From boolean to probabilistic boolean networks as models of genetic regulatory networks

Proceedings of the IEEE

Volumn 90, Issue 11, 2002, Pages 1778-1792

  Shmulevich, Ilya ^a,b   Dougherty, Edward R ^c,d,e,f   Zhang, Wei ^b,g  

^a IEEE   (United States)

^b UNIVERSITY OF TEXAS   (United States)

^c TEXAS A AND M UNIVERSITY   (United States)

^d Genomic Signal Processing Laboratory   (United States)

^e UNIVERSITY OF TEXAS MD ANDERSON CANCER CENTER   (United States)

^f NATIONAL INSTITUTES OF HEALTH   (United States)

^g National Institutes of Health ^*

Author keywords

Attractor; Best fit extension; Boolean nehvork; Cell differentiation; Coefficient of determination; Consistency problem; Gene; Genetic nehvork; Influence; Markov chain; Microarray; Nonlinear filter; Probabilistic boolean network; Root signal

Indexed keywords

BOOLEAN ALGEBRA; COMPUTATIONAL COMPLEXITY; GENES; MARKOV PROCESSES; MATHEMATICAL MODELS; PERTURBATION TECHNIQUES; SIGNAL PROCESSING;

ATTRACTOR; BEST-FIT EXTENSION; CELL DIFFERENTIATION; COEFFICIENT OF DETERMINATION; CONSISTENCY PROBLEM; INFLUENCE; MICROARRAY; NONLINEAR FILTER; PROBABILISTIC BOOLEAN NETWORK; ROOT SIGNAL;

GENETIC ENGINEERING;

EID: 0345983657     PISSN: 00189219     EISSN: None     Source Type: Journal    
DOI: 10.1109/JPROC.2002.804686     Document Type: Article

References (102)

