How to recognize monofunctional units in a metabolic system.

In intracellular metabolic networks, it is often useful to discern subsystems (modules) of which the metabolites are only produced or consumed by reactions within that subsystem or by a limited number of fluxes crossing the borders of the subsystem. In many cases such subsystems function as units with respect to their effect on the remainder of the system. In this paper we show that the co-response of two metabolic variables outside that subsystem to a perturbation of a subsystem reaction does not depend on which subsystem reaction is perturbed if three conditions are fulfilled: (1) the reactions outside the subsystem are not affected directly by metabolites belonging to the subsystem; (2) there are no conservation relations linking the subsystem to the rest; and (3) the subsystem is linked to the remainder of the system only via one degree of freedom in fluxes. We propose the name "monofunctional units" for subsystems fulfilling these three criteria. Identification of such units greatly simplifies metabolic control analysis. Only one reaction per unit needs to be perturbed to analyse control in the system. Difficulties, such as the inaccessibility of some reactions to experimental perturbation, may be circumvented by perturbing another reaction within the unit that leads to the same co-response coefficients. The analysis can also serve to identify unsuspected regulatory interactions in the metabolic network. The differences in the behaviour between metabolic units and other types of subsystems are illustrated by numerical examples.