Figure 3.

Autocorrelation of fluctuations for YFP-LuxO, qrr4-cfp, and mCherry-LuxR concentrations. (A, B, D, and E) Heat maps of concentration fluctuation autocorrelation matrixes for YFP-LuxO in the WT strain (A), YFP-LuxO in the luxO-ar strain (B), qrr4-cfp in the WT strain (D), and mCherry-LuxR in the WT strain (E). AI concentrations are indicated in the figure. (C) Autocorrelation curves inferred from A (green dashed) and B (black solid). The gray curve is the theoretical prediction of autocorrelation for a stable protein with noisy production ($R\left(\tau \right)=e^{-{\beta }_0\left|\tau \right|}$, where β₀ = (log 2)/2, is half of the basic dilution rate). (F) Autocorrelation curves inferred from D (blue dashed) and E (red solid). The lower gray curve is the same as the gray curve in C. The upper dashed curve is the theoretical autocorrelation for proteins whose production rate depends on an upstream stable protein with noisy production, $R\left(\tau \right)=\left(1+{\beta }_0\left|\tau \right|\right)e^{-{\beta }_0\left|\tau \right|}$ 10 (also Eq. S47). (G–I) Single-molecule fluorescence squared SD (σ²) versus mean (〈N〉) at the beginning of image acquisition for qrr4-cfp (G), YFP-LuxO (H), and mCherry-LuxR (I). σ² is proportional to 〈N〉 if intrinsic noise dominates. Such a relation is observed for YFP-LuxO but not for qrr4-cfp or mCheery-LuxR, which are known to be regulated by multiple upstream factors. Symbols: WT 0 nM AI (dot), WT 50 nM AI (circle), WT 1 μM AI (square), luxO-ar 0 nM AI (cross), luxO-ar 50 nM AI (triangle), and luxO-ar 0 nM AI (pentagram). The insets show SD (σ) versus mean (〈N〉) on a linear scale.