Fig. 5: Genetic circuit with positive and negative feedback on a single DNA molecule.

a Schematic of a DNA molecule encoding the gene for T7 RNAP producing a downstream strong single-chain dimeric Cro (dCro) repressor to repress HT-T7 RNAP synthesis. b Two-color fluorescent images of HT-T7 RNAP signal co-localized to two surface-immobilized DNA molecules. Scale bar, 2 µm. c Exemplary trace of a single DNA molecule (shown in panel b) encoding the gene circuit in panel a with dCro and highlighted in panel d (Trace I). The black line is a moving average over the raw data in light gray. A second construct with a weak monomeric Cro (mCro) repressor, replacing dCro, was probed as a proxy for no/weak negative feedback. The HT-T7 RNAP expression signals were transformed into frequency space using the Fast-Fourier-Transformation (FFT). The ensemble-averaged power spectrum (the black line indicates \({f}^{-3/2}\) decay) is given as median and error bars representing 32th and 68th percentiles from a total number of DNA molecules (n = 108 for dCro and n = 56 for mCro) examined over n = 5 (dCro) and n = 4 (mCro) independent experiments. d Scatter plot showing the maximal FFT amplitude (\({{{{{{\mathscr{F}}}}}}}_{\max }\)) against signal drift computed as a linear trend in the HT-T7 RNAP expression traces. The dashed ellipse estimates the reference distribution without negative feedback from the construct with mCro. Traces outside the ellipse were classified as pulses (filled markers). The inset shows the fraction of HT-T7 RNAP expression traces classified as pulses for the two constructs. Projected histograms are overlaid with bimodal Gaussian fits to guide the eye. The same number of DNA molecules were used as in panel c. e Pulsing factor is defined as the ratio between \({{{{{{\mathscr{F}}}}}}}_{\max }\) and signal accumulation (drift). The pulsing factor distributions for the two constructs from panel d, excluding the traces with negative HT-T7 RNAP signal accumulation. The violin plot shows the Gaussian kernel density estimate as gray area and error bars indicate minimum and maximum values. The p-value is computed by two-sided Welch’s t-test. The same number of DNA molecules were used as in panel c. f Exemplary HT-T7 RNAP synthesis traces for the three highlighted traces in panel d (Trace II–IV). The insets show individual traces overlaid with the average signal found from population classes in panel d (Class 1–3). Individual pulses were aligned in time with the phase shift computed at \({{{{{{\mathscr{F}}}}}}}_{\max }\). Source data are provided as a Source Data file.