mRNA transcriptional dynamics is governed by a complex network of transcription factor (TF) proteins. Experimental and theoretical analysis of this process is hindered by the fact that measurements of TF activity in vivo is very challenging. Current models that jointly infer TF activities and model parameters rely on either of the two main simplifying assumptions: either the dynamics is simplified (e.g. assuming quasi-steady state) or the interactions between TFs are ignored, resulting in models accounting for a single TF.