Higher Order Periodic Base Pairs Opening in a Finite Stacking Enthalpy DNA Model

The dynamics of periodic base pairs opening in a finite stacking enthalpy DNA is investigated in this work. This is achieved by using the Joyeux-Buyukdagli DNA model, in which the polynomial approximations of the stacking interaction and Morse potential are expanded up to the fifth order nonlinear terms by using the Taylor series expansion technique. By incorporating the continuum limit approximation and the extended multiple scale asymptotic methods, higher order nonlinear Schrödinger amplitude equations are derived. In the limit of cubic nonlinearity, the periodic base pair configurations clearly depict the open state; with linear stability analysis exposing other periodic background modes that are vital in the DNA transcription, replication, and transmission of genetic codes. The higher order modes generally display a more robust and structurally stable wave profile, which epitomizes the base pair dynamics of the DNA molecule observed from experimental investigations. Prolonged time evolution of base pairs stretching greatly modifies the higher order modes of the DNA molecule, strongly suggesting that such modes may induce abnormalities like gene mutation which is responsible for numerous diseases.