缠绕方程在DNA模型中的应用

Applications of Tangle Equations for DNA Model

本文所要解决的问题是如何解缠绕方程组.缠绕方程组的每个方程的左边都是未知的缠绕的和的分子构造的形式,右边是已知的纽结或链环.这样的方程组主要来源于DNA的特异性位点重组实验中的缠绕模型.在DNA的特异性位点重组的过程中,DNA分子的两条链在拓扑异构酶的作用下断开并把不同的端点重新连接起来,从而得到新的DNA分子.本文的数学模型是:N(O)=K_0,N(O+R)=K_1,其中O是有理缠绕或者是两个有理缠绕的和,R是整缠绕,并且O和R都是未知的缠绕,N是缠绕的分子的构造,K_i(i=0,1)是已知的纽结或链环.本文给出了这些缠绕方程组的解,从而得到DNA分子在重组后的模型.

In this paper,we give methods of solving tangle equations.The left side of the tangle equations are the numerator construction of the sum of the unknown tangles,the right side of the tangle equations are the known knots or links.These tangle equations come from the tangle model of the DNA site-specific recombination.During the DNA sitespecific recombination,double-stranded DNA breaks and recombines different ends under the function of the topoisomerase,then one can get a new DNA molecule.We consider the following mathematical model：N（O）=K_0,N（O＋R）=K_1,where O is a rational tangle or the sum of two rational tangles,and R is a rational tangle,in addition,O and R are unknown tangles,N is the numerator construction of the tangle,and K_i（i=0,1）are the known knots or links.We give the solutions of these tangle equations.Furthermore,one can obtain the DNA recombination model.