This page contains the abstract, introduction and reference list from the following paper: Luis Acerenza and Athel Cornish-Bowden (1997) "Generalization of the double-modulation method for in situ determination of elasticities", Biochem. J. 327, 217-223
The double-modulation method [Kacser, H. and Burns, J. A. (1979) Biochem. Soc. Trans. 7, 1149-1160] was the first method proposed for determining elasticities in situ. It is based on measuring changes in steady-state metabolite concentrations and fluxes induced by parameter modulations. It has the important advantage that it is not necessary to know the values of the changes in the parameters. Here we develop a matrix formulation of the double-modulation method that allows it to be applied to metabolic systems of any structure and size. It also shows which parameters need to be modulated and which variables need to be measured in order to calculate the elasticities that correspond to particular rates. Some suggestions for the practical implementation of the method are given, including various ways of testing the reliability of the results.
Since the first development of metabolic control analysis from the pioneering work of Kacser and Burns [1] and Heinrich and Rapoport [2], much effort has been devoted to delineating the relationships between the properties of metabolic systems and the kinetic properties of their components. Instead of the familiar kinetic constants used in mechanistic studies metabolic control analysis expresses the latter in terms of elasticities, which define the sensitivities of the rates of individual reactions to the concentrations of metabolites. Although in principle elasticities can be measured on an isolated enzyme, such measurements are always open to doubts as to whether the artificial system truly reproduces the properties of the same enzyme in situ, because metabolites that interact with it in situ may be omitted, or present but quantitatively different. These are probably more important than the more obvious difficulty that the enzyme may be altered during isolation, because this is more easily checked. There has accordingly been much interest in developing experimental methods for measuring both control coefficients and elasticities in intact systems.
The simplest type of such method is one involving a single modulation, in which the activity of one enzyme is perturbed, for example by addition of an inhibitor that is specific for one enzyme. Such a perturbation can yield a value for the flux control coefficient of the perturbed step, and values for other steps can be estimated if the elasticities of neighbouring enzymes with respect to common intermediates are known. For example, in a study of the urea cycle in rat hepatocytes, Wanders and co-workers [3] used norvaline to inhibit ornithine carboxylase, and estimated the flux control coefficient for this enzyme; from this they calculated the flux control coefficient of carbamoyl-phosphate synthase by taking account of the elasticities of the two enzymes with respect to their common intermediate, carbamoyl phosphate.
The double-modulation method of Kacser and Burns [4] represented a major step forward. It offered the hope that modulation of two steps would allow analysis of a pathway segment without prior knowledge of the intermediate elasticities, which could, instead, be obtained from the analysis itself, and it avoided any assumption that enzyme elasticities are unity, i.e. that rates are necessarily proportional to enzyme concentrations. For several years after it was proposed this method was little used, but subsequently a number of groups [5-7] applied it to various systems. Fell [8, 9] has reviewed these and other applications.
Giersch [10-11] has generalized the double-modulation method into the multiple-modulation method, and a somewhat different but related procedure known as co-response analysis has also been described [12-14]: this involves modulating all of the enzymes in the system and measuring all of the fluxes and metabolite concentrations. Although one can in this way obtain the complete set of control coefficients and elasticities that characterize the system it demands more experimental effort than is strictly necessary, as in many systems one can obtain all of the information from a much smaller number of modulations. For this reason, Giersch and Cornish-Bowden [15] have recently explored ways of defining the precise sets of reactions that need to be modulated in order to allow determination of particular elasticities. In this paper we also address this question, as part of a more general formulation of the multiple-modulation method. The matrix method that we propose is completely general, as it can be applied to systems of any structure and size.
A somewhat different but related approach to the control analysis of larger systems is found in the top-down method [16], recently reviewed by one of its originators [17], and in the conceptually similar modular analysis [18]. These were motivated by a desire to determine what information could be obtained from limited experiments in which groups of enzymes are considered together as blocks, in systems too large and complicated to allow a complete analysis. Such methods have recently been extended to systems with more than one intermediate connecting the blocks [19] or more than one flux connecting the intermediates [20]. We believe that the combination of top-down or modular approaches and the general principles developed in the present paper would give a more solid ground to the design of modulation experiments.