MECHANICAL APPROACH IN THE STUDIES OF DNA BASE PAIR OSCILLATIONS
The rotational oscillations of the DNA bases around the sugar-phosphate chains make an important contribution to the process of DNA base pairs opening that in turn plays a crucial role in the process of the DNA-protein recognition. As a result, the study of these oscillations helps to understand better the dynamical mechanisms of the biological activity of the DNA molecule. In this work, we study rotational oscillations of two coupled DNA bases that form a base pair: adenine-thymine (AT) or guanine-cytosine (GC). We show that the problem can be reduced to the mechanical problem of two coupled nonsymmetrical nonlinear pendulums oscillating in the horizontal plane. We obtain the Lagrange equations, estimate the values of the coefficients of the equations and use the results of estimations to construct the potential energy surface. We consider in detail the case of small amplitudes of angular displacements, find the general solution of corresponding Lagrange equations and present graphs using Maple 13.