Table 1 Kinetic equations used in the model. Reactions 1, 2, and 3 are reversible Henri-Michaelis-Menten reactions with one substrate and one product. Reaction 4 is an irreversible Henri-Michaelis-Menten reaction with one substrate and one product. Reaction 5 is a mass action reaction with 2 substrates and one product.

1

$\frac{d[X_2]}{dt}=\frac{(K_{11}{K}_{12}[X_1]-K_{13}{K}_{14}[X_2])[E_1]}{K_{14}[X_2]+K_{12}[X_1]+K_{14}{K}_{12}}-\frac{(K_{21}{K}_{22}[X_2]-K_{23}{K}_{24}[X_3])[E_2]}{K_{24}[X_3]+K_{22}[X_2]+K_{24}{K}_{22}}$

2

$\frac{d[X_3]}{dt}=\frac{(K_{21}{K}_{22}[X_2]-K_{23}{K}_{24}[X_3])[E_2]}{K_{24}[X_3]+K_{22}[X_2]+K_{24}{K}_{22}}-\frac{(K_{31}{K}_{32}[X_3]-K_{33}{K}_{34}[X_4])[E_3]}{K_{34}[X_4]+K_{32}[X_3]+K_{34}{K}_{32}}$

3

$\frac{d[X_4]}{dt}=\frac{(K_{31}{K}_{32}[X_3]-K_{33}{K}_{34}[X_4])[E_3]}{K_{34}[X_4]+K_{32}[X_3]+K_{34}{K}_{32}}-\frac{K_{41}[X_4][E_4]}{K_{42}+[X_4]}+K_{52}[X_6]-K_{51}[X_4][E_2]$

4

$\frac{d[X_5]}{dt}=\frac{K_{41}[X_4][E_4]}{K_{42}+[X_4]}$

5

$\begin{array}{l}\frac{d[X_6]}{dt}=K_{51}[X_4][E_2]-K_{52}[X_6]\\ \frac{d[E_2]}{dt}=K_{52}[X_6]-K_{51}[X_4][E_2]\end{array}$