Garimella Ramesh, Garimella Uma, Liu Weijiu
Department of Mathematics, University of Central Arkansas, 201 Donaghey Avenue, Conway, AR 72035, USA.
Math Biosci Eng. 2007 Jul;4(3):471-88. doi: 10.3934/mbe.2007.4.471.
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 path ways can be controlled and regulated. Finally observer-based and proportional output feedback controllers are designed to regulate the end product to its de sired level. Applications to the regulation of blood glucose levels are discussed.
细胞利用信号转导机制来调节某些代谢途径。在本文中，对该调节机制进行了数学分析。为了进行此分析，首先使用微分方程组为这些途径建立了一个数学模型。然后研究了该系统的线性稳定性、可控性和可观测性。我们表明线性化系统是可控且可观测的，并且使用劳斯稳定性判据可知线性化系统所有特征值的实部均为非正。可控性和可观测性是动态系统的结构特性。因此我们的结果可能解释了代谢途径为何能够被控制和调节。最后设计了基于观测器的比例输出反馈控制器，以将终产物调节到其期望水平。还讨论了在血糖水平调节方面的应用。
