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NONLINEAR OSCILLATIONS OF TWO COUPLED COMPLEMENTARY DNA BASES Yakushevich L. V., Gapa S.1, Awrejcewicz J.
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Institute of Cell Biophysics of the Russian Academy of Sciences, Institutskaya str. 3, Pushchino, 142290, Russia, +7 4967 739252, yakushev@icb.psn.ru Technical University of Lodz, ul. Stefanowskiego 1/15, Lodz, Poland, 90-924, +48 042 6312225, awrejcew@o.lodz.pl

Nonlinear large amplitude oscillations of DNA base pairs, in which adenine forms two hydrogen bonds with thymine, and guanine forms three hydrogen bonds with cytosine, are of special interest, because they made substantial contribution to the process of opening DNA base pairs and that, in turn, is considered as one of important elements of the process of the DNA-protein recognition. In order to study the oscillations we develop and modify the recently proposed approach, and we apply it to study nonlinear oscillations of single DNA bases: Adenine (A), Thymine (T), Guanine (G) and Cytosine (C) (see [1]). We show that the dynamical equations that govern the DNA base pair oscillations have the form d 2 1 1 d I1 + K 12 [ A1 sin 1 - B sin(1 + 2 )] = - 1 + F , 2 dt 2 dt 2 d 2 1 d 2 + K 12 [ A2 sin 2 - B sin(1 + 2 )] = - + F, I1 2 2 dt dt where 1 and 2 are the angles of inclination of the 1-st and 2-nd complementary bases from their equilibrium positions; I1 and I2 are the moments of inertia of the bases; K12 is the parameter characterizing interactions between the bases; A1 = 2 r1(r1 + r2 + a ); A2 = 2 r2(r1 + r2 + a ); B = 2 r1r2; r1 and r2 are the distances between the centers of mass of the bases and the sugar-phosphate chains; a is the distance between masses of pendulums in the equilibrium state (1 = 2 = 0); is the coefficient of dissipation, and F is an external generalized force. We obtain the solutions of the equations and the trajectories of the investigated system in the phase space for both cases: AT and GC base pairs. The work has been partially supported by the grant N 08-04-00197 of the Russian Foundation for Basic Research. In addition, this research has been co-financed by the European Social Fund and the State Budget within the Activity 2.6 of the Integrated Operational Program for Regional Development in connection with the execution of the project "Fellowships to support innovative research of PhD students". References 1. Yakushevich L. V., Gapa S., Awrejcewicz J. Mathematical analysis of equations imitating DNA base oscillations, Proceedings of the conference "Mathematics. Computer. Education", Ed. Riznichenko G.Yu., V. 16, 2009, (to appear).