Interferon-γ (IFNγ)-mediated signal transduction via upregulation of signal transducer and activator of transcription (STAT) 1 leads to the expression of the mucin (MUC) 4 gene in pancreatic cancer cells. Upregulation of STAT1 may also implicate STAT1 tyrosine- or serine-phosphorylation. Experimental data indicate that reaction steps involved in IFN-γ induced serine-phosphorylation of STAT1 vary between cell types in contrast to conserved IFN-γ induced tyrosine-phosphorylation of STAT1. The above observations raise the following two questions: (i) How does IFNγ stimulation regulates serine-phosphorylation of STAT1 in the pancreatic cancer cell line CD18/HPAF? (ii) Which type of STAT1 acts as a transcription factor of MUC4? Our objective is to address these two questions by data-driven mathematical modelling. Simulation results of the parameterised ordinary differential equation models show that serine-phosphorylation of unphosphorylated STAT1 occurs in the cytoplasm. In contrast, serine-phosphorylation of tyrosine-phosphorylated STAT1 can take place in the cytoplasm or in the nucleus. In addition, our results propose that unphosphorylated or serine-phosphorylated STAT1 can act as transcription factors of MUC4, either alone by progressive binding to different sites in the promoter or both together.