TAILIEUCHUNG - Ebook Control theory and systems biology: Part 2
(BQ) Part 2 book "Control theory and systems biology" has contents: A control-theoretic interpretation of metabolic control analysis, structural robustness of biochemical networks, robustness of oscillations in biological systems, a theory of approximation for stochastic biochemical processes,.and other contents. | 8 A Control-Theoretic Interpretation of Metabolic Control Analysis Brian P. Ingalls In this chapter, the main results of metabolic control analysis (MCA) are reinterpreted from the point of view of engineering control theory. To begin, the standard model of metabolic systems is identified as redundant in both state dynamics and input e¤ects. A key feature of these systems is that, whereas the dynamics are typically nonlinear, these redundancies appear linearly, through the stoichiometry matrix. This means that the e¤ect of the input can be linearly decomposed into a component driving the state and a component driving the output. A statement of this separation principle is shown to be equivalent to the main theorems of MCA. Presenting a control-theoretic treatment of stoichiometric systems, the chapter arrives at an alternative derivation of some of the fundamental results in the theory of control of biochemical systems. Background Biochemical mechanisms for implementation of feedback control were first discovered in the biosynthetic pathways of metabolism (Pardee and Reddy, 2003), and it was within the study of metabolism that a quantitative theory of the control and regulation of biochemical networks was first developed. In the 1970s, researchers on both sides of the Atlantic, led by Michael Savageau in the United States and by Henrik Kacser and Reinhart Heinrich in Europe, elucidated theoretical frameworks for addressing issues of regulation in metabolic networks. A fundamental tool used by both groups was local parametric sensitivity analysis, applied primarily at steady state. The European camp, whose theory was dubbed metabolic control analysis (MCA), or sometimes metabolic control theory (MCT), made use of a standard linearization technique in addressing steady state behavior (Heinrich and Rapoport, 1974a,b; Kacser and Burns, 1973). Savageau’s work, known as biochemical systems theory (BST), makes use of a more sophisticated log linearization that .
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