On the sign pattern of metabolic control coefficients

The sign of a flux (concentration) control coefficient of an enzyme determines if the metabolic flux (metabolite concentration) will increase or decrease when the enzyme concentration is increased/decreased. In general, the sign of a control coefficient depends on the magnitudes of the enzyme elasticities, fluxes etc. It is shown that in many pathways some (or all) of the control coefficients may have fixed signs irrespective of the magnitudes of the elasticities and fluxes. The remaining control coefficients are sign-indeterminate. The enzymes and metabolites whose control coefficients are sign-indeterminate can be identified in a heuristic fashion directly from the topology of the metabolic pathway, i.e., location of feedback-feedforward loops, location of branches, presence of isoenzymes etc. In other pathways such as those containing a substrate cycle, none of the control coefficients of the enzymes can have a fixed sign; a control coefficient may be positive, negative or zero depending on the actual magnitudes of the elasticities and velocities.