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 Kremling (2007), 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 to show that, under assumptions of time scales separation, it is possible to reduce the models to much smaller ones.