Implementation of an Ultrasensitive Biomolecular Controller for Enzymatic Reaction Processes With Delay Using DNA Strand Displacement

In this article, a set of abstract chemical reactions has been employed to construct a novel nonlinear biomolecular controller, i.e, the Brink controller (BC) with direct positive autoregulation (DPAR) (namely BC-DPAR controller). In comparison to dual rail representation-based controllers such as the quasi sliding mode (QSM) controller, the BC-DPAR controller directly reduces the number of CRNs required for realizing an ultrasensitive input-output response because it does not involve the subtraction module, reducing the complexity of DNA implementations. Then, the action mechanism and steady-state condition constraints of two nonlinear controllers, BC-DPAR controller and QSM controller, are investigated further. Considering the mapping relationship between CRNs and DNA implementation, a CRNs-based enzymatic reaction process with delay is constructed, and a DNA strand displacement (DSD) scheme representing time delay is proposed. The BC-DPAR controller, when compared to the QSM controller, can reduce the number of abstract chemical reactions and DSD reactions required by 33.3% and 31.8%, respectively. Finally, an enzymatic reaction scheme with BC-DPAR controller is designed using DSD reactions. According to the findings, the enzymatic reaction process’s output substance can approach the target level at a quasi-steady state in both delay-free and non-zero delay conditions, but the target level can only be achieved during a finite-time period, mainly due to the fuel stand depletion.