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Homeostatic controllers compensating for growth and perturbations
Fig 20
Performance of the antithetic controller when the compensatory flux is homogeneously generated within the cellular volume (Eqs 56 and 22–27).
Phase 1: constant volume V and constant k3. Initial concentrations and rate constant values: V0 = 25.0, 
, A0 = 0.0, E1,0 = 0.0, E2,0 = 0.0, M0 = 2 × 105, N0 = 1 × 106, O0 = 2 × 105, k2 = 1.0, k3 = 2.0, 
, k4 = 10.0, k5 = 1 × 10−6, k6 = 20.0, k7 = 1 × 10−5, k8 = 20.0, k9 = 1 × 10−5. The controller moves A to 
(Eq 57 when 
). Phase 2: rate constants remain the same as in phase 1, but V increases linearly with 
, while k3 remains constant at k3 = 2.0. The controller is able to maintain A at 
in agreement with Eq 57. Phase 3: V continues to increase with the same speed while k3 now linearly increases with 
. As indicated by Eq 57 the controller is no longer able to keep A at 
but shows a constant steady state value below its theoretical set-point.
doi: https://doi.org/10.1371/journal.pone.0207831.g020