Quantitative modeling of transcription and translation of an all-E. coli cell-free system

Cell-free transcription-translation (TXTL) is expanding as a polyvalent experimental platform to engineer biological systems outside living organisms. As the number of TXTL applications and users is rapidly growing, some aspects of this technology could be better characterized to provide a broader description of its basic working mechanisms. In particular, developing simple quantitative biophysical models that grasp the different regimes of in vitro gene expression, using relevant kinetic constants and concentrations of molecular components, remains insufficiently examined. In this work, we present an ODE (Ordinary Differential Equation)-based model of the expression of a reporter gene in an all E. coli TXTL that we apply to a set of regulatory elements spanning several orders of magnitude in strengths, far beyond the T7 standard system used in most of the TXTL platforms. Several key biochemical constants are experimentally determined through fluorescence assays. The robustness of the model is tested against the experimental parameters, and limitations of TXTL resources are described. We establish quantitative references between the performance of E. coli and synthetic promoters and ribosome binding sites. The model and the data should be useful for the TXTL community interested either in gene network engineering or in biomanufacturing beyond the conventional platforms relying on phage transcription.