A model of a nonlinear DNA-protein interaction system with Killingbeck potential and its stability

8th International Conference on Physics and its Applications

Syahroni, E.^1 ; Suparmi, A.^1 ; Cari, C.^1 ; Fuad, A.^1

Physics Department, Graduate Program, Sebelas Maret University, Jl. Ir. Sutami 36A, Kentingan Jebres Surakarta

57126, Indonesia^1

关键词: DNA-protein interaction;    Equilibrium point;    General model;    Hamiltonian equations;    Interaction model;    Interaction systems;    Protein molecules;    Single chains;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/776/1/012086/pdf
DOI  :  10.1088/1742-6596/776/1/012086

来源: IOP

【 摘 要 】

In this paper, we presented a model of a nonlinear DNA-protein interaction system. The interaction system consisted of a molecule of protein bound with a single chain of DNA. The interaction between DNA chain, especially adenine and thymine, and DNA-protein bound to glutamine and adenine. The forms of these bonds are adapted from the hydrogen bonds. The Killingbeack potential were used to describe both of the interactions. We proposed the Hamiltonian equation to describe the general model of interaction. The interaction model is satisfied when a protein molecule triggers pulses on a DNA chain. An initial shift in position of protein xmshould trigger the shift in position of DNA ym, or alter the state. However, an initial shift in DNA, yn, should not alter the state of a rest protein (i.e. xm= 0), otherwise, the protein would not steadily bind. We also investigated the stability of the model from the DNA-protein interaction with Lyapunov function. The stability of system can be determined when we obtained the equilibrium point.