A two-scale mathematical model for DNA transcription

Unlike the earlier description of regulation of DNA transcription as a biological switch which simply turns on and off, scientists now understand that DNA transcription is a much more complex process. It can depend on several transcription factors (proteins) and DNA regulatory elements (transcription factor binding sites). The combination of these two groups of different scaled factors determines the transcription outcome. In this paper, we propose a two-scale mathematical model for the DNA transcription processes, which integrates the characteristics of both transcription factors and DNA cis-regulatory elements. The model was tested on a well designed synthetic system during early development stage of Drosophila embryo. The system involves three transcription factors (two activators and one repressor) and a reporter gene. The predicted results using the model were compared with the real experimental data using both graphical methods and statistical methods. Parameter estimation will also be discussed in the paper.