Reconciling kinetic and thermodynamic models of bacterial transcription

Abstract

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.

Cis-Regulatory Logic Produces Gene-Expression Noise Describing Phenotypic Heterogeneity in Bacteria

“…Previous studies have highlighted the mechanisms of multiple TF-mediated gene regulation ( Browning and Busby, 2004 ; Morrison et al, 2021 ) which consists of deterministic biochemical kinetics. Then, several mechanisms have been tested in vitro and in vivo to estimate the level of gene expression as a function of available TF concentrations ( Dodd et al, 2004 ; Bintu et al, 2005b ; Kuhlman et al, 2007 ; Garcia and Phillips, 2011 ; Garcia et al, 2012 ; Ahsendorf et al, 2014 ; Morrison et al, 2021 ). This strengthens the construction of additional mathematical models accounting for all feasible states a promoter can adopt.…”

“…Despite considerable research, the extensive roles of TFs in transcriptional dynamics remain unclear. Previous studies have highlighted the mechanisms of multiple TF-mediated gene regulation (Browning and Busby, 2004;Morrison et al, 2021) which consists of deterministic biochemical kinetics. Then, several mechanisms have been tested in vitro and in vivo to estimate the level of gene expression as a function of available TF concentrations (Dodd et al, 2004;Bintu et al, 2005b;Kuhlman et al, 2007;Garcia and Phillips, 2011;Garcia et al, 2012;Ahsendorf et al, 2014;Morrison et al, 2021).…”

“…Diversified interaction patterns among those limited number of regulators against a single binding site introduce randomness in the system, and thus the higher level of noise ( Yan et al, 2017 ). The physical architecture of the promoter region and the influence of CREs support the understanding of combinatorial associations, although the mechanism is poorly understood ( Sun et al, 2020 ; Mejía-Almonte et al, 2020 ; Morrison et al, 2021 ).…”

Sequence specificity in DNA binding is determined by association rather than dissociation

“…Consequently, the rate of protein dissociation would depend on the DNA sequence, while the association rate would be invariant with respect to sequence. Indeed, the rate of protein association with DNA has often been assumed to be sequence-independent (3)(4)(5)(6). However, single-molecule measurements have shown that when a protein scans the DNA for binding sites, the association rate does depend on the sequence (7), and that different target sequences can be bypassed with distinct probabilities (8).…”

“…4 and 5 for 1/t1,3 and 1/t3,1, which are the sought macroscopic association and dissociation rates. We then obtain (6) and , (7) where [R] is the concentration of the searching protein. We now solve for p2,3 (= ptot) in both Eq.…”