New Approach to Frequency Response Analysis of Biomolecular Circuits

In this study, we propose a new approach to the frequency response analysis of biomolecular circuits. We consider the following biomolecular circuit: an enzyme-free DNA reaction system that utilizes DNA strand displacement reactions. Because biomolecular circuits are nonlinear in nature, it is generally difficult to apply linear control theory without linearization. In a class of DNA circuits, the DNA strands in the reaction system can be divided into two groups: fuel strands and signal strands. Herein, we show that frequency response analysis is applicable by transforming the original nonlinear model into a two-time-scale model. The novelty of our method is demonstrated by using two practical examples.