Reconciling kinetic and thermodynamic models of bacterial transcription

The study of transcription remains one of the centerpieces of modern biology with implications in settings from development to metabolism to evolution to disease. Precision measurements using a host of different techniques including fluorescence and sequencing readouts have raised the bar for what it means to quantitatively understand transcriptional regulation. In particular our understanding of the simplest genetic circuit is sufficiently refined both experimentally and theoretically that it has become possible to carefully discriminate between different conceptual pictures of how this regulatory system works. This regulatory motif, originally posited by Jacob and Monod in the 1960s, consists of a single transcriptional repressor binding to a promoter site and inhibiting transcription. In this paper, we show how seven distinct models of this so-called simple-repression motif, based both on thermodynamic and kinetic thinking, can be used to derive the predicted levels of gene expression and shed light on the often surprising past success of the thermodynamic models. These different models are then invoked to confront a variety of different data on mean, variance and full gene expression distributions, illustrating the extent to which such models can and cannot be distinguished, and suggesting a two-state model with a distribution of burst sizes as the most potent of the seven for describing the simple-repression motif.Author summary: With the advent of new technologies allowing us to query biological activity with ever increasing precision, the deluge of quantitative biological data demands quantitative models. Transcriptional regulation—a feature that lies at the core of our understanding of cellular control in myriad context ranging from development to disease—is no exception, with single-cell and single-molecule techniques being routinely deployed to study cellular decision making. These data have served as a fertile proving ground to test models of transcription that mainly come in two flavors: thermodynamic models (based on equilibrium statistical mechanics) and kinetic models (based on chemical kinetics). In this paper we study the correspondence between these theoretical frameworks in the context of the simple repression motif, a common regulatory architecture in prokaryotes in which a repressor with a single binding site regulates expression. We explore the consequences of different levels of coarse-graining of the molecular steps involved in transcription, finding that, at the level of mean gene expression, the different models cannot be distinguished. We then study higher moments of the gene expression distribution which allows us to discard several of the models that disagree with experimental data and supporting a minimal kinetic model.