Biomolecular Implementation of a Quasi Sliding Mode Controller Using an Ultrasensitive Cell Signalling Pathway

A fundamental aim of synthetic biology is to achieve the capability to design and implement robust embedded biomolecular feedback control circuits. An approach to realize this objective is facilitated by using abstract "chemical reaction networks" (CRNs).  This approach can impart a good degree of predictive functionality to the wet-lab circuits since these networks can model a large class of chemical and biological processes, and can be well analysed using advanced mathematical techniques.  The existing work within this framework concerns the design and implementation of linear time-invariant systems only: an example of such systems is the well-known "proportional+integrator" (PI) controller derived recently by Yordanov et al.  In practice, however, the PI controllers must be combined with a nonlinearity to overcome the wind-up effect associated with the integrator action. Here, we extend this approach to allow the implementation of nonlinear controllers using the sliding mode control theory whose strong performance and robustness characteristics have been widely recognised for a number of decades in the more traditional control engineering application domains. We show how a signalling cycle with ultrasensitive response dynamics can provide a biomolecular implementation of a nonlinear quasi sliding mode controller. We implement our controller on a prototype of a biological pathway, specifically a first-order low pass filter and demonstrate that our nonlinear controller outperforms a PI controller by facilitating faster response dynamics without introducing overshoots in the transient response.