Fig. 3: The frequency of a periodic input determines the effect of distance on information transmission.

a Model simulations of RFP_p in response to a periodic arabinose input (2 h period). Gray shaded regions denote the presence of arabinose. b GFP as a function of time in response to an oscillatory arabinose input (2 h period). Gray shaded regions denote the presence of 0.1% arabinose. Colored shaded regions represent 1 SD from the mean. c RFP as a function of time in response to a periodic arabinose input (2 h period). d Model simulations of RFP_p in response to a periodic arabinose input (1 h period). e GFP over time in response to an oscillatory arabinose input (1 h period). f RFP in response to an oscillating arabinose input (1 h period). g RFP amplitude as a function of the input period at different distances. Square, plus, and circular data points represent the amplitudes in the step response, 2 h and 1 h forced oscillator experiments, respectively. Error bars represent 1 SD from the mean amplitude. h Top: mean RFP power spectra in response to an input period of 2 h (red dashed line) for 395–1536 min. The gray shaded region denotes a bandwidth of ±10 min around the expected input frequency. Bottom: mean RFP power spectrum in response to an input period of 1 h (blue dashed line) for 500–1249 min. i Signal-to-noise (SNR) ratios computed using bootstrapped power spectra for GFP or RFP for each distance (Methods) in the 1 h forced oscillator experiment. The horizontal lines within boxes denote the median and upper and lower edges represent the upper and lower quartiles, respectively. Upper and lower whiskers represent the 95th and 5th confidence intervals, respectively. Horizontal lines with stars denote statistically significant differences (P < 0.05) based on a one-tailed bootstrapped hypothesis test (Methods). *P < 0.05, **P < 0.01, and ***P < 0.001 (Supplementary Fig. 16). Source data are provided as a Source Data file.