Optimization-based synthesis of stochastic biocircuits with statistical specifications

Model-guided design has become a standard approach to engineering biomolecular circuits in synthetic biology. However, the stochastic nature of biomolecular reactions is often overlooked in the design process. As a result, cell-cell heterogeneity causes unexpected deviation of biocircuit behaviours from model predictions and requires additional iterations of design-build-test cycles. To enhance the design process of stochastic biocircuits, this paper presents a computational framework to systematically specify the level of intrinsic noise using well-defined metrics of statistics and design highly heterogeneous biocircuits based on the specifications. Specifically, we use descriptive statistics of population distributions as an intuitive specification language of stochastic biocircuits and develop an optimization-based computational tool that explores parameter configurations satisfying design requirements. Sensitivity analysis methods are also performed to ensure the robustness of a biocircuit design against extrinsic perturbations. These design tools are formulated with convex optimization programs to enable rigorous and efficient quantification of the statistics. We demonstrate these features by designing a stochastic negative feedback biocircuit that satisfies multiple statistical constraints and perform an in-depth study of noise propagation and regulation in negative feedback pathways.