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Mathematical Biosciences and Engineering

2007, Volume 4, Issue 3: 471-488. doi: 10.3934/mbe.2007.4.471
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A theoretic control approach in signal-controlled metabolic pathways

  • 1.
    Department of Mathematics, University of Central Arkansas, 201 Donaghey Avenue, Conway, AR 72035
  • 2.
    Department of Biology, University of Central Arkansas, 201 Donaghey Avenue, Conway, AR 72035
  • Received: 01 August 2006 Accepted: 29 June 2018 Published: 01 May 2007

  • MSC : 92C45, 92C40, 93D20, 34D05.

  • Cells use a signal transduction mechanism to regulate certain metabolic pathways. In this paper, the regulatory mechanism is analyzed mathematically. For this analysis, a mathematical model for the pathways is first established using a system of differential equations. Then the linear stability, controllability, and observability of the system are investigated. We show that the linearized system is controllable and observable, and that the real parts of all eigenvalues of the linearized system are nonpositive using Routh's stability criterion. Controllability and observability are structural properties of a dynamical system. Thus our results may explain why the metabolic pathways can be controlled and regulated. Finally observer-based and proportional output feedback controllers are designed to regulate the end product to its desired level. Applications to the regulation of blood glucose levels are discussed.

    Citation: Ramesh Garimella, Uma Garimella, Weijiu Liu. A theoretic control approach in signal-controlled metabolic pathways[J]. Mathematical Biosciences and Engineering, 2007, 4(3): 471-488. doi: 10.3934/mbe.2007.4.471

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  • Cells use a signal transduction mechanism to regulate certain metabolic pathways. In this paper, the regulatory mechanism is analyzed mathematically. For this analysis, a mathematical model for the pathways is first established using a system of differential equations. Then the linear stability, controllability, and observability of the system are investigated. We show that the linearized system is controllable and observable, and that the real parts of all eigenvalues of the linearized system are nonpositive using Routh's stability criterion. Controllability and observability are structural properties of a dynamical system. Thus our results may explain why the metabolic pathways can be controlled and regulated. Finally observer-based and proportional output feedback controllers are designed to regulate the end product to its desired level. Applications to the regulation of blood glucose levels are discussed.


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