System identification of gene regulatory networks for perturbation mitigation via feedback control

In Synthetic Biology, the idea of using feedback control for the mitigation of perturbations to gene regulatory networks due to disease and environmental disturbances is gaining popularity. To facilitate the design of such synthetic control circuits, a suitable model that captures the relevant dynamics of the gene regulatory network is essential. Traditionally, Michaelis-Menten models with Hill-type nonlinearities have often been used to model gene regulatory networks. Here, we show that such models are not suitable for the purposes of controller design, and propose an alternative formalism. Using tools from system identification, we show how to build so-called S-System models that capture the key dynamics of the gene regulatory network and are suitable for controller design. Using the identified S-System model, we design a genetic feedback controller for an example gene regulatory network with the objective of rejecting an external perturbation. Using a sine sweeping method, we show how the S-System model can be approximated by a second order linear transfer function and, based on this transfer function, we design our controller. Simulation results using the full nonlinear S-System model of the network show that the designed controller is able to mitigate the effect of external perturbations. Our findings highlight the usefulness of the S-System modelling formalism for the design of synthetic control circuits for gene regulatory networks.