| Summary: | Synthetic biology is an interdisciplinary field that combines principles of engineering, biology, physics, and others to design and construct novel biological parts, devices, and systems that do not exist in nature. It has the potential to revolutionize many industries, including medicine, agriculture, and energy production. Despite its potential, synthetic biology is still mainly confined to laboratory experimentation because the design process is complex and may not consistently yield reliable outcomes when applied to real-world settings. These challenges can be attributed, in part, to a lack of modularity and the inherent stochasticity of biological systems. In the realm of synthetic biology applications, such as diagnosis, multi-input sensors and long-term memory devices that can remember sensory outputs for later analysis are essential. However, these have proved difficult to achieve. In this thesis, through mathematical modeling and stochastic analysis, I present a proof-of-concept design for a robust ratiometric sensor, which is a type of multi-input sensor that is especially useful to sense relative biomarker concentrations for in-gut diagnostics. Additionally, I provide design principles for a long-term, yet reversible, memory device, which can be toggled between two stable states that can be maintained for long time despite stochastic fluctuations. These two circuit designs can be widely applied in many diagnostic applications, such as through engineered bacteria in the gut, and at the same time they offer insight on how natural systems may perform similar tasks.
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