Solution of Equations Based on Analog DNA Strand Displacement Circuits

Deoxyribonucleic acid (DNA) strand displacement can be used to build complex functional circuits due to its highly modular and programmable properties. While DNA strand displacement is most often used to solve logic problems, it can also be used to compute the roots of equations. In this paper, we present the design of novel architectures for catalysis, degradation, and annihilation in ideal formal reaction modules, and we translate these reaction modules to DNA networks. These ideal formal or DNA reaction modules are suitable for building analog circuits for solving tasks. The computing analog DNA circuits are assessed by solving a linear equation, a one-variable quadratic equation, and a set of two simultaneous linear equations. The results were evaluated by simulation.