×
Sun, Yonghui; Wei, Zhinong; Sun, Guoqiang

Positive stability analysis and bio-circuit design for nonlinear biochemical networks. (English) Zbl 1420.92043

Abstr. Appl. Anal. 2013, Article ID 717489, 8 p. (2013).
Summary: This paper is concerned with positive stability analysis and bio-circuits design for nonlinear biochemical networks. A fuzzy interpolation approach is employed to approximate nonlinear biochemical networks. Based on the Lyapunov stability theory, sufficient conditions are developed to guarantee the equilibrium points of nonlinear biochemical networks to be positive and asymptotically stable. In addition, a constrained bio-circuits design with positive control input is also considered. It is shown that the conditions can be formulated as a solution to a convex optimization problem, which can be easily facilitated by using the Matlab LMI control toolbox. Finally, a real biochemical network model is provided to illustrate the effectiveness and validity of the obtained results.

MSC:

92C42 Systems biology, networks
93D20 Asymptotic stability in control theory
93C10 Nonlinear systems in control theory
93C95 Application models in control theory

Keywords:

nonlinear biochemical networks; positive stability; bio-circuit design

Software:

LMI toolbox; Matlab
PDF BibTeX XML Cite
\textit{Y. Sun} et al., Abstr. Appl. Anal. 2013, Article ID 717489, 8 p. (2013; Zbl 1420.92043)
Full Text: DOI

References:

