Optimal Design of Robust Synthetic Biological Oscillators

Abstract

This paper applies a real structural genetic algorithm (RSGA) to simultaneously identify network structure and estimate system parameters for a robust biological oscillator with specific oscillation frequency. At present, a repressilator with oscillation phenomenon has been successfully built in Escherichia coli (E. coli) and its function is to harmonize cell-cell communication. However, stochastic molecular perturbations may affect the oscillatory behaviors and the network structure is unknown beforehand. We use a stochastic S-system model to capture the dynamic behavior and the network topology for the biological oscillator under the perturbational environments, transform a robust synthetic design problem to a robust multi-objective optimization problem, and introduce the RSGA to solve this problem based on the design specification. The optimal parameters and the simplest structure are simultaneously searched such that the cost function related to tracking error of sinusoidal signal and the number of reaction pathways is minimized. Numerical experimental results in silico show that the proposed method is effective to synthesize robust biological oscillators implementing the particular oscillatory functions when the networks are influenced by intrinsic and extrinsic stochastic molecular perturbations.