Quantitative Steady-State Bounds in Biomolecular Circuits Due to Bounded Multi-Parametric Perturbations

Biomolecular circuit performance depends upon the reaction rate parameters. Any perturbation in these parameters can propagate to the output of the system, altering its performance. A rigorous quantitation of the extent of such deviations in response to variations in one or more parameters, especially in nonlinear settings, is generally unclear. To address this, we developed theoretical frameworks based on the Banach Contraction Theorem and Interval Analysis. We used a parametrized version of the Banach Contraction Theorem to develop a method to bound steady-state variations in terms of variations in multiple parameters, in the linearized and in the nonlinear settings. We extended this to propose a solution to the design problem of obtaining parametric bounds given steady-state bound specifications. We developed a complementary method based on Interval Analysis to rigorously obtain steady-state intervals given parametric intervals. These methods are illustrated using benchmark biomolecular circuit examples. These results contribute to the analysis and design of biomolecular systems in the presence of uncertainties.