One of the essential parts of synthetic biology is the modeling of systems which it aspires to describe. These models can be of varying natures, they describe the very small; the behaviour of single molecules, up ot the very large; dynamics of whole organisms. These models allow for the prediction of the behaviour of said systems, which supports wet lab work and allows to predict the outcomes of experiments. In this project we tried to implement a deterministic model of the transcription and translation of our expression system. This kind of model is based on numerically solving differential equations, that each describe the concentration of a species of the system over time. The model is meant to give us clues about how our expression system is regulated and behaves over time and to be experimentally validated.