(A) Histogram of CW bias of wild-type cells. Grey bars are bins covering the average CW bias regime of wild-type cells. We sorted cells by their CW bias before stimulus and grouped them into the CW bias intervals (Methods). CW bias bins h and i are absent from the histogram because cells with CW bias greater than 0.4 require extra CheR from plasmid pZE21-CheR. We observed that most wild-type cells had CW biases between 0.05 and 0.2. To increase the chance to obtain cells with CW bias higher than 0.2, we transformed wild-type cells with pZE21-CheR (Methods). The first (B) and second (C) mean post-stimulus CCW interval lengths vs. pre-stimulus CW bias for all wild-type (RP437 and RP437 expressing CheR from pZE21-CheR) cells. (See Supplementary Fig. 1 for post-stimulus CCW interval lengths in individual cells.) Black circles, cells exposed to a small stimulus (10 nM stepwise increase of L-aspartate). Grey triangles, cells exposed to a large stimulus (1 µM stepwise increase of L-aspartate). Black line, power-law fit of the geometric mean of pre-stimulus CCW interval lengths calculated over 1500 s for all wild-type (RP437 and RP437 expressing extra CheR from pZE21-CheR) cells as a function of the pre-stimulus CW bias (Supplementary Fig. 1b). Error bars show the standard error associated with the average CCW interval length in each bin. Dark grey dotted line, geometric mean of the CCW interval lengths following a randomly chosen time point in non-stimulated cells. As the CW interval order after stimulus increases, the mean CCW interval lengths after stimulus approaches the mean CCW interval lengths (See also Supplementary Fig. 1).

(A) Low frequency noise in individual wild-type RP437 cells (black) and RP437 cells expressing CheR from pZE21-CheR (grey) versus CW bias. (Inset) Power spectral density (black) averaged over wild-type cells (RP437 and RP437 cells expressing CheR from pZE21-CheR) with CW bias = 0.15–0.20 (see Supplementary Fig. 5 for all CW bias bins). Power spectral density (dark grey line) of the motor decoupled from the signalling network³ (See Supplementary Fig. 5 for all CW bias bins). We determined the low frequency noise for the region between the dotted lines.
(B) Signalling noise as a function of CW bias for wild-type RP437 cells and RP437 cells expressing CheR from pZE21-CheR. Signalling noise is defined as the variance of the fluctuating [CheY-P]. Letters correspond to the CW bias bins (Methods). The power spectral densities and CW biases are averaged over cells within the same CW bias. Error bars show the standard error associated with the estimated signalling noise within each bin.

(A) Average response time for wild-type (RP437 and RP437 expressing extra CheR from pZE21-CheR) cells exposed to a stepwise small (black circles, 10 nM L-aspartate) or large (inset; grey triangles, 1 µM L-aspartate) stimulus. Error bars show the standard error associated with the average response time within each bin (a–i, Methods). (B) Average response time to a small (black circles) or large (inset, grey triangles) stimulus as a function of the correlation time for wild-type (RP437 and RP437 expressing CheR from pZE21-CheR) cells. For the large stimulus, the average response time was adjusted by a correction factor (Supplementary Fig. 2d). The solid lines are linear fit functions forced through the origin. Black line: Response time = C*Correlation time. C≈0.98±0.10 (R²=0.75). Inset grey line: Relaxation time = C*Correlation time. C≈12.23±1.83 (R²=0.07). The letters correspond to CW bias bins (Methods). Error bars for the correlation time are the half lengths of the first uncorrelated CCW intervals. Error bars for the response time are the standard error associated with the average response time within each bin. Grey area, peaks of wild-type cell population.

(A) Inverse of the coupling coefficient averaged over the long timescale for which this ratio is constant for the small (black circles) or large (grey triangles) stimulus. We computed the geometric mean over frequencies ranging from 1 s to 5 min for a small stimulus (from 10 s to 5 min for a large stimulus) in each CW bias bin. Standard error of the mean is smaller than the marker size. Lines, mean value of |K̃(ω)|_{CW bias} computed over CW biases ranging from ~0.05 to 0.5 for a small stimulus (black) and from ~0.1 to 0.3 a large stimulus (grey). (Inset) Inverse of |K̃(ω)|_{CW bias} for CW bias ranging from 0.15 to 0.20 for a small stimulus (10 nM L-aspartate increase) released at t = 0. See Supplementary Fig. 7 for all CW bias bins. (B) Average response times of wild-type (RP437 and RP437 expressing inducible CheR) cells to small (black circles) or large (inset, grey triangles) stimulus versus mean pre-stimulus signalling noise. Solid lines, linear fits forced through the origin: . Black line: C=259±25 sec/µM² (R²=0.8) for small stimulus. Inset, grey line: C=3215 ±307 sec/µM² (R²=0.4) for large stimulus. Grey area, average functioning state of wild-type population. (C) The correlation time as a function of the mean signalling noise before stimulus for wild-type (RP437 and RP437 expressing CheR from pZE21-CheR) cells. Black line, linear fit function forced through the origin (; C≈257 ±21 sec/µM² (R²=0.9)). Error bars for the correlation time are the average half-lengths of the first uncorrelated CCW intervals. Error bars for the signalling noise are the standard error associated with the signalling noise in each bin. Grey area is the average functioning state of wild-type population. Letters correspond to the CW bias bins (Methods).