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Intervention in Biological Phenomena via Feedback Linearization

DOI: 10.1155/2012/534810

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Abstract:

The problems of modeling and intervention of biological phenomena have captured the interest of many researchers in the past few decades. The aim of the therapeutic intervention strategies is to move an undesirable state of a diseased network towards a more desirable one. Such an objective can be achieved by the application of drugs to act on some genes/metabolites that experience the undesirable behavior. For the purpose of design and analysis of intervention strategies, mathematical models that can capture the complex dynamics of the biological systems are needed. S-systems, which offer a good compromise between accuracy and mathematical flexibility, are a promising framework for modeling the dynamical behavior of biological phenomena. Due to the complex nonlinear dynamics of the biological phenomena represented by S-systems, nonlinear intervention schemes are needed to cope with the complexity of the nonlinear S-system models. Here, we present an intervention technique based on feedback linearization for biological phenomena modeled by S-systems. This technique is based on perfect knowledge of the S-system model. The proposed intervention technique is applied to the glycolytic-glycogenolytic pathway, and simulation results presented demonstrate the effectiveness of the proposed technique. 1. Introduction Biological systems are complex processes with nonlinear dynamics. S-systems are proposed in [1, 2] as a canonical nonlinear model to capture the dynamical behavior of a large class of biological phenomena [3, 4]. They are characterized by a good tradeoff between accuracy and mathematical flexibility [5]. In this modeling approach, nonlinear systems are approximated by products of power-law functions which are derived from multivariate linearization in logarithmic coordinates. It has been shown that this type of representation is a valid description of biological processes in a variety of settings. S-systems have been proposed in the literature to mathematically capture the behavior of genetic regulatory networks [6–13]. Moreover, the problem of estimating the S-system model parameters, the rate coefficients and the kinetic orders, has been addressed by several researchers [12, 14–16]. In [17], the authors studied the controllability of S-systems based on feedback linearization approach. Recently, the authors in [18] developed two different intervention strategies, namely, indirect and direct, for biological phenomena modeled by S-systems. The goal of these intervention strategies is to transfer the target variables from an initial steady-state level

