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Stability analysis of a reduced transcription-translation model of RNA polymerase

I. Belgacem, E. Grac, D. Ropers, J.-L. Gouzé

Proceedings of the 53rd IEEE Conference on Decision and Control (CDC), Dec 2014, Los Angeles, CA, United States.

The aim of this paper is to analyse the dynamical behaviour of models of gene transcription-translation for the synthesis of RNA polymerase in a cell, with a closed loop from the produced RNA polymerase (end-product) to the transcription step (RNA polymerase is needed to transcribe itsown gene). Using monotone system theory we study a reduced version of this model with two variables (mRNA and protein),and show that it has either a single globally stable trivial equilibrium in (0, 0), or has an unstable zero equilibrium anda globally stable positive one. This dynamical behaviour can be related to biological observations on the bacterium Escherichia coli.