Fig. 4.

Birhythmicity in the expression of a genetic oscillator. (A) Binary expression of a protein P that activates a kinase of an ultrasensitive signaling cascade involving kinases Y and R. The latter also down-regulates gene expression through negative feedback, causing the expression levels of all involved proteins to oscillate. Promoter switching is caused by DNA damage and repair triggered by weak irradiation. (B) Sample paths for all protein concentrations from stochastic simulation are shown for DNA damage and repair events. We observe that the oscillation baseline of P (blue) displays only little variation over large variations in the oscillator period. By contrast, the binary behavior of the oscillation baseline is amplified downstream in the ultrasensitive cascade, leading to switching between oscillatory and silent oscillator modes (blue). (C) Baseline variations are quantified by probability distributions which discriminate well the binary switch in the oscillator output (R, blue) that is not present in the input distribution (P, green; concentration scaled by a factor of 2). (D) We analyze the power spectra of both kinases, observing birhythmic behavior in Y (red), but only a single frequency in R (blue), the oscillator output, which demonstrates the amplification of the all-or-none response. We note the increase at low frequencies, which is a reminiscence of phenotypic switching over long timescales. Our theoretical predictions for the distributions and power spectra (solid) agree well with stochastic simulation of the full network via SSA (dotted). Parameter values are given in SI Appendix, Table S3.