1. M. Schena, D. Shalon, R. W. Davis, and P. O. Brown, "Quantitative monitoring of gene expression patterns with a complementary DNA microarray," Science, vol. 270, pp. 467-470, 1995.
2. J. E. Cells, M. Kruhøffer, I. Gromova, C. Frederiksen, M. Østergaard, T. Thykjaer, P. Gromov, J. Yu, H. Pálsdóttir, N. Magnusson, and T. F. Ørntoft, "Gene expression profiling: Monitoring transcription and translation products using DNA microarrays and proteomics," FEES Lett., vol. 480, no. 1, pp. 2-16, 2000.
3. T. R. Hughes, M. Mao, A. R. Jones, J. Burchard, M. J. Marton, K. W. Shannon, S. M. Lefkowitz, M. Ziman, J. M. Schelter, M. R. Meyer, S. Kobayashi, C. Davis, H. Dai, Y. D. He, S. B. Stephaniants, G. Cavet, W. L. Walker, A. West, E. Coffey, D. D. Shoemaker, R. Stoughton, A. P. Blanchard, S. H. Friend, and P. S. Linsley, "Expression profiling using microarrays fabricated by an ink-jet oligonucleotide synthesizer," Nature BiotechnoL, vol. 19, pp. 342-347, 2001.
4. R. J. Lipshutz, S. P. A. Fodor, T. R. Gingeras, and D. J. Lockhart, "High density synthetic oligonucleotide arrays," Nature Genetics, vol. 21, pp. 20-24, 1999.
5. D. J. Lockhart and E. A. Winzeler, "Genomics, gene expression and DNA arrays," Nature, vol. 405, pp. 827-836, 2000.
6. T. R. Golub, D. K. Slonim, P. Tamayo, C. Huard, M. Gaasenbeek, J. P. Mesirov, H. Coller, M. L. Loh, J. R. Downing, M. A. Caligiuri, C. D. Bloomfield, and E. S. Lander, "Molecular classification of cancer: Class discovery and class prediction by gene expression monitoring," Science, vol. 286, pp. 531-537, 1999.
7. A. Ben-Dor, L. Bruhn, N. Friedman, I. Nachman, M. Schummer, and Z. Yakhini, "Tissue classification with gene expression profiles," J. Comput. Biol, vol. 7, pp. 559-583, 2000.
8. J. Khan, J. S. Wei, M. Ringner, L. H. Saal, M. Ladanyi, F. Westermann, F. Berthold, M. Schwab, C. R. Antonescu, C. Peterson, and P. S. Meltzer, "Classification and diagnostic prediction of cancers using gene expression profiling and artificial neural networks," Nature Medicine, vol. 7, pp. 673-679, 2001.
9. I. Hedenfalk-, D. Duggan, Y. Chen, M. Radmacher, M. Bittner, R. Simon, P. Meltzer, B. Gusterson, M. Esteller, M. Raffeid, Z. Yakhini, A. Ben-Dor, E. Dougherty, J. Kononen, L. Bubendorf, W. Fehrle, S. Pittaluga, S. Gruvverger, N. Loman, O. Johannsson, H. Olsson, B. Wifond, G. Sauter, O. P. Kallioniemi, A. Borg, and J. Trent, "Gene expression profiles distinguish hereditary breast cancers," New England J. Med., vol. 34, pp.539-548, 2001.
10. M. Anthony and N. Biggs, Computational Learning Theory. Cambridge, U.K.: Cambridge Univ. Press, 1992.
11. L. Ljung, System Identification: Theory for the User. Upper Saddle River, NJ: Prentice-Hall, 1999.
12. P. Smolen, D. Baxter, and J. Byrne, "Mathematical modeling of gene networks," Neuron, vol. 26, pp. 567-580, 2000.
13. J. Hasty, D. McMillen, F. Isaacs, and J. J. Collins, "Computational studies of gene regulatory networks: In numero molecular biology," Nature Reviews Genetics, vol. 2, pp. 268-279, 2001.
14. H. de Jong, "Modeling and simulation of genetic regulatory systems: A literature review,"J. Comput. Biol, vol. 9, no. 1, pp. 69-103, 2002.
15. J. M. Bower and H. Bolouri, Eds., Computational Modeling of Genetic and Biochemical Networks. Cambridge, MA: MIT Press, 2001.
16. S. A. Kauffman, "Metabolic stability and epigenesis in randomly constructed genetic nets," J. Theoret. Biol, vol. 22, pp. 437-467, 1969.
17. _, "Homeostasis and differentiation in random genetic control networks," Nature, vol. 224, pp. 177-178, 1969.
18. K. Glass and S. A. Kauffman, "The logical analysis of continuous, nonlinear biochemical control networks," J. Theoret. Biol., vol. 39, pp. 103-129, 1973.
19. S. A. Kauffman, "The large scale structure and dynamics of genetic control circuits: an ensemble approach," J. Theoret. Biol., vol. 44, pp. 167-190, 1974.
20. _, The Origins of Order: Self-Organization and Selection in Evolution. New York: Oxford Univ. Press, 1993.
21. S. Huang, "Gene expression profiling, genetic networks, and cellular states: An integrating concept for tumorigenesis and drug discovery," J. Mol. Med., vol. 77, pp. 469-480, 1999.
22. R. Somogyi and C. Sniegoski, "Modeling the complexity of gene networks: Understanding multigenic and pleiotropic regulation," Complexity, vol. 1, pp. 45-63, 1996.
23. C.-H. Yuh, H. Bolouri, and E. H. Davidson, "Genomic cis-regulatory logic: Experimental and computational analysis of a sea urchin gene," Science, vol. 279, pp. 1896-1902, 1998.
