Deterministic and chance-constrained interpretation of an upper bound on reaction flux. The dotted lines represent the upper bound for the flux of a reaction j in a deterministic (left panel) and chance-constrained interpretation (right panel). The arrows show the flux ranges. If the upper bound is a random variable, the deterministic interpretation forces the flux v
below the lowest value in the upper bound distribution. The chance-constrained interpretation allows v
to exceed the lowest value in the upper bound distribution by some probability specified by the parameter ε.