Robustness analysis of DNA-based biomolecular feedback controllers to parametric and time delay uncertainties

Recent advances in DNA computing have greatly facilitated the design of bimolecular circuitry based on DNA strand displacement reactions. An important issue to consider in the design process for such circuits is the effect of biological and experimental uncertainties on the functionality and reliability of the overall circuit. In the case of bimolecular feedback control circuits, such uncertainties could lead to a range of adverse effects, including achieving wrong concentration levels, sluggish performance and even instability. In this paper, we analyse the robustness properties of two biomolecular feedback controllers; a classical linear proportional integral (PI) and a recently proposed nonlinear quasi sliding mode (QSM) controller, subject to uncertainties in the experimentally implemented rates of their underlying chemical reactions, and to variations in accumulative time delays in the process to be controlled. Our results show that the nonlinear QSM controller is significantly more robust against investigated uncertainties, highlighting its potential as a practically implementable bimolecular feedback controller for future synthetic biology applications.