Fig. 2. Dynamics and phase diagram of the free oscillator.

a Experimental (full) and simulated (dashed) time traces of the free oscillator for different refresh ratios R(δ) and DNA concentrations as indicated in b. b Simulated phase diagram of the free oscillator. Color overlay of different metrics as indicated in the legend reveals regions of sustained, damped and overdamped oscillations. A_∞, γ, and τ_eq are the normalized equilibrium amplitude, damping ratio, and equilibration time constant for trajectories with less than one detectable maximum, respectively. Experimental data were mapped onto the diagram using α as a fitting parameter proportional to the DNA concentration. System parameters: n = 3, K_a = 20 nM, K_h = 2 nM, k_TL = 0.02 s⁻¹, ${\tau }_m=12\min$. DNA concentrations are 0.1–1 nM (α = 0.3–3 pMs⁻¹) for the circuit plasmids and 2 nM for reporter plasmids.