Robust H∞-stabilization design in gene networks under stochastic molecular noises: Fuzzy-interpolation approach

IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics

Volumn 38, Issue 1, 2008, Pages 25-42

  Chen, Bor Sen ^a   Chang, Yu Te ^a   Wang, Yu Chao ^a  

^a NATIONAL TSING HUA UNIVERSITY   (Taiwan)

Author keywords

Fuzzy approximation; Gene circuit design; Gene network; Molecular noise; Robust H filtering; Robust H stabilization

Indexed keywords

GENES; INTERPOLATION; LINEAR MATRIX INEQUALITIES; ROBUSTNESS (CONTROL SYSTEMS); STOCHASTIC MODELS; SYSTEM STABILITY;

GENE CIRCUIT DESIGN; GENE NETWORK; MOLECULAR NOISE;

SIGNAL FILTERING AND PREDICTION;

PROTEOME;

ARTICLE; BIOLOGICAL MODEL; COMPUTER SIMULATION; FUZZY LOGIC; GENE EXPRESSION; METABOLISM; PHYSIOLOGY; SIGNAL TRANSDUCTION; STATISTICAL MODEL; STATISTICS;

COMPUTER SIMULATION; FUZZY LOGIC; GENE EXPRESSION; MODELS, BIOLOGICAL; MODELS, STATISTICAL; PROTEOME; SIGNAL TRANSDUCTION; STOCHASTIC PROCESSES;

EID: 39649116670     PISSN: 10834419     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSMCB.2007.906975     Document Type: Article

References (63)

