Robust state estimation for stochastic genetic regulatory networks

International Journal of Systems Science

Volumn 41, Issue 1, 2010, Pages 47-63

  Liang, Jinling ^a   Lam, James ^b  

^a SOUTHEAST UNIVERSITY   (China)

^b UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Genetic regulatory networks; Parameter uncertainty; Robust state estimation; State estimation; Stochastic disturbance; Stochastic systems

Indexed keywords

CONCENTRATION OF; DESIGN PROCEDURE; ESTIMATION ERRORS; EXTRACELLULAR; FEEDBACK REGULATION; GENETIC REGULATORY NETWORKS; LINEAR MATRIX INEQUALITY TECHNIQUES; LYAPUNOV-KRASOVSKII FUNCTIONAL METHOD; MODELLING ERROR; NETWORK PARAMETERS; NOISE PERTURBATION; NUMERICAL SOFTWARE; PARAMETER FLUCTUATIONS; PARAMETER UNCERTAINTY; ROBUST STATE ESTIMATION; STATE ESTIMATORS; STOCHASTIC DISTURBANCES; STOCHASTIC STABILITY; SUFFICIENT CONDITIONS; TIME VARYING; TRANSLATION PROCESS;

CONVERGENCE OF NUMERICAL METHODS; ENZYME ACTIVITY; LAWS AND LEGISLATION; LINEAR MATRIX INEQUALITIES; LYAPUNOV FUNCTIONS; STATE ESTIMATION; STOCHASTIC SYSTEMS; TIME VARYING NETWORKS; UNCERTAIN SYSTEMS;

PARAMETER ESTIMATION;

EID: 77649240657     PISSN: 00207721     EISSN: 14645319     Source Type: Journal    
DOI: 10.1080/00207720903141434     Document Type: Article

References (43)

