The College of Education for Pure Sciences, Department of Mathematics, discussed a master’s thesis on (Taylor Analytical Technique to Solve Gene Expression Model)
The thesis presented by the researcher (Angham Ahmed Jabbar Abdel-Sayed) included the study of gene expression models of the Escherichia coli strain and solving these models by applying a new analytical approximation method for linear ordinary differential equations using Taylor expansion technique, as this method uses compounds derived from Taylor chain expansion as a key in its construction. . The solutions resulting from the application of this method are in the form of a power series. The effectiveness of the method has been confirmed by two models of gene expression, the first includes three ordinary differential equations representing the equations for the change in the concentration of DNA, mRNA and protein. The second model is a development of the first model, which consists of four ordinary differential equations representing the equations for the change in the concentration of the activating gene, the repressor gene, RNA and protein, as they are studied in two cases, the first case when the activated protein and the inhibitor protein compete to bind to the same regulatory sites of DNA , the second case when the link is to different regulatory sites.
The computational results showed the preference of the method used to solve these models over the method of fog analysis that was used previously to solve the first model in terms of time and ease of application. Either the second model sheds light on the problem of the first model that neglects the time delay that occurs during the transcription and translation process by adding a differential delay limit, studying the results and testing the convergence of solutions. Surface and graphs.