Kinetics and mechanisms of catalyzed dual-E (antithetic) controllers
Fig 32
Switching between single-E control (Fig 31) and dual-E control (Fig 29) as a function of k6 for different values of k9, k11, k13, and k15.
Panel (a): high value (1 × 109) of k9, k11, k13, and k15. The dual-E controller shows its maximum operational range. In this case the switch occurs when k6 > k7Eztot. Panels (b)-(d): for the lower values of k9, k11, k13, and k15 (indicated inside the figure) the ternary-complex concentration (E1⋅Ez⋅E2) is lower than Eztot and the switch occurs at lower k6 values, which leads to a decreased operational range of the dual-E controller. Due to the lower (E1⋅Ez⋅E2) concentration the single-E control mode (which occurs analogous to the red-outlined part in Fig 9e) shows an offset below k7Eztot/k5. Note however, that Ass will depend on the perturbation k1 and move towards Aset with increasing k1, thereby reducing the single-E controller’s offset. Other rate constants: k1=500.0, k2=1.0, k3=0.0, k4=1.0, k5=40.0, k7=1 × 108, k10=k12=k14=k16=1 × 103. Initial concentrations: A0=2.0, E1,0=5.49 × 10−2, E2,0=5.21 × 103, Ez0=7.4 × 10−14, (E1⋅Ez)0=9.09 × 10−8, (E1⋅Ez⋅E2)0=9.09 × 10−7, (EzE2)0=1.66 × 10−10.