Solution of state transfer matrix based on DNA strand displacement circuits

In recent years, DNA strand displacement (DSD) circuits have been developed in leaps and bounds. The high storage and parallelism of DNA give it an inherent advantage in the field of DNA computations. DSD is widely used in analog computations and neural network computations. However, there are few studies on solving state transfer matrix using DSD circuits. Aiming at the above problems, a scheme for solution of state transfer matrix based on DSD circuits is proposed. In this paper, the summation, subtraction, multiplication, division and exponential reaction modules are built by the DSD reactions. Based on the reaction modules, DNA chemical reaction networks of state transfer matrix are constructed. DSD circuits are built by cascading the DNA chemical reaction networks. The solution of the state transfer matrix is implemented through the DSD circuits. The Visual DSD is used to verify the practicality of DSD circuits. This scheme may provide a reference to analog computations based on DSD circuits.