Chance-constrained reaction flux bounds with or without enzyme level changes. When there is no modification in the enzyme level, the flux for reaction j lies within the reference state range (a). When the reaction is up-regulated, the upper bound distribution shifts above the reference state upper bound (b). When the reaction is down-regulated, the upper bound distribution shifts below the reference state upper bound and the new (modified state) lower bound may also shift below the reference state lower bound (c). The red dashed lines in (b) and (c) show the range of possible flux capacity values equaling the spread of the capacity distributions.