Metabolic control analysis. An application of signal flow graphs

In this paper the method of signal-flow graphs is used for calculating the Control Coefficients of metabolic pathways in terms of enzyme elasticities. The method is applied to an unbranched pathway (a) without feedback or feedforward regulation and (b) with feedback inhibition of the first enzyme by the last variable metabolite. It is shown that, by using a signal-flow graph, the control structure of a metabolic pathway can be represented in a graphical manner directly from the configuration of the pathway, without the necessity of writing the governing equations in a matrix form. From a signal-flow graph the various Control Coefficients can be evaluated in an easy and straightforward fashion without recourse to matrix inversion or other algebraic techniques. A signal-flow graph also provides a visual framework for analysing the cause-effect relationships of the individual enzymes.