Optimization-based synthesis of stochastic biocircuits with statistical specifications

Model-guided design has become a standard approach to engineering biomolecular circuits in current 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 behaviors 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 developed to ensure the robustness of a biocircuit design. These design tools are formulated using convex optimization programs to enable efficient and rigorous quantification of the statistics without approximation, and thus, they are amenable to the synthesis of stochastic biocircuits that require high reliability. We demonstrate these features by designing a stochastic negative feedback biocircuit that satisfies multiple statistical constraints. In particular, we use a rigorously quantified parameter map of feasible design space to perform in-depth study of noise propagation and regulation in negative feedback pathways.