The purpose of this study was to determine the model of a interaction system between the DNA with protein. 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 Cornell potential was used to describe both of the interactions. We proposed the Hamiltonian equation to describe the general model of interaction. Interaction system is divided into three parts. The interaction model is satisfied when a protein molecule triggers pulses on a DNA chain. An initial shift in position of protein xm should 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.
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