Quantitative analysis of metabolic regulation. A graph-theoretic approach using spanning trees.

A graph-theoretic technique using spanning trees is described for the evaluation of Flux Control Coefficients of metabolic pathways. The technique is illustrated by investigating a linear pathway (a) in the absence of feedback and feedforward regulation. (b) with its first enzyme inhibited by the end product and (c) with multiple feedback loops. It is shown that the Flux Control Coefficients of a linear pathway with one or more feedback loops can be derived in a systematic manner by superimposing the effect of the feedback loop(s) on the expressions pertaining to the Flux Control Coefficients of the unregulated pathway.