References

[1]  M. A. Savageau, “Biochemical systems analysis. I. Some mathematical properties of the rate law for the component enzymatic reactions,” Journal of Theoretical Biology, vol. 25, no. 3, pp. 365–369, 1969.
[2]  E. O. Voit, Canonical Nonlinear Modeling: S-System Approach to Understanding Complexity, Van Nostrand/Reinhold, New York, NY, USA, 1991.
[3]  E. O. Voit, “A systems-theoretical framework for health and disease: inflammation and preconditioning from an abstract modeling point of view,” Mathematical Biosciences, vol. 217, no. 1, pp. 11–18, 2009.
[4]  E. O. Voit, F. Alvarez-Vasquez, and Y. A. Hannun, “Computational analysis of sphingolipid pathway systems,” Advances in Experimental Medicine and Biology, vol. 688, pp. 264–275, 2010.
[5]  R. Gentilini, “Toward integration of systems biology formalism: the gene regulatory networks case,” Genome informatics. International Conference on Genome Informatics., vol. 16, no. 2, pp. 215–224, 2005.
[6]  E. O. Voit and J. Almeida, “Decoupling dynamical systems for pathway identification from metabolic profiles,” Bioinformatics, vol. 20, no. 11, pp. 1670–1681, 2004.
[7]  I. C. Chou, H. Martens, and E. O. Voit, “Parameter estimation in biochemical systems models with alternating regression,” Theoretical Biology and Medical Modelling, vol. 3, article 25, 2006.
[8]  T. Kitayama, A. Kinoshita, M. Sugimoto, Y. Nakayama, and M. Tomita, “A simplified method for power-law modelling of metabolic pathways from time-course data and steady-state flux profiles,” Theoretical Biology and Medical Modelling, vol. 3, article 24, 2006.
[9]  L. Qian and H. Wang, “Inference of genetic regulatory networks by evolutionary algorithm and H∞ filtering,” in Proceedings of the IEEE/SP 14th WorkShoP on Statistical Signal Processing (SSP '07), pp. 21–25, August 2007.
[10]  J. Vera, R. Curto, M. Cascante, and N. V. Torres, “Detection of potential enzyme targets by metabolic modelling and optimization: application to a simple enzymopathy,” Bioinformatics, vol. 23, no. 17, pp. 2281–2289, 2007.
[11]  H. Wang, L. Qian, and E. R. Dougherty, “Steady-state analysis of genetic regulatory networks modeled by nonlinear ordinary differential equations,” in Proceedings of the IEEE Symposium on Computational Intelligence in Bioinformatics and Computational Biology (CIBCB '09), pp. 182–185, April 2009.
[12]  H. Wang, L. Qian, and E. Dougherty, “Inference of gene regulatory networks using S-system: a unified approach,” IET Systems Biology, vol. 4, no. 2, pp. 145–156, 2010.
[13]  A. Marin-Sanguino, S. K. Gupta, E. O. Voit, and J. Vera, “Biochemical pathway modeling tools for drug target detection in cancer and other complex diseases,” Methods in Enzymology, vol. 487, pp. 319–369, 2011.
[14]  O. R. Gonzalez, C. Küper, K. Jung, P. C. Naval, and E. Mendoza, “Parameter estimation using simulated annealing for S-system models of biochemical networks,” Bioinformatics, vol. 23, no. 4, pp. 480–486, 2007.
[15]  Z. Kutalik, W. Tucker, and V. Moulton, “S-system parameter estimation for noisy metabolic profiles using Newton-flow analysis,” IET Systems Biology, vol. 1, no. 3, pp. 174–180, 2007.
[16]  I. C. Chou and E. O. Voit, “Recent developments in parameter estimation and structure identification of biochemical and genomic systems,” Mathematical Biosciences, vol. 219, no. 2, pp. 57–83, 2009.
[17]  A. Ervadi-Radhakrishnan and E. O. Voit, “Controllability of non-linear biochemical systems,” Mathematical Biosciences, vol. 196, no. 1, pp. 99–123, 2005.
[18]  N. Meskin, H. N. Nounou, M. Nounou, A. Datta, and E. R. Dougherty, “Intervention in biological phenomena modeled by S-systems,” IEEE Transactions on Biomedical Engineering, vol. 58, no. 5, pp. 1260–1267, 2011.
[19]  A. G. Hernández, L. Fridman, A. Levant, Y. Shtessel, S. I. Andrade, and C. R. Monsalve, “High order sliding mode controller for blood glucose in type 1 diabetes, with relative degree fluctuations,” in Proceedings of the 11th International Workshop on Variable Structure Systems (VSS '10), pp. 416–421, June 2010.
[20]  A. Isidori, A. J. Krener, C. Gori-Giorgi, and S. Monaco, “Nonlinear decoupling via feedback: a differential geometric approach,” IEEE Transactions on Automatic Control, vol. 26, no. 2, pp. 331–345, 1981.
[21]  A. Isidori, Nonlinear Control Systems, Springer, 1989.
[22]  A. Isidori and M. D. Benedetto, Feedback Linearization of Nonlinear Systems, Taylor Francis Group-CRC Press, 2010.
[23]  T. L. Chien, C. C. Chen, and C. J. Huang, “Feedback linearization control and its application to MIMO cancer immunotherapy,” IEEE Transactions on Control Systems Technology, vol. 18, no. 4, pp. 953–961, 2010.
[24]  B. Jakubczyk and W. Respondek, “On linearization of control systems,” Bulletin de l'Académie Polonaise des Sciences, Série des Sciences Mathématiques, vol. 28, pp. 517–522, 1980.
[25]  E. O. Voit, Computational Analysis of Biochemical Systems. A Practical Guide for Biochemists and Molecular Biologists, Cambridge University Press, 2000.
[26]  J. J. E. Slotine and W. Li, Applied Nonlinear Control, Pearson Education, 1991.
[27]  S. Sastry, Nonlinear Systems: Analysis, Stability and Control, Springer, 1999.
[28]  R. Marino and P. Tomei, “Global adaptive output-feedback control of nonlinear systems, part II. Nonlinear parameterization,” IEEE Transactions on Automatic Control, vol. 38, no. 1, pp. 33–48, 1993.
[29]  N. V. Torres, “Modelization and experimental studies on the control of the glycolytic- glycogenolytic pathway in rat liver,” Molecular and Cellular Biochemistry, vol. 132, no. 2, pp. 117–126, 1994.

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