The Structural Approach to Metabolic Control Analysis I: Theoretical Aspects

  • Christine Reder
Part of the NATO ASI Series book series (NSSA, volume 190)


In the study of a biochemical system, it is interesting to emphasize its invariants, i.e. the characteristics or properties that depend neither on the state of its environment nor on its internal state, but only on its structure. The models used in metabolic control theory, or more generally in biochemical kinetic theory, can be constructed in two steps: defining first the stoicheiometric reaction scheme, and giving then the expressions of the rate functions of each of the reactions. As the reaction scheme is generally supposed not to depend on the state of the system, it is natural to define the structural properties of a model as those that depend only on this scheme, and not on the rate functions. Then the study of the structural properties of a model can be used into two different ways: either to test directly the reaction network on which a model is based, or to use the network structure of a model, assuming it to be valid, to calculate coefficients that cannot be measured experimentally. This can be done without making any assumptions about the rate functions or about the state of the system. In this paper, we will explain in the context of a simple example how the structural properties of the control coefficients can be constructed, and also how the elasticity coefficients can be calculated from the control coefficients, providing that their structural properties are satisfied. [These results are presented and proved in a general framework in Reder (1988)].


Rate Function External Parameter Elasticity Coefficient Biochemical System Elasticity Matrix 
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  1. Mazat, J.-P. & Reder, C. (1988), Aspects Géométriques de la Théorie du Contrôle du Métabolisme (Mazat, J.-P. & Reder, C., eds. ), BordeauxGoogle Scholar
  2. Reder, C. (1986) Mimodrame mathématique sur les systèmes biochimiques, Université Bordeaux I. Mathématiques Appliquées. Publication N° 8608Google Scholar
  3. Reder, C. (1988) J. theor. Biol.135,175–201Google Scholar

Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Christine Reder
    • 1
  1. 1.UER de Mathématique et InformatiqueUniversité de Bordeaux ITalence CedexFrance

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