The relative change in the flux through the metabolic system can be related to the relative change in enzyme activity through the global control coefficient:

_{}. (A.1)

Rearranging this equation leads to Eq. 22 in the paper:

_{}, (22)

Similarly

_{} (A.2)

leads to Eq. 23:

_{}. (23)

Because the flux leads through enzyme 6,

_{}. (A.3)

Rearranging this equation leads to Eq. 24 in the paper:

** _{},** (24)

Similarly

_{} (A.4)

leads to Eq. 25 in the paper:

_{}. (25)

For the system with two variable enzymes the expressions for the global control coefficients are identical. The expressions for the intra-modular control coefficients include an extra term accounting for the change in the enzyme of reaction 5:

_{}. (A.5)

Using the summation theorem for flux control this equation can be written as:

_{}. (A.6)

which rearranges to Eq. 27 in the paper.

_{}, (27)

Doing the same for the concentration of the metabolite

_{}, (A.7)

_{}, (A.8)

leads to Eq. 28:

_{}. (28)