Kinetics and mechanisms of catalyzed dual-E (antithetic) controllers
Fig 34
Metastable single-E controller and critical slowing down in the autonomous transition from single-E to dual-E control mode.
(a) Step-wise change of k1 at t = 100.0 from 500.0 (phase 1) to 1000.0 (phase 2). (b) Metastable single-E control mode. The single-E controller defends its set-point (=2.5), but transition to dual-E control mode (indicated by arrow) occurs at approximately 1600 time units when E2 reaches its steady state. (c) The metastable single-E control mode is operative as long as E2 is above its steady state value. The transition from single-E to dual-E control mode occurs when E2 has reached its steady state (indicated by arrow). Rate constants: k1=500.0 (phase 1), k1=1000.0 (phase 2), k2=1.0, k3=0.0, k4=1.0, k5=40.0, k6=40.0 k7=1 × 108, k9=k11=k13=k15=1 × 109, k10=k12=k14=k16=1 × 103. Initial concentrations: A0=2.5, E1,0=199.1, E2,0=9.52 × 104, Ez0=1.08 × 10−12, (E1⋅Ez)0=2.37 × 10−15, (E1⋅Ez⋅E2)0=9.995 × 10−7, (EzE2)0=5.01 × 10−10. (d) Transition time T as a function of k6. k1=500.0; all other rate constants and initial concentrations as for (a)-(c).