Robustness analysis of a nucleic acid controller for a dynamic biomolecular process using the structured singular value.

• The structured singular value (μ) robustness analysis framework is extended to evaluate nucleic acid controllers for biomolecular processes. • We show that representation of linear feedback controllers with chemical reaction networks introduces nonlinear dynamics, with equilibria that move due to parametric uncertainty. • μ -analysis identifies worst-case parameterisations missed by Monte Carlo simulations. In the field of synthetic biology, theoretical frameworks and software tools are now available that allow control systems represented as chemical reaction networks to be translated directly into nucleic acid-based chemistry, and hence implement embedded control circuitry for biomolecular processes. However, the development of tools for analysing the robustness of such controllers is still in its infancy. An interesting feature of such control circuits is that, although the transfer function of a linear system can be easily implemented via a chemical network of catalysis, degradation and annihilation reactions, this introduces additional nonlinear dynamics, due to the annihilation kinetics. We exemplify this problem for a dynamical biomolecular feedback system, and demonstrate how the structured singular value (μ) analysis framework can be extended to rigorously analyse the robustness of this class of system. We show that parametric uncertainty in the system affects the location of its equilibrium, and that this must be taken into account in the analysis. We also show that the parameterisation of the system can be scaled for experimental feasibility without affecting its robustness properties, and that a statistical analysis via Monte Carlo simulation fails to uncover the worst-case uncertainty combination found by μ -analysis. [ABSTRACT FROM AUTHOR]