The College of Education for Pure Sciences, Department of Mathematics, organized a scientific lecture on (Taylor's analytical technique for solving the gene expression model). The lecture, presented by the lecturer (Angham Ahmed Jabbar), included a study or gene expression model for an Escherichia coli strain and solving this model by applying an analytical method for linear ordinary differential equations using the Taylor technique, as this method uses the derivatives of the Taylor series expansion as a key in its construction. The solutions resulting from applying this method are in the form of a power series. The computational results showed the superiority of the method used to solve this model over the previously used method in terms of time and ease of use.