Robust and structural ergodicity analysis of stochastic biomolecular networks involving synthetic antithetic integral controllers
For researchers designing synthetic biological circuits, this provides more precise theoretical tools to ensure stable and controllable behavior under parameter uncertainty.
The paper develops exact algebraic and polynomial methods for robustly verifying ergodicity and output controllability of stochastic biomolecular networks with antithetic integral controllers, extending prior linear programming-based conditions that were potentially conservative.
Ergodicity and output controllability have been shown to be fundamental concepts for the analysis and synthetic design of closed-loop stochastic reaction networks, as exemplified by the use of antithetic integral feedback controllers. In [Gupta, Briat & Khammash, PLoS Comput. Biol., 2014], some ergodicity and output controllability conditions for unimolecular and certain classes of bimolecular reaction networks were obtained and formulated through linear programs. To account for context dependence, these conditions were later extended in [Briat & Khammash, CDC, 2016] to reaction networks with uncertain rate parameters using simple and tractable, yet potentially conservative, methods. Here we develop some exact theoretical methods for verifying, in a robust setting, the original ergodicity and output controllability conditions based on algebraic and polynomial techniques. Some examples are given for illustration.