Estimating the multi-scale effects of extrinsic noise on genes and circuits activity from an empirically validated model of transcription kinetics

Recent studies of Escherichia coli transcription dynamics using time-lapse confocal microscopy and in vivo single-RNA detection confirmed that transcription initiation has two main rate-limiting steps. Here, we argue that this allows selective ‘tuning’ of the effects of extrinsic noise on a multi-scale level that ranges from individual genes to large-scale gene networks. First, using empirically validated stochastic models of transcription and translation, we show that the effects of RNA polymerase numbers’ cell-to-cell variability on the cell-to-cell diversity in RNA numbers decrease as the relative time-length of the open complex formation increases. Next, using a stochastic model of a 2-genes symmetric toggle switch, we show that the cell-to-cell diversity of the switching frequency due to cell-to-cell variability in RNA polymerase numbers also depends on the promoter kinetics. Finally, from the binarized protein numbers over time of 50-gene network models where genes interact by repression, we calculate the cell-to-cell variability of the mutual information and Lempel-Ziv complexity of the networks dynamics, and find that, while arising from the cell-to-cell variability in RNA polymerase numbers, these variability levels also depend on the promoter initiation kinetics. Given this, we hypothesize that E. coli may be capitalizing on the 2 rate-limiting steps’ nature of transcription initiation to tune the effects of extrinsic noise at the single gene, motifs, and large gene regulatory network levels.