Biochemical control theory

The examples to be presented illustrate the diversity of fields of applications, but they are mentioned in outline form only. Many biological phenomena used to be modelled by real or formal kinetic models. A biochemical control theory that is partially based on non-mass-action-type enzyme kinetics seems to be under elaboration, and certain aspects will be illustrated. A few specific models of fluctuation and oscillation phenomena in neurochemical systems will be presented. The formal structure of population dynamics is quite similar to that of chemical kinetics, and models referring to different hierarchical levels from elementary genetics to ecology are well-known examples. Polymerisation, cluster formation and recombination kinetics from the physical literature will be mentioned briefly. Another question to be discussed is how electric-circuit-like elements can be constructed in terms of chemical kinetics. Finally, kinetic theories of selection will be mentioned. 

Enzyme kinetics traditionally deviates from mass-action kinetics. This deviation results from the early enzyme kinetic measurements, which were 

The mass-action kinetic model of the interaction among four molecule populations, namely enzyme (E), substrate (S), complex (C) and product (P) is described by 

The usual initial concentrations are e(0) = Cq, 5(0) = 5q, c(0) = Cq, / (0) = Pq. Since the enzyme molecules are always either in free (E) or complexed (C) form the enzyme concentration can be eliminated. Since the substrate molecules are always in original (S), complexed (C) or product (P) form they can be eliminated too  

The system of differential equations obtained by the elimination cannot be solved analytically. Assuming that the substrate concentration changes slowly , the complex concentration can be expressed by the quasi-steady equation 

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Biochemical control theory Michaelis- Menten-like equations Qualitative, numerical... 

Hafher, R.P., Brown, G.C.. Brand, M.D. (1990). Analysis of the control of respiration rate, phosphorylation rate, proton leak rate and proton motive force in isolated mitochondria using the top-down approach of metabolic control theory. Eur. J. Biochem. 188,313-319. 

Although the importance of a systemic perspective on metabolism has only recently attained widespread attention, a formal frameworks for systemic analysis has already been developed since the late 1960s. Biochemical Systems Theory (BST), put forward by Savageau and others [142, 144 147], seeks to provide a unified framework for the analysis of cellular reaction networks. Predating Metabolic Control Analysis, BST emphasizes three main aspects in the analysis of metabolism [319] (i) the importance of the interconnections, rather than the components, for cellular function (ii) the nonlinearity of biochemical rate equations (iii) the need for a unified mathematical treatment. Similar to MCA, the achievements associated with BST would warrant a more elaborate treatment, here we will focus on BST solely as a tool for the approximation and numerical simulation of complex biochemical reaction networks. 

M. A. Savageau, Biochemical systems theory and metabolic control theory 1. Fundamental similarities and differences. Math. Biosci. 86, 127 145 (1987). 

Bottom-up systems biology does not rely that heavily on Omics. It predates top-down systems biology and it developed out of the endeavors associated with the construction of the first mathematical models of metabolism in the 1960s [10, 11], the development of enzyme kinetics [12-15], metabolic control analysis [16, 17], biochemical systems theory [18], nonequilibrium thermodynamics [6, 19, 20], and the pioneering work on emergent aspects of networks by researchers such as Jacob, Monod, and Koshland [21-23]. 

Kholodenko, B.N., Cascante, M. and Westerhoff, H.V. (1994a) Control theory of metabolic channelling. Mol. Cell. Biochem. 733-734,313-331. 

Sorribas, A. Savageau, M. A. (1989a). A comparison ofvariant theories of intact biochemical systems 1 Enzyme-enzyme interactions and biochemical systems theory. Math. Biosci. 94, 161-193. Sorribas, A. Savageau, M. A. (1989b). A comparison of variant theories of intact biochemical systems 2 Flux oriented and metabolic control theaies. Math. Biosci. 94,195-238. 

The object of metabolic control theory is to provide a sound mathematical foundation for the quantitative estimation of the role played by individual enzymes on the control of flux through a metabolic pathway and also the control exerted by individual enzymes on the concentration of intermediate metabolites in the pathway. The general principles of metabolic control theory and biochemical systems theory can be visualized by considering the simple metabolic pathway in Fig. 6. The numbers above the arrows... 

Metabolic control analysis Kinetic modeling Biochemical systems theory Cybernetic modeling... 

Although there has been a substantial body of pharmacological evidence in support of the monoamine theory of depression, clinical biochemical data have been less convincing (Luchins, 1976) this is where differences in the concentrations of NA and 5-HT and their metabolites or hormones, which are ultimately under the control of brain monoaminergic neurons (neuroendocrine markers), have been compared between depressed patients and normal controls. However, by the early 1970s a major difficulty with the theory was becoming apparent this was the time lag between the immediate... 

Volumes 1, 2 and 3 form an integrated series with the fundamentals of fluid flow, heat transfer and mass transfer in the first volume, the physical operations of chemical engineering in this, the second volume, and in the third volume, the basis of chemical and biochemical reactor design, some of the physical operations which are now gaining in importance and the underlying theory of both process control and computation. The solutions to the problems listed in Volumes 1 and 2 are now available as Volumes 4 and 5 respectively. Furthermore, an additional volume in the series is in course of preparation and will provide an introduction to chemical engineering design and indicate how the principles enunciated in the earlier volumes can be translated into chemical plant. 

Westerhoff, H. V. Chen, Y. D. How do enzyme activities control metabolite concentrations An additional theorem in the theory of metabolic control. Eur J Biochem 1984,142 425-430. 

Coulson, R.A. (1993). The flow theory of enzyme kinetics role of solid geometry in the control of reaction velocity in live animals. Inti. J. Biochem. 25 1445-1474. 

As most chemical and virtually all biochemical processes occur in liquid state, solvation of the reaction partners is one of the most prominent topics for the determination of chemical reactivity and reaction mechanisms and for the control of reaction conditions and resulting materials. Besides an exhaustive investigation by various experimental methods [1,2,3], theoretical approaches have gained an increasing importance in the treatment of solvation effects [4,5,6,7,8], The reason for this is not only the need for sufficiently accurate models for a physically correct interpretation of the experimental data (Theory determines, what we observe ), but also the limitation of experimental methods in dealing with ultrafast reaction dynamics in the pico- or even subpicosecond regime. These processes have become more and more the domain of computational simulations and a critical evaluation of the accuracy of simulation methods covering experimentally inaccessible systems is of utmost importance, therefore. 

The final section of this chapter develops various methods and theories to explore control and regulation in biochemical networks. 

Metabolic control analysis (MCA) is a specialized theory that is concerned with particular sensitivity coefficients, elasticity coefficients and control coefficients. These coefficients tell us how a steady state of a biochemical system shifts in response to perturbation in enzyme activities or external (clamped) substrate concentration [53, 209],... 

It is widely appreciated that chemical and biochemical reactions in the condensed phase are stochastic. It has been more than 60 years since Delbriick studied a stochastic chemical reaction system in terms of the chemical master equation. Kramers theory, which connects the rate of a chemical reaction with the molecular structures and energies of the reactants, is established as a central component of theoretical chemistry [77], Yet study of the dynamics of chemical and biochemical reaction systems, in terms of either deterministic differential equations or the stochastic CME, is not the exclusive domain of chemists. Recent developments in the simulation of reaction systems are the work of many sorts of scientists, ranging from control engineers to microbiologists, all interested in the dynamic behavior of biochemical reaction systems [199, 210],... 

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