Fig. 6. Intracellular activity response function constructed from single-cell measurements on Dictyostelium.

a Upper panel: The average cytosolic cAMP level (the activity $a$, arbitrary unit) in response to a step increase of 1 nM extracellular cAMP at $t=0$ (reproduced from Fig. 2a in ref. ³). Lower panel: The response function $R_a\left(t\right)$ estimated from the derivative of the response data in the upper panel. b The corresponding phase shift ${\varphi }_a$ in the low frequency regime (red curve), obtained from the Fourier transform of $R_a\left(t\right)$. Onset oscillation frequencies in experiments reside in the green region (see Fig. 2b in ref. ²). Also shown is the phase shift $-{\varphi }_s$ from Eq. (6) at ${\tau }_s=0.35$ min (blue curve), the extracellular signal clearance time to yield an onset oscillation period of about 8 min. Faster signal clearance shortens the oscillation period towards the theoretical lower bound at around 6.28 min.