When Activators Repress and Repressors Activate: A Qualitative Analysis of the Shea-Ackers Model

Abstract

The concept of activation in transcriptional regulation is based on the assumption that product mRNA increases monotonically as a function of regulator concentration. We analyze the Shea-Ackers model of transcription and find this assumption to be correct only for the simplest of promoters. We define a new regulatory constant that is a nonlinear combination of association and transcription initiation constants characterizing activation and repression for more complicated promoters. Our results can guide the synthesis of new promoters and lead to a deeper understanding of the constraints guiding the natural promoters evolution.