Figure 9.

Noise-induced oscillations in the gene network. Comparison of the predictions of noise-induced oscillations in the mRNA concentrations by ssLNA and hLNA methods. Panel (a) shows a stochastic bifurcation diagram depicting the regions in the translation rate (k_s) versus transcription rate (k₀) parameter space where both methods predict no oscillations (black), both predict oscillations (red) and only the ssLNA correctly predicts an oscillation (blue). There is no steady-state in the white region. Panels (b), (c) and (d) show spectra at 3 points in the blue, red and black regions of the bifurcation plot in (a) (these points are marked by roman numbers). The solid and dashed lines show the predictions of the ssLNA and the hLNA respectively, while the dots and circles show the results of stochastic simulations of the full and coarse-grained network using the CME and the heuristic CME, respectively. The parameters are given by Ω=1000, $\left[E_T\right]=0.01$, $\left[G_T\right]=1/\mathrm{\Omega }$ and k_dM=0.01, k₁=0.001, k₋₁=100, k₂=1000, k₋₂=1, k₋₃=10, k₃=0.1, k₄=10. These parameters guarantee timescale separation (validity of the deterministic QSSA) and cooperative behavior in the feedback loop. Note that the hLNA spectrum in (b) and (c) is scaled up 5000 and 1000 times, respectively