Determination of control coefficients in intact metabolic systems

The control structure of a metabolic system can in principle be determined without the need for purification of the component enzymes and study of their kinetic properties, provided that their activities can be perturbed by amounts sufficient to produce measurable changes in the steady-state variables, i.e. the fluxes through the system and the concentrations of the intermediates. Each perturbation is characterized in terms of the co-response coefficients of all pairs of variables, i.e. the slopes of the lines produced when the logarithm of one variable is plotted against the logarithm of another, both varying in response to the same perturbation. If all the co-response coefficients are assembled into a matrix, the inverse of this matrix can be transformed into a matrix containing all the component elasticities, which can be inverted to provide the complete matrix of control coefficients. In a simple three-enzyme pathway studied, the analysis proves not to require unrealistically high accuracy in the original co-response measurements: even with errors with standard deviation +/- 5.77 degrees in the angles to the horizontal of the lines in the co-response plots (equivalent at best to errors of +/- 20% in the corresponding co-response coefficients), the final control coefficient matrix may be adequate for assessing the control structure of the system. Examination of literature data from studies of mitochondrial respiration and of gluconeogenesis indicates that considerably higher precision than this is achievable.