Since mammalian target of rapamycin (mTOR) and N-myristoltransferase (NMT) have been shown to be potentially related to breast cancer, mTOR-NMT signalling pathway is taken into specific consideration. In this thesis, mathematical models are developed to not only describe the mTORNMT signalling pathways, but also to analyze and predict the response to a treatment. Based on different biological hypotheses, candidate models are obtained by using an ordinary differential equation formalism. An optimization method called the Differential Evolution algorithm is applied to find the best parameter sets for our candidates. Doing so, will give the smallest distance between experimental data and simulated results. The experimental data are provided by Dr Shrivastav’s laboratory, Department of Biology, University of Winnipeg. Furthermore, the mathematical analysis for our candidate models has been found to show their asymptotic behaviours.To determine which candidate model is most likely to be the ”best” among the subgroup of models, model selection is used. Ultimately, the collaboration with Dr Shrivastav’s laboratory let us understand the simplified mTOR-NMT signalling pathway. / October 2016