Ebook Control theory and systems biology: Part 2
➤ Gửi thông báo lỗi ⚠️ Báo cáo tài liệu vi phạmNội dung chi tiết: Ebook Control theory and systems biology: Part 2
Ebook Control theory and systems biology: Part 2
8 A Control-Theoretic Interpretation of Metabolic Control AnalysisBrian p. IngallsIn this chapter, the main results of metabolic control analysis (MCA Ebook Control theory and systems biology: Part 2A) arc 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 effects. /X key feature of these systems is that, whereas the dynamics are typically nonlinear, these redundancies Ebook Control theory and systems biology: Part 2appear linearly, through the stoichiometry matrix. This means that the effect of the input can be linearly decomposed into a component driving the staEbook Control theory and systems biology: Part 2
le 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 co8 A Control-Theoretic Interpretation of Metabolic Control AnalysisBrian p. IngallsIn this chapter, the main results of metabolic control analysis (MCA Ebook Control theory and systems biology: Part 2 of control of biochemical systems.8.1BackgroundBiochemical 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 Ebook Control theory and systems biology: Part 2of biochemical networks was first developed. In the 1970s. researchers on both sides of the Atlantic, led by Michael Savageau in the United Stales andEbook Control theory and systems biology: Part 2
by Henrik Kacscr and Reinhart Heinrich in Europe, elucidated theoretical frameworks for addressing issues of regulation in metabolic networks. A fund8 A Control-Theoretic Interpretation of Metabolic Control AnalysisBrian p. IngallsIn this chapter, the main results of metabolic control analysis (MCA Ebook Control theory and systems biology: Part 2bed 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 m Ebook Control theory and systems biology: Part 2ore sophisticated log linearization that provides an improved approximation of nonlinear dynamics (Savageau. 1976). With respect to local parametric sEbook Control theory and systems biology: Part 2
ensitivity analysis, the two approaches yield identical results.146Brian Ỉ*. IngallsThe analysis in the present ehapler follows the linearization meth8 A Control-Theoretic Interpretation of Metabolic Control AnalysisBrian p. IngallsIn this chapter, the main results of metabolic control analysis (MCA Ebook Control theory and systems biology: Part 2 sensitivity analysis. Moreover, linearization leaves intact the stoichiometric relationships that arc exploited in studies of these networks. Indeed, as will be shown below, it is this stoichiometric nature that distinguishes the mathematics of metabolic control analysis from that of standard sensi Ebook Control theory and systems biology: Part 2tivity analysis. As first shown by Reder (1988), an application of some basic linear algebra provides an extension of sensitivity analysis that capturEbook Control theory and systems biology: Part 2
es the features of stoichiometry. Beyond these mathematical underpinnings, the field of metabolic control analysis deals with myriad intricacies of ap8 A Control-Theoretic Interpretation of Metabolic Control AnalysisBrian p. IngallsIn this chapter, the main results of metabolic control analysis (MCA Ebook Control theory and systems biology: Part 2nd Schuster. 1996).Local parametric sensitivity analysis addresses the behavior of dynamical systems under small perturbations in system parameters. Such analysis plays an important role in control theory', and several texts on sensitivity analysis have been written with control applications in mind Ebook Control theory and systems biology: Part 2 (see, for example, Frank, 1978; Roscnwasscr and Yusupov, 2000; Tomovic, 1963; and Varma et al., 1999).The analysis in this chapter is based on the stEbook Control theory and systems biology: Part 2
andard ordinary differential equation based description of biochemical systems (chapter 1) in which the states arc the concentrations of the chemical 8 A Control-Theoretic Interpretation of Metabolic Control AnalysisBrian p. IngallsIn this chapter, the main results of metabolic control analysis (MCA Ebook Control theory and systems biology: Part 2ke enzyme activity as the parameter input. This choice of input channel typically results in an overactuated system with more inputs than states. Additionally, the reaction rates are important outputs. Because they depend directly on the parameter inputs, these rates enjoy some autonomy from the sta Ebook Control theory and systems biology: Part 2te dynamics and can. to a degree, be manipulated separately.The discussion that follows highlights a procedure for making explicit the separation betwEbook Control theory and systems biology: Part 2
