Estimation of promoter activity from time-lapse data

This protocol is extracted from research article:

Stochastic transcriptional pulses orchestrate flagellar biosynthesis in Escherichia coli

**
Sci Adv**,
Feb 5, 2020;
DOI:
10.1126/sciadv.aax0947

Stochastic transcriptional pulses orchestrate flagellar biosynthesis in Escherichia coli

Procedure

Promoter activity was estimated as previously described (*24*, *65*). Briefly, if the total area of the cell is *A*(*t*) and the average pixel intensity is *C*(*t*), then *F*_{total} = *A*(*t*)*C*(*t*). It follows that$$\frac{1}{A}\frac{{\mathit{dF}}_{\text{total}}}{\mathit{dt}}=C\frac{1}{A}\frac{\mathit{dA}}{\mathit{dt}}+\frac{\mathit{dC}}{\mathit{dt}}$$

The left term $\frac{1}{A}\frac{d{F}_{\text{total}}}{\mathit{dt}}$, i.e., the “cell size normalized” production rate, was operationally defined as the promoter activity. To compute promoter activity, $\frac{1}{A}\frac{\mathit{dA}}{\mathit{dt}}$, i.e., the relative growth rate of the cell, was estimated by taking the log ratio of the initial and final area of the cell for each cell division. $\frac{\mathit{dC}}{\mathit{dt}}$ was estimated by smoothing our fluorescence traces with a Savitzky-Golay filter and taking the numerical derivative. See the “Estimation of promoter activity” section in the Supplementary Materials for more details.

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