1. C. V. Rao, M. Wolf, and A. P. Arkin, "Control, exploitation and tolerance of intracellular noise," Nature, vol. 420, no. 6912, pp. 231-237, Nov. 2002.
2. O. G. Berg, "A model for the statistical fluctuations of protein numbers in a microbial population," J. Theor. Biol., vol. 71, no. 4, pp. 587-603, Apr. 1978.
3. M. S. Ko, "A stochastic model for gene induction," J. Theor. Biol. vol. 153, no. 2, pp. 181-194, Nov. 1991.
4. H. H. McAdams and A. P. Arkin, "Stochastic mechanisms in gene expression," Proc. Nat. Acad. Sci., vol. 94, no. 3, pp. 814-819, Feb. 1997.
5. J. Hasty, D. McMillen, and J. J. Collins, "Engineered gene circuits," Nature, vol. 420, no. 6912, pp. 224-230, Nov. 14, 2002.
6. C. W. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry, and the Natural Sciences. Berlin, Germany: Springer-Verlag, 1990.
7. R. Z. Has'minskii, Stochastic Stability of Differential Equations. Alphen, Sweden: Sijthoff and Noordhoff, 1980.
8. D. T. Gillespie, "Exact stochastic simulation of coupled chemical reactions," J. Phys. Chem., vol. 81, no. 25, pp. 2340-2361, Jan. 1977.
9. N. Le Novere and T. S. Shimizu, "STOCHSIM: Modelling of stochastic biomolecular processes," Bioinformatics, vol. 17, no. 6, pp. 575-576, Jun. 2001.
10. T. S. Shimizu and D. Bray, Foundations of Systems Biology, H. Kitano, Ed. Cambridge, MA: MIT Press, 2001, pp. 213-232.
11. D. T. Gillespie, "Approximate accelerated stochastic simulation of chemically reacting systems," J. Chem. Phys., vol. 115, no. 4, pp. 1716-1733, Jul. 2001.
12. M. A. Gibson and J. Bruck, "Efficient exact stochastic simulation of chemical systems with many species and many channels," J. Phys. Chem. A, vol. 104, no. 9, pp. 1876-1889, 2000.
13. E. I. Haseltine and J. B. Rawlings, "Approximate simulation of coupled fast and slow reactions for stochastic chemical kinetics," J. Chem. Phys., vol. 117, no. 15, pp. 6959-6969, Oct. 2002.
14. M. Thattai and A. Van Oudenaarden, "Intrinsic noise in gene regulatory networks," Proc. Nat. Acad. Sci., vol. 98, no. 15, pp. 8614-8619, Jul. 2001.
15. T. S. Kepler and T. C. Elston, "Stochasticity in transcriptional regulation: Origins, consequences, and mathematical representations," Biophys J., vol. 81, no. 6, pp. 3116-3136, Dec. 2001.
16. E. M. Ozbudak, M. Thattai, I. Kurtser, A. D. Grossman, and A. Van Oudenaarden, "Regulation of noise in the expression of a single gene," Nat. Genet., vol. 31, no. 1, pp. 69-73, May 2002.
17. M. B. Elowitz, A. J. Levine, E. D. Siggia, and P. S. Swain, "Stochastic gene expression in a single cell," Science, vol. 297, no. 5584, pp. 1183-1186, Aug. 2002.
18. A. P. Arkin, Self-Organized Biological Dynamics and Nonlinear Control J. Walleczek, Ed. London, U.K.: Cambridge Univ. Press, 2000, pp. 112-144.
19. M. Samoilov, A. Arkin, and J. Ross, "Signal processing by simple chemical systems," J. Phys. Chem. A, vol. 106, no. 43, pp. 10205-10221, 2002.
20. P. B. Detwiler, S. Ramanathan, A. Sengupta, and B. I. Shraiman, "Engineering aspects of enzymatic signal transduction: Photoreceptors in the retina," Biophys. J., vol. 79, no. 6, pp. 2801-2817, Dec. 2000.
21. M. Thattai and A. Van Oudenaarden, "Attenuation of noise in ultrasensitive signaling cascades," Biophys. J., vol. 82, no. 6, pp. 2943-2950, Jun. 2002.
22. P. Smolen, D. A. Baxter, and J. H. Byrne, "Modeling transcriptional control in gene networks-methods, recent results, and future directions," Bull. Math. Biol., vol. 62, no. 2, pp. 247-292, Feb. 2000.
23. D. Fell, Understanding the Control of Metabolism. London, U.K.: Portland, 1997.
24. R. Heinrich and S. Schuster, The Regulation of Cellular System. London, U.K.: Portland, 1996.
25. B. S. Chen and Y. C. Wang, "On the attenuation and amplification of molecular noise in gene regulatory networks," BMC Bioinf., vol. 7, no. 52, pp. 1-14, 2006.
26. H. H. McAdams and A. Arkin, "It is a noisy business! Genetic regulation at the nanomolar scale," Trends Genet., vol. 15, no. 2, pp. 65-69, Feb. 1999.
27. J. Hasty, J. Pradines, M. Dolnik, and J. J. Collins, "Noise-based switches and amplifiers for gene expression," Proc. Nat. Acad. Sci. vol. 97, no. 5, pp. 2075-2080, Feb. 2000.
28. T. M. Yi, Y. Huang, M. I. Simon, and J. Doyle, "Robust perfect adaptation in bacterial chemotaxis through integral feedback control," Proc. Nat. Acad. Sci., vol. 97, no. 9, pp. 4649-4653, Apr. 2000.
29. D. M. Wolf and A. P. Arkin, "Fifteen minutes of fim: Control of type 1 pili expression in E. coh," OMICS, vol. 6, no. 1, pp. 91-114, 2002.
30. N. Barkai and S. Leibler, "Circadian clocks limited by noise," Nature, vol. 403, no. 6767, pp. 267-268, Jan. 2000.
31. J. M. Vilar, H. Y. Kueh, N. Barkai, and S. Leibler, "Mechanisms of noise-resistance in genetic oscillators," Proc. Nat. Acad. Sci., vol. 99, no. 9, pp. 5988-5992, Apr. 2002.