1. Akutsu, T., Miyano, S., and Kuhara, S. (1999), 'Identification of Genetic Networks from a Small Number of Gene Expression Patterns Under the Boolean Network Model', Proceedings of Pacific Symposium on Biocomputing, 4, 17-28.
2. Arkin, A., Ross, J., and McAdams, H.H. (1998), 'Stochastic Kinetic Analysis of Development pathway Bifurcation in Phage -infected Escherichia coli Cells', Genetics, 149, 1633-1648.
3. Beal, M., Falciani, F., Ghahramani, Z., Rangel, C., and Wild, D. (2005), 'A Bayesian Approach to Reconstructing Genetic Regulatory Networks with Hidden Factors', Bioinformatics, 21(3), 349-356.
4. Bolouri, H., and Davidson, E. (2002), 'Modelling Transcriptional Regulatory Networks', BioEssay, 24, 1118-1129.
5. Boyd, S., Ghaoui, L., Feron, E., and Balakrishnan, V. (1994), Linear Matrix Inequalities in System and Control Theory, Philadephia: SIAM.
6. Cao, J., and Ren, F. (2008), 'Exponetial Stability of Discretetime Genetic Regulatory Networks with Delays', IEEE Transactions on Neural Networks, 19, 520-523.
7. Chen, L., and Aihara, K. (2002), 'Stability of Genetic Regulatory Networks with Time Delay', IEEE Transactions on Circuits and Systems-I, 49(5), 602-608.
8. Chen, T., He, H., and Church, G. (1999), 'Modeling Gene Expression with Differential Equations', Proceedings of Pacific Symposium on Biocomputing, 4, 29-40.
9. Cook, D., Gerber, A., and Tapscott, S. (1998), 'Modeling Stochastic Gene Expression: Implications for Haploinsufficiency', Proceedings of the National Academy of Science, USA, 95, 15641-15646.
10. D'haeseleer, P., Liang, S., and Somogyi, R. (2000), 'Genetic Network Inference: from Co-expression Clustering to Reverse Engineering', Bioinformatics, 16(8), 707-726.
11. D'haeseleer, P., Wen, X., Fuhrman, S., and Somogyi, R. (1999), 'Linear Modelling of mRNA Expression Levels During CNS Development and Injury', Proceedings of Pacific Symposium on Biocomputing, 4, 41-52.
12. Eisen, M., Spellman, P., Brown, P., and Botstein, D. (1998), 'Cluster Analysis and Display of Genome-wide Expression Patterns', Proceedings of the National Academy of Science, USA, 95, 14863-14868.
13. Elowitz, M.B., and Leibler, S. (2000), 'A Synthetic Oscillatory Network of Transcriptional Regulators', Nature, 403, 335-338.
14. Hale, J., and Lunel, S.M.V. (1993), Introduction to Functional Differential Equations, Berlin, Germany: Springer.
15. Hoon, M., Imoto, S., Kobayashi, K., Ogasawara, N., and Miyano, S. (2003), 'Infering Gene Regulatory Networks from Time-ordered Gene Expression Data of Bacillus using Differential Equations', Proceedings of Pacific Symposium on Biocomputing, 8, 17-28.
16. Huang, S. (1999), 'Gene Expression Profilling, Genetic Networks, and Cellular States: An Integrating Concept for Tumorigenesis and Drug Discovery', Journal of Molecular Medicine, 77, 469-480.
17. Jong, H. (2002), 'Modeling and Simulation of Genetic Regulatory Systems: A Literature Review', Journal of Computational Biology, 9(1), 67-103.
18. Kellam, P., Liu, X., Martin, N., Orengo, C., Swift, S., and Tucker, A. (2002), 'A Framework for Modelling Virus Gene Expression Data', Intelligent Data Analysis, 6, 265-279.
19. Kushur, H. (1976), Stochastic Stability and Control, New York: Academic Press.
20. Li, C., Chen, L., and Aihara, K. (2006), 'Stability of Genetic Networks with SUM Regulatory Logic: Lur'e System and LMI Approach', IEEE Transactions on Circuits Systems-I, 53(11), 2451-2458.
21. Li, P., Lam, J., and Shu, Z. (in press), 'On the Transient and Steady-state Estimation of Interval genetic Regulatory Networks', IEEE Transactions on Systems, Man and Cybernetics-B .
22. Liang, J., Wang, Z., and Liu, X. (2009), 'State Estimation for Coupled Uncertain Stochastic Networks with Missing Measurements and Time-varying Delays: the Discretetime Case', IEEE Transactions on Neural Networks, 20(5), 781-793.
23. Liu, Y., Wang, Z., and Liu, X. (2008), 'State Estimation for Discrete-time Markovian Jumping Neural Networks with Mixed Mode-dependent Delays', Physics Letters A, 372(48), 7147-7155.
24. Murphy, K., and Mian, S. (1999), 'Modeling Gene Expression Data Using Dynamic Bayesian Networks', Technical Report, Berkeley: University of California.
25. Paulsson, J. (2004), 'Summing up the Noise in Gene Networks', Nature, 427, 415-418.
26. Pease, A.C., Solas, D., Sullivan, E.J., Cronin, M.T., Holmes, C.P., and Fodor, S.P. (1994), 'Light-generated Oligonucleotide Arrays for Rapid DNA Sequence Analysis', Proceedings of the National Academy of Sciences of the USA, 91(11), 5022-5026.
27. Rangel, C., Angus, J., Ghahramani, Z., Lioumi, M., Sotheran, E., Gaiba, A., Wild, D., and Falciani, F. (2004), 'Modeling T-cell Activation Using Gene Expression Profilling and State Space Models', Bioinformatics, 20(9), 1361-1372.
28. Raser, J.M., and O'Shea, E.K. (2005), 'Noise in Gene Expression: Origins, Consequences, and Control', Science, 309, 2010-2013.
29. Ren, F., and Cao, J. (2008), 'Asymptotic and Robust Stability of Genetic Regulatory Networks with Timevarying Delays', Neurocomputing, 71, 834-842. (Pubitemid 351168429)
30. Shen, B., Wang, Z., Shu, H., and Wei, G. (2008), 'On Nonlinear H1 Filtering for Discrete-time Stochastic Systems with Missing Measurements', IEEE Transactions on Automatic Control, 53(9), 2170-2180.
31. Smolen, P., Baxter, D., and Byrne, J. (2000), 'Mathematical Modelling of Genetics Networks Review', Neuron, 26(3), 567-580.
32. Tamayo, P., Slonim, D., Mesirov, J., Zhu, Q., Kitareewan, S., Dmitrovsky, E., Lander, E.S., and Golub, T.R. (1999), 'Interpreting Patterns of Gene Expression with Selforganizing Maps: Methods and Application to Hematopoietic Differentiation', Proceedings of the National Academy of Science, USA, 96, 2907-2912.
33. Tian, T., and Burrage, K. (2003), 'Stochastic Neural Network Models for Gene Regulatory Networks', Proceedings of IEEE Congress on Evolutionary Computation, 1, 162-169.
34. Wang, Z. (2000), 'Robust State Estimation for Perturbed Systems with Error Variance and Circuits Pole Constraints: The Continuous-time Case', International Journal of Control, 73(4), 303-311.
35. Wang, Z., Gao, H., Cao, J., and Liu, X. (2008), 'On Delayed Genetic Regulatory Networks with Polytopic Uncertainties: Robust Stability Analysis', IEEE Transactions on NanoBioscience, 7(2), 154-163. (Pubitemid 351835963)
36. Wang, Z., Ho, D.W.C., and Liu, X. (2005), 'State Estimation for Delayed Neural Networks', IEEE Transactions on Neural Networks, 16(1), 279-284.
37. Wang, Z., Lam, J., Wei, G., Fraser, F., and Liu, X. (2008), 'Filtering for Nonlinear Genetic Regulatory Networks with Stochastic Disturbances', IEEE Transactions on Automatic Control, 53(10), 2448-2457.
38. Wang, Z., Liu, Y., and Liu, X. (2009), 'State Estimation for Jumping Recurrent Neural Networks with Discrete and Distributed Delays', Neural Networks, 22(1), 41-48.
39. Wang, Z., Yang, F., Ho, D.W.C., Swift, S., Tucker, A., and Liu, X. (2008), 'Stochastic Dynamic Modelling of Short Gene Expression Time Series Data', IEEE Transactions on NanoBioscience, 7(1), 44-55.
40. Wei, G., Wang, Z., Shu, H., Karl, F., and Liu, X. (2007), 'Robust Filtering for Gene Expression Time Series Data with Variance Constraints', International Journal Computer Mathematics, 84(5), 619-633.
41. Wu, F., Zhang, W., and Kusalik, A. (2004), 'Modeling Gene Expression From Microarray Expression Data with State-space Equations', Proceedings of Pacific Symposium on Biocomputing, 9, 581-592.
42. Xiong, J., and Lam, J. (2009), 'Robust H2 Control of Markovian Jump Systems with Uncertain Switching Probabilities', International Journal of Systems Science, 40(3), 255C265.
43. Yuh, C.H., Bolouri, H., and Davidson, E.H. (1998), 'Genetic Cis-regulatory Logic: Experimental and Computational Analysis of a Sea Urchin Gene', Science, 279, 1896-1902.