An algebraic approach to parameter optimization in biomolecular bistable systems

In a synthetic biological network it may often be desirable to maximize or minimize parameters such as reaction rates, fluxes and total concentrations of reagents, while preserving a given dynamic behavior. We consider the problem of parameter optimization in biomolecular bistable circuits. We show that, under some assumptions often satisfied by bistable biological networks, it is possible to derive algebraic conditions on the parameters that determine when bistability occurs. These (global) algebraic conditions can be included as nonlinear constraints in a parameter optimization problem. We derive bistability conditions using Sturm's theorem for Gardner and Collins toggle switch. Then we optimize its nominal parameters to improve switching speed and robustness to a subset of uncertain parameters.