Choudhary,M. L. Bittner, and E. R. Dougherty, "External control in Markovian genetic regulatory networks," Mach. Learn., vol.52, pp. 169-191, 2003.
35. A. Datta, A. Choudhary,M. L. Bittner, and E. R. Dougherty, "External control in Markovian genetic regulatory networks: The imperfect information case," Bioinformatics, vol.20, pp. 924-930, 2004.
36. R. Pal, A. Datta, and E. R. Dougherty, "Optimal infinite horizon control for probabilistic Boolean networks," IEEE Trans. Signal Process., vol.54, no.6, pp. 2375-2387, 2006.
37. D. P. Bertsekas, Dynamic Programming and Optimal Control, 2nd ed. Nashua, NH: Athena Scientific, 2001.
38. C. Sawyers, "Targeted cancer therapy," Nature, vol.432, pp. 294-297, 2004.
39. M. R. Green, "Targeting targeted therapy," New Eng. J. Med., vol.350, no.21, pp. 2191-2193, 2004.
40. N. V. Zhukov and S. A. Tjulandin, "Targeted therapy in the treatment of solid tumors: Practice contradicts theory," Biochemistry (Mosc)., vol.73, p. 605-1188, 2008.
41. D. Coppersmith and S.Winograd, "Matrix multiplication via arithmetic progressions," J. Symbol. Comput., vol.9, pp. 251-280, 1990.
42. T. Kailath, Linear Systems. Englewood Cliffs, NJ: Prentice-Hall, 1979.