Soliton Dynamics Analysis of Peyrard-Bishop-Dauxois DNA Model Using 4th Order Morse Potential Approach

Abstract

Research has been carried out to analyze the dynamics of the soliton DNA of the Peyrard-Bishop-Dauxois (PBD) model with 4th-order-approximation Morse Potential. The aim of research is to know physical changes of PBD model with  4th-order-approximation Morse Potential on stable and unstable state in describing denaturation process of DNA. The Process was carried out by finding a numerical solution of the 4th-order NLS  as stable equation using finite-difference method. Then, the result was be simulated on Matlab. The results show that on the stable state, expand Morse Potential for 4th-order than for 3th-order rastically increased amplitude of oscillation from 1,89 pm to 16 pm. On the first unstable state, the stable equation  was multiplied by (1+ ) where the value of  = 0.25. On the second unstable state, the stable equation  was multiplied two times by (1+ ) where the value of  = 0.25. On three of them, amplitude of oscillation decreased from 16 pm, 2,9 pm to 2,5 pm. Comparing to previous order, there is a new addtion to the 4th-order Morse Potential coefficient  which have physical meaning that larger expansion requires larger dissociation energy as well. So it can be concluded that the PBD model of DNA is descriptively able to explain the biological phenomenon of denaturation in DNA.