Figure 2. A diverse range of biochemical oscillators show the trade-off between resistance to external and internal noise.

For each oscillator, the regime (green) of largest free running amplitude relative to the driving strength is most robust to external fluctuations but is most fragile to internal noise. In contrast, damped oscillations (red) are robust to internal noise and thus preferable at sufficiently high internal noise. Regimes (purple) of intermediate free running amplitude are preferred at intermediate internal noise levels. (a–g) Diverse biochemical oscillators from the literature were simulated with increasing internal noise ${ϵ}_{int}=1/\sqrt{N}$ while driven by a periodic square wave light signal with fixed strength external noise, using the external coupling and parameters specified in the original publications (Leloup et al., 1999; Schmal et al., 2014; Locke et al., 2005; Leloup and Goldbeter, 2003; Goldbeter, 1991; Goodwin, 1965; Gonze and Abou-Jaoudé, 2013; Kondepudi and Prigogine, 2014; Elowitz and Leibler, 2000; Buşe et al., 2009). Clock precision is defined as mutual information between outputs and time. The original publications identified a Hopf bifurcation parameter in these models, with free running oscillations on one side and damped oscillations on the other. Green and purple data correspond to parameter regimes with large and smaller amplitude free running oscillations relative to driving amplitude while the red data corresponds to a damped oscillator. Details in Appendix 2.