24. J. W. Bodnar, "Programming the Drosophila embryo," J. Theoret. Biol., vol. 188, pp. 391-445, 1997.
25. L. Mendoza, D. Thieffry, and E. R. Alvarez-Buylla, "Genetic control of flower morphogenesis in Arabidopsis thaliana: A logical analysis," Bioinfonnat., vol. 15, pp. 593-606, 1999.
26. S. Huang and D. E. Ingber, "Shape-dependent control of cell growth, differentiation, and apoptosis: Switching between attractors in cell regulatory networks," Exp. Cell Res., vol. 261, no. 1, pp. 91-103, 2000.
27. I. Shmulevich and W. Zhang, "Binary analysis and optimizationbased normalization of gene expression data," Bioinformatics, vol. 18, no. 4, pp. 555-565, 2002.
28. Y. Chen, E. R. Dougherty, and M. Bittner, "Ratio-based decisions and the quantitative analysis of cDNA microarray images," Blamed. Opt., vol. 2, pp. 364-374, 1997.
29. M. K. Kerr, E. H. Leiter, L. Picard, and G. A. Churchill, "Sources of variation in microarray experiments," in Computational and Statistical Approaches to Genomics, W. Zhang and I. Shmulevich, Eds. Boston, MA: Kluwer, 2002.
30. H. H. McAdams and A. Arkin, "It's a noisy business! Genetic regulation at the nanomolar scale," Trends in Genetics, vol. 15, pp. 65-69, 1999.
31. 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," in Proc. Pacific Symp. Biocomputing 3, 1998, pp. 66-76.
32. A. Wuensche, "Genomic regulation modeled as a network with basins of attraction," in Proc. Pacific Symp. Biocomputing, vol. 3, 1998, pp. 89-102.
33. R. Thomas, D. Thieffry, and M. Kaufman, "Dynamical behavior of biological 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.
34. 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, no. 2, pp. 261-274, 2002.
35. A. L. Cartel and A. L. Tyner, "Transcriptional regulation of the ' p21(WAFl/CIPl) gene," Exp. Cell Res, vol. 246, no. 2, pp. 280-289, 1999.
36. E. Schneider, M. Montenarh, and P. Wagner, "Regulation of CAK kinase activity by p53," Oncogens, vol. 17, pp. 2733-2741, 1998.
37. J. P. Fitch, E. J. Coyle, and N. C. Gallagher, "Root properties and convergence rates of median filters," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-33, no. 1, pp. 230-240, 1985.
38. P. Wendt, E. Coyle, and N. C. Gallagher, "Stack filters," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-34, pp. 898-911, 1986.
39. N. C. Gallagher and G. L. Wise, "A theoretical analysis of the properties of median filters," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-29, no. 6, 1981.
40. P.-T. Yu and E. J. Coyle, "Convergence behavior and N-roots of stack filters," IEEE Trans. Acoust., Speech, Signal Processing, vol. 38, no. 9, pp. 888-888, 1990.
41. M. Gabbouj, M. P-T., M. Yu, and E. J. Coyle, "Convergence behavior and root signal sets of stack filters," Circuits, Syst., Signal Process., vol. 11, no. 1, pp. 888-888, 1992.
42. Q. Wang, M. Gabbouj, and Y. Neuvo, "Root properties of morphological filters," Signal Processing, vol. 34, pp. 131-148, 1993.
43. J. Serra, Image Analysis and Malhemalical Morphology. London, U.K.: Academic, 1982, vol. 1.
44. E. R. Dougherty, An Introduction to Morphological Image Processing. Bellingham, WA: SPIE, 1992.
45. G. Moran, "On the period-two-property of the majority operator in infinite graphs," Trans. Amer. Math. Soc., vol. 347, no. 5, pp. 1649-1667, 1995.
46. P.-T. Yu and E. J. Coyle, "The classification and associative memory capability of stack filters," IEEE Trans. Acoust., Speech, Signal Processing, vol. 40, no. 10, pp. 2483-2497, 1992.
47. _, "On the existence and design of the best stack filter based associative memory," IEEE Trans. Circuits Syst., vol. 39, no. 3, pp. 171-184, 1992.
48. E. F. Codd, Cellular Automata. New York: Academic, 1968.
49. M. Mitchell, J. P. Crutchfield, and P. T. Hraber, "Evolving cellular automata to perform computations: Mechanisms and impediments," Physica D, vol. 75, pp. 361-391, 1994.
50. F. Jiménez Morales, J. P. Crutchfield, and M. Mitchell, "Evolving two-dimensional cellular automata to perform density classification: A report on work in progress," Parallel Comput., vol. 27, no. 5, pp. 539-553, 2001.
51. A. W. Burks, "Von Neumann's self-reproducing automata," in Essays on Cellular Automata, A. W. Burks, Ed. Champaign, IL: Univ. Illinois Press, 1970, pp. 3-74.
