Figure 4.

Application of constraints on the bounds of exchange reactions. Infinite bounds (here, −1000 to 1000) express the unlimited supply and removal of metabolites to and from the system. A negative flux through an exchange reactions corresponds to an uptake (red) and a positive flux corresponds to the secretion of a metabolite (blue). Maximal uptake can be constraint by restricting the lower bound (lb = −600). The directionality of the exchange can be defined by setting a negative value as the upper bound (ub) for an uptake or by setting a positive value as the lower bound for secretion. These constraints could be based on the limit of detection (LOD) or quantification for the metabolite. Relative differences in the uptake and secretion of a metabolite can be expressed as the relative difference from maximal possible uptake rate (purple as compared to red) and as the relative difference from the minimal secretion rate. Absolute concentration changes over time can be converted to flux values and added to the constraints, considering a user-defined error to the flux to define lower bound and upper bound.