Robust Design of Biological Circuits: Evolutionary Systems Biology Approach

Figure 8

Monte Carlo simulation of biological repressilator by the proposed evolutionary systems biology method. (a) TetR; (b) CI; (c) LacI. The parameters are specified as follows. The standard deviations of uncertain kinetic parameters and decay rates to be robustly tolerated are specified as Δ𝑘₁=0.2, Δ𝑘₂=0.2, Δ𝑘₃=0.2, Δ𝑘₄=0.02, Δ𝑘₅=0.02, Δ𝑘₆=0.02, Δ𝜆₁=0.04, Δ𝜆₂=0.04, Δ𝜆₃=0.04, Δ𝜆₄=0.05, Δ𝜆₅=0.05, and Δ𝜆₆=0.05. The variance of external disturbance 𝑣_𝑖 is 𝜎²_𝑖=(0.03)². The Monte Carlo simulations are performed by 50 rounds. The mean errors e are 0.85, 0.90, and 0.90 with standard deviations of 0.38, 0.38, and 0.37 for TetR, CI, and LacI, respectively.

(a)

(b)

(c)