On mathematical model of DNA mobility

The superhelical DNA molecule is a linearly extendet elastic polimer made from repeating nucleotides. It is start from of a two-chain interwound structure DNA molecules. The DNA double helix is stabilited of the hydrogen bonds between the nitrous bases (nucleobases) align perpendicular to the axis of the molecule. The backbone of the DNA molecule strand is made from alternating phosphate and sugar residues. In a prosesses named replication and transcription the enzymes break the hydrogen bonds and originate the so-called open states. With due regart for a quantum mechanical effect the forces of the self-cotact-atoms into the superhelikal molecule is completaty unstated. In part because, the mechanical methods inability to account explicitle for interactions spiraling sulvent. As enzymes unwinds the DNA double helix, they inducte the forced rotation round tangents to the spiral. This suggest the double helix modeled as two linear chans of penduls (the nucleobases) connected by springs (the sugar- phocphate backbones). It is known such the coupled-pendulum system is then an example of the sine-Gordon model. There the problem of the angular mobility nucleobases redices to the soliton solutions of the sine-Gordon (SG) equation. From a more biology viewpoint, solton may bewiewed, as solitary excitation arising from large-amplitude, the refore nonlinear effect produce, which can migrate as particle. The principal features of the solitonic exctations are stable dynamic and static mode in extended system. In this article an direct analytical construction one-solution (kink) and oscillating-soliton (bion) solutions of SG equation is given. The soliton solutions SG equation applicability on the description of the DNA mobility 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 levet are realized for the different conditions DNA. Bibliogr. 23.