Finite-time regulation property of DNA feedback regulator

In dynamic DNA nanotechnology, the DNA strand displacement technique provides the cornerstone for the bottom-up design of a man-made DNA molecular system. Practically, a feedback controller for regulating the concentration of a target DNA strand to the desired level is indispensable for mediating the kinetic momentum of a molecular actuator. However, such a regulator system operates by consuming fuel strands and requires sufficient supplies of these consumables for its normal execution, indicating that, in practice, optimal controller design requires the period of time during which the regulator proceeds with normal operation to be as long as possible. The fact that the system is naturally high dimensional and nonlinear complicates the analysis of properties emerging during a finite-time period in terms of their theoretical aspects. In this paper, we first define the new concept of a “finite-time regulation property” of DNA systems in the regulation problem. Then, to theoretically analyze this regulation property, we present two-time-scale modeling based on the difference in the initial distribution of the abundance of DNA strands. Focusing on the fast mode as a subsystem with a positive quadratic structure, we propose a new method for analyzing the regulation property observed in a finite period of time