52. J. P. Fitch, E. J. Coyle, and N. C. Gallagher, "Median filtering by threshold decomposition," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-32, no. 6, pp. 1183-1188, 1984.
53. J. H. Holl, Hidden Order: How Adaptation Builds Complexity. Reading, MA: Helix Books, 1995.
54. D. M. Wolf and F. H. Eeckman, "On the relationship between genomic regulatory element organization and gene regulatory dynamics,"J. Theoret. Biol., vol. 195, pp. 167-186, 1998.
55. A. Alberts, D. Bray, J. Lewis, M. Raff, K. Roberts, and J. D. Watson, Molecular Biology of the Cell. New York: Garland, 1983.
56. S. A. Kauffman, At Home in the Universe. New York: Oxford Univ. Press, 1995.
57. P. T. Spellman, G. Sherlock, M. Q. Zhang, V. R. Iyer, K. Anders, M.B. Eisen, P. O. Brown, D. Botstein, and B. Futcher, "Comprehensive identification of cell cycle-regulated genes of the yeast Saccharomyces cerevisiae by microarray hybridization," Mol. Biol. Cell, vol. 9, pp. 3273-3297, 1998.
58. S. Huang, "Genomics, complexity and drug discovery: Insights from Boolean network models of cellular regulation," Pharmacogenomics, vol. 2, no. 3, pp. 203-222, 2001.
59. S. Huang, "Cell state dynamics and tumorigenesis in Boolean regulatory networks," Inter Journal Genetics. MS: 416, [Online]. Available: http://www.interjournal.org.
60. S. Liang, S. Fuhrman, and R. Somogyi, "REVEAL, a general reverse engineering algorithm for inference of genetic network architectures," in Proc. Pacific Symp. Biocomputing 3, 1998, pp. 18-29.
61. T. Akutsu, S. Kuhara, O. Maruyama, and S. Miyano, "Identification of gene regulatory networks by strategic gene disruptions and gene overexpressions," in Proc. 9th Ann. ACM-SIAM Symp. Discrete Algorithms (SODA'98), 1998, pp. 695-702.
62. T. Akutsu, S. Miyano, and S. Kuhara, "Identification of genetic networks from a small number of gene expression patterns under the Boolean network model," in Proc. Pacific Symp. Biocomputing 4, 1999, pp. 17-28.
63. _, "Inferring qualitative relations in genetic networks and metabolic pathways," Bioinformatics, vol. 16, pp. 727-734, 2000.
64. T. E. Ideker, V. Thorsson, and R. M. Karp, "Discovery of regulatory interactions through perturbation: Inference and experimental design," in Proc. Pacific Symp. Biocomputing 5, 2000, pp. 302-313.
65. R. M. Karp, R. Stoughton, and K. Y. Yeung, "Algorithms for choosing differential gene expression experiments," in Proc. RECOMB99 (ACM), 1999, pp. 208-217.
66. Y. Maki, D. Tominaga, M. Okamoto, S. Watanabe, and Y. Eguchi, "Development of a system for the inference of large scale genetic networks," in Proc. Pacific Symp. Biocomputing, vol. 6, 2001, pp. 446-458.
67. K. Noda, A. Shinohara, M. Takeda, S. Matsumoto, S. Miyano, and S. Kuhara, "Finding genetic network from experiments by weighted network model," Genome Informatics, vol. 9, pp. 141-150, 1998.
68. I. Shmulevich, A. Saarinen, O. Yli-Harja, and J. Astola, "Inference of genetic regulatory networks under the best-fit extension paradigm," in Computational and Statistical Approaches To Genomics, W. Zhang and I. Shmulevich, Eds. Boston, MA: Kluwer, 2002.
69. L. G. Valiant, "A theory of the learnable," Commun. Assoc. Comput. Mach., vol. 27, pp. 1134-1142, 1984.
70. Y. Crama, P. Hammer, and T. Ibaraki, "Cause-effect relationships and partially defined Boolean functions," Ann. Oper. Res., vol. 16, pp. 299-326, 1988.
71. L. Pitt and L. G. Valiant, "Computational limitations on learning from examples," J. ACM, vol. 35, pp. 965-984, 1988.
72. E. Boros, T. Ibaraki, and K. Makino, "Error-free and best-fit extensions of partially defined Boolean functions," Inform. Computat., vol. 140, pp. 254-283, 1998.
73. I. Shmulevich, M. Gabbouj, and J. Astola, "Complexity of the consistency problem for certain post classes," IEEE Trans. Syst., Man, Cybernet. B, vol. 31, no. 2, pp. 251-253, Apr. 2001.
74. E. J. Coyle and J. H. Lin, "Stack filters and the mean absolute error criterion," IEEE Trans. Acoust., Speech, Signal Processing, vol. 36, no. 8, pp. 1244-1254, Aug. 1988.
75. E. J. Coyle, J. H. Lin, and M. Gabbouj, "Optimal stack filtering and the estimation and structural approaches to image processing," IEEE Trans. Acoust., Speech, Signal Processing, vol. 37, no. 12, pp. 2037-2066, 1989.
76. R. Yang, L. Yin, M. Gabbouj, J. Astola, and Y. Neuvo, "Optimal weighted median filtering under structural constraints," IEEE Trans. Signal Processing, vol. 43, pp. 591-604, Mar. 1995.
