Like engineered systems, biological systems naturally exhibit a remarkable degree of robustness to both external perturbations and internal fluctuations. Indeed, understanding quantitative principles of biological control is a key goal of systems biology and is necessary for engineering cellular systems.

Unlike electro-mechanical systems, cellular processes are fundamentally discrete and stochastic due to the randomness associated with individual (bio)chemical events at low copy numbers. This limits the applicability of classical control theory to understanding biological control systems. Moreover, individual components of interest are typically embedded within complex and sparsely characterized networks. This makes it difficult to develop reliable models of natural regulatory processes and to engineer molecular control circuits for synthetic biology applications.

In this dissertation talk, I will discuss several approaches to overcoming these challenges. First, I will present a theoretical characterization of the stochastic noise properties of biomolecular “integral feedback” modules, which ensure robust adaptation of cellular abundances in arbitrary reaction networks. I will then discuss the application of statistical moment invariants to derive universal efficiency-fluctuation trade-offs in broad classes of molecular assembly processes, which are ubiquitous in cellular life. Finally, I will present a phenomenological model of signalling robustness in embryonic development and describe planned experiments to test model predictions in zebrafish.