Metabolic control analysis: a survey of its theoretical and experimental development.

As the details of the chemical transformations in metabolism have become increasingly clear, and the enzymes catalysing many of the reactions have been characterized, it is understandable that biochemists should want to explain at the molecular level the metabolic homeostasis observed at the physiological level. How are the rates of synthesis and degradation of metabolites kept in close balance over a very wide range of external conditions without catastrophic rises or falls in the metabolite concentrations? The discoveries of feedback inhibition, co-operativity and covalent modification in enzymes, and of mechanisms for the control of enzyme synthesis and degradation, have disclosed a repertoire of molecular effects that potentially alter the fluxes in metabolic pathways. With such a range of effects to choose from, it is not surprising that disputes arise over explanations for the changes in flux through particular pathways under given circumstances. Since the explanations are usually verbal and qualitative, discrimination between different explanations, or assessment of their adequacy, is difficult. More recently, several groups have attempted theoretical analysis of the potential of these different molecular mechanisms to contribute to the control of metabolic flux. Since these theories can be given a mathematical formulation, they can be used in combination with appropriate experimental measurements to provide quantitative explanations and, potentially, predictions. The theories have often been controversial. Matters at issue have included the extent to which it is feasible to perform experiments to obtain the necessary data, the adequacy of the theories for making useful predictions, and the degree to which the quantitative measures of the theories do actually capture the relevant aspects of regulation and control. To some extent, this is a matter of semantics; a mathematical theory is more explicit about its underlying assumptions and the meaning of its statements, but regulation and control are two terms that have been used without strict adherence to any agreed definition in many different contexts (as noted in [1]). It is therefore inevitable that some will find that the use of these terms in the context of a mathematical theory places a narrower construction on them than they would like. These theories all include a form of sensitivity analysis; that is, the magnitude of the effect of some small change in a parameter (such as an enzyme activity) on a metabolic system property (such as the flux or the concentration of a metabolite) is mathematically related to the properties of the components of the system. Sensitivity analysis is widely used for analogous problems in other fields, including economics, ecology [2], engineering [3] and chemical kinetics [4-6]. Its application in biochemistry was pioneered by Higgins [7], but three variants subsequently arose: Metabolic Control Analysis, Biochemical Systems Theory and Crabtree and Newsholme's 'flux-oriented' theory (the term used in [8]). It is not possible to give a succinct account of the differences between the approaches, which is a controversial area [9-18] even though the underlying mathematics is equivalent to a considerable extent. One area of difference is the choice of the type of parameter that is changed for the determination of sensitivities. In Metabolic Control Analysis, enzyme concentration (or activity) is usually chosen; the response to an external modifier of a metabolic pathway is derived from the resulting sensitivities. In Biochemical Systems Theory [19-25], the primary parameters for the sensitivities are the 'rate constants' for synthesis and degradation of metabolite pools. Savageau has given many reasons for this choice of parameter; Cornish-Bowden has articulated some of the problems with it [15]. Although using these 'rate constants' simplifies the analysis procedures within Biochemical Systems Theory, there is not a one-to-one relationship between them and the enzymes of the system, which can create a slight complication in determining the sensitivity to variation of an enzyme activity. Savageau's theory is part of an integrated system for stability analysis and simulation, in addition to sensitivity analysis. Crabtree and Newsholme's theory [8,10,26-30] is intermediate between the two others, and the primary sensitivities are to an external modifier (a hypothetical one if necessary), but its mathematical development is less rigorous. In this review, I shall concentrate on Metabolic Control Analysis. This is because, apart from considerations of space, approximately two-thirds of the literature citations of theories of metabolic regulation in the past 5 years have been to Metabolic Control Analysis. This may relate to perceived ease of use, which has been compared using the different approaches on the same set of experimental results [31]. In the following review, I will not give a complete derivation and description of the basic concepts of Metabolic Control Analysis; clear accounts can be found in previous articles and reviews [9,32-39]. Instead I will try to indicate areas of disagreement, the scope of the basic theory and where it has been modified or extended, and recent approaches to experimental applications.