An outstanding challenge in the design of synthetic biocircuits is the development of a robust and efficient strategy for interconnecting functional modules. Recent work demonstrated that a phosphorylation-based insulator (PBI) implementing a dual strategy of high gain and strong negative feedback can be used as a device to attenuate retroactivity. This paper describes the implementation of such a biological circuit in a cell-free transcription-translation system and the structural identifiability of the PBI in the system. We first show that the retroactivity also exists in the cell-free system by testing a simple negative regulation circuit. Then we demonstrate that the PBI circuit helps attenuate the retroactivity significantly compared to the control. We consider a complex model that provides an intricate description of all chemical reactions and leveraging specific physiologically plausible assumptions. We derive a rigorous simplified model that captures the output dynamics of the PBI. We performed standard system identification analysis and determined that the model is globally identifiable with respect to three critical parameters. These three parameters are identifiable under specific experimental conditions and we performed these experiments to estimate the parameters. Our experimental results suggest that the functional form of our simplified model is sufficient to describe the reporter dynamics and enable parameter estimation. In general, this research illustrates the utility of the cell-free expression system as an alternate platform for biocircuit implementation and system identification and it can provide interesting insights into future biological circuit designs.
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