Chemical Reaction Networks’ Programming for Solving Equations

Abstract

The computational ability of the chemical reaction networks (CRNs) using DNA as the substrate has been verified previously. To solve more complex computational problems and perform the computational steps as expected, the practical design of the basic modules of calculation and the steps in the reactions have become the basic requirements for biomolecular computing. This paper presents a method for solving nonlinear equations in the CRNs with DNA as the substrate. We used the basic calculation module of the CRNs with a gateless structure to design discrete and analog algorithms and realized the nonlinear equations that could not be solved in the previous work, such as exponential, logarithmic, and simple triangle equations. The solution of the equation uses the transformation method, Taylor expansion, and Newton iteration method, and the simulation verified this through examples. We used and improved the basic calculation module of the CRN++ programming language, optimized the error in the basic module, and analyzed the error’s variation over time.

Chemical Integration of ODEs using Idealized Abstract Solutions

“…To realize mass-action kinetic systems in laboratory settings as synthetic biochemical processes, such as to compute roots of nonlinear equations [18,19] (or in our case, to solve differential equations by measuring chemical concentrations), we must perform our analysis under the assumption that the rate coefficients of reaction channels as well as measured solution concentrations have been contaminated.…”

“…Circuitry for representing primitive calculations such as addition, division, and m-th root finding in chemical matter have been proposed [18], and biomolecule-based programming languages for computing roots of a small range of algebraic functions (such as polynomials) and nonlinear equations (exponential, logarithmic, and a subset of trigonometric equations) have been developed. In particular, the paper [19] depicts the implementation of Newton iterations for root-finding in an idealized abstract solution.…”