Abstract
Accurate predictive mathematical models are urgently needed in synthetic biology to support the bottom-up design of complex biological systems, minimizing trial-and-error approaches. The majority of models used so far adopt empirical Hill functions to describe activation and repression in exogenously-controlled inducible promoter systems. However, such equations may be poorly predictive in practical situations that are typical in bottom-up design, including changes in promoter copy number, regulatory protein level, and cell load. In this work, we derived novel mechanistic steady-state models of the lux inducible system, used as case study, relying on different assumptions on regulatory protein (LuxR) and cognate promoter (Plux) concentrations, inducer-protein complex formation, and resource usage limitation. We demonstrated that a change in the considered model assumptions can significantly affect circuit output, and preliminary experimental data are in accordance with the simulated activation curves. We finally showed that the models are identifiable a priori (in the analytically tractable cases) and a posteriori, and we determined the specific experiments needed to parametrize them. Although a larger-scale experimental validation is required, in the future the reported models may support synthetic circuits output prediction in practical situations with unprecedented details.
Highlights
Recent advances in the construction and characterization of DNA encoded synthetic circuits have enabled to boost the design-build-test engineering cycle applied to biological systems, in terms of time and economic resources
We presented different mechanistic models of the widely used lux inducible system [29], derived under different key assumptions on molecule abundances and resource limitation, thereby obtaining mathematical tools able to describe copy number changes and the burden effects caused by individual parts
We extended the work by studying the usability of such models in terms of structural and practical identifiability, given experimental measurements commonly available in synthetic biology in vivo studies
Summary
Recent advances in the construction and characterization of DNA encoded synthetic circuits have enabled to boost the design-build-test engineering cycle applied to biological systems, in terms of time and economic resources This process has led to the engineering of complex engineering-inspired information processing and control systems, as well as solutions to numerous problems in industrial biotechnology and medicine [1,2,3]. The mentioned circuits are characterized by an elegant design and have real-world impact, the final correctly working systems were obtained only after random selection steps—e.g., to tune the expression levels of key proteins—or the affinity of repressors exerting feedback control [10] These and a number of other examples suggest that a bottom-up design process is desirable to increase the success rate in the construction of working biological systems that behave as intended. Accurate predictive models are needed to support this design step
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