Innovation in synthetic biology often still depends on large-scale experimental trial-and-error, domain expertise, and ingenuity. The application of rational design engineering methods promise to make this more efficient, faster, cheaper and safer. But this requires mathematical models of cellular systems. And for these models we then have to determine if they can meet our intended target behaviour. Here we develop two complementary approaches that allow us to determine whether a given molecular circuit, represented by a mathematical model, is capable of fulfilling our design objectives. We discuss algebraic methods that are capable of identifying general principles guaranteeing desired behaviour; and we provide an overview over Bayesian design approaches that allow us to choose from a set of models, that model which has the highest probability of fulfilling our design objectives. We discuss their uses in the context of biochemical adaptation, and then consider how robustness can and should affect our design approach.
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