32. P. Smolen, D. A. Baxter, and J. H. Byrne, "Modeling circadian oscillations with interlocking positive and negative feedback loops," J. Neurosci., vol. 21, no. 17, pp. 6644-6656, Sep. 2001.
33. J. W. Little, D. P. Shepley, and D. W. Wert, "Robustness of a gene regulatory circuit," EMBO J., vol. 18, no. 15, pp. 4299-4307, Aug. 1999.
34. M. E. Csete and J. C. Doyle, "Reverse engineering of biological complexity," Science, vol. 295, no. 5560, pp. 1664-1669, Mar. 2002.
35. ∞ control problems," IEEE Trans. Autom. Control, vol. 34, no. 8, pp. 831-847, Aug. 1989.
36. B. S. Chen, Y. C. Wang, W. S. Wu, and W. H. Li, "A new measure of the robustness of biochemical networks," Bioinformatics, vol. 21, no. 11, pp. 2698-2705, Jun. 2005.
37. ∞ filtering for non-linear stochastic systems," IEEE Trans. Signal Process., vol. 53, no. 2, pp. 589-598, Feb. 2005.
38. ∞ filters for equalization designs of nonlinear communication systems: Fuzzy interpolation approach," IEEE Trans. Fuzzy Syst., vol. 11, no. 3, pp. 384-398, Jun. 2003.
39. ∞ filtering design in multirate transmultiplexer systems: LMI approach," IEEE Trans. Signal Process., vol. 49, no. 11, pp. 2693-2701, Nov. 2001.
40. ∞ control with state-dependent noise," IEEE Trans. Autom. Control, vol. 49, no. 1, pp. 45-57, Jan. 2004.
41. ∞ control for nonlinear stochastic systems," SIAM J. Control Optim., vol. 44, no. 6, pp. 1973-1991, 2006.
42. K. M. Passino and S. Yurkovich, Fuzzy Control. Menlo Park, CA: Addison-Wesley, 1998.
43. B. S. Chen, C. S. Tseng, and H. J. Uang, "Robustness design of nonlinear dynamic systems via fuzzy linear control," IEEE Trans. Fuzzy Syst., vol. 7, no. 5, pp. 571-585, Oct. 1999.
44. S. P. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory. Philadelphia, PA: SIAM, 1994.
45. M. A. Savageau, Biochemical Systems Analysis: A Study of Function and Design in Molecular Biology. Reading, MA: Addison-Wesley, 1976.
46. E. O. Voit, Computational Analysis of Biochemical Sysems: A Practical Guide for Biochemists and Molecular Biologists. Cambridge, U.K.: Cambridge Univ. Press, 2000.
47. J.-J. E. Slotine and W. Li, Applied Nonlinear Control. Englewood Cliffs, NJ: Prentice-Hall, 1991.
48. W. S. Hlavacek and M. A. Sauageau, "Rules for coupled expression of regulator and effector genes in inducible circuits," J. Mol. Biol. vol. 255, no. 1, pp. 121-139, Jan. 1996.
49. S. R. Veflingstand, J. Almeida, and E. O. Voit, "Priming nonlinear searches for pathway indentification," Theor. Biol. Med. Model, vol. 1, pp. 8-20, 2004.
50. S. Kikuchi, D. Tominaga, M. Arita, K. Takahashi, and M. Tomita, "Dynamic modeling of genetic networks using genetic algorithm and S-system," Bioinformatics, vol. 19, no. 5, pp. 643-650, Mar. 2003.
51. J. H. Schwacke and E. O. Voit, "Computation and analysis of time-dependent sensitivities in generalized mass action systems," J. Theor. Biol., vol. 236, no. 1, pp. 21-38, Sep. 2005.
52. E. O. Voit, "Design principles and operating principles: The yin and yang of optimal functioning," Math. Biosci., vol. 182, no. 1, pp. 81-92, Mar. 2003.
53. E. Klipp, R. Herwig, A. Kowald, C. Wierling, and H. Lehrach, Systems Biology in Practice: Concepts, Implementation and Application. Hoboken, NJ: Wiley, 2005.
54. N. G. Coplland, N. A. Jenkins, and D. L. Court, "Recombineering: A powerful new tool for mouse functional genomics," Nat. Rev. Genet. vol. 2, no. 10, pp. 769-779, Oct. 2001.
55. D. L. Court, J. A. Sawitzke, and L. C. Thomason, "Genetic engineering using homologous recombination," Annu. Rev. Genet., vol. 36, pp. 361-388, 2002.
56. T. Takagi and M. Sugeno, "Fuzzy identification of systems and its applications to modeling and control," IEEE Trans. Syst., Man, Cybern., vol. SMC-15, no. 1, pp. 116-132, Jan./Feb. 1985.
57. L. Hood, J. R. Heath, M. E. Phelps, and B. Lin, "Systems biology and new technologies enable predictive and preventative medicine," Science, vol. 306, no. 5696, pp. 640-643, Oct. 2004.
58. 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, Jun. 2006.
59. A. Datta, R. Pal, A. Choudhary, and E. R. Dougherty, "Control approaches for probabilistic gene regulatory networks," IEEE Signal Process. Mag., vol. 24, no. 1, pp. 54-63, Jan. 2007.
60. M. Chaves, E. D. Sontag, and R. Albert, "Methods of robustness analysis for Boolean models of gene control networks," Proc. Inst. Electr. Eng. - Systems Biology, vol. 153, no. 4, pp. 154-167, Jul. 2006.
61. K. Y. Tsai and F. S. Wang, "Evolutionary optimization with data collocation for reverse engineering of biological networks," Bioinformatics, vol. 21, no. 7, pp. 1180-1188, Apr. 2005.
62. H. C. Chen, H. C. Lee, T. Y. Lin, W. H. Li, and B. S. Chen, "Quantitative characterization of transcriptional regulatory network in the yeast cell cycle," Bioinfonnatics, vol. 20, no. 12, pp. 1914-1927, Aug. 2004.
63. B. S. Chen and C. W. Li, "Analyzing microarray data in drug discovery using systems biology," Expert Opin. Drug Discovery, vol. 2, no. 5, pp. 755-768, 2007.