System identification of the phosophorylation based insulator in an in vitro cell-free expression system

An outstanding challenge in the design of synthetic biocircuits is the development of a robust and efficient strategy for interconnecting functional modules. Recent theoretical work demonstrated that a phosphorylation based insulator implementing a dual strategy of high gain and strong negative feedback could potentially serve as a device to attenuate retroactivity. This research investigates the structural identifiability of the phoshorylation based insulator when implemented in a transcription-translation (TXTL) cell free expression system. 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 phosphorylation based insulator. We perform standard system identification analysis and determine that the model is globally identifiable with respect to three critical parameters. These three parameters are identifiable under specific experimental conditions and we perform these experiments to estimate the parameters. Our experimental results suggest that the functional form of our simplified model is sufficient to describe reporter dynamics and enable parameter estimation. In general, this research illustrates the utility of the TXTL cell free expression system as a platform for system identification, as it provides extra control inputs for parameter estimation that typically are unavailable in vivo.