Abstract
This chapter is the introduction to part III of the book. This chapter contains a short survey of the current research approaches to the field of control of biochemical pathways which is dominated by the BST [Biochemical System Theory] and the MCA [Metabolic Control Analysis] theories, which constitute the mainstream of system biology in the latter aspect. Alongside these theoretical frameworks, there is a host of other research frameworks that are aided by a great number of numerical software packages and which are based on different and various aspects of optimization techniques. In Chap. 16, a humble attempt is conducted in order to explore the possible optimality of biochemical pathways via the worst-case approach of the \(H_\infty \) control theory. Starting from simple enzymatic reactions and applying linearization, a simple pathway is considered which contains a negative feedback loop, upon which various aspects of linear modern control theory are applied. The theory developed is demonstrated via the threonine synthesis pathway which contains three negative feedback loops. In Chap. 17, a further study of other optimal measures is conducted, including the peak-to-peak and the energy-to-peak optimal measures. The latter optimal measures are applied and demonstrated on the threonine synthesis pathway and the glycolytic pathway in yeast. The third part of the book culminates in a conjecture according to which biochemical feedback control systems may apply either a worst-case strategy or a peak-to-peak strategy accounting for their inherent robustness in the face of parameter uncertainties.
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Gershon, E., Shaked, U. (2019). Introduction and Literature Survey. In: Advances in H∞ Control Theory. Lecture Notes in Control and Information Sciences, vol 481. Springer, Cham. https://doi.org/10.1007/978-3-030-16008-1_15
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