[1] Carson, E. R.; Cobelli, C.; Finkelstein, L., The Mathematical Modeling of Metabolic and Endocrine Systems (1983), New York, NY, USA: John Wiley & Sons, New York, NY, USA
[2] de Jong, H., Modelling and simulation of genetic regulatory systems: a literature review, Journal of Computational Biology, 9, 1, 67-103 (2002)
[3] Hasty, J.; Millen, M.; Collins, J. J., Engineered gene circuits, Nature, 420, 6912, 224-230 (2002)
[4] Sontag, E. D., Molecular systems biology and control, European Journal of Control, 11, 4-5, 396-435 (2005) · Zbl 1293.93571
[5] Klipp, E.; Herwig, R.; Kowald, A.; Wierling, C.; Lehrach, H., Systems Biology in Practice: Concepts, Implementation and Application (2005), New York, NY, USA: John Wiley & Sons, New York, NY, USA
[6] D’haeseleer, P.; Liang, S.; Somogyi, R., Tutorial on gene expression data analysis and modeling, Proceedings of the Pacific Symposium on Biocomputing
[7] Smolen, P.; Baxter, D. A.; Byrne, J. H., Mathematical modeling of gene networks, Neuron, 26, 3, 567-580 (2000)
[8] Wu, F. X.; Zhang, W. J.; Kusalik, A. J., Modeling gene expression from microarray expression data with state-space equations, Pacific Symposium on Biocomputing, 9, 581-592 (2004)
[9] Sun, Y.; Feng, G.; Cao, J., A new approach to dynamic fuzzy modeling of genetic regulatory networks, IEEE Transactions on Nanobioscience, 9, 4, 263-272 (2010)
[10] Xiong, H.; Choe, Y., Structural systems identification of genetic regulatory networks, Bioinformatics, 24, 4, 553-560 (2008)
[11] Angeli, D.; Ferrell, J. E.; Sontag, E. D., Detection of multistability, bifurcations, and hysteresis in a large class of biological positive-feedback systems, Proceedings of the National Academy of Sciences of the United States of America, 101, 7, 1822-1827 (2004)
[12] Keener, J.; Sneyd, J., Mathematical Physiology (1998), New York, NY, USA: Springer, New York, NY, USA · Zbl 0913.92009
[13] Hood, L.; Heath, J. R.; Phelps, M. E.; Lin, B., Systems biology and new technologies enable predictive and preventative medicine, Science, 306, 5696, 640-643 (2004)
[14] Farina, L.; Rinaldi, S., Positive Linear Systems: Theorey and Applications (2000), New York, NY, USA: John Wiley & Sons, New York, NY, USA
[15] Gao, H.; Lam, J.; Wang, C.; Xu, S., Control for stability and positivity: equivalent conditions and computation, IEEE Transactions on Circuits and Systems II, 52, 9, 540-544 (2005)
[16] Rami, M. A.; Tadeo, F., Controller synthesis for positive linear systems with bounded controls, IEEE Transactions on Circuits and Systems II, 54, 2, 151-155 (2007)
[17] Liu, X.; Wang, L.; Yu, W.; Zhong, S., Constrained control of positive discrete-time systems with delays, IEEE Transactions on Circuits and Systems II, 55, 2, 193-197 (2008)
[18] Jacquez, J. A.; Simon, C. P., Qualitative theory of compartmental systems, SIAM Review, 35, 1, 43-79 (1993) · Zbl 0776.92001
[19] Haddad, W. M.; Chellaboina, V., Stability and dissipativity theory for nonnegative dynamical systems: a unified analysis framework for biological and physiological systems, Nonlinear Analysis: Real World Applications, 6, 1, 35-65 (2005) · Zbl 1074.93030
[20] Chen, L.; Aihara, K., Stability of genetic regulatory networks with time delay, IEEE Transactions on Circuits and Systems I, 49, 5, 602-608 (2002) · Zbl 1368.92117
[21] Li, C.; Chen, L.; Aihara, K., Stability of genetic networks with SUM regulatory logic: lur’e system and LMI approach, IEEE Transactions on Circuits and Systems I, 53, 11, 2451-2458 (2006) · Zbl 1374.92045
[22] Li, C.; Chen, L.; Aihara, K., Stochastic stability of genetic networks with disturbance attenuation, IEEE Transactions on Circuits and Systems II, 54, 10, 892-896 (2007)
[23] Ren, F.; Cao, J., Asymptotic and robust stability of genetic regulatory networks with time-varying delays, Neurocomputing, 71, 4-6, 834-842 (2008)
[24] Wang, Z.; Gao, H.; Cao, J.; Liu, X., On delayed genetic regulatory networks with polytopic uncertainties: robust stability analysis, IEEE Transactions on NanoBioscience, 7, 2, 154-163 (2008)
[25] Sun, Y.; Feng, G.; Cao, J., Robust stochastic stability analysis of genetic regulatory networks with disturbance attenuation, Neurocomputing, 79, 39-49 (2012)
[26] Takagi, T.; Sugeno, M., Fuzzy identification of systems and its applications to modeling and control, IEEE Transactions on Systems, Man, and Cybernetics, 15, 1, 116-132 (1985) · Zbl 0576.93021
[27] Chen, B. S.; Chang, Y. T.; Wang, Y. C., Robust H∞-stabilization design in gene networks under stochastic molecular noises: fuzzy-interpolation approach, IEEE Transactions on Systems, Man, and Cybernetics B, 38, 1, 25-42 (2008)
[28] Hasty, J.; Pradines, J.; Dolnik, M.; Collins, J. J., Noise-based switches and amplifiers forgene expression, Proceedings of the National Academy of Sciences of the United States of America, 97, 5, 2075-2080 (2000)
[29] Chen, B. S.; Wu, W. S.; Wang, Y. C.; Li, W. H., On the robust circuit design schemes of biochemical networks: steady-state approach, IEEE Transactions on Biomedical Circuits and Systems, 1, 2, 91-104 (2007)
[30] Chen, B. S.; Chen, P. W., Robust engineered circuit design principles for stochastic biochemical networks with parameter uncertainties and disturbances, IEEE Transactions on Biomedical Circuits and Systems, 2, 2, 114-132 (2008)
[31] Chappell, M. J.; Godfrey, K. R., Structural identifiability of the parameters of a nonlinear batch reactor model, Mathematical Biosciences, 108, 2, 241-251 (1992) · Zbl 0738.92010
[32] Wen, F.; Li, Z.; Xie, C.; Shaw, D., Study on the fractal and chaotic features of the Shanghai composite index, Fractals, 20, 2, 133-140 (2012) · Zbl 1250.91084
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.