een manipulating metabolite concentrations, on the one hand, and reaction rates, on the other, which complements investigations of metabolic “redesign8 A Control-Theoretic Interpretation of Metabolic Control AnalysisBrian p. IngallsIn this chapter, the main results of metabolic control analysis (MCA Ebook Control theory and systems biology: Part 2alysis community, a significant step in this direction was taken by Kacscr and Accrcnza (1993), who described a “universal method” for altering pathway flux. Ijitcr, the goal of increasing specific metabolite concentrations was taken up by Kacser and Small (1994). A local description of the combined Ebook Control theory and systems biology: Part 2 problem was given by Westcrhoff and Kell (1996). These results can all be seen as contained within the “metabolic design” approach described by KholoEbook Control theory and systems biology: Part 2
denko Ct al. (1998, 20ÍM)). In the sections that follow, equivalent results arc derived from a control-engineering viewpoint, culminating in a control8 A Control-Theoretic Interpretation of Metabolic Control AnalysisBrian p. IngallsIn this chapter, the main results of metabolic control analysis (MCA Ebook Control theory and systems biology: Part 2n of Metabolic Control Analysis1478.2Redundancy in C ontrol EngineeringThe results presented here arc a consequence of redundancies that appear in stoichiometric systems. Before addressing these, let US briefly review the standard manner in which such redundancies arc treated in control engineering. Ebook Control theory and systems biology: Part 28.2.1State Redundancy: Nonminimal RealizationsRecall from chapter 1 the standard description of a linear, lime-invariant system:= ^x(z) +(8.1a)j(0 = CEbook Control theory and systems biology: Part 2
x(0 + D«(/),(8.1b)where are R'1", lie R"111, y e R/A> and A. B. c and D are constant matrices of the appropriate dimensions. In systems theory, one is8 A Control-Theoretic Interpretation of Metabolic Control AnalysisBrian p. IngallsIn this chapter, the main results of metabolic control analysis (MCA Ebook Control theory and systems biology: Part 2 choices of the input //(•) with initial condition ar(O) 0. Given a particular system of the form (8.1), the associated input-output behavior can be equally generated from a whole class of systems of this form. That is, the representation, or realization, of these input-output behaviors is not uniqu Ebook Control theory and systems biology: Part 2e.A realization is said to be minimal if there arc no alternative systems of smaller order that represent the same behavior. Nonminimal realizations eEbook Control theory and systems biology: Part 2
xhibit redundancy (typically due to a symmetry or to decoupled behavior); they can be improved by removal of the redundant components. /X simple insta8 A Control-Theoretic Interpretation of Metabolic Control AnalysisBrian p. IngallsIn this chapter, the main results of metabolic control analysis (MCA Ebook Control theory and systems biology: Part 2ly exhibit such simple redundancies, as will be seen in section 8.3.8.2.2Input Redundancy: OveractuationIn control engineering, much effort has gone into the analysis of system (8.1) in the underactuated case (mo > /Mo), w here one attempts to manipulate a system for w hich there are fewer input cha Ebook Control theory and systems biology: Part 2nnels than degrees of freedom. In the case that the number of input channels equals the number of degrees of freedom (mo — /Mo) the system is fully acEbook Control theory and systems biology: Part 2
tuated, and much of that analysis is trivial. Finally, if Mo < /Mo. the system is overactuated, in which case a redundancy in the control inputs prese8 A Control-Theoretic Interpretation of Metabolic Control AnalysisBrian p. IngallsIn this chapter, the main results of metabolic control analysis (MCA Ebook Control theory and systems biology: Part 2egrees of freedom in the input can then be used to meet further performance criteria (llãrkcgârd and Glad, 2(M)5).In the overactuated case, system (8.1) can be treated as follows. For simplicity, lake the case that B has rank Mo (so there arc exactly Mo - M/o redundancies amongI4XBrian 1». Ingallsth Ebook Control theory and systems biology: Part 2e inputs). Because B docs not have lull column rank, it can be factored as B — Bf)B\, where Bo is «0 X Wo and has full rank, while Bl is no X mo and hEbook Control theory and systems biology: Part 2
as rank «0. The control input II can them be mapped to a virtual control input Ú r R"° by Ù — Bu. resulting in the fully actuated system^x(l) - .4x(f)8 A Control-Theoretic Interpretation of Metabolic Control AnalysisBrian p. IngallsIn this chapter, the main results of metabolic control analysis (MCA Ebook Control theory and systems biology: Part 2tate dynamics because they give rise to the same virtual input u.This redundancy can be made explicit by writing M as the sum of two terms that lie inside and outside of the nullspacc of R respectively:!/(/) = Â'đi(r) I .v/a?(r),where the columns of matrix K form a basis for the nullspacc of B and t Ebook Control theory and systems biology: Part 2he columns of A/ are linearly independent of one another and of the columns of A. Through this decomposition, the stale dynamics can be manipulated byEbook Control theory and systems biology: Part 2
the choice of «?(•), while «|( ) can be chosen to satisfy other design criteria. In particular, if the system output involves a feedthrough term (thaGọi ngay
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