Robust Design of Biological Circuits: Evolutionary Systems Biology Approach

Figure 6

Simulation result of biological AND gate. (a) In order to confirm the robustness and filtering ability of the synthetic gene network, 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=0.02, Δ𝑘₄=0.02, Δ𝑘₅=0.000005, Δ𝑘₆=0.2, Δ𝑘₇=0.02, Δ𝜆₁=0.04, Δ𝜆₂=0.04, Δ𝜆₃=0.05, Δ𝜆₄=0.05, Δ𝜆₅=0.05, Δ𝜆₆=0.04, and Δ𝜆₇=0.05. The variance of external disturbance 𝑣_𝑖 is 𝜎²_𝑖=(0.1)². The Monte Carlo simulations are performed by 50 rounds. The mean error is 𝑒=(1/50)∑⁵⁰_𝑖=1𝑒_𝑖=121.95 with a standard deviation of 9.93, where 𝑒_𝑖 is the root mean squared error of the ith Monte Carlo simulation. (b) In contrast to the above design case, the design parameters are specified aside the optimal design parameter 𝑘^∗, with 𝑘₁=0.9, 𝑘₂=0.6, 𝑘₃=0.95, 𝑘₄=0.25, 𝑘₅=0.00002, 𝑘₆=0.6, and 𝑘₇=0.15. In this design case, the mean error is 𝑒=165.90 with standard deviation of 18.67.

(a)

(b)