Figure 3

Verification of LNA predictions by stochastic simulations.

In (a) and (c) we plot the power spectra of the concentration fluctuations in X₁ and X₂ respectively using the LNA (solid lines) and also from stochastic simulations using the stochastic simulation algorithm (data points). Note that in (a) burstiness in the input reaction promotes noise-induced oscillations (induces a peak in the spectrum of X₁) and in (c) it destroys them (removes the peak in the spectrum of X₂ for non-bursty input). In (b) and (d) we plot the quality of the noise-induced oscillations whose spectra are shown in (a) and (c) respectively. See text for definition of the quality factor Q^99%. Note that the quality of the noise-induced oscillations can only be improved by burstiness in the input reaction to a certain extent (saturation of Q^99% with mean burst size μ₁). The constants are (a) h₁Ω N_A = 1000 molecules s⁻¹, k₁ = 2.805 × 10¹¹ M⁻² s⁻¹, k₂ = 0.375 s⁻¹ and k₃ = 0.25 s⁻¹; (b) h₁Ω N_A = 500 molecules s⁻¹, k₁ = 6.528 × 10¹⁰ M⁻² s⁻¹, k₂ = 0.01 s⁻¹ and k₃ = 1 s⁻¹. The compartment volume in each case is Ω = 3 × 10⁻¹⁵ l, which gives mean molecule numbers of (a) molecules and (b) molecules. Note that the units for concentration, time and frequency ω are Molar (M), second (s) and radians per second (rad s⁻¹) respectively. See Methods for a discussion of biologically relevant parameter ranges.