  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.
