Solving The Tangle Equations Of DNA Molecular Model

This article focuses on the problem of tangle equations in the DNA molecular model.Through some related knowledge of rational tangle and how enzymes act on the DNA strand and the mathematical model established in the process of recombination.This model is a kind of rational tangle equation,the left side of equation is the N structure of the unknown tangle sum molecule,and the right side is the known second bridge knot.Then the definition rational tangle,the definition and properties of continued fraction and the second bridge knot are classified properties applied to this model,and the proof process of the solution of some tangle equations is given.First,introduce the definition of rational tangle,Conway’s representation and some basic properties,such as the nature and operation of continued fractions,and the relationship between rational tangle equivalence classes;through some theorems and lemmas,mathe-matical models of DNA can be established and equations can be obtained(1)N(X+T)=b(1,1);(2)N(X+R)=b(α,β);(3)N(X+R+R)=b(α’,β’);And verified the correctness of these solutions.Next,from the general solution of the mathematical modelN(O+iR)=Ki(i=0,1,2,3),the specific winding equation K0=b(1,0)K1=b(9+x,9)=b(9+x,x)and winding equation are given(1)N(X+T)=b(1,1);(2)N(X+R)=b(x,1);(3)N(X+R+R)=b(2x+1,2);Among them,x satisfies x+1 a prime number,2x+1 is a prime number,the process of solving an equation.In addition to this method,another method is also used to find the following tangle equation and its possible solutions,(1)N(X+T)=<x>(2)N(X+R)=<x,1>(3)N(X+R+R)=<x,1,y>.Among them,x>1,x,y are positive integer,xy+y is a prime number,xy+2x-yis a prime number.