Analysis and reduction of transcription translation coupled models for gene expression

The aim of this paper is to analyze and to reduce coupled transcription-translation models developed in (Kremling (2007)), which are a detailed representation of the process describing how the information in DNA turns into proteins in a cell, with polymerase and ribosomes. The full model is of high dimensions, and may be complex to deal with. Under assumptions on the parameters, we can write the full system in the form of a slow fast system. The fast part is a monotone system and we prove its global stability. We put this fast part to its quasi steady state, and show that it is possible to obtain a small reduced model (with three variables) having essentially the same dynamical behavior.