Living cells are exquisite systems. They are strongly regulated to perform in highly specific ways, but are at the same time wonderfully robust. This combination arises from the sophistication of their construction and operation: their internal variables are carefully controlled by complex networks of dynamic biochemical interactions, crafted and refined by billions of years of evolution. Using modern DNA engineering technology, scientists have begun to circumvent the long process of evolution by employing a rational design-based approach to construct novel gene networks inside living cells. Currently, these synthetic networks are relatively simple when compared to their natural counterparts, but future prospects are promising, and synthetic biologists would one day like to be able to control cells using genetic circuits much in the way that electronic devices are controlled using electrical circuits. The importance of precise dynamical behaviour in living organisms suggests that this endeavour would benefit greatly from the insights of control theory. However, the nature of biochemical networks can make the implementation of even basic control structures challenging. This thesis focusses specifically on the concept of integral control in this context. Integral control is a fundamental strategy in control theory that is central to regulation, sensory adaptation, and long-term robustness. Consequently, its implementation in a synthetic gene network is an attractive prospect. Here, the general challenges and important design considerations associated with engineering an in-cell synthetic integral controller are laid out. Specific implementations using transcriptional regulation are studied analytically and then in silico using models constructed with commonly available parts from the bacterium Escherichia coli. Finally, using a controller based on post-translational signalling, an on-paper design is proposed for an integral-controlled biosynthesis network intended to allow a population of engineered Saccharomyces cerevisiae cells to actively regulate the extracellular concentration of a small molecule.
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