The kink–antikink relationship in DNA replication

We proceed from of a two-chain interwound structure of DNA molecules. With due regard for a quantum mechanical effect the forces of the self-contact-atoms into the superhelical molecule are unstated, partly because the mechanical methods inability to account explicitly for interactions spiraling subvent. As enzymes unwind the DNA double helix, they induce the forced rotation on round tangents to the spiral. From here we draw a conclusion: the double helix modeled as two chans of pendulums (the nucleobases), connected by springs (the sugar-phocphate backbones). It is known that such a coupled-pendulum system is then an example of the sine-Gordon model. There the problem of the angular mobility nucleobases is reduced to the soliton solutions of the sine-Gordon (sG) equation. In the preceding article a direct analytical construction of one-solution ($p$-kink) and oscillating-soliton (bion) solutions of sG equation are given. In the same place the soliton solutions sG equation applicability in a processes replication and transcription is discussed. On the basis of the sine-Gordon model we show that when the probability density of the excitations and of the kinetic equation coefficients are considered. The comparison of energy level is carried out for the different DNA conditions. In this article a direct general analytical construction one-solution of sG equation in the form of $p$-soliton and $n$-soliton is given. One of the properties of solitons is their localizaiton within a region. For the one-soliton solutions the corresponding region is usually each half-pitch of the DNA helix. In order to analyse the soliton-antisoliton interaction in the DNA replication we directly construct the exact general analytical two-soliton solutions of sG equation with the help of the Hirota method. Special cases of two-soliton solutions of sG equation are considered. For the two-soliton solutions the corresponding regions are usually distinct half-pitches of the DNA helix. The two-soliton solutions of sG equation allow to receive the DNA two-sided replication are determined. DNA chains have a directionality, and the chains of the double helix are anti-parallel. Unter the solution impact at first the “leading” branches may occur, later the “lagging” branches. The “leading” is the helix so that moves along in the replication process. The “lagging” helix have a inverse direction of the growth. In this article the double-sided DNA replication with the help of the kink–antikink interaction is considered. Refs 13.