An implementation method for solving a circle and straight line equation set intersection point based on DNA strand displacement

Abstract

The invention provides an implementation method for solving a circle and straight line equation set intersection point based on DNA strand displacement, which comprises the following steps: firstly, constructing a quadratic logic gate, a first-order logic gate and a constant logic gate based on a reaction mechanism of DNA strand displacement, and determining a small fulcrum domain of each logic gate, a base sequence of each logic gate, an auxiliary object, a DNA strand structure of a reactant and a structural domain of each logic gate; secondly, respectively determining DNA chemical reaction networks of a binary quadratic equation and a binary linear equation according to a conversion relation between each logic gate biochemical reaction and a mathematical differential expression, and respectively designing DNA chemical reaction networks of a circle equation set and a linear equation set; and finally, solving the DNA chemical reaction network of the circle and straight line equation set by adjusting the concentration of the auxiliary substance, and carrying out simulation verification on the solving result by using Visual DSD software. The method provided by the invention has reasonability and effectiveness, and can be used as a basis for researching the solution of a high-order high-order equation set based on DNA strand displacement in the future.

Description

technical field [0001] The invention relates to the technical field of solving DNA strand displacement equations, in particular to a realization method for solving the intersection of circle and straight line equations based on DNA strand displacement. Background technique [0002] DNA strand replacement is a dynamic DNA nanotechnology that releases DNA single-strand products through the adhesion and initiation of chain reactions between single strands of DNA molecules. DNA strand displacement has the characteristics of self-organization, sensitivity and accuracy. in 1989, The stochastic Brussels model proposed by et al. established a corresponding relationship between DNA chemical reaction expressions and mathematical ordinary differential equations, making it possible to construct mathematical equations based on DNA strand displacement. The chemical reaction expression (1-1) expresses the stochastic Brussels model, and the kinetic behavior of this model is expressed by ...

AI Technical Summary

Problems solved by technology

[0012] The equations solved by the existing DNA strand replacement technology are one-dimensional equations such as one-dimensional one-dimensional equations, one-dimensional quadratic equations, etc., which do not involve the solution of binary and above equations, and do not consider the technical problem of the situation that the equation has no solution. The present invention proposes An implementation method based on DNA strand replacement for circle and straight line equations, AX based on DNA strand replacement 2 , BX, -C three DNA chemical calculation modules, according to the influence of the chemical reaction rate on the DNA reaction pool, construct circle and straight line equations and solve them, solve mathematical problems from the biological point of view, and provide more theories for DNA calculation Support, use Visual DSD simulation software to verify and clarify the working process of DNA strand displacement reaction, realize the expected function, and the results prove its effectiveness

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