77. E. R. Dougherty and R. P. Loce, "Precision of morphological- representation estimators for translation-invariant binary filters: Increasing and nonincreasing," Signal Processing, vol. 40, pp. 129-154, 1994.
78. R. P. Loce and E. R. Dougherty, "Optimal morphological restoration:-The morphological filter mean-absolute-error theorem," Vis. Commun. Image Representation, vol. 3, no. 4, 1992.
79. E. R. Dougherty and J. T. Astola, Nonlinear Filters for Image Processing. Piscataway, NJ: SPIE/IEEE Press, 1999.
80. E. R. Dougherty and Y. Chen, "Optimal and adaptive design of logical granulometric filters," Adv. Imaging Electron Phys., vol. 117, pp. 1-71, 2001.
81. E. R. Dougherty, S. Kim, and Y. Chen, "Coefficient of determination in nonlinear signal processing," Signal Processing, vol. 80, no. 10, pp. 2219-2235, 2000.
82. S. Kim, E. R. Dougherty, Y. Chen, K. Sivakumar, P. Meltzer, J. M. Trent, and M. Bittner, "Multivariate measurement of gene expression relationships," Genomics, vol. 67, pp. 201-209, 2000.
83. S. Kirn, E. R. Dougherty, M. L. Bittner, Y. Chen, K. Sivakumar, P. Meltzer, and J. M. Trent, "General nonlinear framework for the analysis of gene interaction via multivariate expression arrays," J. Biomed. Opt., vol. 5, no. 4, pp. 411-424, 2000.
84. L. L. Scharf, Statistical Signal Processing. Reading, MA: Addison-WesIey, 1991.
85. E. B. Suh, E. R. Dougherty, S. Kim, M. L. Bittner, Y. Chen, D. E. Russ, and R. Martino, "Parallel computation and visualization tools for codetermination analysis of multivariate gene-expression relations," in Computational and Statistical Approaches to Genomics, W. Zhang and I. Shmulevich, Eds. Boston, MA: Kluwer, 2002.
86. S. E. Wildsmith and F. J. Elcock, "Microarrays under the microscope," J. Clin. Pathol: Mol. Pathol., vol. 54, pp. 8-16, 2001.
87. J. Pearl, Probabilistic Reasoning in Intelligent Systems: Nertvorks of Plausible Inference. San Mateo, CA: Morgan Kaufmann, 1997.
88. V. Vapnik, The Nature of Statistical Leaming Theory, 2nded. New York: Springer-Verlag, 2000.
89. I. Tabus and J. Astola, "On the use of the MDL principle in gene expression prediction," J. Appl. Signal Process., vol. 4, pp. 297-303, 2001.
90. I. Tabus, J. Rissanen, and J. Astola, "Normalized maximum likelihood models for Boolean regression with application to prediction and classification in genomics," in Computational and Statistical Approaches to Genomics, W. Zhang and I. Shmulevich, Eds. Boston, MA: Kluwer, 2002.
91. B. Plateau and J-M. Fourneau, "A methodology for solving Markov models of parallel systems," J. Parallel Distrib. Comput., vol. 12, pp. 370-387, 1991.
92. P. L. Hammer, A. Kogan, and U. G. Rothblum, "Evaluation, strength, and relevance of variables of Boolean functions," SIAM J. Discrete Math., vol. 13, no. 3, pp. 302-312, 2000.
93. A. Wagner, "How to reconstruct a large genetic network from n gene perturbations in fewer than n2 easy steps," Bioinformatics, vol. 17, no. 12, pp. 1183-1197, 2001.
94. S. A. Kauffman and S. Levin, 'Toward a general theory of adaptive walks on rugged landscapes," J. Theoret. Biol., vol. 128, pp. 11-45, 1987.
95. D. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning. Reading, MA: Addison-Wesley, 1989.
96. I. Shmulevich, E. R. Dougherty, and W. Zhang, "Gene perturbation and intervention in probabilistic Boolean networks," Bioinformatics, vol. 18, no. 10, pp. 1319-1331, 2002.
97. G. E. Cho and C. D. Meyer, "Markov chain sensitivity measured by mean first passage times," Linear Algebra and Its Applications, vol. 316, pp. 21-28, 2000.
98. T. Kobayashi, S.-B. Ruan, J. R. Jabbur, U. Consoli, K. Clodi, H. Shiku, L. Owen-Schaub, M. Andreeff, J. Reed, and W. Zhang, "Differential p53 phosphorylation and activation of apoptosis-promoting genes Bax and Fas/APO-1 by radiation and ara-C treatment," Cell Death and Differentiation, vol. 5, pp. 584-591, 1998.
99. C. B. Harley, "Telomere loss: Mitotic clock or genetic time bomb?," Mutation Res., vol. 256, pp. 271-282, 1991.
100. I. Shmulevich, E. R. Dougherty, and W. Zhang, "Control of stationary behavior in probabilistic Boolean networks by means of structural intervention," J. Biologic. Syst., to be published.
101. M. D. Stern, "Emergence of homeostasis and noise imprinting in an evolution model," Proc. Nat. Acad. Sciences USA, vol. 96, pp. 10746-10751, 1999.
102. S. Bornholdt and K. Sneppen, "Robustness as an evolutionary principle," Proc. Royal Soc. London B, vol. 266, pp. 2281-2286, 2000.