Stability analysis and reduction of gene transcription models

The aim of this paper is to analyze the dynamical behaviour of models of gene transcription in a cell, developed in [1], which are a detailed representation of transcription process from DNA to RNA with action of polymerase. Using monotone system theory and compartmental systems theory, we study several versions of these models. We use our results of global stability of the fast part of the full system to show that, under assumptions of time scales separation, it is possible to reduce the full models to much smaller ones.