Fig. 3. The period of the free oscillator is determined by the dilution rate.

a A sensitivity analysis was performed by analyzing the change in the period ΔT in response to a 30% change in individual model parameters⁹. b Example of an auto-correlation function (ACF) that was used to estimate experimental periods for both reporters, corresponding to sample 4 in Fig. 2a. The red triangle indicates the first maximum. c Period as a function of the dilution rate T(δ). The experimentally measured periods are compared to predictions by our ODE model, an analytical solution by Hori et al.³⁵, both with an mRNA lifetime of $12\min$³², and with the phenomenological T(δ) = Cπ/δ with C ≈ 1. While the predictions are in good agreement with the data at higher dilution rates, the measured periods are systematically higher at lower dilution rates. Data shows means ± SD of N = 2, or N = 4 technical replicates, as indicated by individual data points (jittered). As time traces with periods > 6 h only contain 2-3 maxima, we additionally accounted for a systematic measurement uncertainty that scales inversely with the number of maxima. System parameters are as in Fig. 2, with α = 3 pMs⁻¹.