Fig 16. Performance of the motif 1 antithetic, motif 1 autocatalytic and motif 2 zero-order controllers with respect to surface to volume ratio related growth and an exponential increase of k3.
(a) Perturbation profile. Phase 1: constant V (25.0) and k3 (2.0); phase 2: V increases according to Eq 2 (η = 1 and ξ = 0.2) and k3 remains constant; phase 3: V continues to increase and k3 starts to increase exponentially as described by Eq 49. (b) Behavior of the antithetic controller (Eqs 21–27). Rate constant values as in Fig 9. Initial concentrations: A0 = 2.0, E1,0 = 0.01, E2,0 = 100, M0 = O0 = 1 × 106. (c) Behavior of the autocatalytic controller (Eqs 33–35). Rate constant values as in Fig 11. Initial concentrations: A0 = 2.0, E0 = 0.01, M0 = 1 × 106. (d) Behavior of the motif 2 zero-order controller (Eqs 43–46). Initial concentrations: A0 = 2.0, E0 = 1.0, M0 = 1 × 103. Note the breakdown of the controller at the very end of phase 3 due to low E (arrow).