Generalization of the double-modulation method for in situ determination of elasticities

The double-modulation method [Kacser and Burns (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.