Bayesian and Algebraic Strategies to Design in Synthetic Biology

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 promises to make this more efficient, faster, cheaper, and safer. However, this requires mathematical models of cellular systems. For these models, we then have to determine if they can meet our intended target behavior. 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 behavior; we provide an overview of Bayesian design approaches that allow us to choose a model that has the highest probability of fulfilling our design objectives from a set of models. We discuss their uses in the context of biochemical adaptation and, then, consider how robustness can and should affect our design approach.