A Model for Analysis of Gene Expression in the Cell Involving Protein Degradation

Abstract

The gene expression is responsible for the initiation sustenance and termination of various processes taking place in a cell in order to maintain the structure and the function of the cell. In the present paper, a model is proposed to analyze the gene expression in terms of temporal variation of DNA, mRNA and protein concentration along with the stability of molecular processes taking place in the cell. The model incorporates the parameters like replication, transcription, reverse transcription, translation and degradation of the protein. The model is obtained in terms of a system of differential equations along with initial conditions based on the physical and physiological conditions of the problem. The analytical solution is obtained for the model. The results have been obtained for a dataset of E. coli TJK16 strain and E. coli B/r strain, and employed to study the relationships of the parameters involved with the concentration of DNA, mRNA and protein. The asymptotic stability analysis at the equilibrium point has been performed for the molecular processes in the cell. The information generated from the model can be useful for developing the protocols for healthcare.