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Publications of Eduardo D. Sontag jointly with Z. An
Articles in journal or book chapters
and E.D. Sontag.
Inferring causal connections through embedded physics-informed neural networks (ePINNs): An application to synthetic biology resource competition.
Note: In preparation.
Biological systems have been widely studied as complex dynamic systems that evolve with time in response to the internal resources abundance and external perturbations due to their common features. Integration of systems and synthetic biology provides a consolidated framework that draws system-level connections among biology, mathematics, engineering, and computer sciences. One major problem in current synthetic biology research is designing and controlling the synthetic circuits to perform reliable and robust behaviors as they utilize common transcription and translational resources among the circuits and host cells. While cellular resources are often limited, this results in a competition for resources by different genes and circuits, which affect the behaviors of synthetic genetic circuits. The manner competition impacts behavior depends on the “bottleneck” resource. With knowledge of physics laws and underlying mechanisms, the dynamical behaviors of the synthetic circuits can be described by the first principle models, usually represented by a system of ordinary differential equations (ODEs). In this work, we develop the novel embedded PINN (ePINN), which is composed of two nested loss-sharing neural networks to target and improve the unknown dynamics prediction from quantitative time series data. We apply the ePINN approach to identify the mathematical structures of competition phenotypes. Firstly, we use the PINNs approach to infer the model parameters and hidden dynamics from partially known data (including a lack of understanding of the reaction mechanisms or missing experimental data). Secondly, we test how well the algorithms can distinguish and extract the unknown dynamics from noisy data. Thirdly, we study how the synthetic and competing circuits behave in various cases when different particles become a limited resource.
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