Mathematical Modeling: Bridging the Gap between Concept and Realization in Synthetic Biology
Figure 4
Sensitivity and bifurcation analyses of the metabolator model in Fung et al. [6]. (a) Sensitivity analysis: increase in glycolytic rate increases the oscillatory capability of the metabolator. The glycolytic rate is equal to 0.001, 0.01, 0.05, and 0.5 in the top four panels from left to right. (b) Phase plots obtained by perturbing the steady-state solution at show that the oscillatory dynamics is limit cycle oscillation irrespective of the initial condition. The initial state of the oscillator is depicted with squares. (c) Hopf bifurcation analysis was used to construct a phase diagram of glycolytic rate versus external acetate concentration. The flux-sensitive nature of the oscillations is evident here; low glycolytic fluxes lead to a stable steady state with oscillations setting in beyond a threshold value of the glycolytic flux. (d) Another phase diagram suggests that at , specific combinations of three protein levels are required to sustain oscillation. The variable represents rate of synthesis of protein i (i: LacI, Pta or Acs) (from Fung et al. [6], with permission).
